- MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.122522 0.425999 0.000000 0.000000 0.000000 0.943917 0.000000 0.000000 0.000000 0.000000 0.830559 0.000000 0.170021 0.048964 0.000000 0.000000 0.000000 0.420512 0.711706 0.915946 0.000000 0.000000 0.000000 0.000000 0.000000 0.021282 0.000000 0.000000 0.567938 0.000000 0.000000 0.000000 0.777417 0.000000 0.000000 0.000000 0.732155 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.058944 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.142976 0.665758 0.000000 0.000000 0.000000 0.000000 0.701077 0.000000 0.000000 0.000000 0.000000 0.000000 0.024139 0.613804 0.079940 0.000000 0.578710 0.914534 0.000000 0.148076 0.902427 0.000000 0.492305 0.000000 0.000000 0.000000 0.000000 0.000000 0.316853 0.000000 0.000000 0.000000 0.000000 0.962823 0.000000 0.418666 0.557892 0.000000 0.000000 0.529265 0.000000 0.431082 0.000000 0.128894 0.000000 0.000000 0.123966 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.371072 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.455367 0.000000 0.000000 0.000000 0.806590 0.834728 0.000000 0.000000 0.000000 0.265486 0.000000 0.000000 0.000000 0.000000 0.000000 0.593944 0.000000 0.000000 0.000000 0.709177 0.000000 0.334651 0.439176 0.000000 0.091002 0.000000 0.000000 0.000000 0.945788 0.120871 0.000000 0.347219 0.000000 0.000000 0.292264 0.164044 0.472937 0.000000 0.000000 0.771318 0.000000 0.689625 0.268671 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.437933 0.590610 0.000000 0.000000 0.987449 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.853167 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.608666 0.952681 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.750743 0.000000 0.594166 0.000000 0.000000 0.000000 0.470938 0.000000 0.048036 0.208888 0.702573 0.000000 0.734994 0.000000 0.699704 0.524827 0.113873 0.803860 0.000000 0.000000 0.000000 0.000000 0.857079 0.000000 0.440781 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.769280 0.000000 0.932010 0.000000 0.000000 0.000000 0.678285 0.000000 0.000000 0.318150 0.065676 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.642196 0.000000 0.537971 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.790146 0.967924 0.178677 0.000000 0.844868 0.000000 0.597654 0.966523 0.000000 0.000000 0.837141 0.000000 0.000000 0.000000 0.000000 0.956534 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.880646 0.000000 0.479727 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.287272 0.000000 0.644173 0.000000 0.000000 0.164169 0.000000 0.444038 0.000000 0.000000 0.000000 0.000000 0.000000 0.998294 0.000000 0.000000 0.764414 0.692973 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.381383 0.574587 0.000000 0.000000 0.000000 0.301161 0.000000 0.000000 0.000000 0.000000 0.000000 0.380295 0.000000 0.319183 0.735679 0.000000 0.746254 0.255445 0.112619 0.000000 0.000000 0.580904 0.000000 0.644340 0.000000 0.000000 0.000000 0.000000 0.000000 0.358010 0.000000 0.086763 0.452411 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 103 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.701077 0.000000 0.000000 0.000000 0.000000 0.771318 0.000000 0.000000 0.699704 0.769280 0.642196 0.000000 0.000000 0.000000 0.000000 0.255445 0.000000 Row indices: 0 8 13 16 24 30 33 37 44 52 56 58 67 70 73 79 82 85 90 98 103 Column indices: 1 2 6 11 13 14 18 19 0 6 9 13 17 4 17 18 9 10 11 13 14 16 17 19 5 10 12 13 16 18 0 3 11 9 13 14 18 4 8 10 11 13 17 18 0 3 4 5 10 11 18 19 2 11 18 19 17 19 3 5 6 7 9 12 13 14 19 1 14 18 1 2 15 11 12 13 15 17 18 1 6 18 0 17 19 2 4 10 13 14 1 2 6 12 14 15 17 19 2 4 10 12 13 Off-diagonal values: 0.122522 0.425999 0.943917 0.830559 0.170021 0.048964 0.420512 0.711706 0.915946 0.021282 0.567938 0.777417 0.732155 0.058944 0.142976 0.665758 0.024139 0.613804 0.079940 0.578710 0.914534 0.148076 0.902427 0.492305 0.316853 0.962823 0.418666 0.557892 0.529265 0.431082 0.128894 0.123966 0.371072 0.455367 0.806590 0.834728 0.265486 0.593944 0.709177 0.334651 0.439176 0.091002 0.945788 0.120871 0.347219 0.292264 0.164044 0.472937 0.689625 0.268671 0.437933 0.590610 0.987449 0.853167 0.608666 0.952681 0.750743 0.594166 0.470938 0.048036 0.208888 0.702573 0.734994 0.524827 0.113873 0.803860 0.857079 0.440781 0.932010 0.678285 0.318150 0.065676 0.537971 0.790146 0.967924 0.178677 0.844868 0.597654 0.966523 0.837141 0.956534 0.880646 0.479727 0.287272 0.644173 0.164169 0.444038 0.998294 0.764414 0.692973 0.381383 0.574587 0.301161 0.380295 0.319183 0.735679 0.746254 0.112619 0.580904 0.644340 0.358010 0.086763 0.452411 . x x - - - x - - - - x - x x - - - x x x . - - - - x - - x - - - x - - - x - - | | . - x - - - - - - - - - - - - x x - | | | x - - - - - x x x - x x - x x - x | | | | . x - - - - x - x x - - x - x - x | | x | . - - - - - x - - - - - - - - | | | | | | . - - x - - - x x - - - x - | | | | x | | . x - x x - x - - - x x - x | | x x x | | x - x x - - - - - - x x | | x | | | | | | . - x - - - - - - x x | | | | | | | | | | . - - - - - - x - x | | | x | x x x | x | x x x x - - - - x | x | | | | | | | | | | x - x - - - x - | x x | | | | | | | | | | x - x - - - - | | | | | | | | | | | x x x . x - x x - | x | | | | x | | | | | | | | . - - x - x | | | | | | | | | | | | | | | . x - x | | x | x | | | | | x | | x x | | . - - | x x | | | x | | | | | x | x x | x x x | | x | x | | | | | x | x x | | | | | . The error in solving: 5.220797e-16 The error in solving: 2.604455e-16 The error in solving: 7.714665e-16 The error in solving: 3.703706e-16 The error in solving: 3.974599e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 0.474754 0.953909 0.819534 0.000000 0.000000 0.000000 0.000000 0.000000 0.286424 0.000000 0.000000 0.714897 0.000000 0.345217 0.695766 0.061379 0.948711 0.311664 0.007604 0.543059 0.100701 0.000000 0.622082 0.138452 0.000000 0.000000 0.000000 0.000000 0.978331 0.000000 0.000000 0.969911 0.000000 0.000000 0.000000 0.532723 0.000000 0.000000 0.000000 0.000000 0.669489 0.000000 0.000000 0.841287 0.262314 0.422880 0.989097 0.141856 0.000000 0.000000 0.730669 0.000000 0.000000 0.158652 0.000000 0.900157 0.000000 0.000000 0.000000 0.645852 0.000000 0.000000 0.874461 0.000000 0.000000 0.000000 0.235110 0.202654 0.000000 0.737131 0.000000 0.000000 0.000000 0.636905 0.906395 0.000000 0.000000 0.000000 0.769634 0.000000 0.000000 0.051457 0.626501 0.000000 0.522186 0.000000 0.475353 0.000000 0.000000 0.000000 0.000000 0.000000 0.129508 0.770262 0.469147 0.380006 0.811004 0.000000 0.000000 0.008276 0.000000 0.005870 0.481511 0.279233 0.918442 0.000000 0.687372 0.342380 0.116506 0.071054 0.230343 0.000000 0.000000 0.000000 0.000000 0.000000 0.949674 0.819882 0.500975 0.942532 0.014530 0.000000 0.336895 0.000000 0.000000 0.299684 0.000000 0.757211 0.433893 0.000000 0.000000 0.064924 0.505120 0.000000 0.880102 0.288882 0.269866 0.242515 0.461915 0.734192 0.000000 0.000000 0.000000 0.000000 0.000000 0.885938 0.000000 0.018455 0.323200 0.223944 0.776519 0.000000 0.131013 0.000000 0.933789 0.265117 0.000000 0.000000 0.000000 0.000000 0.535510 0.000000 0.491358 0.000000 0.000000 0.000000 0.853556 0.000000 0.000000 0.000000 0.000000 0.000000 0.271350 0.000000 0.861416 0.061567 0.134508 0.058160 0.042219 0.000000 0.000000 0.832451 0.608589 0.000000 0.272302 0.979067 0.586145 0.969503 0.000000 0.000000 0.000000 0.235577 0.941249 0.692903 0.000000 0.679610 0.452855 0.000000 0.348395 0.000000 0.000000 0.687546 0.000000 0.000000 0.000000 0.000000 0.000000 0.976356 0.000000 0.032469 0.000000 0.822508 0.000000 0.000000 0.836414 0.000000 0.000000 0.780741 0.492775 0.000000 0.445688 0.000000 0.418986 0.000000 0.000000 0.996479 0.160446 0.000000 0.000000 0.024582 0.000000 0.000000 0.000000 0.686033 0.659583 0.000000 0.666741 0.140745 0.000000 0.930474 0.000000 0.410712 0.000000 0.894088 0.000000 0.105241 0.000000 0.000000 0.000000 0.000000 0.385647 0.752826 0.000000 0.105841 0.000000 0.000000 0.454441 0.000000 0.000000 0.581803 0.000000 0.906070 0.000000 0.818450 0.221941 0.489747 0.000000 0.161106 0.398514 0.870545 0.681350 0.152836 0.000000 0.000000 0.000000 0.000000 0.000000 0.379759 0.000000 0.726345 0.000000 0.256855 0.000000 0.000000 0.000000 0.039356 0.000000 0.962559 0.504314 0.934964 0.000000 0.865902 0.000000 0.737747 0.485027 0.000000 0.866539 0.000000 0.519142 0.166586 0.000000 0.020085 0.000000 0.047258 0.109113 0.000000 0.000000 0.429033 0.000000 0.076590 0.000000 0.305398 0.000000 0.000000 0.094531 0.000000 0.436550 0.000000 0.002800 0.000000 0.000000 0.000000 0.999469 0.000000 0.000000 0.000000 0.000000 0.772270 0.000000 0.000000 0.000000 0.638875 0.000000 0.000000 0.000000 0.000000 0.950364 0.605869 0.000000 0.784806 0.324356 0.638574 0.529922 0.961638 0.695977 0.000000 0.414743 0.572247 0.623221 0.337411 0.000000 0.296075 0.000000 0.552924 0.000000 0.000000 0.445328 0.000000 0.000000 0.000000 0.000000 0.338880 0.000000 0.000000 0.371829 0.248452 0.000000 0.000000 0.520734 0.000000 0.000000 0.733646 0.377261 0.969420 0.000000 0.000000 0.975561 0.000000 0.000000 0.753014 0.602701 0.000000 0.000000 0.795794 0.000000 0.538119 0.000000 0.000000 0.000000 0.695930 0.328276 0.000000 0.187791 0.000000 0.804579 0.000000 0.007275 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 180 (max 380) Diagonal entries: 0.000000 0.543059 0.669489 0.000000 0.626501 0.279233 0.000000 0.885938 0.853556 0.969503 0.000000 0.024582 0.385647 0.152836 0.000000 0.000000 0.000000 0.000000 0.975561 0.000000 Row indices: 0 10 17 25 32 41 52 65 74 81 92 99 108 115 125 135 145 151 164 171 180 Column indices: 2 3 4 10 13 15 16 17 18 19 0 2 4 5 10 13 17 5 6 7 8 9 12 15 17 1 4 8 9 11 15 16 0 3 6 8 14 15 16 17 18 1 3 4 6 8 9 10 11 12 18 19 0 1 2 4 7 9 10 13 14 16 17 18 19 0 1 9 10 11 12 14 16 17 2 4 14 16 17 18 19 0 3 4 6 7 8 13 14 15 17 18 0 3 9 11 13 16 19 0 2 4 7 8 15 16 18 19 1 3 5 7 13 15 18 1 3 5 6 7 9 10 11 12 19 1 3 7 9 10 11 13 15 16 18 0 1 3 5 6 9 11 13 16 18 0 4 9 13 18 19 1 2 3 4 5 6 8 9 10 11 13 15 18 3 6 7 10 13 14 15 1 2 5 7 11 12 14 16 18 Off-diagonal values: 0.474754 0.953909 0.819534 0.286424 0.714897 0.345217 0.695766 0.061379 0.948711 0.311664 0.007604 0.100701 0.622082 0.138452 0.978331 0.969911 0.532723 0.841287 0.262314 0.422880 0.989097 0.141856 0.730669 0.158652 0.900157 0.645852 0.874461 0.235110 0.202654 0.737131 0.636905 0.906395 0.769634 0.051457 0.522186 0.475353 0.129508 0.770262 0.469147 0.380006 0.811004 0.008276 0.005870 0.481511 0.918442 0.687372 0.342380 0.116506 0.071054 0.230343 0.949674 0.819882 0.500975 0.942532 0.014530 0.336895 0.299684 0.757211 0.433893 0.064924 0.505120 0.880102 0.288882 0.269866 0.242515 0.461915 0.734192 0.018455 0.323200 0.223944 0.776519 0.131013 0.933789 0.265117 0.535510 0.491358 0.271350 0.861416 0.061567 0.134508 0.058160 0.042219 0.832451 0.608589 0.272302 0.979067 0.586145 0.235577 0.941249 0.692903 0.679610 0.452855 0.348395 0.687546 0.976356 0.032469 0.822508 0.836414 0.780741 0.492775 0.445688 0.418986 0.996479 0.160446 0.686033 0.659583 0.666741 0.140745 0.930474 0.410712 0.894088 0.105241 0.752826 0.105841 0.454441 0.581803 0.906070 0.818450 0.221941 0.489747 0.161106 0.398514 0.870545 0.681350 0.379759 0.726345 0.256855 0.039356 0.962559 0.504314 0.934964 0.865902 0.737747 0.485027 0.866539 0.519142 0.166586 0.020085 0.047258 0.109113 0.429033 0.076590 0.305398 0.094531 0.436550 0.002800 0.999469 0.772270 0.638875 0.950364 0.605869 0.784806 0.324356 0.638574 0.529922 0.961638 0.695977 0.414743 0.572247 0.623221 0.337411 0.296075 0.552924 0.445328 0.338880 0.371829 0.248452 0.520734 0.733646 0.377261 0.969420 0.753014 0.602701 0.795794 0.538119 0.695930 0.328276 0.187791 0.804579 0.007275 . - x x x - - - - - x - - x - x x x x x x x x - x x - - - - x - - x - - - x - - | | x - - x x x x x - - x - - x - x - - | x | . x - - - x x - x - - - x x - - - x | | x x - x - x - - - - - x x x x x - | x | x x x x - x x x x x - - - - - x x x x x | x | . x - x x - - x x - x x x x x x | | | | | x - x x x x - x - x x - - | | x | x | | | x - - - - - x - x x x x x | | x x | x x x x - - - x x x - x x - x | | x | | | | | x . x - x - - x - - x x | x | x | | x x | | x - - - x x - x x | x | x | x | x | | | | x x - x - - x - | x | x | x x x | x x x x x - - - - - x | x | x | | | x | x x x | x . x x - x - x x | x | x x | | x | x | x | . x - x - x | | | x | | | | x | | | x | | . - x x | x x x x x x | x x x x | x | x | . x - | | | x | | x x | | x | | x x x | | x - | x x | | x | x | | | x x | x | x | x . The error in solving: 7.376145e-16 The error in solving: 4.386692e-16 The error in solving: 4.443195e-16 The error in solving: 5.477003e-16 The error in solving: 5.275157e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.750000 [ 0.733237 0.211917 0.000000 0.000000 0.000000 0.000000 0.839325 0.121553 0.305254 0.000000 0.046854 0.000000 0.631365 0.066965 0.837362 0.000000 0.217741 0.688113 0.917752 0.772173 0.986666 0.492616 0.094869 0.224433 0.385467 0.503944 0.853886 0.389182 0.000000 0.886300 0.652631 0.889194 0.662508 0.801935 0.572434 0.006978 0.164654 0.000000 0.498596 0.807091 0.339517 0.709235 0.163649 0.000000 0.329801 0.000000 0.155040 0.000000 0.715212 0.818622 0.716749 0.452246 0.599526 0.680563 0.000000 0.073567 0.954828 0.052522 0.304635 0.297662 0.966939 0.475172 0.000000 0.389917 0.000000 0.801421 0.189123 0.000000 0.008255 0.353927 0.879085 0.618898 0.000000 0.689614 0.775622 0.118393 0.511431 0.021788 0.000000 0.000000 0.245626 0.474894 0.000000 0.414983 0.371179 0.291293 0.756791 0.739269 0.041629 0.425517 0.467005 0.000000 0.041318 0.186674 0.194271 0.000000 0.000000 0.929431 0.000000 0.707854 0.236123 0.000000 0.000000 0.069181 0.672268 0.852566 0.690280 0.390040 0.156928 0.269446 0.666615 0.777377 0.569150 0.523695 0.113677 0.062646 0.000000 0.503774 0.785314 0.941392 0.243321 0.305657 0.199547 0.517789 0.394363 0.291832 0.576378 0.480096 0.149393 0.000000 0.545340 0.000000 0.451303 0.120846 0.535670 0.000000 0.000000 0.000000 0.696581 0.638213 0.208849 0.000000 0.950200 0.000000 0.971110 0.098708 0.000000 0.140303 0.565796 0.000000 0.306140 0.309446 0.682028 0.074977 0.187192 0.152603 0.990539 0.871120 0.000000 0.539191 0.226887 0.000000 0.033352 0.645043 0.000000 0.176764 0.000000 0.469980 0.699291 0.797869 0.439139 0.458451 0.682768 0.000000 0.000000 0.740884 0.000000 0.384695 0.025725 0.336049 0.000000 0.914898 0.855527 0.055456 0.163402 0.550746 0.060116 0.349533 0.132856 0.010535 0.092490 0.000000 0.025168 0.978099 0.000000 0.975448 0.872861 0.428830 0.809180 0.360067 0.420284 0.614284 0.000000 0.405742 0.094433 0.067712 0.911845 0.388506 0.000000 0.003474 0.014743 0.824968 0.000000 0.790360 0.136166 0.169685 0.611374 0.024590 0.000000 0.151841 0.591775 0.052269 0.898314 0.228095 0.807938 0.707791 0.000000 0.294332 0.240484 0.940293 0.626556 0.464060 0.766859 0.896405 0.556428 0.000000 0.374835 0.137341 0.868625 0.000000 0.315676 0.892745 0.023193 0.812584 0.057324 0.848835 0.902237 0.507668 0.204338 0.000000 0.700616 0.063856 0.782614 0.929199 0.163380 0.000000 0.967619 0.096591 0.591506 0.000000 0.745441 0.000000 0.893508 0.423243 0.701107 0.308991 0.342721 0.627541 0.000000 0.734041 0.647150 0.120596 0.000000 0.935191 0.007592 0.928623 0.876169 0.426560 0.232297 0.935350 0.681445 0.896623 0.203587 0.120523 0.894946 0.000000 0.927811 0.000000 0.000000 0.408900 0.350041 0.114719 0.320266 0.786942 0.000000 0.441652 0.298851 0.459148 0.741712 0.424038 0.000000 0.600996 0.218529 0.227457 0.210966 0.717993 0.000000 0.374668 0.106699 0.075414 0.983738 0.397292 0.000000 0.764794 0.814195 0.096863 0.438378 0.412178 0.000000 0.962979 0.000000 0.000000 0.946696 0.837719 0.655468 0.272354 0.974589 0.241640 0.615792 0.100163 0.501091 0.046600 0.605095 0.468543 0.908119 0.210888 0.000000 0.902563 0.316590 0.427013 0.073249 0.075870 0.000000 0.897928 0.204282 0.599956 0.493570 0.000000 0.284922 0.718339 0.333043 0.867907 0.000000 0.065648 0.185672 0.529271 0.870625 0.283955 0.335169 0.027612 0.023891 0.000000 0.311925 0.000000 0.548307 0.597530 0.515989 0.272350 0.109122 0.961201 0.156783 0.521622 0.529307 0.512567 0.280049 0.167550 0.035834 0.237219 0.591578 0.000000 0.000000 0.639399 0.394252 0.256864 0.380143 0.077238 0.000000 0.000000 0.000000 0.725350 0.235190 0.730958 0.955168 0.884742 0.000000 0.001764 0.748786 0.459956 0.389447 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 301 (max 380) Diagonal entries: 0.733237 0.492616 0.163649 0.389917 0.371179 0.852566 0.576378 0.140303 0.699291 0.010535 0.014743 0.464060 0.782614 0.935191 0.000000 0.096863 0.000000 0.283955 0.591578 0.000000 Row indices: 0 12 29 44 57 71 87 101 115 128 144 159 175 191 207 223 238 255 271 287 301 Column indices: 1 6 7 8 10 12 13 14 16 17 18 19 0 2 3 4 5 6 7 9 10 11 12 13 14 15 16 18 19 0 1 4 6 8 9 10 11 12 13 15 16 17 18 19 0 1 5 6 8 9 10 11 13 14 15 16 17 0 1 3 5 6 7 8 9 10 12 13 14 17 19 0 3 4 6 7 8 9 10 11 12 13 14 15 17 18 19 0 1 2 3 4 5 7 8 10 12 13 14 18 19 0 2 4 5 8 10 11 12 13 14 15 16 17 19 0 2 3 5 7 9 10 11 12 15 17 18 19 1 2 3 4 5 6 7 8 10 12 13 15 16 17 18 19 0 1 3 4 5 6 7 9 11 13 14 15 16 17 19 0 1 2 3 4 5 7 8 9 10 12 13 14 16 17 18 0 1 2 3 4 5 6 7 8 10 11 13 14 16 17 18 0 2 3 4 5 6 7 9 10 11 14 15 16 17 18 19 0 1 2 3 4 6 9 10 11 12 13 15 16 17 18 19 1 2 3 4 5 7 8 9 10 11 13 14 16 17 19 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 0 1 3 4 5 6 8 9 10 11 13 14 15 16 18 19 0 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 2 3 4 5 9 10 11 12 13 15 16 17 18 Off-diagonal values: 0.211917 0.839325 0.121553 0.305254 0.046854 0.631365 0.066965 0.837362 0.217741 0.688113 0.917752 0.772173 0.986666 0.094869 0.224433 0.385467 0.503944 0.853886 0.389182 0.886300 0.652631 0.889194 0.662508 0.801935 0.572434 0.006978 0.164654 0.498596 0.807091 0.339517 0.709235 0.329801 0.155040 0.715212 0.818622 0.716749 0.452246 0.599526 0.680563 0.073567 0.954828 0.052522 0.304635 0.297662 0.966939 0.475172 0.801421 0.189123 0.008255 0.353927 0.879085 0.618898 0.689614 0.775622 0.118393 0.511431 0.021788 0.245626 0.474894 0.414983 0.291293 0.756791 0.739269 0.041629 0.425517 0.467005 0.041318 0.186674 0.194271 0.929431 0.707854 0.236123 0.069181 0.672268 0.690280 0.390040 0.156928 0.269446 0.666615 0.777377 0.569150 0.523695 0.113677 0.062646 0.503774 0.785314 0.941392 0.243321 0.305657 0.199547 0.517789 0.394363 0.291832 0.480096 0.149393 0.545340 0.451303 0.120846 0.535670 0.696581 0.638213 0.208849 0.950200 0.971110 0.098708 0.565796 0.306140 0.309446 0.682028 0.074977 0.187192 0.152603 0.990539 0.871120 0.539191 0.226887 0.033352 0.645043 0.176764 0.469980 0.797869 0.439139 0.458451 0.682768 0.740884 0.384695 0.025725 0.336049 0.914898 0.855527 0.055456 0.163402 0.550746 0.060116 0.349533 0.132856 0.092490 0.025168 0.978099 0.975448 0.872861 0.428830 0.809180 0.360067 0.420284 0.614284 0.405742 0.094433 0.067712 0.911845 0.388506 0.003474 0.824968 0.790360 0.136166 0.169685 0.611374 0.024590 0.151841 0.591775 0.052269 0.898314 0.228095 0.807938 0.707791 0.294332 0.240484 0.940293 0.626556 0.766859 0.896405 0.556428 0.374835 0.137341 0.868625 0.315676 0.892745 0.023193 0.812584 0.057324 0.848835 0.902237 0.507668 0.204338 0.700616 0.063856 0.929199 0.163380 0.967619 0.096591 0.591506 0.745441 0.893508 0.423243 0.701107 0.308991 0.342721 0.627541 0.734041 0.647150 0.120596 0.007592 0.928623 0.876169 0.426560 0.232297 0.935350 0.681445 0.896623 0.203587 0.120523 0.894946 0.927811 0.408900 0.350041 0.114719 0.320266 0.786942 0.441652 0.298851 0.459148 0.741712 0.424038 0.600996 0.218529 0.227457 0.210966 0.717993 0.374668 0.106699 0.075414 0.983738 0.397292 0.764794 0.814195 0.438378 0.412178 0.962979 0.946696 0.837719 0.655468 0.272354 0.974589 0.241640 0.615792 0.100163 0.501091 0.046600 0.605095 0.468543 0.908119 0.210888 0.902563 0.316590 0.427013 0.073249 0.075870 0.897928 0.204282 0.599956 0.493570 0.284922 0.718339 0.333043 0.867907 0.065648 0.185672 0.529271 0.870625 0.335169 0.027612 0.023891 0.311925 0.548307 0.597530 0.515989 0.272350 0.109122 0.961201 0.156783 0.521622 0.529307 0.512567 0.280049 0.167550 0.035834 0.237219 0.639399 0.394252 0.256864 0.380143 0.077238 0.725350 0.235190 0.730958 0.955168 0.884742 0.001764 0.748786 0.459956 0.389447 x x - - - - x x x - x - x x x - x x x x x x x x x x x x - x x x x x x x x - x x x x x - x - x - x x x x x x - x x x x x x x | x - x x - x x x x - x x x x x - - x x | x x x x x x x x - x x x - - x - x x | | x x x x x x x x x x x x x - x x x x x x x x x x x x - x - x x x - - - x x x | x | x x | x x - x x x x x x x x - x x | x x | x | x x x x x x - - x - x x x | x x x x x x x x x x - x x - x x x x x x x | x x x x x | x x x - x x x x x - x x x x x x x | x x x x x x x x - x x x - x x x x x x x x x | x x x x x - x x x - x | x x x x x x | x x x | x x x x x x x x x x x x | x | | x x x x x . x x x x x | x x x x x | x x x x x | x x x x x - x | | x x x x x x x x x x x x x x . x x x x x | x x x x | x x x x | x x x x x x x x | x | x x x x x x x x x x x x x x x - | x x x x x | | | x x x x x | x x x x . The error in solving: 8.968369e-16 The error in solving: 4.024708e-16 The error in solving: 5.696659e-16 The error in solving: 3.750936e-16 The error in solving: 7.713104e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.774612 0.000000 0.000000 0.000000 0.373688 0.000000 0.305521 0.995671 0.000000 0.000000 0.000000 0.000000 0.963021 0.000000 0.757712 0.654706 0.130905 0.000000 0.000000 0.000000 0.000000 0.828147 0.000000 0.633677 0.000000 0.172344 0.000000 0.213992 0.000000 0.000000 0.391397 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.774744 0.000000 0.665954 0.000000 0.100234 0.309827 0.000000 0.426522 0.000000 0.000000 0.920718 0.847042 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.305873 0.000000 0.000000 0.000000 0.440808 0.000000 0.000000 0.688508 0.000000 0.000000 0.000000 0.000000 0.000000 0.650002 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.122309 0.527607 0.000000 0.685675 0.219315 0.000000 0.000000 0.000000 0.645899 0.000000 0.000000 0.000000 0.000000 0.000000 0.120948 0.679070 0.945030 0.000000 0.459213 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.747678 0.000000 0.237583 0.000000 0.629537 0.000000 0.000000 0.000000 0.779114 0.000000 0.000000 0.000000 0.420238 0.507964 0.929230 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.473385 0.000000 0.011081 0.894834 0.000000 0.000000 0.000000 0.000000 0.000000 0.863332 0.000000 0.731710 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.803349 0.000000 0.000000 0.796981 0.000000 0.000000 0.270322 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.612795 0.000000 0.252931 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.422372 0.000000 0.492792 0.000000 0.963982 0.000000 0.000000 0.000000 0.000000 0.355458 0.000000 0.000000 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Dimension: 20 x 20 Off-diagonal entries: 102 (max 380) Diagonal entries: 0.774612 0.828147 0.100234 0.688508 0.645899 0.629537 0.011081 0.796981 0.492792 0.787624 0.330825 0.151350 0.738473 0.248435 0.217104 0.549273 0.635549 0.927492 0.877657 0.471001 Row indices: 0 7 12 18 23 28 34 38 42 45 48 55 62 67 72 75 82 92 94 97 102 Column indices: 4 6 7 12 14 15 16 3 5 7 10 18 0 3 5 8 9 16 0 9 16 17 19 0 10 11 12 14 1 3 9 13 14 15 4 7 13 15 4 10 17 19 6 10 15 1 4 15 0 1 4 6 9 14 17 3 4 5 9 10 16 18 2 3 9 10 17 3 7 10 15 19 1 12 15 0 3 12 13 14 17 19 0 2 4 5 7 8 9 14 18 19 5 11 0 17 19 0 4 9 14 18 Off-diagonal values: 0.373688 0.305521 0.995671 0.963021 0.757712 0.654706 0.130905 0.633677 0.172344 0.213992 0.391397 0.774744 0.665954 0.309827 0.426522 0.920718 0.847042 0.305873 0.440808 0.650002 0.122309 0.527607 0.685675 0.219315 0.120948 0.679070 0.945030 0.459213 0.747678 0.237583 0.779114 0.420238 0.507964 0.929230 0.473385 0.894834 0.863332 0.731710 0.803349 0.270322 0.612795 0.252931 0.422372 0.963982 0.355458 0.941964 0.743256 0.137403 0.059705 0.401878 0.048495 0.931244 0.301429 0.927783 0.212813 0.059360 0.725076 0.886022 0.398734 0.672490 0.748019 0.800628 0.373708 0.419689 0.455315 0.752469 0.194054 0.375320 0.455084 0.478585 0.108072 0.203651 0.708363 0.846649 0.521779 0.499014 0.829526 0.975851 0.782740 0.224523 0.177215 0.756031 0.600300 0.472717 0.102003 0.921888 0.725991 0.439416 0.414116 0.410833 0.338379 0.039735 0.609733 0.326890 0.235798 0.965929 0.077777 0.298001 0.215621 0.826562 0.299048 0.187742 x - - - x - x x - - - - x - x x x - - - | x - x - x - x - - x - - - - - - - x - x | x x - x - - x x - - - - - - x - - - x | | x - - - - - x - - - - - - x x - x x | | | x - - - - - x x x - x - - - - - | x | x | x - - - x - - - x x x - - - - | | | | x | x x - - - - - x - x - - - - | | | | x | | x - - x - - - - - - x - x | | | | | | x | x - x - - - - x - - - - | x | | x | | | | x - - - - - x - - - - x x | | x | x | | x x - - - x - - x - - | | | x x x | | | x x x - - - - x - x - | | x x | | | | | x x | x - - - - x - - | | | x | | | x | | x | | x - x - - - x | x | | | | | | | | | | x | x x - - - - x | | x | | | | | | | | x x x x - x - x x | x | x x | x x x | | | | x | x - x x | | | | | x | | | | | x | | | | | x - - x | | | | | | | | | | | | | | | | x x x x | | | x | | | | x | | | | x | | | x x The error in solving: 7.244418e-16 The error in solving: 6.295063e-16 The error in solving: 2.941469e-16 The error in solving: 3.557833e-16 The error in solving: 4.621533e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.174631 0.000000 0.370978 0.089369 0.389498 0.000000 0.237268 0.000000 0.000000 0.000000 0.631646 0.450326 0.234822 0.766212 0.806966 0.353118 0.413537 0.000000 0.000000 0.000000 0.481128 0.708389 0.153541 0.000000 0.000000 0.685670 0.230317 0.003562 0.000000 0.302713 0.760983 0.000000 0.000000 0.570192 0.000000 0.000000 0.519586 0.000000 0.000000 0.838318 0.766553 0.048134 0.487778 0.000000 0.000000 0.379318 0.146554 0.887368 0.622446 0.000000 0.573641 0.068655 0.000000 0.000000 0.000000 0.773481 0.305310 0.000000 0.000000 0.166639 0.423923 0.000000 0.000000 0.850548 0.000000 0.905999 0.395355 0.000000 0.000000 0.000000 0.848686 0.987509 0.000000 0.000000 0.000000 0.000000 0.419871 0.000000 0.993779 0.380458 0.087669 0.556072 0.065402 0.000000 0.651057 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.273015 0.000000 0.823929 0.000000 0.000000 0.497607 0.000000 0.000000 0.000000 0.000000 0.504326 0.265018 0.000000 0.608737 0.000000 0.637810 0.000000 0.000000 0.154628 0.365748 0.484849 0.474705 0.392378 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.022610 0.000000 0.000000 0.000000 0.000000 0.749967 0.000000 0.000000 0.045860 0.408599 0.000000 0.793961 0.481907 0.000000 0.927493 0.868183 0.000000 0.519752 0.210624 0.143198 0.095222 0.000000 0.000000 0.000000 0.852996 0.000000 0.311070 0.011256 0.000000 0.000000 0.009750 0.000000 0.228587 0.000000 0.000000 0.214788 0.000000 0.000000 0.000000 0.851409 0.000000 0.000000 0.358556 0.568859 0.000000 0.000000 0.771374 0.733003 0.524587 0.384214 0.132962 0.036328 0.000000 0.094673 0.730969 0.887560 0.699516 0.478403 0.660923 0.415641 0.000000 0.000000 0.106217 0.263511 0.000000 0.949918 0.925836 0.942867 0.464518 0.000000 0.435418 0.399186 0.555513 0.743631 0.707473 0.429684 0.000000 0.000000 0.000000 0.000000 0.501100 0.000000 0.000000 0.000000 0.000000 0.074351 0.000000 0.000000 0.497008 0.988284 0.000000 0.809757 0.485537 0.668121 0.000000 0.000000 0.000000 0.790689 0.729071 0.000000 0.764893 0.000000 0.000000 0.703844 0.345903 0.139374 0.000000 0.856895 0.397247 0.000000 0.463316 0.000000 0.000000 0.000000 0.343855 0.000000 0.000000 0.284090 0.000000 0.118789 0.000000 0.000000 0.000000 0.000000 0.999296 0.000000 0.878684 0.356041 0.797880 0.670810 0.699446 0.817735 0.000000 0.000000 0.000000 0.000000 0.722684 0.000000 0.344608 0.000000 0.000000 0.000000 0.000000 0.435924 0.607303 0.251283 0.000000 0.565551 0.547029 0.127859 0.843500 0.000000 0.845887 0.038634 0.534536 0.576374 0.000000 0.085569 0.332169 0.000000 0.000000 0.298239 0.082822 0.000000 0.890529 0.202458 0.325742 0.000000 0.550232 0.490302 0.000000 0.620471 0.000000 0.144567 0.509401 0.000000 0.000000 0.000000 0.000000 0.614136 0.000000 0.394853 0.000000 0.532490 0.905472 0.993589 0.053799 0.101840 0.269171 0.000000 0.000000 0.000000 0.000000 0.000000 0.588704 0.000000 0.539594 0.657765 0.734570 0.835095 0.812910 0.000000 0.000000 0.000000 0.056643 0.854502 0.976920 0.000000 0.000000 0.360866 0.856850 0.000000 0.914044 0.115204 0.178180 0.635553 0.870378 0.041206 0.000000 0.000000 0.619987 0.000000 0.000000 0.500705 0.597766 0.177049 0.058430 0.000000 0.000000 0.000000 0.000000 0.510505 0.000000 0.000000 0.000000 0.000000 0.915573 0.000000 0.000000 0.000000 0.294632 0.462930 0.339798 0.000000 0.000000 0.000000 0.000000 0.902346 0.000000 0.000000 0.000000 0.000000 0.456779 0.000000 0.000000 0.000000 0.051685 0.208331 0.415055 0.474798 0.000000 0.321091 0.000000 0.000000 0.000000 0.553845 0.000000 0.819783 0.000000 0.000000 0.196781 0.257843 0.000000 0.578721 0.000000 0.000000 0.000000 0.000000 0.028058]; Dimension: 20 x 20 Off-diagonal entries: 185 (max 380) Diagonal entries: 0.174631 0.708389 0.487778 0.850548 0.651057 0.608737 0.749967 0.311070 0.733003 0.464518 0.988284 0.463316 0.817735 0.845887 0.144567 0.588704 0.635553 0.915573 0.208331 0.028058 Row indices: 0 11 21 32 40 46 54 63 70 84 96 104 112 121 133 142 153 165 171 178 185 Column indices: 2 3 4 6 10 11 12 13 14 15 16 0 2 5 6 7 9 10 13 16 19 0 1 5 6 7 8 10 11 15 16 19 0 5 6 10 11 16 18 19 0 1 2 12 14 17 2 3 7 10 11 12 13 14 1 9 10 12 13 15 16 18 19 0 1 5 8 11 13 16 0 3 4 7 9 10 11 12 14 15 16 17 18 19 0 3 4 6 7 8 11 12 13 14 15 16 1 6 9 12 13 14 18 19 1 4 5 6 8 9 15 18 0 5 7 8 9 10 11 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0.399186 0.555513 0.743631 0.707473 0.429684 0.501100 0.074351 0.497008 0.809757 0.485537 0.668121 0.790689 0.729071 0.764893 0.703844 0.345903 0.139374 0.856895 0.397247 0.343855 0.284090 0.118789 0.999296 0.878684 0.356041 0.797880 0.670810 0.699446 0.722684 0.344608 0.435924 0.607303 0.251283 0.565551 0.547029 0.127859 0.843500 0.038634 0.534536 0.576374 0.085569 0.332169 0.298239 0.082822 0.890529 0.202458 0.325742 0.550232 0.490302 0.620471 0.509401 0.614136 0.394853 0.532490 0.905472 0.993589 0.053799 0.101840 0.269171 0.539594 0.657765 0.734570 0.835095 0.812910 0.056643 0.854502 0.976920 0.360866 0.856850 0.914044 0.115204 0.178180 0.870378 0.041206 0.619987 0.500705 0.597766 0.177049 0.058430 0.510505 0.294632 0.462930 0.339798 0.902346 0.456779 0.051685 0.415055 0.474798 0.321091 0.553845 0.819783 0.196781 0.257843 0.578721 x - x x x - x - - - x x x x x x x - - - x x x - - x x x - x x - - x - - x - - x x x x - - x x x x - x x - - - x x - - x x | | x - x x - - - x x - - - - x - x x x x x | x - - - - - - - x - x - - x - - | | x x | x - x - - x x x x x - - - - - | x | | | | x - - x x - x x - x x - x x x x | | | x | x x - - x - x - - x - - - x | | x x | | x x x x x x - x x x x x x x | | x x | x x x x - x x x x x x - - - | x | | | | x | | x x - x x x - - - x x | x | | x x x | x x | x - - - x - - x - x | | | | x | x x x x x x - - - - x - x | | | | x x x | x x x x | x x x x - x x | | x x | x x x | x x | x | x x - - - - x | x | x x x x x x | | | | | x - x x x x x | | | x x x | | x x | x x x x x x - | x | | x x x x | | | | x | | | | x - - | x x x | | | | x | | | | x | | | x x x x | x | | | x | x | | x x | x | | | | x The error in solving: 1.003198e-15 The error in solving: 7.473417e-16 The error in solving: 4.562817e-16 The error in solving: 5.649129e-16 The error in solving: 4.072688e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.066018 0.108216 0.000000 0.000000 0.396568 0.000000 0.673447 0.000000 0.804260 0.000000 0.313716 0.000000 0.438942 0.395863 0.484286 0.659820 0.957083 0.000000 0.149525 0.072474 0.477698 0.749775 0.963090 0.000000 0.699703 0.101021 0.334363 0.000000 0.844615 0.000000 0.722314 0.856421 0.845247 0.000000 0.016836 0.485782 0.305472 0.399742 0.000000 0.000000 0.433514 0.000000 0.922856 0.477961 0.352062 0.401936 0.027893 0.854351 0.730170 0.433057 0.000000 0.304966 0.322516 0.023861 0.103611 0.678785 0.000000 0.000000 0.740338 0.619923 0.688790 0.090257 0.346062 0.711894 0.348143 0.371219 0.000000 0.000000 0.326242 0.255850 0.225690 0.000000 0.344478 0.741943 0.685658 0.679134 0.000000 0.467045 0.416253 0.000000 0.975159 0.094847 0.649064 0.000000 0.937242 0.000000 0.491185 0.841273 0.014755 0.229220 0.006458 0.380336 0.898206 0.000000 0.127427 0.217897 0.072347 0.520579 0.282411 0.693575 0.000000 0.000000 0.601576 0.000000 0.665494 0.614552 0.876941 0.835270 0.132745 0.000000 0.085722 0.824716 0.107606 0.624626 0.798960 0.000000 0.922947 0.247180 0.401219 0.000000 0.000000 0.219102 0.041947 0.000000 0.294676 0.337035 0.129272 0.270374 0.891609 0.572688 0.697519 0.847220 0.000000 0.000000 0.267800 0.623296 0.428913 0.882632 0.000000 0.144736 0.000000 0.722037 0.442273 0.000000 0.570967 0.502564 0.000000 0.795341 0.394248 0.000000 0.000000 0.000000 0.625911 0.000000 0.215126 0.462659 0.220370 0.120134 0.000000 0.467554 0.915157 0.536731 0.743153 0.283013 0.702199 0.000000 0.237809 0.781939 0.078753 0.345368 0.490690 0.685684 0.000000 0.164761 0.443004 0.000000 0.475575 0.000000 0.108104 0.000000 0.898538 0.945302 0.000000 0.037872 0.757891 0.356001 0.328774 0.985623 0.380523 0.523565 0.802241 0.379013 0.175832 0.899431 0.926119 0.336871 0.893174 0.000000 0.000000 0.806112 0.106382 0.372555 0.000000 0.108223 0.923569 0.000000 0.813757 0.636401 0.000000 0.813095 0.589589 0.222988 0.520835 0.000000 0.000000 0.376080 0.000000 0.994845 0.000000 0.335198 0.000000 0.950105 0.214068 0.330231 0.844769 0.025456 0.919276 0.665499 0.863882 0.000000 0.000000 0.799613 0.000000 0.468310 0.039466 0.911977 0.545172 0.883054 0.081058 0.488234 0.635510 0.000000 0.000000 0.831993 0.066117 0.049962 0.598018 0.110115 0.097888 0.503307 0.339710 0.436843 0.406838 0.000000 0.751234 0.000000 0.787535 0.030276 0.000000 0.755113 0.380178 0.057022 0.000000 0.000000 0.000000 0.111061 0.994308 0.665593 0.859140 0.421685 0.234018 0.164324 0.434163 0.220557 0.000000 0.336242 0.000000 0.724598 0.404648 0.754596 0.225136 0.000000 0.000000 0.028772 0.000000 0.443230 0.000000 0.641581 0.000000 0.308250 0.000000 0.315315 0.305914 0.816624 0.684117 0.812513 0.370250 0.000000 0.605885 0.595250 0.000000 0.029696 0.619294 0.053321 0.553099 0.000000 0.719812 0.249871 0.914591 0.029655 0.490864 0.244578 0.650755 0.281502 0.249040 0.875725 0.308436 0.510923 0.154725 0.000000 0.000000 0.000000 0.217511 0.000000 0.643099 0.215950 0.000000 0.512009 0.011045 0.000000 0.282895 0.110627 0.000000 0.000000 0.762032 0.000000 0.531195 0.450540 0.988456 0.659903 0.863340 0.451136 0.000000 0.281341 0.325088 0.111869 0.560115 0.018345 0.924391 0.191828 0.000000 0.226121 0.622684 0.000000 0.416009 0.909172 0.471043 0.844920 0.000000 0.158974 0.055976 0.000000 0.000000 0.110202 0.000000 0.000000 0.257227 0.680058 0.508935 0.957602 0.547472 0.497558 0.453094 0.782270 0.715749 0.238539 0.633019 0.000000 0.953365 0.293585 0.000000 0.012772 0.924958 0.290836 0.784834 0.056160 0.000000 0.000000 0.000000 0.194153 0.494046 0.623744 0.313270 0.751652 0.083748 0.417323 0.000000 0.991840 0.002605 0.067177]; Dimension: 20 x 20 Off-diagonal entries: 275 (max 380) Diagonal entries: 0.066018 0.749775 0.922856 0.711894 0.937242 0.614552 0.129272 0.795341 0.078753 0.523565 0.589589 0.799613 0.406838 0.220557 0.684117 0.875725 0.531195 0.844920 0.953365 0.067177 Row indices: 0 12 25 40 54 70 83 97 108 122 138 150 165 179 193 205 221 232 247 261 275 Column indices: 1 4 6 8 10 12 13 14 15 16 18 19 0 2 4 5 6 8 10 11 12 14 15 16 17 0 3 4 5 6 7 8 9 11 12 13 14 15 18 19 0 1 2 4 5 8 9 10 12 13 14 15 17 18 0 1 2 6 7 8 9 10 11 12 14 15 16 17 18 19 2 4 6 7 8 10 11 12 13 14 16 17 18 1 2 4 5 7 8 9 10 11 14 15 16 17 19 1 2 4 5 8 12 14 15 16 17 19 0 1 2 3 4 6 7 9 10 11 13 14 16 18 0 1 3 4 5 6 7 8 10 11 12 13 14 15 16 19 0 1 3 4 6 7 9 11 12 15 17 19 1 2 3 4 5 6 7 8 13 14 15 16 17 18 19 0 3 4 5 6 7 8 9 10 11 14 16 17 19 0 1 5 6 7 8 9 10 11 12 15 17 18 19 0 3 5 7 9 11 12 13 15 16 18 19 1 2 3 4 6 7 8 9 10 11 12 13 14 16 17 18 2 4 5 7 8 10 11 14 17 18 19 0 1 3 4 5 6 7 8 9 11 12 14 15 16 19 0 3 6 7 8 9 10 11 12 13 14 15 16 19 1 2 3 4 5 9 10 11 12 13 14 15 17 18 Off-diagonal values: 0.108216 0.396568 0.673447 0.804260 0.313716 0.438942 0.395863 0.484286 0.659820 0.957083 0.149525 0.072474 0.477698 0.963090 0.699703 0.101021 0.334363 0.844615 0.722314 0.856421 0.845247 0.016836 0.485782 0.305472 0.399742 0.433514 0.477961 0.352062 0.401936 0.027893 0.854351 0.730170 0.433057 0.304966 0.322516 0.023861 0.103611 0.678785 0.740338 0.619923 0.688790 0.090257 0.346062 0.348143 0.371219 0.326242 0.255850 0.225690 0.344478 0.741943 0.685658 0.679134 0.467045 0.416253 0.975159 0.094847 0.649064 0.491185 0.841273 0.014755 0.229220 0.006458 0.380336 0.898206 0.127427 0.217897 0.072347 0.520579 0.282411 0.693575 0.601576 0.665494 0.876941 0.835270 0.132745 0.085722 0.824716 0.107606 0.624626 0.798960 0.922947 0.247180 0.401219 0.219102 0.041947 0.294676 0.337035 0.270374 0.891609 0.572688 0.697519 0.847220 0.267800 0.623296 0.428913 0.882632 0.144736 0.722037 0.442273 0.570967 0.502564 0.394248 0.625911 0.215126 0.462659 0.220370 0.120134 0.467554 0.915157 0.536731 0.743153 0.283013 0.702199 0.237809 0.781939 0.345368 0.490690 0.685684 0.164761 0.443004 0.475575 0.108104 0.898538 0.945302 0.037872 0.757891 0.356001 0.328774 0.985623 0.380523 0.802241 0.379013 0.175832 0.899431 0.926119 0.336871 0.893174 0.806112 0.106382 0.372555 0.108223 0.923569 0.813757 0.636401 0.813095 0.222988 0.520835 0.376080 0.994845 0.335198 0.950105 0.214068 0.330231 0.844769 0.025456 0.919276 0.665499 0.863882 0.468310 0.039466 0.911977 0.545172 0.883054 0.081058 0.488234 0.635510 0.831993 0.066117 0.049962 0.598018 0.110115 0.097888 0.503307 0.339710 0.436843 0.751234 0.787535 0.030276 0.755113 0.380178 0.057022 0.111061 0.994308 0.665593 0.859140 0.421685 0.234018 0.164324 0.434163 0.336242 0.724598 0.404648 0.754596 0.225136 0.028772 0.443230 0.641581 0.308250 0.315315 0.305914 0.816624 0.812513 0.370250 0.605885 0.595250 0.029696 0.619294 0.053321 0.553099 0.719812 0.249871 0.914591 0.029655 0.490864 0.244578 0.650755 0.281502 0.249040 0.308436 0.510923 0.154725 0.217511 0.643099 0.215950 0.512009 0.011045 0.282895 0.110627 0.762032 0.450540 0.988456 0.659903 0.863340 0.451136 0.281341 0.325088 0.111869 0.560115 0.018345 0.924391 0.191828 0.226121 0.622684 0.416009 0.909172 0.471043 0.158974 0.055976 0.110202 0.257227 0.680058 0.508935 0.957602 0.547472 0.497558 0.453094 0.782270 0.715749 0.238539 0.633019 0.293585 0.012772 0.924958 0.290836 0.784834 0.056160 0.194153 0.494046 0.623744 0.313270 0.751652 0.083748 0.417323 0.991840 0.002605 x x - - x - x - x - x - x x x x x - x x x x x - x x x - x - x x x - x x x x - - x | x x x x x x x x - x x x x x - - x x x x x x x x - - x x x - x x x x - x x - x x x | x - x x x x x x x - x x x x x x | | x | x x x x x - x x x x x - x x x - | x x | x x x x x x x x - - x x x x - x | x x | x x | x x - - - x - x x x x - x x x x x x | x x x x x x - x x - x - x - x x | x x x x x x x x x x x x x x - - x x x | x x | x x | x x x x - - x - x - x | x x x x x x x x | | x - x x x x x x x x | | x x x x x x x x x x - x - x x - x x x | | | x x x x x x x x x - x - x x x x | | x | x | x | x | x x x x x x - x x | x x x x | x x x x x x x x x x x x x - | | x | x x | x x | x x | | x | x x x x x x | x x x x x x x | x x | x x x x - x x | | x | | x x x x x x x x x x x | x x | x x x x x | | | x x x x x x x | x x x The error in solving: 7.441863e-16 The error in solving: 5.454871e-16 The error in solving: 3.090730e-16 The error in solving: 5.621789e-16 The error in solving: 4.029938e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.257052 0.868170 0.160768 0.000000 0.446273 0.000000 0.116534 0.882303 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.697652 0.067957 0.022419 0.000000 0.000000 0.926831 0.000000 0.702716 0.327463 0.000000 0.000000 0.377491 0.250757 0.596482 0.000000 0.000000 0.000000 0.318622 0.000000 0.000000 0.000000 0.000000 0.938037 0.433111 0.000000 0.944226 0.283315 0.088007 0.000000 0.460987 0.000000 0.000000 0.000000 0.962273 0.000000 0.000000 0.653169 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.172467 0.000000 0.020831 0.000000 0.893513 0.000000 0.000000 0.000000 0.000000 0.282185 0.359899 0.000000 0.000000 0.714946 0.747848 0.000000 0.000000 0.000000 0.000000 0.461685 0.000000 0.000000 0.865429 0.065047 0.000000 0.403189 0.000000 0.000000 0.000000 0.000000 0.538240 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.808912 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.822964 0.925066 0.000000 0.000000 0.000000 0.863978 0.000000 0.000000 0.486427 0.000000 0.000000 0.000000 0.000000 0.077476 0.526651 0.000000 0.000000 0.000000 0.760965 0.000000 0.000000 0.559502 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.558192 0.002338 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.314685 0.000000 0.402131 0.000000 0.000000 0.000000 0.000000 0.000000 0.264296 0.000000 0.000000 0.000000 0.000000 0.222199 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0.000000 0.751263 0.000000 0.000000 0.906881 0.000000 0.000000 0.000000 0.000000 0.000000 0.960575 0.481308 0.000000 0.464754 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.072929 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.847258 0.000000 0.000000 0.000000 0.718397 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.937363 0.000000 0.000000 0.000000 0.492799 0.000000 0.000000 0.000000 0.764503 0.000000 0.000000 0.000000 0.000000 0.808917 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.078180 0.000000 0.000000 0.863035 0.000000 0.000000 0.000000 0.000000 0.044165 0.026140 0.000000 0.000000 0.000000 0.415885 0.760721 0.000000 0.000000 0.000000 0.000000 0.633680 0.000000 0.000000 0.583394 0.000000 0.000000 0.000000 0.000000 0.000000 0.138281 0.000000 0.462058 0.000000 0.000000 0.000000 0.978377 0.866672 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 105 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 6 15 23 29 36 41 45 47 52 54 61 65 70 78 84 87 90 93 100 105 Column indices: 8 9 10 12 14 15 4 5 6 9 11 12 15 16 17 1 6 7 9 10 11 13 17 0 7 9 11 16 17 0 1 6 9 10 12 17 4 11 12 16 19 4 5 9 12 15 16 4 6 12 17 18 10 19 0 1 2 5 12 14 18 1 5 6 10 2 13 17 18 19 7 8 9 10 11 15 16 17 0 6 8 10 13 19 0 2 13 5 9 17 1 5 10 0 3 8 9 13 14 19 2 8 10 14 15 Off-diagonal values: 0.257052 0.868170 0.160768 0.446273 0.116534 0.882303 0.697652 0.067957 0.022419 0.926831 0.702716 0.327463 0.377491 0.250757 0.596482 0.318622 0.938037 0.433111 0.944226 0.283315 0.088007 0.460987 0.962273 0.653169 0.172467 0.020831 0.893513 0.282185 0.359899 0.714946 0.747848 0.461685 0.865429 0.065047 0.403189 0.538240 0.808912 0.822964 0.925066 0.863978 0.486427 0.077476 0.526651 0.760965 0.559502 0.558192 0.002338 0.314685 0.402131 0.264296 0.222199 0.061040 0.439968 0.882302 0.475052 0.929054 0.027952 0.839605 0.703573 0.328712 0.792387 0.150383 0.330964 0.021373 0.345209 0.268433 0.025824 0.449421 0.700160 0.912986 0.841119 0.323376 0.394710 0.898423 0.544426 0.148331 0.558021 0.173719 0.118916 0.225333 0.505366 0.751263 0.906881 0.960575 0.481308 0.464754 0.072929 0.847258 0.718397 0.937363 0.492799 0.764503 0.808917 0.078180 0.863035 0.044165 0.026140 0.415885 0.760721 0.633680 0.583394 0.138281 0.462058 0.978377 0.866672 . - - - - - - - x x x - x - x x - - - - | . - - x x x - - x - x x - - x x x - - | x . - - - x x - x x x - x - - - x - - x | | . - - - x - x - x - - - - x x - - x x | | . - x - - x x - x - - - - x - - | | | | x . - - - - - x x - - - x - - x | | | | x x . - - x - - x - - - - - - - | | | | | | | . - - - - - - - x x - - - | | | | x | x | . - - - x - - - - x x - | | | | | | | | | . x - - - - - - - - x x x x | | x | | | | . - x - x - - - x - | x | | | x x | | | x . - - - - - - - - | | x | | | | | | | | | . x - - - x x x | | | | | | | x x x x x | . - x x x - - x | | | | | x | x | x | | x . - - - - x x | x | | | | | | | | | | x | . - - - - | | | | | x | | | x | | | | | | . x - - | x | | | x | | | | x | | | | | | . - - x | | x | | | | x x | | | x x | | | . x | | x | | | | | x | x | | | x x | | | . The error in solving: 3.513575e-16 The error in solving: 3.791075e-16 The error in solving: 6.918046e-16 The error in solving: 6.093597e-16 The error in solving: 5.665831e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.855222 0.986504 0.642918 0.128547 0.071285 0.152281 0.000000 0.000000 0.000000 0.301879 0.292947 0.000000 0.000000 0.550531 0.000000 0.748080 0.000000 0.000000 0.000000 0.000000 0.860925 0.000000 0.000000 0.301010 0.017098 0.479150 0.780300 0.939919 0.374834 0.000000 0.352180 0.852416 0.000000 0.000000 0.528639 0.000000 0.000000 0.000000 0.736367 0.771017 0.000000 0.802252 0.000000 0.955288 0.094010 0.975256 0.000000 0.619919 0.954362 0.443586 0.924003 0.539340 0.000000 0.287252 0.000000 0.506890 0.000000 0.212502 0.000000 0.000000 0.987041 0.000000 0.000000 0.793019 0.000000 0.000000 0.099326 0.000000 0.118704 0.625454 0.388464 0.000000 0.000000 0.000000 0.573817 0.000000 0.000000 0.000000 0.865253 0.000000 0.050593 0.000000 0.000000 0.562498 0.000000 0.000000 0.873228 0.000000 0.000000 0.000000 0.691784 0.881317 0.761143 0.172152 0.603614 0.700677 0.025748 0.000000 0.170082 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.411111 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.813040 0.595290 0.000000 0.362378 0.431964 0.000000 0.974047 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.786156 0.670897 0.332351 0.000000 0.000000 0.000000 0.000000 0.075178 0.823847 0.000000 0.162197 0.000000 0.877568 0.000000 0.042699 0.457584 0.000000 0.000000 0.000000 0.323178 0.780967 0.000000 0.037257 0.684808 0.210806 0.316327 0.434260 0.450216 0.004905 0.746641 0.993388 0.000000 0.000000 0.000000 0.857973 0.890281 0.000000 0.000000 0.495494 0.119208 0.883356 0.197485 0.000000 0.785916 0.000000 0.952239 0.000000 0.000000 0.000000 0.466863 0.000000 0.000000 0.955881 0.000000 0.457926 0.836797 0.045917 0.364692 0.000000 0.000000 0.447160 0.700847 0.252609 0.000000 0.000000 0.000000 0.736287 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.142544 0.161917 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.631256 0.307270 0.000000 0.000000 0.890331 0.000000 0.000000 0.529425 0.383708 0.616150 0.000000 0.000000 0.000000 0.837125 0.000000 0.704171 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.697814 0.949963 0.149809 0.000000 0.000000 0.000000 0.000000 0.000000 0.357211 0.000000 0.000000 0.391923 0.251100 0.000000 0.000000 0.945997 0.000000 0.008671 0.000000 0.000000 0.000000 0.000000 0.343979 0.000000 0.000000 0.097293 0.000000 0.617403 0.101996 0.000000 0.358643 0.342411 0.515341 0.750334 0.000000 0.095212 0.000000 0.939917 0.381234 0.000000 0.000000 0.763070 0.035964 0.340277 0.000000 0.000000 0.000000 0.000000 0.000000 0.092392 0.000000 0.000000 0.000000 0.000000 0.505940 0.651805 0.864231 0.000000 0.956115 0.572243 0.000000 0.000000 0.435209 0.000000 0.182097 0.101581 0.094481 0.525739 0.221746 0.000000 0.381857 0.575870 0.000000 0.166404 0.000000 0.000000 0.518654 0.414019 0.000000 0.415451 0.873661 0.000000 0.000000 0.105514 0.327300 0.207608 0.347282 0.158339 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.664784 0.000000 0.204464 0.000000 0.015402 0.010535 0.000000 0.000000 0.000000 0.817515 0.814318 0.000000 0.868706 0.000000 0.059856 0.000000 0.000000 0.982948 0.000000 0.000000 0.000000 0.957503 0.000000 0.256617 0.063458 0.946925 0.471432 0.000000 0.000000 0.297065 0.634798 0.512392 0.721629 0.019423 0.000000 0.000000 0.724170 0.000000 0.706311 0.456324 0.756001 0.000000 0.771834 0.567899 0.000000 0.456407 0.000000 0.144119 0.994470 0.000000 0.000000 0.660402 0.179039 0.407390 0.000000 0.085436 0.963655 0.377209 0.044170 0.262662 0.000000 0.947980 0.287559 0.000000 0.000000 0.241104 0.556374 0.560722 0.546673 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 195 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 10 20 34 41 52 56 64 77 87 97 103 110 117 129 138 151 159 169 181 195 Column indices: 2 3 4 5 6 7 11 12 15 17 2 5 6 7 8 9 10 12 13 16 0 1 3 5 6 7 9 10 11 12 13 15 17 19 2 5 8 10 11 12 16 0 2 5 8 12 13 14 15 16 17 18 0 9 17 18 0 1 3 11 12 13 18 19 1 3 5 6 10 11 13 14 15 16 17 18 19 0 1 5 6 9 10 11 12 14 16 0 3 5 6 7 8 11 12 13 17 4 5 12 13 16 19 0 1 5 7 14 15 16 2 5 6 9 11 16 19 1 2 4 5 6 7 9 11 12 15 16 17 3 8 9 10 12 13 16 18 19 0 1 2 4 5 7 10 11 13 14 17 18 19 0 1 9 11 13 14 18 19 1 3 6 10 12 13 14 15 18 19 0 1 2 5 7 8 9 11 12 14 16 17 0 1 2 4 5 6 7 8 10 11 14 15 16 17 Off-diagonal values: 0.855222 0.986504 0.642918 0.128547 0.071285 0.152281 0.301879 0.292947 0.550531 0.748080 0.860925 0.301010 0.017098 0.479150 0.780300 0.939919 0.374834 0.352180 0.852416 0.528639 0.736367 0.771017 0.802252 0.955288 0.094010 0.975256 0.619919 0.954362 0.443586 0.924003 0.539340 0.287252 0.506890 0.212502 0.987041 0.793019 0.099326 0.118704 0.625454 0.388464 0.573817 0.865253 0.050593 0.562498 0.873228 0.691784 0.881317 0.761143 0.172152 0.603614 0.700677 0.025748 0.170082 0.411111 0.813040 0.595290 0.362378 0.431964 0.974047 0.786156 0.670897 0.332351 0.075178 0.823847 0.162197 0.877568 0.042699 0.457584 0.323178 0.780967 0.037257 0.684808 0.210806 0.316327 0.434260 0.450216 0.004905 0.746641 0.993388 0.857973 0.890281 0.495494 0.119208 0.883356 0.197485 0.785916 0.952239 0.466863 0.955881 0.457926 0.836797 0.045917 0.364692 0.447160 0.700847 0.252609 0.736287 0.142544 0.161917 0.631256 0.307270 0.890331 0.529425 0.383708 0.616150 0.837125 0.704171 0.697814 0.949963 0.149809 0.357211 0.391923 0.251100 0.945997 0.008671 0.343979 0.097293 0.617403 0.101996 0.358643 0.342411 0.515341 0.750334 0.095212 0.939917 0.381234 0.763070 0.035964 0.340277 0.092392 0.505940 0.651805 0.864231 0.956115 0.572243 0.435209 0.182097 0.101581 0.094481 0.525739 0.221746 0.381857 0.575870 0.166404 0.518654 0.414019 0.415451 0.873661 0.105514 0.327300 0.207608 0.347282 0.158339 0.664784 0.204464 0.015402 0.010535 0.817515 0.814318 0.868706 0.059856 0.982948 0.957503 0.256617 0.063458 0.946925 0.471432 0.297065 0.634798 0.512392 0.721629 0.019423 0.724170 0.706311 0.456324 0.756001 0.771834 0.567899 0.456407 0.144119 0.994470 0.660402 0.179039 0.407390 0.085436 0.963655 0.377209 0.044170 0.262662 0.947980 0.287559 0.241104 0.556374 0.560722 0.546673 . - x x x x x x - - - x x - - x - x - - | . x - - x x x x x x - x x - - x - - - x x . x - x x x - x x x x x - x - x - x | | x . - x - - x - x x x - - - x - - - x | x | . x - - x - - - x x x x x x x - x | | | | . - - - x - - - - - - - x x - x x | x | | . - - - - x x x - - - - x x | x | x | x x . - - x x - x x x x x x x x x | | | x x | . x x x x - x - x - - - x | | x | x x x x . - x x x - - - x - - | | | | x x | | | | . - x x - - x - - x x x | | | x | x | | | . - - x x x - - - | | x | | x x | | x | x . - - - x - - x | x x | x x x x | x | x x . - x x x - - | | | x | | | | x x x | x x . - x - x x x x x | x x | x | | x x | x x . - x x x x x | | | | | | | x | x | x x | . - x x | x | x | | x | | | x | x x x x | . x x x x x | | x | x x x | x x | x | x x . - x x x | x x x x x | x x | | x x x x | . The error in solving: 3.388624e-16 The error in solving: 4.693894e-16 The error in solving: 4.941740e-16 The error in solving: 4.654824e-16 The error in solving: 5.474255e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.021108 0.531853 0.197328 0.000000 0.000000 0.000000 0.000000 0.116731 0.618286 0.085938 0.000000 0.781230 0.400505 0.000000 0.405293 0.619403 0.000000 0.979198 0.483326 0.367264 0.000000 0.664694 0.385642 0.017436 0.815667 0.770816 0.979659 0.924968 0.546608 0.000000 0.383997 0.000000 0.000000 0.000000 0.399871 0.983136 0.687233 0.087019 0.000000 0.000000 0.000000 0.000000 0.759943 0.000000 0.479864 0.831610 0.391222 0.908733 0.729069 0.000000 0.288193 0.646788 0.495022 0.000000 0.000000 0.000000 0.000000 0.000000 0.469672 0.588433 0.244439 0.307565 0.000000 0.000000 0.604069 0.000000 0.333781 0.436827 0.000000 0.721379 0.811067 0.922854 0.000000 0.000000 0.833030 0.031587 0.130870 0.217319 0.919800 0.630778 0.933681 0.682939 0.000000 0.000000 0.314991 0.333770 0.871078 0.826588 0.161677 0.920595 0.695694 0.755102 0.895805 0.000000 0.000000 0.436005 0.204322 0.589568 0.262443 0.918765 0.745335 0.455186 0.811344 0.937779 0.000000 0.694826 0.157593 0.000000 0.090440 0.022728 0.000000 0.000000 0.432570 0.613100 0.581185 0.000000 0.466800 0.467981 0.998855 0.500733 0.134591 0.662796 0.000000 0.000000 0.000000 0.000000 0.226151 0.405555 0.953887 0.000000 0.557421 0.278825 0.211438 0.797789 0.389132 0.556455 0.059676 0.824103 0.580009 0.112443 0.803902 0.000000 0.361777 0.000000 0.407016 0.000000 0.000000 0.772714 0.331406 0.000000 0.000000 0.109853 0.000000 0.177989 0.000000 0.000000 0.183191 0.906470 0.000000 0.416618 0.172794 0.022832 0.015171 0.701462 0.000000 0.746259 0.000000 0.000000 0.536835 0.000000 0.519506 0.000000 0.000000 0.000000 0.000000 0.124476 0.338924 0.315903 0.967681 0.695936 0.000000 0.537185 0.262903 0.817078 0.435987 0.479730 0.262371 0.568860 0.000000 0.490135 0.454914 0.000000 0.202928 0.677978 0.000000 0.392163 0.150962 0.710803 0.000000 0.342930 0.477026 0.560102 0.119034 0.037429 0.466679 0.000000 0.077040 0.000000 0.911415 0.000000 0.476862 0.601439 0.000000 0.203079 0.133049 0.960852 0.000000 0.997015 0.134481 0.028795 0.735915 0.652554 0.056578 0.310988 0.000000 0.000000 0.816820 0.000000 0.090523 0.232423 0.000000 0.960538 0.788564 0.682331 0.405274 0.000000 0.404204 0.026691 0.328196 0.314299 0.236916 0.452624 0.000000 0.595373 0.583045 0.487823 0.216341 0.000000 0.127577 0.000000 0.050510 0.000000 0.000000 0.475593 0.910349 0.179109 0.523197 0.000000 0.000000 0.662401 0.434887 0.768445 0.110626 0.631226 0.300283 0.322400 0.204197 0.183911 0.000000 0.062128 0.464560 0.453578 0.000000 0.295729 0.000000 0.712878 0.056207 0.209979 0.272856 0.808079 0.676859 0.976070 0.000000 0.000000 0.021008 0.530115 0.399696 0.000000 0.949985 0.378878 0.803253 0.242117 0.562214 0.000000 0.356174 0.754292 0.334735 0.948039 0.292189 0.803127 0.026929 0.239808 0.000000 0.275047 0.238662 0.232922 0.000000 0.481258 0.648626 0.341806 0.000000 0.635458 0.120571 0.675938 0.000000 0.524190 0.782943 0.774154 0.614892 0.112238 0.000000 0.662926 0.000000 0.102254 0.682123 0.391338 0.365542 0.685401 0.000000 0.000000 0.578168 0.389002 0.517614 0.000000 0.619409 0.000000 0.446970 0.119070 0.200402 0.631270 0.000000 0.284694 0.267406 0.242797 0.149002 0.274379 0.017302 0.019514 0.412016 0.000000 0.335387 0.969979 0.534796 0.290236 0.000000 0.986233 0.000000 0.296681 0.255089 0.000000 0.578244 0.565435 0.745386 0.000000 0.000000 0.327941 0.000000 0.172154 0.000000 0.942036 0.209154 0.317751 0.000000 0.950863 0.195682 0.013132 0.466953 0.000000 0.882259 0.427795 0.073000 0.656013 0.000000 0.151910 0.621181 0.000000 0.000000 0.842935 0.951078 0.064749 0.000000 0.472917 0.000000 0.000000 0.000000 0.000000 0.791803 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 278 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 12 26 36 50 66 81 96 106 118 133 148 163 176 193 209 225 239 255 268 278 Column indices: 1 2 3 8 9 10 12 13 15 16 18 19 0 2 3 4 5 6 7 8 9 11 15 16 17 18 3 5 6 7 8 9 11 12 13 19 0 1 2 5 7 8 10 11 12 15 16 17 18 19 0 1 2 5 6 7 8 9 10 11 12 13 16 17 18 19 0 1 2 3 4 6 7 9 10 13 14 15 17 18 19 0 1 2 7 8 9 11 12 13 14 15 16 17 18 19 0 1 3 5 8 9 12 14 17 18 0 1 2 3 4 6 9 11 16 17 18 19 0 2 3 4 5 6 7 8 10 11 13 14 16 17 18 0 1 2 3 4 5 7 9 11 12 14 15 16 18 19 0 1 2 3 4 7 9 10 12 13 14 15 17 18 19 0 1 2 4 5 6 7 9 11 14 15 16 17 0 1 2 3 4 5 6 7 8 10 11 12 14 16 17 18 19 0 1 2 5 6 7 9 10 11 12 13 15 16 17 18 19 0 1 2 4 5 6 8 9 10 12 13 14 16 17 18 19 0 2 4 5 6 7 8 11 12 13 15 17 18 19 0 2 3 4 5 6 7 8 9 11 12 13 14 16 18 19 1 2 3 6 8 10 11 12 14 15 16 17 19 0 1 2 4 5 8 9 10 12 17 Off-diagonal values: 0.021108 0.531853 0.197328 0.116731 0.618286 0.085938 0.781230 0.400505 0.405293 0.619403 0.979198 0.483326 0.367264 0.664694 0.385642 0.017436 0.815667 0.770816 0.979659 0.924968 0.546608 0.383997 0.399871 0.983136 0.687233 0.087019 0.759943 0.479864 0.831610 0.391222 0.908733 0.729069 0.288193 0.646788 0.495022 0.469672 0.588433 0.244439 0.307565 0.604069 0.333781 0.436827 0.721379 0.811067 0.922854 0.833030 0.031587 0.130870 0.217319 0.919800 0.630778 0.933681 0.682939 0.314991 0.333770 0.871078 0.826588 0.161677 0.920595 0.695694 0.755102 0.895805 0.436005 0.204322 0.589568 0.262443 0.918765 0.745335 0.455186 0.811344 0.937779 0.694826 0.157593 0.090440 0.022728 0.432570 0.613100 0.581185 0.466800 0.467981 0.998855 0.500733 0.134591 0.662796 0.226151 0.405555 0.953887 0.557421 0.278825 0.211438 0.797789 0.389132 0.556455 0.059676 0.824103 0.580009 0.112443 0.803902 0.361777 0.407016 0.772714 0.331406 0.109853 0.177989 0.183191 0.906470 0.416618 0.172794 0.022832 0.015171 0.701462 0.746259 0.536835 0.519506 0.124476 0.338924 0.315903 0.967681 0.695936 0.537185 0.262903 0.817078 0.435987 0.479730 0.262371 0.568860 0.490135 0.454914 0.202928 0.677978 0.392163 0.150962 0.710803 0.342930 0.477026 0.560102 0.119034 0.037429 0.466679 0.077040 0.911415 0.476862 0.601439 0.203079 0.133049 0.960852 0.997015 0.134481 0.028795 0.735915 0.652554 0.056578 0.310988 0.816820 0.090523 0.232423 0.960538 0.788564 0.682331 0.405274 0.404204 0.026691 0.328196 0.314299 0.236916 0.452624 0.595373 0.583045 0.487823 0.216341 0.127577 0.050510 0.475593 0.910349 0.179109 0.523197 0.662401 0.434887 0.768445 0.110626 0.631226 0.300283 0.322400 0.204197 0.183911 0.062128 0.464560 0.453578 0.295729 0.712878 0.056207 0.209979 0.272856 0.808079 0.676859 0.976070 0.021008 0.530115 0.399696 0.949985 0.378878 0.803253 0.242117 0.562214 0.356174 0.754292 0.334735 0.948039 0.292189 0.803127 0.026929 0.239808 0.275047 0.238662 0.232922 0.481258 0.648626 0.341806 0.635458 0.120571 0.675938 0.524190 0.782943 0.774154 0.614892 0.112238 0.662926 0.102254 0.682123 0.391338 0.365542 0.685401 0.578168 0.389002 0.517614 0.619409 0.446970 0.119070 0.200402 0.631270 0.284694 0.267406 0.242797 0.149002 0.274379 0.017302 0.019514 0.412016 0.335387 0.969979 0.534796 0.290236 0.986233 0.296681 0.255089 0.578244 0.565435 0.745386 0.327941 0.172154 0.942036 0.209154 0.317751 0.950863 0.195682 0.013132 0.466953 0.882259 0.427795 0.073000 0.656013 0.151910 0.621181 0.842935 0.951078 0.064749 0.472917 0.791803 . x x x - - - - x x x - x x - x x - x x x . x x x x x x x x - x - - - x x x x - | | . x - x x x x x - x x x - - - - - x x x x . - x - x x - x x x - - x x x x x x x x | . x x x x x x x x x - - x x x x x x x x x . x x - x x - - x x x - x x x x x x | | | . x x x - x x x x x x x x x x x | x | x | . x x - - x - x - - x x - x x x x x | x | . x - x - - - - x x x x x | x x x x x x x . x x - x x - x x x - x x x x x x | x | x . x x - x x x - x x x x x x x | | x | x x . x x x x - x x x x x x | x x x x | x | x . - x x x x - - x x x x x x x x x | x x x . x - x x x x x x x | | x x x | x x x x x . x x x x x x x x | x x x | x x x | x x x . x x x x x | x | x x x x x | | x x x | x . x x x x | x x x x x x x x | x x x x | x . x x | x x x | | x | x | x x x | x x x x . x x x x | x x | | x x x | x | | | | x | . The error in solving: 3.106463e-16 The error in solving: 5.268078e-16 The error in solving: 7.959093e-16 The error in solving: 6.097152e-16 The error in solving: 3.368224e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.250000 [ -0.015563 0.000000 0.000000 0.706350 0.000000 0.000000 0.000000 0.000000 0.000000 -0.260873 0.000000 0.000000 0.271599 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.498096 -0.268330 0.000000 0.000000 0.000000 0.000000 0.000000 0.181499 0.475900 0.000000 0.000000 0.000000 0.806346 0.000000 0.124578 0.000000 -0.685045 0.000000 0.370556 0.000000 0.000000 0.000000 0.000000 0.411365 0.000000 -0.916892 0.060648 0.000000 0.000000 0.000000 0.206958 0.000000 0.000000 0.000000 0.050464 0.000000 0.000000 0.000000 -0.145610 0.000000 0.391845 0.000000 0.000000 0.000000 0.000000 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- - - - - - | | | | | x o | . x x - - - o - - - - - o | | | | | | | | . - - - - o - o o o - | x o | | | x | x x . - - - - - o - - - | | o | | | | o x | o . - - x - x - - o | | | o x o o | | | | | . x - - o - - - | | | | | | x | | | | | x . x - - o - - | | | | | | | | | x x | | | . o - - - - | | | x | x | | | | x | x | | . - - o - | | | o x | x | o | | o | | | | . - o - | | | | | | x | | | o o | | x | x . - - | x | | | | | | | | o | | | | | | | . - | x o | o x | | x | o | | | x | x | | x The error in solving: 6.231111e-16 The error in solving: 5.467490e-16 The error in solving: 9.028282e-16 The error in solving: 6.385291e-16 The error in solving: 3.805653e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 -0.877200 0.000000 -0.047329 0.000000 0.000000 0.000000 0.000000 -0.364632 0.182571 0.707919 -0.882355 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17 1 3 7 8 11 14 16 17 1 4 12 13 14 16 17 1 5 6 7 8 9 11 12 13 14 15 17 0 3 4 6 7 10 11 12 13 17 19 0 3 4 12 13 14 15 17 18 0 4 5 8 11 17 18 19 0 1 2 5 11 12 13 16 1 2 3 4 7 8 14 19 1 5 7 8 11 17 18 3 6 8 9 10 12 14 15 16 17 19 1 2 3 4 6 7 11 15 16 19 1 3 5 7 8 9 10 11 12 15 16 17 18 19 4 5 9 13 15 0 2 4 7 10 11 12 14 19 0 7 12 13 15 18 1 4 5 7 10 11 13 15 16 18 19 1 6 10 12 15 16 0 1 3 4 5 8 9 10 13 16 Off-diagonal values: -0.877200 -0.047329 -0.364632 0.182571 0.707919 -0.882355 0.380799 -0.420622 0.909031 0.798168 0.056836 0.001137 -0.919413 -0.583655 -0.586486 0.084314 -0.806528 -0.155995 0.101076 0.212619 -0.451193 0.466521 0.818322 -0.961983 -0.841564 0.109872 -0.926428 -0.206943 -0.549489 0.210230 0.336834 0.611886 -0.449411 -0.155737 0.743958 0.830246 -0.524342 0.702165 0.645801 0.107662 0.577199 0.982831 0.122777 -0.363512 -0.000656 -0.888842 0.653817 -0.498527 -0.464289 -0.604839 -0.638419 -0.057030 -0.717850 0.593131 0.448818 0.782434 0.612449 -0.770146 0.488280 -0.683183 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0.104755 0.373356 -0.918122 0.831752 0.245992 -0.155055 -0.568977 0.957770 -0.968386 0.536110 0.023072 -0.128538 -0.979065 . o - o - - - - o x x o x o x - - - x - x x - x - o - - - - - - o - o - x o - - | o o x - - - x o - - x - - x - o o - - | x | . o - - - - - - - o o x - x x - - | o | | . o x x o x - x x x x x - o - - o | | o x . o o - - o o o o - - - x - x x | | x o | . - - - - - x o o o - o o - x | | | o x | x x - - x - - - - - x x x o o x | | x | | . - - o o o - - o - - - | o o x x | | o o o - - - - x - - - - x | o | | | x | o x | x x - - - - - o x - | | | o | | o | o o x . o - o x o o - o | o o o x | o x | | | x o - - x o - - o | o | o | x | x x o o o x x - o o x x x | | | | o o | | | o | | | x o o - - - - o | x | o | | x | | o o o | o x - - - x x | | | | | | x | | | | x o | o . - x - | o | | x o | o | | o x | x | o x . x x | x | | | | o | | | o | x | | x o | . - x x | o o x | | o x x | | o | | o | | o The error in solving: 6.632363e-16 The error in solving: 4.695945e-16 The error in solving: 6.181460e-16 The error in solving: 7.598960e-16 The error in solving: 5.394516e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.750000 [ -0.155488 0.496616 -0.271978 0.000000 0.610154 0.209855 0.515313 0.218108 0.000000 0.000000 0.579213 -0.790474 0.000000 0.823148 0.965380 0.000000 -0.539533 0.000000 -0.388153 0.723649 0.000000 0.000000 -0.470454 0.000000 0.835137 0.000000 -0.633114 -0.999233 -0.265232 0.248592 -0.060797 0.000000 0.304242 0.000000 0.000000 0.491143 0.000000 -0.619854 -0.108385 -0.730624 -0.671404 -0.789445 0.338726 0.000000 0.072092 0.000000 0.992918 -0.943451 0.462330 -0.812211 0.000000 0.152855 0.593859 0.393049 0.398772 0.103099 0.000000 0.595087 -0.064439 -0.760503 0.000000 -0.397092 0.000000 -0.127525 -0.596889 0.448874 -0.696451 -0.245726 0.987874 0.532439 0.976567 0.922205 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0.597348 -0.494045 0.925357 0.517502 0.000000 0.375823 0.667229 0.518147 -0.570899 0.838310]; Dimension: 20 x 20 Off-diagonal entries: 292 (max 380) Diagonal entries: -0.155488 0.000000 0.338726 -0.127525 0.929913 0.252125 -0.728764 -0.268750 0.832482 0.000000 0.270214 -0.977316 0.000000 0.000000 -0.332076 0.000000 0.561976 -0.608389 -0.888311 0.838310 Row indices: 0 13 25 40 54 68 83 96 111 124 141 156 171 188 201 216 231 244 258 275 292 Column indices: 1 2 4 5 6 7 10 11 13 14 16 18 19 2 4 6 7 8 9 10 12 15 17 18 19 0 1 4 6 7 8 9 11 12 13 14 15 17 18 19 1 4 5 6 7 8 9 10 11 12 14 16 18 19 0 3 5 7 8 9 10 12 13 14 15 16 18 19 0 1 3 4 6 7 8 9 10 11 13 14 16 18 19 0 1 3 5 7 10 11 12 13 14 15 17 18 1 2 3 4 6 8 9 10 11 12 13 14 15 17 18 0 3 4 5 6 7 9 11 12 13 15 17 18 0 2 3 4 6 7 8 10 11 12 13 14 15 16 17 18 19 1 2 4 5 6 7 8 9 13 14 15 16 17 18 19 0 1 2 3 5 6 7 8 10 12 13 15 16 18 19 0 1 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 1 3 4 5 7 8 9 10 11 15 16 17 18 0 1 2 3 4 7 8 10 11 12 15 16 17 18 19 0 2 4 5 6 7 8 9 10 11 13 16 17 18 19 0 2 3 6 8 9 10 12 13 15 17 18 19 0 1 2 3 5 6 8 9 11 13 14 15 16 18 0 1 2 3 4 5 6 8 9 10 12 13 14 15 16 17 19 0 1 2 3 4 5 6 7 9 10 11 12 13 15 16 17 18 Off-diagonal values: 0.496616 -0.271978 0.610154 0.209855 0.515313 0.218108 0.579213 -0.790474 0.823148 0.965380 -0.539533 -0.388153 0.723649 -0.470454 0.835137 -0.633114 -0.999233 -0.265232 0.248592 -0.060797 0.304242 0.491143 -0.619854 -0.108385 -0.730624 -0.671404 -0.789445 0.072092 0.992918 -0.943451 0.462330 -0.812211 0.152855 0.593859 0.393049 0.398772 0.103099 0.595087 -0.064439 -0.760503 -0.397092 -0.596889 0.448874 -0.696451 -0.245726 0.987874 0.532439 0.976567 0.922205 -0.017730 -0.166836 0.026317 -0.325578 -0.822965 -0.463287 0.875805 -0.661484 -0.711259 -0.031534 -0.687011 -0.091148 0.083875 -0.694048 0.650745 0.387726 0.095878 0.020496 0.742436 0.165288 -0.991411 -0.383126 -0.662225 0.121269 -0.116206 -0.529972 0.850049 0.952308 0.263391 0.712524 -0.525598 0.157334 0.608957 -0.070792 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x x - - x o - x x - o - o x | . o - x - o o o x o - x - - x - o o o o o x - x - x o x o - x x x x x - x o o | o | o o x o o x x x x o - o - x - o o o | | x x o - o o o o - x o x x x - x x x o | o o x x o o x x x - x o - x - x o o o | o | x o o - - o o x o x o - x o - | o x o o | o o x o o o x x o x - o o - x | | o o o o x x x - x o x - x - o o - x | o x o | o o o . o x x x x x o x o o | x x | o x o x x o x - - o o o x o o x x o o o | o o o o | o o o o - x o - o o o x | | x x x o o x o x . o x x o o x x | x | o x x | o o o x x | . - x x o o - o o x o o | | x x | x o x | o x o o x x o | x | o o o o o o o x | x | . x x o x x | o x | | o | x o x | x o | x x o o x o x x o | x x | o x | x | x x o o o x - x x x x o x x | x x o | o x x x o x o x x x o x o x x o | o x o x x | x x x o x The error in solving: 6.615281e-16 The error in solving: 5.032612e-16 The error in solving: 7.551608e-16 The error in solving: 7.870064e-16 The error in solving: 6.025661e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.774113 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.249320 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.842798 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.968930 -0.145117 -0.838282 -0.125572 0.000000 0.000000 0.000000 0.000000 0.000000 -0.704706 -0.629695 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.914773 0.000000 0.000000 -0.446161 -0.646455 -0.091489 0.000000 0.000000 0.000000 0.000000 0.000000 -0.109885 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.466096 0.000000 0.000000 -0.717758 0.000000 0.238873 0.000000 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0.248990 0.578655 -0.812719 -0.846398 0.093844 0.656635 0.713401 -0.720434 -0.905374 -0.888218 0.592690 0.276631 0.800765 0.857175 -0.131076 0.381376 0.364562 0.682823 -0.343845 -0.374678 -0.314483 -0.781433 0.032463 0.705824 0.531025 -0.255265 -0.351506 0.489503 -0.600253 0.526784 0.201178 -0.780199 -0.075432 -0.526968 0.990158 -0.154545 -0.123680 x - - - - - - o - - - - - - - - - - - - | x - - - - - - - - - - - x o o o - - - | | o o - - - - - - - - - - - - - - o - | o o o - - - - - o - - - - - - - - - o | | o | x - x - - - - - - - o - - - - - | | | | | o - o x x o o - - - - - o - - o | | | x | o x x - - - - - o - - - o - o | | o o x | o x - x - - - - x - - - - | | | x | | | | o x x - - - x o x - o - x | | x x | x | o o x - - - - - - - - - x | o | | x | | | | o - - - - - x - - - o x o | | x | x x | | x - - - - - - x - | | | | | | | | | | x o x - - - - - - - | o | | | | | | x | | | | x x - x o - - o | o x x | | | | | x x o | x x - - x - x | | | o | o | | | | | | | | x - - o - | | | | | o | | | | | | | | | x o - - - | | | | x | | | x o | | | | o | | x - - | x o | x x | o | o | | | | | | | | o - o | | | | | | x | | | | | | o | o | | o The error in solving: 2.877759e-16 The error in solving: 5.028664e-16 The error in solving: 7.562121e-16 The error in solving: 6.033248e-16 The error in solving: 8.693302e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.120460 0.134809 0.000000 0.524977 0.000000 -0.784504 0.000000 0.000000 -0.320890 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.209163 0.958481 0.000000 0.172376 0.683801 0.000000 0.916615 0.000000 0.000000 0.702129 0.000000 0.000000 0.000000 0.000000 0.000000 0.371042 -0.834006 0.777405 0.059514 0.826138 0.228972 0.000000 0.105519 0.000000 0.354554 0.000000 -0.328461 0.000000 -0.616595 0.000000 0.000000 0.094885 0.000000 0.000000 0.168128 0.000000 0.852044 0.869029 0.000000 0.000000 -0.906301 -0.253414 0.384417 -0.639060 0.000000 0.000000 0.000000 0.000000 -0.568750 -0.535664 -0.942780 0.513094 -0.984071 0.699231 -0.483767 0.000000 -0.329700 0.000000 0.621939 0.000000 -0.681395 0.202097 -0.031320 0.000000 0.449069 0.273323 -0.515745 0.000000 0.000000 0.000000 0.000000 0.000000 -0.388741 0.000000 0.744113 0.000000 -0.358143 0.000000 -0.732484 0.735412 0.000000 0.425480 0.000000 0.560284 0.000000 0.942643 0.981618 0.404791 0.000000 0.000000 0.943425 0.069968 0.000000 -0.570570 -0.994628 0.000000 0.000000 0.620201 0.293442 0.000000 0.000000 0.000000 0.919029 0.000000 0.000000 0.996601 0.244909 -0.323682 0.000000 0.113834 -0.816447 0.000000 0.075763 0.745697 -0.066872 0.949939 -0.362446 0.000000 0.000000 -0.676570 0.461997 0.000000 0.000000 0.000000 -0.734366 0.000000 0.000000 -0.127502 0.000000 0.491701 -0.724172 -0.966763 0.000000 0.000000 -0.054668 0.087978 0.000000 0.000000 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0.433437 -0.951352 -0.130611 0.000000 0.000000 -0.966805 0.000000 0.000000 -0.251044 0.303636 0.000000 0.709098 0.000000 0.357015 -0.349731 0.206931 -0.731835 0.922175 0.000000 0.000000 -0.949010 0.000000 0.000000 0.000000 0.000000 -0.320935 -0.416084 0.000000 0.000000 -0.982527 0.000000 -0.263267 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.610482 -0.153954 -0.679020 -0.859202 -0.523472 0.703324 0.000000 0.000000 -0.808743 0.000000 0.000000 0.128753 0.761739 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.170578 0.000000 -0.455507 0.000000 -0.197059 0.418488 0.000000 0.000000 0.000000 0.000000 0.987119 -0.064722 0.588397 0.000000 -0.794820 0.723719 0.181593 0.775773 0.000000 0.000000 0.000000 0.000000 0.000000 -0.267745 -0.560729 0.000000 -0.509970 -0.179181 0.008237 -0.600679 0.000000 -0.355968 0.000000 0.000000 -0.851653 -0.935896 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.820967 0.000000 0.000000 0.000000 0.000000 0.860802 0.000000 -0.539125 -0.127105 0.000000 -0.570663 -0.285994 0.000000 0.000000 -0.290618 0.000000 0.462163 -0.161821 0.512037 0.249024 0.000000 0.000000 0.000000 -0.816675 0.030766 -0.842018 -0.468069 0.385544 -0.424613 0.000000 0.000000 0.000000 0.224908 -0.092607 0.000000 -0.304570]; Dimension: 20 x 20 Off-diagonal entries: 186 (max 380) Diagonal entries: 0.120460 0.958481 0.105519 -0.639060 0.449069 0.942643 0.244909 -0.127502 0.697036 0.923997 -0.153623 0.467678 -0.262782 -0.251044 -0.982527 0.761739 -0.794820 -0.935896 -0.290618 -0.304570 Row indices: 0 4 14 22 34 44 54 65 73 85 93 101 111 122 135 142 150 160 168 174 186 Column indices: 1 3 5 8 0 3 4 6 9 15 16 17 18 19 0 4 6 8 11 14 16 17 0 1 2 8 9 10 11 12 13 14 16 18 0 1 2 5 6 12 14 16 18 19 1 3 6 7 10 11 13 14 17 18 2 5 7 9 10 12 13 14 15 16 19 0 4 9 10 11 14 15 18 2 3 4 5 6 7 9 12 14 15 17 19 0 1 2 3 7 12 16 18 0 1 9 11 12 14 16 19 1 2 3 4 8 12 15 16 18 19 3 5 7 9 10 11 13 14 16 18 19 0 1 2 3 4 5 6 7 10 14 16 18 19 0 1 2 5 10 11 16 3 4 5 6 7 8 11 14 2 4 6 7 12 13 14 17 18 19 5 6 8 9 10 11 13 16 4 9 11 12 14 15 0 1 2 3 7 8 9 10 11 12 16 17 Off-diagonal values: 0.134809 0.524977 -0.784504 -0.320890 0.209163 0.172376 0.683801 0.916615 0.702129 0.371042 -0.834006 0.777405 0.059514 0.826138 0.228972 0.354554 -0.328461 -0.616595 0.094885 0.168128 0.852044 0.869029 -0.906301 -0.253414 0.384417 -0.568750 -0.535664 -0.942780 0.513094 -0.984071 0.699231 -0.483767 -0.329700 0.621939 -0.681395 0.202097 -0.031320 0.273323 -0.515745 -0.388741 0.744113 -0.358143 -0.732484 0.735412 0.425480 0.560284 0.981618 0.404791 0.943425 0.069968 -0.570570 -0.994628 0.620201 0.293442 0.919029 0.996601 -0.323682 0.113834 -0.816447 0.075763 0.745697 -0.066872 0.949939 -0.362446 -0.676570 0.461997 -0.734366 0.491701 -0.724172 -0.966763 -0.054668 0.087978 -0.293459 0.547799 -0.075449 0.379909 -0.945657 -0.634981 -0.571074 -0.032673 0.619862 0.825852 0.719727 0.177187 0.330469 -0.253294 0.963209 0.259160 0.998265 0.561255 0.379883 -0.371219 0.374064 -0.601891 0.986073 -0.372102 0.606401 -0.335055 -0.692186 -0.176605 -0.066959 -0.854103 0.359453 0.037125 -0.183958 -0.980507 -0.853850 -0.427312 -0.593575 -0.376262 0.624114 0.586543 0.878879 -0.028880 -0.196639 -0.429990 0.523798 -0.267217 -0.549281 -0.703215 0.003833 -0.549988 -0.261352 0.811494 -0.275544 -0.313831 0.477902 0.433437 -0.951352 -0.130611 -0.966805 0.303636 0.709098 0.357015 -0.349731 0.206931 -0.731835 0.922175 -0.949010 -0.320935 -0.416084 -0.263267 0.610482 -0.153954 -0.679020 -0.859202 -0.523472 0.703324 -0.808743 0.128753 0.170578 -0.455507 -0.197059 0.418488 0.987119 -0.064722 0.588397 0.723719 0.181593 0.775773 -0.267745 -0.560729 -0.509970 -0.179181 0.008237 -0.600679 -0.355968 -0.851653 0.820967 0.860802 -0.539125 -0.127105 -0.570663 -0.285994 0.462163 -0.161821 0.512037 0.249024 -0.816675 0.030766 -0.842018 -0.468069 0.385544 -0.424613 0.224908 -0.092607 x x - x - o - - o - - - - - - - - - - - x x - x x - x - - x - - - - - x o x x x x | x - x - o - o - - x - - x - x x - - o o x o - - - - o o o x o x o - o - x - o x o | x x o - - - - - o - x - o - o x | x | x | x x x - - x x - o o - - x x - | | x | | x x o - x o - x x o x o - - o x | | | o | | o - x o o - - o x - - o - | | x o x o o o x o - - x - x x - x - x o x x x | | | x | x - - x - - - o - x - o x | | | | | | | o o x o - o - o - - o | o x x o | | | o | | x o - - o o - o x | | | x | x | o | o o x o o o - o - x o o x o o x x o o | | o | | o x - x - x o x o x | | o | | | | o o | | o - o - - - | | | x o o o o x | | o | | x x - - - - | | x | o | o x | | | | x o x | o x x x | | | | | o o | o o x o | o | | o o - - | | | | x | | | | x | o o | o o | | o - x o x x | | | o x o o x o | | | x o | o The error in solving: 6.268091e-16 The error in solving: 6.798722e-16 The error in solving: 5.663414e-16 The error in solving: 6.474029e-16 The error in solving: 4.304911e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.750000 [ -0.488652 0.286142 -0.124729 -0.844917 -0.209987 0.199200 -0.594070 -0.401997 -0.541030 0.000000 0.759681 0.971822 0.000000 0.000000 0.000000 0.000000 -0.690493 0.432319 0.773458 -0.920263 0.000000 0.865014 0.253239 0.554694 0.997283 -0.644512 0.939387 0.334118 0.000000 0.000000 -0.851538 0.000000 -0.043280 0.037638 -0.129663 -0.574336 -0.418243 -0.457819 0.260174 0.212790 0.047375 0.211636 0.334831 -0.944837 -0.914151 -0.343501 -0.573993 0.109010 -0.269673 0.505235 0.028806 0.000000 0.000000 -0.600093 0.000000 0.000000 -0.017379 -0.788917 -0.185292 0.000000 0.179860 0.000000 -0.542442 0.084312 -0.729119 -0.369290 0.643348 0.995968 0.992027 -0.292824 0.000000 0.390628 0.099589 -0.360988 0.739305 0.487804 -0.826763 0.000000 0.480383 -0.520573 0.076482 0.133228 -0.624865 -0.978089 0.467861 -0.809978 0.000000 0.959735 0.227162 0.681264 0.053308 -0.143584 0.687886 0.000000 -0.804608 -0.625174 0.074216 0.575316 0.827312 0.000000 -0.025432 0.323120 0.000000 -0.442685 0.695869 0.420575 0.000000 0.395977 0.829449 0.641324 0.146380 -0.911171 -0.030502 0.000000 0.000000 -0.249762 0.000000 0.007057 -0.026040 0.000000 -0.535825 0.150825 -0.506113 0.000000 0.000000 -0.411909 -0.799128 0.027289 0.570606 0.000000 -0.254776 0.000000 -0.432104 0.052696 -0.719377 -0.869353 0.000000 0.316862 0.110903 0.000000 0.732046 -0.891358 0.000000 0.000000 0.000000 0.682025 0.000000 0.056840 0.000000 0.935816 0.000000 -0.681996 0.350047 -0.059636 -0.640534 0.925638 0.563583 0.471134 0.476408 0.163674 -0.498709 0.252433 -0.156939 0.138836 0.237665 -0.916659 0.647550 0.787125 -0.040569 -0.206393 0.000000 -0.805115 0.000000 0.494700 0.786099 0.000000 0.815535 0.193827 0.021872 0.919143 -0.700999 -0.392020 0.745378 0.000000 0.000000 0.000000 0.000000 0.711912 -0.607025 0.326957 -0.028813 0.783667 0.936768 -0.701719 0.000000 0.177338 -0.605333 0.000000 -0.729151 0.000000 -0.779678 0.340658 -0.555000 0.000000 0.282883 0.000000 -0.333012 0.000000 -0.005032 0.038989 0.298772 0.417402 -0.676722 -0.811510 0.000000 0.730758 0.782904 -0.838253 0.480234 -0.314037 0.000000 -0.921024 0.583525 0.168452 -0.951830 0.956730 0.000000 0.759622 -0.762634 -0.049290 0.000000 0.585955 0.506557 0.000000 0.153914 0.000000 0.691677 0.648143 0.310810 0.257661 -0.526940 0.173737 -0.434863 -0.734498 0.000000 0.000000 -0.427570 0.000000 -0.552988 -0.898050 -0.175277 -0.791026 0.103319 -0.380173 -0.844804 0.043899 0.024409 -0.477457 0.000000 -0.979947 0.762387 -0.716950 0.202999 -0.640683 0.570282 0.351256 0.364026 0.000000 0.781881 0.739947 -0.203666 0.000000 0.031237 -0.766827 -0.186087 0.000000 -0.713630 -0.592553 0.719070 -0.192100 0.498543 0.514099 -0.174090 -0.186145 0.690448 -0.964293 0.940267 0.452084 -0.096145 0.000000 0.985683 0.534326 0.000000 0.000000 -0.386986 0.000000 0.000000 0.000000 0.930344 0.728091 0.941943 -0.676739 -0.284960 -0.258503 -0.335087 0.000000 0.000000 0.811896 0.995210 0.933021 0.042343 0.261107 0.000000 0.657100 0.000000 -0.985218 0.097752 0.378963 0.666188 -0.380813 0.668762 -0.270399 0.579618 0.000000 0.376259 0.085922 -0.455974 0.000000 -0.279614 -0.216621 0.000000 0.142007 0.688096 0.000000 -0.071358 0.485393 -0.017423 -0.165345 0.000000 -0.354311 -0.915409 0.000000 0.072563 -0.609431 0.846009 0.336187 0.606728 -0.981072 -0.422569 -0.489232 -0.279028 -0.935097 -0.879037 -0.791499 0.000000 0.917888 -0.824183 -0.629468 0.950718 -0.918595 0.014740 0.047393 -0.901584 0.000000 0.000000 -0.943741 0.378811 -0.230329 0.547134 0.809905 0.389765 0.518345 0.456871 0.977930 0.749033 -0.471749 0.919321 -0.027173 -0.930610 0.000000 0.000000 0.556424 -0.547575 -0.666255 -0.575356 -0.097969 0.240081 0.837948 0.680485 -0.399318 -0.263942 -0.762848 0.066082 0.000000 -0.247097 0.010381 0.000000 -0.716464 0.373985 -0.227914]; Dimension: 20 x 20 Off-diagonal entries: 293 (max 380) Diagonal entries: -0.488652 0.865014 0.334831 0.084312 0.467861 0.420575 -0.799128 0.056840 -0.040569 0.326957 0.298772 0.585955 0.103319 -0.766827 -0.386986 -0.985218 -0.017423 -0.629468 -0.930610 -0.227914 Row indices: 0 14 29 43 59 75 88 101 114 130 142 157 171 186 202 215 230 244 261 277 293 Column indices: 1 2 3 4 5 6 7 8 10 11 16 17 18 19 2 3 4 5 6 7 10 12 13 14 15 16 17 18 19 0 1 3 4 5 6 7 8 9 10 13 16 17 18 0 2 4 5 6 7 8 9 11 12 13 14 15 16 18 19 0 1 2 3 5 7 8 9 10 11 12 14 15 16 17 18 0 1 3 4 7 8 9 10 11 12 15 17 18 0 1 2 5 7 8 10 12 13 14 15 17 18 0 1 5 9 11 12 13 14 15 16 17 18 19 0 1 2 3 4 5 6 7 9 11 13 14 16 17 18 19 0 1 2 7 8 10 11 12 13 15 16 18 0 1 2 4 6 8 9 11 12 13 15 16 17 18 19 1 2 3 4 5 7 8 9 12 14 16 17 18 19 0 1 2 3 6 8 9 10 11 13 14 15 16 17 19 0 1 2 3 4 5 6 8 9 10 12 14 16 17 18 19 0 1 2 3 4 5 6 7 8 10 11 18 19 0 1 2 3 4 7 8 9 10 11 13 16 17 18 19 0 1 2 4 5 6 8 9 11 12 14 15 17 19 0 2 3 4 5 6 7 8 9 10 11 12 13 15 16 18 19 0 1 2 5 6 7 8 9 10 11 12 13 14 15 16 17 1 2 3 4 5 6 7 8 9 10 11 12 14 15 17 18 Off-diagonal values: 0.286142 -0.124729 -0.844917 -0.209987 0.199200 -0.594070 -0.401997 -0.541030 0.759681 0.971822 -0.690493 0.432319 0.773458 -0.920263 0.253239 0.554694 0.997283 -0.644512 0.939387 0.334118 -0.851538 -0.043280 0.037638 -0.129663 -0.574336 -0.418243 -0.457819 0.260174 0.212790 0.047375 0.211636 -0.944837 -0.914151 -0.343501 -0.573993 0.109010 -0.269673 0.505235 0.028806 -0.600093 -0.017379 -0.788917 -0.185292 0.179860 -0.542442 -0.729119 -0.369290 0.643348 0.995968 0.992027 -0.292824 0.390628 0.099589 -0.360988 0.739305 0.487804 -0.826763 0.480383 -0.520573 0.076482 0.133228 -0.624865 -0.978089 -0.809978 0.959735 0.227162 0.681264 0.053308 -0.143584 0.687886 -0.804608 -0.625174 0.074216 0.575316 0.827312 -0.025432 0.323120 -0.442685 0.695869 0.395977 0.829449 0.641324 0.146380 -0.911171 -0.030502 -0.249762 0.007057 -0.026040 -0.535825 0.150825 -0.506113 -0.411909 0.027289 0.570606 -0.254776 -0.432104 0.052696 -0.719377 -0.869353 0.316862 0.110903 0.732046 -0.891358 0.682025 0.935816 -0.681996 0.350047 -0.059636 -0.640534 0.925638 0.563583 0.471134 0.476408 0.163674 -0.498709 0.252433 -0.156939 0.138836 0.237665 -0.916659 0.647550 0.787125 -0.206393 -0.805115 0.494700 0.786099 0.815535 0.193827 0.021872 0.919143 -0.700999 -0.392020 0.745378 0.711912 -0.607025 -0.028813 0.783667 0.936768 -0.701719 0.177338 -0.605333 -0.729151 -0.779678 0.340658 -0.555000 0.282883 -0.333012 -0.005032 0.038989 0.417402 -0.676722 -0.811510 0.730758 0.782904 -0.838253 0.480234 -0.314037 -0.921024 0.583525 0.168452 -0.951830 0.956730 0.759622 -0.762634 -0.049290 0.506557 0.153914 0.691677 0.648143 0.310810 0.257661 -0.526940 0.173737 -0.434863 -0.734498 -0.427570 -0.552988 -0.898050 -0.175277 -0.791026 -0.380173 -0.844804 0.043899 0.024409 -0.477457 -0.979947 0.762387 -0.716950 0.202999 -0.640683 0.570282 0.351256 0.364026 0.781881 0.739947 -0.203666 0.031237 -0.186087 -0.713630 -0.592553 0.719070 -0.192100 0.498543 0.514099 -0.174090 -0.186145 0.690448 -0.964293 0.940267 0.452084 -0.096145 0.985683 0.534326 0.930344 0.728091 0.941943 -0.676739 -0.284960 -0.258503 -0.335087 0.811896 0.995210 0.933021 0.042343 0.261107 0.657100 0.097752 0.378963 0.666188 -0.380813 0.668762 -0.270399 0.579618 0.376259 0.085922 -0.455974 -0.279614 -0.216621 0.142007 0.688096 -0.071358 0.485393 -0.165345 -0.354311 -0.915409 0.072563 -0.609431 0.846009 0.336187 0.606728 -0.981072 -0.422569 -0.489232 -0.279028 -0.935097 -0.879037 -0.791499 0.917888 -0.824183 0.950718 -0.918595 0.014740 0.047393 -0.901584 -0.943741 0.378811 -0.230329 0.547134 0.809905 0.389765 0.518345 0.456871 0.977930 0.749033 -0.471749 0.919321 -0.027173 0.556424 -0.547575 -0.666255 -0.575356 -0.097969 0.240081 0.837948 0.680485 -0.399318 -0.263942 -0.762848 0.066082 -0.247097 0.010381 -0.716464 0.373985 o x o o o x o o o - x x - - - - o x x o | x x x x o x x - - o - o x o o o o x x x x x o o o o x o x x - - o - - o o o - x | o x o o x x x o - x x o x x o - x o x x o o x o - x x x x o x - o o x x x - o x | o x x - x x x x o o - - o - x o - o x o | | o o x x - o - o x o o - x x - x o | | | x | x - x - o x o o x x x x x o x o x x o x x o o - o - x x - x x x x o o x | | | | x o x o x x o - x o - o - o x o | x | o | o x x x o o - x x o x o | o x x o x | x o o | x x - x - x x x x o x o o | | o | o o o o x o o x x o - o x o x o x x x | x x o | x o o - o o x o x x o o x o x x o | x x | | o - - - x x x o o o o | | x x x x x | x | o x x x o x o x | x x o | o o | x x | o x o o - o o | x o x x x o o o o o o o | x o o x o x x o | | o x o x x x x x x x o x o o - | x o o o o x x x o o o x | o x | o x o The error in solving: 7.233194e-16 The error in solving: 7.043880e-16 The error in solving: 6.018866e-16 The error in solving: 6.866350e-16 The error in solving: 4.380993e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 -0.801170 0.000000 0.000000 0.000000 0.000000 -0.108922 -0.714436 0.000000 0.000000 -0.396385 -0.835875 0.000000 0.000000 0.000000 0.307652 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.415280 0.000000 0.000000 0.000000 0.908169 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.982835 0.000000 0.000000 0.000000 -0.187575 0.000000 -0.198983 0.000000 0.000000 0.779257 0.000000 0.000000 0.000000 -0.727015 0.000000 0.000000 0.000000 0.055972 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.745869 0.000000 0.000000 0.000000 0.000000 0.000000 0.708036 0.656362 0.000000 0.000000 0.000000 0.000000 0.000000 0.889277 -0.383292 0.000000 0.000000 0.114849 0.000000 -0.007124 0.000000 0.000000 0.000000 0.000000 0.099317 0.000000 0.000000 0.000000 0.000000 -0.221668 0.000000 -0.660290 -0.490051 0.000000 0.000000 0.916351 -0.813701 0.000000 0.000000 0.000000 0.000000 0.000000 -0.438555 0.000000 0.000000 0.000000 0.000000 -0.571230 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.615099 0.000000 0.000000 0.000000 0.458509 0.000000 0.389246 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.036054 0.000000 0.000000 0.822663 0.000000 0.000000 0.000000 0.680367 0.792139 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.960014 -0.951737 0.000000 0.000000 0.473021 0.007209 -0.924893 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.708870 0.461831 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.465196 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.845202 0.994393 0.000000 0.000000 -0.703681 0.412087 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.577750 -0.535274 0.000000 0.000000 0.000000 0.000000 0.000000 0.966995 0.000000 0.000000 0.000000 0.000000 0.000000 0.465691 -0.780493 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.043051 -0.939068 0.000000 0.000000 0.000000 0.000000 0.553600 0.892633 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.646502 0.000000 0.000000 0.000000 -0.855461 0.563160 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.924447 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.391027 -0.166344 0.000000 -0.029935 0.584490 0.000000 0.000000 0.000000 0.000000 0.000000 -0.613364 0.263545 0.000000 0.000000 0.078521 0.000000 0.000000 -0.767748 0.000000 0.083090 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 92 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 6 9 14 19 26 29 33 38 43 48 53 53 58 62 67 74 75 80 84 92 Column indices: 1 6 7 10 11 15 4 8 17 1 3 6 10 14 4 10 11 17 18 1 3 8 13 15 16 19 0 6 11 1 5 7 18 1 5 6 17 18 1 2 3 15 16 4 11 12 15 16 5 6 12 18 19 2 5 8 11 13 3 5 9 17 6 7 13 18 19 2 3 4 7 12 18 19 5 3 4 9 10 18 2 3 11 19 0 2 3 9 10 13 16 18 Off-diagonal values: -0.801170 -0.108922 -0.714436 -0.396385 -0.835875 0.307652 0.415280 0.908169 0.982835 -0.187575 -0.198983 0.779257 -0.727015 0.055972 -0.745869 0.708036 0.656362 0.889277 -0.383292 0.114849 -0.007124 0.099317 -0.221668 -0.660290 -0.490051 0.916351 -0.813701 -0.438555 -0.571230 0.615099 0.458509 0.389246 -0.036054 0.822663 0.680367 0.792139 0.960014 -0.951737 0.473021 0.007209 -0.924893 -0.708870 0.461831 0.465196 -0.845202 0.994393 -0.703681 0.412087 0.577750 -0.535274 0.966995 0.465691 -0.780493 0.786544 -0.796987 -0.494465 -0.807776 -0.711820 -0.109969 0.928724 0.707311 0.250805 -0.446803 0.422200 -0.275764 -0.869409 -0.427841 0.271094 -0.356357 -0.326165 0.416059 -0.819594 0.508225 -0.951216 -0.401497 0.043051 -0.939068 0.553600 0.892633 -0.646502 -0.855461 0.563160 0.924447 -0.391027 -0.166344 -0.029935 0.584490 -0.613364 0.263545 0.078521 -0.767748 0.083090 . o - - - - o o - - o o - - - x - - - - | . - - x - - - x - - - - - - - - x - - | o . o - - x - - - o - - - x - - - - - | | | . o - - - - - x x - - - - - x o - | x | o . - - - x - - - - o - o o - - x o | | | | . o - - - - o - - - - - - - - | x | | | x . x - - - - - - - - - - o - | x | | | x x . - - - - - - - - - x o - | x x o | | | | . - - - - - - o x - - - | | | | x | | | | . - o x - - o x - - - | | | | | x o | | | . - x - - - - - x o | | | | | | | | | | | . - - - - - - - - | | x | | o | | o | | o . o - - - - - - | | | o | x | | | x | | | . - - - x - - | | | | | | o x | | | | | o . - - - o o | | x o o | | x | | | | o | | . - - x o | | | | | o | | | | | | | | | | . - - - | | | x o | | | | x x | | | | | | . o - | | o x | | | | | | | x | | | | | | . o o | o x | | | | | o x | | x | | o | x . The error in solving: 8.789108e-16 The error in solving: 6.080942e-16 The error in solving: 5.097136e-16 The error in solving: 4.728641e-16 The error in solving: 4.957304e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 -0.005001 0.000000 -0.580276 0.403316 0.000000 -0.370009 0.524743 0.919069 0.000000 -0.755875 0.000000 0.000000 0.000000 -0.817450 0.000000 0.221125 0.772868 0.568335 -0.253305 0.000000 0.000000 -0.628053 0.000000 -0.894950 0.000000 0.000000 0.538999 0.000000 0.254076 0.000000 0.000000 -0.593583 0.000000 0.000000 0.000000 0.000000 0.111398 -0.160729 0.848174 0.000000 0.000000 0.000000 0.544665 0.444886 0.000000 0.000000 0.000000 -0.929124 0.074711 0.000000 0.000000 -0.752213 -0.172078 0.000000 -0.870016 0.000000 0.000000 0.000000 -0.898682 0.085272 0.000000 0.000000 0.000000 -0.421460 0.895023 0.189995 0.432518 0.432403 0.723654 0.000000 0.000000 0.000000 0.000000 0.000000 0.837715 0.067551 0.000000 0.238442 -0.938349 -0.789632 0.000000 0.168572 0.000000 -0.321237 0.000000 0.000000 -0.948965 -0.768712 0.000000 -0.954880 0.000000 0.998072 0.000000 0.738948 0.000000 0.000000 0.000000 0.999920 0.000000 -0.911535 0.003891 -0.618647 0.406759 0.000000 0.000000 0.133585 -0.940764 0.000000 0.745696 0.701829 -0.556654 0.000000 -0.255415 0.000000 0.000000 0.620180 0.852960 -0.721454 0.000000 0.385752 -0.769484 -0.906459 -0.103078 0.325018 0.000000 0.000000 0.562916 0.000000 0.194831 0.000000 0.000000 0.000000 0.000000 -0.610404 0.519210 0.000000 0.000000 -0.908695 0.000000 -0.868727 0.000000 0.925937 -0.183537 -0.838665 0.664855 0.000000 0.276964 -0.808636 0.000000 0.000000 0.864362 0.000000 0.000000 0.428278 0.032011 0.670627 0.000000 0.229575 0.000000 0.000000 0.058497 0.000000 -0.821056 0.062808 -0.991988 0.000000 0.000000 0.000000 0.000000 0.000000 -0.106577 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.133552 0.051397 -0.871071 -0.659115 0.000000 0.000000 0.768253 0.722739 0.000000 -0.062777 0.000000 0.000000 0.000000 0.437402 0.896639 0.000000 -0.717983 0.000000 0.000000 -0.268773 0.000000 -0.521576 0.000000 0.000000 0.000000 0.895657 0.000000 0.000000 -0.569669 0.000000 -0.864854 0.000000 -0.972581 0.000000 0.000000 0.000000 0.000000 0.116955 0.000000 0.687493 -0.826993 -0.388698 0.000000 0.022628 0.000000 -0.146181 0.000000 0.000000 0.000000 0.272626 0.000000 0.711346 0.000000 0.000000 0.000000 -0.999022 0.000000 0.000000 0.000000 0.000000 0.000000 0.997927 0.000000 0.000000 0.000000 -0.879459 0.000000 0.383736 0.000000 -0.096629 -0.076143 0.000000 0.841024 0.000000 0.154518 0.000000 0.000000 0.000000 0.000000 0.000000 -0.574448 0.000000 0.000000 0.856952 0.601141 -0.109764 0.000000 0.000000 0.000000 -0.063064 0.253108 0.000000 0.000000 0.041593 0.000000 0.000000 0.000000 0.000000 0.000000 0.498030 0.000000 0.453595 -0.763147 0.000000 -0.326435 0.434646 0.534646 0.000000 0.649599 -0.213606 0.130302 0.289106 0.958709 0.000000 0.000000 0.000000 0.278125 0.000000 -0.204624 0.000000 0.473824 0.000000 0.159776 0.000000 0.015148 0.000000 -0.421619 -0.611946 0.345765 0.000000 0.000000 0.912528 0.000000 0.000000 -0.642774 0.000000 0.000000 0.000000 0.000000 0.000000 0.270207 0.000000 0.000000 0.892972 0.000000 0.000000 0.000000 0.429861 0.254882 -0.029589 0.000000 0.495175 0.133653 -0.437516 0.894725 0.000000 -0.172887 0.000000 -0.349032 -0.314011 0.000000 -0.309254 -0.746081 -0.750252 0.000000 -0.346045 0.454861 -0.948884 0.307048 -0.068881 0.000000 0.081199 0.000000 0.425732 0.440928 0.000000 0.000000 -0.916045 0.000000 0.478650 0.000000 0.000000 0.000000 0.948788 0.000000 0.773885 -0.434679 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.087082 0.000000 0.000000 0.090848 0.087300 -0.460272 0.000000 0.470835 0.000000 0.000000 -0.100244 0.108327 0.000000 -0.185610 0.000000 0.401769 -0.077681 0.000000 0.120402 0.000000 0.000000 0.498321 0.000000 -0.112639 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 189 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 11 19 27 38 48 61 71 83 89 99 107 113 121 128 141 149 160 173 181 189 Column indices: 2 4 5 7 8 9 11 15 17 18 19 0 3 5 8 10 13 18 19 0 4 5 9 10 13 14 16 0 1 5 6 7 8 9 10 16 17 19 0 1 3 5 8 9 11 13 15 19 1 2 3 4 7 8 10 11 12 14 17 18 19 1 2 3 4 5 8 10 15 16 19 1 3 4 5 6 8 9 12 15 16 17 19 2 4 5 6 12 19 0 1 2 5 6 8 12 13 15 18 0 4 7 9 11 16 18 19 0 2 4 8 10 14 0 4 6 8 9 11 13 19 2 3 4 8 9 12 18 0 1 3 4 5 7 8 9 10 11 15 17 19 1 3 5 6 7 10 13 19 2 6 7 8 10 11 12 13 15 17 18 0 1 2 4 5 6 7 8 10 12 13 16 18 2 4 5 12 15 16 17 19 2 3 5 7 8 10 13 15 Off-diagonal values: -0.005001 -0.580276 0.403316 -0.370009 0.524743 0.919069 -0.755875 -0.817450 0.221125 0.772868 0.568335 -0.253305 -0.628053 -0.894950 0.538999 0.254076 -0.593583 0.111398 -0.160729 0.848174 0.544665 0.444886 -0.929124 0.074711 -0.752213 -0.172078 -0.870016 -0.898682 0.085272 -0.421460 0.895023 0.189995 0.432518 0.432403 0.723654 0.837715 0.067551 0.238442 -0.938349 -0.789632 0.168572 -0.321237 -0.948965 -0.768712 -0.954880 0.998072 0.738948 0.999920 -0.911535 0.003891 -0.618647 0.406759 0.133585 -0.940764 0.745696 0.701829 -0.556654 -0.255415 0.620180 0.852960 -0.721454 0.385752 -0.769484 -0.906459 -0.103078 0.325018 0.562916 0.194831 -0.610404 0.519210 -0.908695 -0.868727 0.925937 -0.183537 -0.838665 0.664855 0.276964 -0.808636 0.864362 0.428278 0.032011 0.670627 0.229575 0.058497 -0.821056 0.062808 -0.991988 -0.106577 -0.133552 0.051397 -0.871071 -0.659115 0.768253 0.722739 -0.062777 0.437402 0.896639 -0.717983 -0.268773 -0.521576 0.895657 -0.569669 -0.864854 -0.972581 0.116955 0.687493 -0.826993 -0.388698 0.022628 -0.146181 0.272626 0.711346 -0.999022 0.997927 -0.879459 0.383736 -0.096629 -0.076143 0.841024 0.154518 -0.574448 0.856952 0.601141 -0.109764 -0.063064 0.253108 0.041593 0.498030 0.453595 -0.763147 -0.326435 0.434646 0.534646 0.649599 -0.213606 0.130302 0.289106 0.958709 0.278125 -0.204624 0.473824 0.159776 0.015148 -0.421619 -0.611946 0.345765 0.912528 -0.642774 0.270207 0.892972 0.429861 0.254882 -0.029589 0.495175 0.133653 -0.437516 0.894725 -0.172887 -0.349032 -0.314011 -0.309254 -0.746081 -0.750252 -0.346045 0.454861 -0.948884 0.307048 -0.068881 0.081199 0.425732 0.440928 -0.916045 0.478650 0.948788 0.773885 -0.434679 0.087082 0.090848 0.087300 -0.460272 0.470835 -0.100244 0.108327 -0.185610 0.401769 -0.077681 0.120402 0.498321 -0.112639 . - o - o x - o x x - o - - - o - x x x o . - o - o - - x - x - - o - - - - x o x | . - x x - - - o x - - o o - o - - - o x | . - o x x x x x - - - - - x x - x o o | x . o - - o o - o - x - x - - - x | o x o x . - x o - x x o - o - - x x o | x o o o x . - x - x - - - - o x - - o | o | x o o x . x o - - x - - x x x - x | | x | o x o | . - - - o - - - - - - o x o o | | x x | o . - - x x - o - - o - o | | | x | | o | o . o - - - - x - x o o | x | o | | | x | x . - - o - - - - - x | | | o | x | o o | x . x - - - - - o | | x x o | | | o x | | x . - - - - x - x o | o x x | x o x x x | | . x - o - x | x | x | o o x | | x | | o | . - - - x | | x | | | x x o | x x o x | o . o o - o o o | o x o x o | x | x x | | o . x - | | x | x o | | | | | | x | | x x o . x | | o x | o | x o | x | | x | o | | | . The error in solving: 4.918301e-16 The error in solving: 6.884907e-16 The error in solving: 6.342923e-16 The error in solving: 4.521609e-16 The error in solving: 4.445904e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.109471 0.435785 -0.649758 0.577114 -0.046923 -0.186319 -0.186312 0.000000 -0.156228 0.195611 0.146246 0.000000 -0.794053 -0.762913 0.000000 -0.885359 -0.483364 0.577356 -0.766183 0.206135 0.000000 -0.972010 0.047151 0.132620 0.000000 0.000000 0.000000 0.278237 0.000000 0.806721 0.000000 0.572727 0.000000 -0.813998 0.125212 0.527690 -0.659016 0.109381 -0.497747 0.000000 -0.448310 0.000000 0.000000 0.000000 -0.768588 -0.084566 0.000000 0.376583 0.000000 0.981128 0.856439 0.594887 0.180828 0.000000 0.000000 -0.923117 0.000000 0.611162 0.000000 0.009217 -0.535387 -0.497161 0.000000 -0.344189 0.000000 0.000000 -0.907802 0.000000 0.960702 -0.933156 0.479075 0.735725 0.152443 0.000000 0.000000 0.000000 0.515308 -0.401811 0.845680 0.000000 -0.737366 -0.150025 -0.502919 0.000000 -0.114428 0.000000 0.764239 0.580630 0.000000 -0.691487 0.591906 -0.064314 0.952710 -0.409505 0.789880 0.000000 -0.404191 0.000000 -0.520270 0.324743 0.576675 0.796643 0.000000 0.863724 0.000000 -0.569436 0.910340 -0.381962 0.773918 0.000000 0.189113 -0.711088 -0.076478 0.000000 0.003875 0.000000 -0.956433 -0.937376 -0.219140 -0.398437 0.000000 -0.122948 0.643631 0.600901 -0.756324 0.000000 0.850877 0.407883 0.000000 0.865500 0.074124 0.000000 0.998656 0.000000 0.000000 0.000000 -0.117443 0.165680 0.000000 0.927543 -0.165256 0.000000 0.685468 0.000000 -0.193506 -0.968918 0.000000 0.971415 -0.210014 -0.353420 0.000000 0.000000 -0.102609 -0.168108 -0.372468 0.000000 -0.926754 -0.752643 -0.865723 -0.738490 0.000000 -0.551732 -0.807012 0.000000 -0.354787 -0.427047 -0.325254 0.000000 0.511247 0.255713 -0.515312 0.000000 0.292245 0.000000 0.000000 0.781592 -0.811309 0.961550 0.937233 0.000000 0.054222 -0.621343 0.000000 -0.468984 -0.376514 -0.682486 0.000000 -0.285774 0.000000 0.000000 -0.150285 0.000000 -0.151355 -0.022719 -0.839548 -0.999004 0.375424 0.000000 -0.823017 0.000000 0.000000 -0.444444 0.000000 0.540664 -0.282524 0.940254 0.464674 -0.782121 -0.417630 0.000000 0.987942 -0.271946 -0.056808 0.533488 0.418693 0.000000 -0.307027 0.000000 0.000000 0.000000 -0.341935 0.266363 -0.845218 0.556869 0.000000 0.109110 -0.787447 0.899348 -0.049040 -0.321650 0.000000 -0.430214 -0.721719 0.000000 -0.959692 0.574117 0.010968 0.320774 0.283965 0.687630 -0.515257 0.045759 0.101702 0.666417 0.467453 -0.399537 -0.455155 0.000000 0.990789 0.000000 -0.295025 0.000000 -0.748722 0.373453 0.148232 -0.276060 0.684526 0.000000 -0.305875 0.000000 0.430005 0.000000 0.000000 0.340538 0.531264 0.917661 0.326339 0.216430 -0.332684 0.000000 -0.554999 0.000000 0.000000 0.000000 0.000000 0.000000 -0.945180 0.501258 0.679407 0.000000 0.000000 0.999145 0.904778 0.030547 -0.228916 0.845918 0.000000 0.000000 -0.142915 0.722896 0.651679 -0.539337 -0.418773 0.000000 0.000000 0.000000 0.000000 0.604413 -0.867917 0.226197 0.718769 -0.884715 -0.627625 0.007039 0.000000 0.000000 -0.993935 0.000000 -0.422002 -0.889755 0.851741 0.000000 -0.124929 -0.704172 0.000000 0.838759 -0.550880 -0.126042 0.000000 -0.902996 -0.803884 0.000000 0.000000 0.000000 -0.883739 -0.473471 0.000000 0.000000 0.054942 0.000000 -0.525572 0.450162 -0.638172 -0.731049 -0.797507 0.000000 0.000000 -0.477564 -0.395114 0.390927 -0.125280 0.311616 0.000000 -0.850882 -0.577576 0.000000 0.630600 -0.282825 0.574359 0.503072 -0.195072 0.356831 0.365489 0.000000 0.000000 0.000000 0.000000 -0.890108 -0.493018 0.689697 0.855469 -0.441372 -0.210025 0.095253 -0.016806 0.330769 0.000000 0.000000 0.583886 0.000000 0.668392 -0.381140 0.041114 0.054956 0.000000 0.760071 -0.417162 0.000000 0.531295 -0.926563 0.860414 -0.592351 -0.085751 -0.543783 -0.523859 0.000000 -0.084024 0.000000 0.482652 -0.908003 0.000000 0.047763 -0.906077 0.000000 0.828375 -0.339415 0.089390 0.839129 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 272 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 16 29 39 52 66 81 93 107 121 134 147 163 179 190 202 216 228 242 257 272 Column indices: 1 2 3 4 5 6 7 9 10 11 13 14 16 17 18 19 0 2 3 4 8 10 12 14 15 16 17 18 19 1 5 6 8 10 11 12 13 16 18 0 1 2 4 7 9 10 11 12 13 17 18 19 1 2 3 5 7 8 10 11 12 13 14 15 17 19 0 1 2 4 6 7 8 9 11 12 13 15 17 18 19 0 2 3 4 5 7 8 10 11 13 17 18 0 1 3 5 6 8 9 10 13 14 15 17 18 19 0 2 3 5 6 7 9 10 11 13 16 17 18 19 1 2 4 5 6 8 11 13 14 15 16 17 19 2 4 5 6 7 8 9 11 12 13 14 15 17 1 2 3 4 6 7 8 9 10 12 13 15 16 17 18 19 0 1 2 3 4 5 6 7 9 11 13 14 15 16 17 19 1 4 5 6 7 8 9 11 17 18 19 2 3 4 5 6 9 10 11 12 13 18 19 0 1 2 3 4 7 9 10 11 13 14 16 17 18 0 1 5 6 9 11 12 13 14 15 18 19 0 1 2 4 5 7 8 9 10 11 12 13 18 19 0 1 2 3 4 5 6 9 11 12 13 14 16 17 19 0 1 2 3 4 5 7 9 10 12 13 15 16 17 18 Off-diagonal values: 0.109471 0.435785 -0.649758 0.577114 -0.046923 -0.186319 -0.186312 -0.156228 0.195611 0.146246 -0.794053 -0.762913 -0.885359 -0.483364 0.577356 -0.766183 0.206135 -0.972010 0.047151 0.132620 0.278237 0.806721 0.572727 -0.813998 0.125212 0.527690 -0.659016 0.109381 -0.497747 -0.448310 -0.768588 -0.084566 0.376583 0.981128 0.856439 0.594887 0.180828 -0.923117 0.611162 0.009217 -0.535387 -0.497161 -0.344189 -0.907802 0.960702 -0.933156 0.479075 0.735725 0.152443 0.515308 -0.401811 0.845680 -0.737366 -0.150025 -0.502919 -0.114428 0.764239 0.580630 -0.691487 0.591906 -0.064314 0.952710 -0.409505 0.789880 -0.404191 -0.520270 0.324743 0.576675 0.796643 0.863724 -0.569436 0.910340 -0.381962 0.773918 0.189113 -0.711088 -0.076478 0.003875 -0.956433 -0.937376 -0.219140 -0.398437 -0.122948 0.643631 0.600901 -0.756324 0.850877 0.407883 0.865500 0.074124 0.998656 -0.117443 0.165680 0.927543 -0.165256 0.685468 -0.193506 -0.968918 0.971415 -0.210014 -0.353420 -0.102609 -0.168108 -0.372468 -0.926754 -0.752643 -0.865723 -0.738490 -0.551732 -0.807012 -0.354787 -0.427047 -0.325254 0.511247 0.255713 -0.515312 0.292245 0.781592 -0.811309 0.961550 0.937233 0.054222 -0.621343 -0.468984 -0.376514 -0.682486 -0.285774 -0.150285 -0.151355 -0.022719 -0.839548 -0.999004 0.375424 -0.823017 -0.444444 0.540664 -0.282524 0.940254 0.464674 -0.782121 -0.417630 0.987942 -0.271946 -0.056808 0.533488 0.418693 -0.307027 -0.341935 0.266363 -0.845218 0.556869 0.109110 -0.787447 0.899348 -0.049040 -0.321650 -0.430214 -0.721719 -0.959692 0.574117 0.010968 0.320774 0.283965 0.687630 -0.515257 0.045759 0.101702 0.666417 0.467453 -0.399537 -0.455155 0.990789 -0.295025 -0.748722 0.373453 0.148232 -0.276060 0.684526 -0.305875 0.430005 0.340538 0.531264 0.917661 0.326339 0.216430 -0.332684 -0.554999 -0.945180 0.501258 0.679407 0.999145 0.904778 0.030547 -0.228916 0.845918 -0.142915 0.722896 0.651679 -0.539337 -0.418773 0.604413 -0.867917 0.226197 0.718769 -0.884715 -0.627625 0.007039 -0.993935 -0.422002 -0.889755 0.851741 -0.124929 -0.704172 0.838759 -0.550880 -0.126042 -0.902996 -0.803884 -0.883739 -0.473471 0.054942 -0.525572 0.450162 -0.638172 -0.731049 -0.797507 -0.477564 -0.395114 0.390927 -0.125280 0.311616 -0.850882 -0.577576 0.630600 -0.282825 0.574359 0.503072 -0.195072 0.356831 0.365489 -0.890108 -0.493018 0.689697 0.855469 -0.441372 -0.210025 0.095253 -0.016806 0.330769 0.583886 0.668392 -0.381140 0.041114 0.054956 0.760071 -0.417162 0.531295 -0.926563 0.860414 -0.592351 -0.085751 -0.543783 -0.523859 -0.084024 0.482652 -0.908003 0.047763 -0.906077 0.828375 -0.339415 0.089390 0.839129 . x x o x o o o - o x x - o o - o o x o x . o x x - - - x - x - x - o x x o x o | o . - - o o - x - x x x x - - o - x - x o o . o - - o - x o x x x - - - x o x | o o o . o - x x - o x o x o x - o - o x x x | x . o x o x - x o o - x - o o o o | o x x o . x x - x x - x - - - o x - x o | x | o o . x o o - - o o o - o o o o | o o | o o o . x x o - x - - x o x x | x o | o o o | o . - o - o o o o x - o | | o | x o x x o o . x o o x x - o - - | o x o x | x o x o o . o o - o x x x x x o x x x x o o | x | o . o x x o x - o | x | | x x x x x o | o | . - - - o x x | | x x x o x | | o x x o o . - - - x o x x o o x | | o | o o x | o o . x o o - o o | | | o o | | x | o x o o o . - o o x o x | o o | x o x x o x x | | | . o o x x o o x o x | | x | x o x x | x o . x o x o o o o | o | x o | x o | x o x x . The error in solving: 5.356477e-16 The error in solving: 3.287747e-16 The error in solving: 5.207588e-16 The error in solving: 3.525204e-16 The error in solving: 4.875036e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a standard normal distribution with a random diagonal and a density of 0.250000 [ -1.229071 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.578067 -1.087021 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.079367 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.868191 1.482759 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.224748 -1.361325 0.000000 0.000000 -1.375920 -0.031836 0.000000 0.000000 0.247620 -0.586183 0.000000 0.000000 -0.949942 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.201164 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1.771776 0.000000 0.000000 0.000000 0.000000 -0.592614]; Dimension: 20 x 20 Off-diagonal entries: 98 (max 380) Diagonal entries: -1.229071 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.489390 0.000000 0.000000 -0.170604 1.046627 0.000000 1.935929 0.000000 0.897570 -0.105692 -0.222638 0.723386 -0.592614 Row indices: 0 2 5 12 15 22 30 37 42 47 53 58 63 68 75 78 82 85 92 95 98 Column indices: 17 18 5 13 14 4 5 8 9 12 13 16 5 8 14 1 5 7 9 12 13 18 0 1 3 11 12 13 14 15 2 7 8 9 12 17 19 4 5 12 15 17 2 5 14 18 19 3 4 5 6 7 16 2 9 15 18 19 1 7 8 10 14 1 6 9 18 19 0 1 7 10 11 17 19 0 13 15 1 6 9 12 1 7 9 1 2 3 7 9 11 16 2 5 10 3 8 14 Off-diagonal values: -0.578067 -1.087021 0.079367 0.868191 1.482759 -0.224748 -1.361325 -1.375920 -0.031836 0.247620 -0.586183 -0.949942 -2.201164 1.037216 1.292533 -0.765413 -0.646739 0.005809 0.282948 -1.063319 -0.504063 -1.535056 0.912953 -0.416297 0.732708 -2.070397 0.164316 0.181922 2.017382 -0.388440 -0.404250 -0.401577 0.015681 0.089055 -0.210504 1.397700 0.747770 -0.394345 -0.191668 1.258674 0.431948 -0.389351 -0.141478 0.368731 -0.658352 -0.355874 -0.421645 0.725651 2.283132 2.135137 -0.037708 -2.076049 -0.094958 0.198402 -0.057103 -1.671439 0.281749 0.720838 0.010294 -0.064213 0.422565 -0.571570 -0.392974 -0.573388 1.357215 0.504873 -0.705409 -2.269141 0.557885 0.712110 -1.974180 0.532960 -1.089717 0.811461 -0.199052 1.340546 0.122709 -0.158119 0.541311 -1.770863 0.918123 1.222437 -0.719245 -0.396250 2.957606 -0.454184 1.570151 -0.556758 -0.600358 1.663777 1.047224 -1.171273 -0.711803 0.740841 0.054233 0.558486 1.422011 1.771776 o - - - - - - - - - - - - - - - - o o - | . - - - x - - - - - - - x x - - - - - | | . - o o - - o o - - x o - - o - - - | | | . - o - - x - - - - - x - - - - - | o | | . o - x - x - - o o - - - - o - x o | x | . - - - - - o x x x o - - - - | | o | | | . o x x - - o - - - - x - x | | | | o o | o - - - - x - - x - o - - | | o | | x | | . - - - - - o - - - o o | | | x x x o o | . - - - - - - o - - - | | x | | | | | | o o - - - - o - - x x | x | | | | | o x | o x - - o - - - - - | o | | | | x | | x | | . - - - - - o o x x | | | | | o | | x o | x - - - x - o x | | | | | | | | | | | | x . o - - - - | x | | | | o | | x | | x | | x - - - - | o | | | | | o | x | | | | | | o - - - | o x o | | | o | x | x | | | | o o - - | | o | | x | | | | x | | | | | | | x - | | | x | | | | x | | | | | x | | | | o The error in solving: 5.822886e-16 The error in solving: 4.135488e-16 The error in solving: 6.967134e-16 The error in solving: 5.016089e-16 The error in solving: 6.587565e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a standard normal distribution with a random diagonal and a density of 0.500000 [ -0.884231 -0.004316 0.000000 0.922885 2.239590 0.000000 1.737848 0.974948 0.000000 0.000000 -0.481193 0.000000 0.518374 -0.325299 0.122911 0.000000 -0.709762 0.000000 -0.590187 0.000000 0.000000 0.000000 0.000000 0.902621 0.000000 0.052511 1.345508 0.000000 0.753393 0.000000 1.057496 0.000000 0.621167 0.702567 -0.202072 0.000000 0.000000 0.586069 0.000000 0.000000 -0.375251 0.828406 0.000000 0.000000 1.025045 -0.395599 -0.785758 0.000000 0.000000 -1.768837 -0.584017 0.248879 0.000000 0.000000 -0.935040 0.688211 1.297471 0.603449 0.552172 0.839778 -0.513638 -0.033424 0.000000 -0.778665 0.173820 -0.120039 0.149023 0.000000 0.000000 0.000000 2.723454 -0.224862 -0.563895 0.000000 0.000000 0.000000 0.370321 1.494520 0.000000 0.000000 0.000000 0.000000 1.751560 0.000000 -0.042955 0.000000 0.000000 0.000000 1.636606 0.000000 0.000000 0.000000 0.404101 0.552876 0.000000 0.000000 0.000000 -0.383048 0.928778 0.000000 -0.070387 0.549957 1.020833 0.661624 0.000000 1.547906 0.000000 1.600231 0.000000 -0.531445 0.000000 0.000000 -1.057679 0.000000 1.065467 0.766209 0.000000 0.000000 0.000000 -1.076941 -0.587042 0.243173 0.000000 0.000000 1.214116 1.308760 0.568354 0.000000 -0.895100 0.000000 -1.642257 0.000000 0.000000 1.623250 0.139539 0.000000 0.000000 -0.420132 0.000000 -0.612889 0.000000 -0.193327 0.000000 0.605340 0.000000 0.000000 2.060758 0.671989 -2.051364 2.123847 -0.655653 1.056388 0.000000 0.000000 -0.593986 1.267370 0.000000 0.000000 0.000000 1.041255 -0.107638 0.191744 0.000000 0.000000 0.000000 -0.281654 0.000000 0.340271 0.000000 -0.140211 0.000000 0.000000 -2.294540 -0.502986 1.035522 0.000000 -1.047253 0.535543 -0.529425 -0.736646 0.000000 0.216604 -0.979672 -0.242790 -1.030574 0.000000 0.000000 -1.358697 0.233948 0.785843 -0.835525 0.000000 0.000000 -0.711979 0.465246 -0.056263 -2.098818 -0.178302 0.000000 1.591585 -1.001366 0.000000 0.000000 0.000000 0.000000 -0.499130 0.000000 0.242811 -0.208366 0.000000 -1.697683 0.000000 0.000000 0.000000 0.944517 0.000000 0.000000 1.012830 0.541161 2.061540 1.487675 0.000000 0.000000 -0.084122 -0.390130 0.000000 0.407927 0.000000 -0.055300 0.000000 1.342241 0.623082 0.000000 0.000000 -0.909946 0.000000 0.000000 -0.423319 0.329314 -0.238983 0.000000 -0.173005 -0.920515 0.146792 0.000000 0.000000 0.000000 -0.469065 -0.985738 0.000000 0.000000 -0.442327 0.000000 -1.472472 1.551040 0.346671 1.095534 0.014775 0.000000 1.642526 0.000000 0.000000 0.000000 0.000000 1.476645 -0.243884 -0.394415 0.000000 -0.113534 0.650325 0.430505 2.403038 -0.048443 0.000000 0.000000 0.000000 0.000000 0.000000 0.738641 0.000000 0.150696 0.000000 -0.070944 0.000000 0.644786 -0.787269 -1.795359 0.000000 0.000000 0.000000 -0.493958 0.000000 0.000000 1.159572 0.180053 0.000000 0.000000 0.000000 -0.212300 0.489383 0.000000 0.622851 0.000000 1.763840 0.000000 0.000000 0.000000 -1.478366 0.000000 -0.015261 -0.099600 0.000000 -0.519558 -0.291068 0.000000 -0.956453 0.537025 -1.555185 0.000000 0.000000 -0.774259 0.000000 -1.629796 0.000000 0.000000 0.000000 0.750807 0.000000 -0.143026 -0.334204 0.000000 0.000000 0.000000 0.000000 -0.737317 -0.338110 0.000000 0.455309 -0.753124 0.000000 0.000000 -0.389331 -0.725112 0.000000 0.000000 -0.542923 0.269812 0.000000 0.000000 0.532627 0.000000 -0.756566 1.399503 -1.168350 2.438360 -2.016292 -0.189245 0.927172 0.050324 0.000000 0.497700 0.000000 0.000000 0.000000 -1.242243 0.000000 0.000000 0.000000 0.640345 -1.278713 -1.653723 0.000000 0.000000 0.963072 -0.105966 0.000000 0.000000 1.214233 -0.211793 0.227281 0.413435 0.000000 0.102207 0.000000 -1.073953 0.000000 -0.346870 0.000000 0.699732 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.175162 0.000000 -0.138006 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 199 (max 380) Diagonal entries: -0.884231 0.000000 0.000000 -0.778665 -0.042955 1.547906 0.568354 0.671989 0.000000 0.785843 -1.697683 0.623082 0.000000 0.000000 0.180053 -0.956453 0.000000 0.927172 -0.211793 0.000000 Row indices: 0 11 20 34 44 50 60 70 80 92 105 113 123 135 144 153 162 171 183 192 199 Column indices: 1 3 4 6 7 10 12 13 14 16 18 3 5 6 8 10 12 13 14 17 0 1 4 5 6 9 10 11 14 15 16 17 18 19 0 1 4 5 6 10 11 12 16 17 2 8 12 13 17 18 0 1 2 3 7 9 12 14 15 19 0 1 4 5 8 10 13 14 17 19 1 3 6 8 9 10 11 14 15 19 0 1 5 7 9 12 13 14 16 17 18 19 1 2 3 4 7 8 10 13 14 15 16 17 19 0 5 7 8 14 17 18 19 0 3 4 6 8 10 14 17 18 19 1 2 3 7 8 11 13 14 15 16 17 19 4 5 6 8 9 10 11 12 18 0 2 4 5 6 10 13 18 19 1 3 7 9 10 12 13 16 17 0 2 6 8 9 14 15 17 18 1 2 5 6 9 11 12 13 14 15 16 18 0 4 8 9 10 13 14 17 19 0 2 4 6 8 15 17 Off-diagonal values: -0.004316 0.922885 2.239590 1.737848 0.974948 -0.481193 0.518374 -0.325299 0.122911 -0.709762 -0.590187 0.902621 0.052511 1.345508 0.753393 1.057496 0.621167 0.702567 -0.202072 0.586069 -0.375251 0.828406 1.025045 -0.395599 -0.785758 -1.768837 -0.584017 0.248879 -0.935040 0.688211 1.297471 0.603449 0.552172 0.839778 -0.513638 -0.033424 0.173820 -0.120039 0.149023 2.723454 -0.224862 -0.563895 0.370321 1.494520 1.751560 1.636606 0.404101 0.552876 -0.383048 0.928778 -0.070387 0.549957 1.020833 0.661624 1.600231 -0.531445 -1.057679 1.065467 0.766209 -1.076941 -0.587042 0.243173 1.214116 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-0.737317 -0.338110 0.455309 -0.753124 -0.389331 -0.725112 -0.542923 0.269812 0.532627 -0.756566 1.399503 -1.168350 2.438360 -2.016292 -0.189245 0.050324 0.497700 -1.242243 0.640345 -1.278713 -1.653723 0.963072 -0.105966 1.214233 0.227281 0.413435 0.102207 -1.073953 -0.346870 0.699732 1.175162 -0.138006 o o - x x - x x - - o - x o x - o - o - | . - x - x x - x - x - x x o - - x - - o x . - x o o - - o o x - - o x x x x x o o | o x o x - - - x o o - - - x x - - | | x | o - - - x - - - x x - - - o x - o x x x | x - x - o - - o - x x - - - o o x | | x x x - o - o - - x x - - o - o | o | x | | x x o x o x - - o x - - - x o x | | | o | x . o - - o o x - o x o o | x o o o | | o x x o - - o x o o o - x o | | | | o | x o | o - - - x - - x x x x | | o o | x | o | x x - - o - - o x o | o o x | | | o o | | o . o x x x x - x | | | | x o o | o x x x o . - - - - x - x | o | x o o | | | o | | x x - - - o x | x | x | | | o | o o | o o | o x o - - o | o | | | x | o o | | | | o o . x o - | o o | | o x | | x | o x o x o o x x - x | | | o | | | x o o | | x o | | x o x x | x | o | o | x | | | | | | x | o | . The error in solving: 5.076786e-16 The error in solving: 3.964289e-16 The error in solving: 4.510815e-16 The error in solving: 6.797482e-16 The error in solving: 6.335328e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a standard normal distribution with a random diagonal and a density of 0.750000 [ 0.000000 0.086840 -0.645231 0.000000 0.283021 -1.266055 -1.880769 0.000000 -1.097512 0.000000 -0.324147 1.409677 0.230017 -1.306201 0.745548 0.348226 0.469323 -0.213884 -0.077356 -1.535094 0.000000 1.702308 -0.050276 -0.216661 0.000000 0.000000 0.449903 0.249347 1.030087 -1.031454 0.555423 0.000000 1.156345 0.000000 -0.175063 0.000000 0.275982 0.000000 -0.956102 -0.020732 0.000000 0.174340 0.666219 0.429226 1.052454 -0.693833 1.420344 1.791273 0.178287 -0.961090 0.000000 -0.332427 0.877818 -0.000672 0.000000 -1.352452 2.076955 1.959259 -2.456128 -0.666716 0.635383 1.120462 0.342929 0.672667 0.567606 1.449108 -0.950366 -0.496590 2.264272 0.423899 0.000000 0.000000 0.278314 0.922974 0.927426 1.282018 1.460745 -1.055448 0.441990 -0.517359 0.000000 0.916196 0.526646 0.224207 -0.020630 0.000000 0.000000 -1.883099 0.000000 -1.366973 -0.307894 0.493618 -0.808050 -0.815247 0.994536 -1.610271 0.000000 -0.805115 0.028133 0.000000 1.129555 -0.394206 0.153111 1.056952 -0.642249 0.871414 0.284059 -0.459712 2.381677 -0.588200 -0.735834 0.000000 0.000000 0.000000 0.293302 -1.130304 -0.267820 -0.630232 -1.047427 -1.262592 -0.228277 -0.528230 0.442309 -1.079395 0.000000 0.998294 -1.217428 1.213867 1.591228 0.297444 1.461348 -1.031624 -0.584683 0.000000 -1.172656 0.128571 0.000000 -2.291295 -0.707799 0.000000 -0.114009 1.174211 2.004691 0.000000 0.076820 1.339208 0.000000 -0.602373 0.520714 1.005027 -0.280055 0.187303 1.385932 0.875362 0.421891 -0.999725 -0.542162 0.531985 -0.144483 0.000000 -0.745653 0.000000 0.000000 0.083365 0.000000 1.270388 -0.075136 1.571927 1.064407 -0.029818 0.000000 0.000000 0.000000 -0.340469 1.114823 -0.705802 -0.678182 0.000000 0.000000 0.000000 0.000000 -0.713819 -0.408273 0.000000 0.258150 -0.190708 0.000000 -0.213593 -0.782098 -0.052258 0.008847 -0.507985 -1.812357 0.160614 1.542035 0.624792 0.000000 0.545952 -0.931223 1.395667 1.159007 0.000000 1.474726 -1.675200 0.494877 0.316513 0.389465 0.517932 -0.906677 -0.062002 0.020577 1.645513 1.281448 -0.511371 -0.558329 0.000000 0.000000 0.527078 0.471506 0.000000 0.052985 0.602625 -0.107860 0.737281 -0.084138 1.165021 0.420365 1.295948 -1.748785 -0.054359 -1.033610 0.353106 -0.129079 1.653812 0.000000 0.928695 -1.172270 0.486627 0.000000 -0.019880 -0.111378 0.000000 -0.437311 0.000000 1.284269 -0.069255 -1.335289 -1.319913 -0.035875 0.000000 0.000000 -0.869061 -0.614031 -2.134685 0.385500 0.000000 1.829430 0.371401 -0.362229 1.888770 0.000000 -0.630379 0.000000 0.173607 -0.136362 0.450250 -0.141483 0.200930 0.000000 -1.754633 -0.476055 -0.266175 -0.188664 -0.223135 -0.500135 1.121266 -0.394497 0.000000 -0.139994 -0.423697 0.190290 -0.572376 -0.375019 -0.210088 0.000000 0.484841 0.707872 -1.700909 0.000000 0.000000 1.327949 0.842642 -0.007785 -0.377126 -0.254720 -1.563404 2.146070 0.146229 0.000000 0.000000 -0.443976 -0.876051 0.000000 -0.220869 0.538810 0.000000 0.398863 1.748010 -0.369311 -1.675143 -0.003432 0.000000 0.000000 -0.492425 0.000000 -0.636153 0.000000 0.187755 0.492163 -0.938629 0.000000 -1.037755 0.080770 -0.002701 -1.007847 0.853987 -0.164478 -0.586833 -1.293584 -0.256036 0.437317 1.393137 0.208788 -0.394750 0.331242 -0.772671 -1.280345 0.340594 0.000000 1.592066 -0.301789 0.000000 -0.844044 0.021706 0.296460 -1.231358 0.160473 -0.245541 -0.196629 -0.438995 -0.481516 1.152915 0.000000 -0.220597 -1.095774 -1.095240 0.150008 0.457830 1.577137 -1.289475 1.372407 0.000000 0.317459 0.000000 0.410006 0.000000 0.312145 0.000000 -0.186980 1.864612 0.000000 -0.169926 -1.451632 -1.194584 -0.135702 0.000000 0.778528 -2.139501 0.574477 -0.234931 0.000000 0.000000 -1.039731 -0.838129 0.000000 0.000000 0.000000 0.000000 -1.151880 0.000000 -0.200349 -0.185952 -0.072594 0.000000 2.106698 0.339477 0.774952 -1.687562 0.381897 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 292 (max 380) Diagonal entries: 0.000000 1.702308 0.666219 0.672667 -0.020630 0.871414 -1.217428 -0.602373 1.064407 -0.052258 0.020577 0.353106 -0.614031 -0.223135 -0.254720 -0.636153 -1.280345 0.457830 0.574477 0.000000 Row indices: 0 16 28 44 61 74 90 105 121 131 146 161 178 192 207 221 234 251 268 281 292 Column indices: 1 2 4 5 6 8 10 11 12 13 14 15 16 17 18 19 2 3 6 7 8 9 10 12 14 16 18 19 1 3 4 5 6 7 8 9 11 12 13 15 16 17 18 19 0 1 2 4 5 6 7 8 9 12 13 14 15 16 17 18 19 1 2 3 7 9 10 11 12 13 14 15 17 18 0 1 2 3 4 6 7 8 9 10 14 15 16 17 18 19 0 1 2 3 5 7 8 9 10 11 12 14 15 17 18 0 1 2 4 5 8 9 10 11 12 13 14 15 16 17 18 0 3 5 6 7 9 13 14 15 16 1 2 4 5 7 8 10 11 12 13 14 15 17 18 19 0 2 3 4 5 6 7 8 9 11 12 13 14 17 18 0 1 2 3 4 5 6 7 8 9 10 12 13 15 16 17 19 0 2 4 5 6 7 8 11 13 14 16 17 18 19 1 3 4 5 6 7 9 10 11 12 14 15 16 18 19 0 1 2 3 5 6 7 10 11 12 13 15 16 17 0 1 3 4 6 7 8 9 10 13 17 18 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 19 0 2 3 4 5 6 7 8 9 10 11 13 14 15 16 18 19 0 2 4 6 8 9 11 12 13 14 16 17 19 2 3 8 10 11 12 14 15 16 17 18 Off-diagonal values: 0.086840 -0.645231 0.283021 -1.266055 -1.880769 -1.097512 -0.324147 1.409677 0.230017 -1.306201 0.745548 0.348226 0.469323 -0.213884 -0.077356 -1.535094 -0.050276 -0.216661 0.449903 0.249347 1.030087 -1.031454 0.555423 1.156345 -0.175063 0.275982 -0.956102 -0.020732 0.174340 0.429226 1.052454 -0.693833 1.420344 1.791273 0.178287 -0.961090 -0.332427 0.877818 -0.000672 -1.352452 2.076955 1.959259 -2.456128 -0.666716 0.635383 1.120462 0.342929 0.567606 1.449108 -0.950366 -0.496590 2.264272 0.423899 0.278314 0.922974 0.927426 1.282018 1.460745 -1.055448 0.441990 -0.517359 0.916196 0.526646 0.224207 -1.883099 -1.366973 -0.307894 0.493618 -0.808050 -0.815247 0.994536 -1.610271 -0.805115 0.028133 1.129555 -0.394206 0.153111 1.056952 -0.642249 0.284059 -0.459712 2.381677 -0.588200 -0.735834 0.293302 -1.130304 -0.267820 -0.630232 -1.047427 -1.262592 -0.228277 -0.528230 0.442309 -1.079395 0.998294 1.213867 1.591228 0.297444 1.461348 -1.031624 -0.584683 -1.172656 0.128571 -2.291295 -0.707799 -0.114009 1.174211 2.004691 0.076820 1.339208 0.520714 1.005027 -0.280055 0.187303 1.385932 0.875362 0.421891 -0.999725 -0.542162 0.531985 -0.144483 -0.745653 0.083365 1.270388 -0.075136 1.571927 -0.029818 -0.340469 1.114823 -0.705802 -0.678182 -0.713819 -0.408273 0.258150 -0.190708 -0.213593 -0.782098 0.008847 -0.507985 -1.812357 0.160614 1.542035 0.624792 0.545952 -0.931223 1.395667 1.159007 1.474726 -1.675200 0.494877 0.316513 0.389465 0.517932 -0.906677 -0.062002 1.645513 1.281448 -0.511371 -0.558329 0.527078 0.471506 0.052985 0.602625 -0.107860 0.737281 -0.084138 1.165021 0.420365 1.295948 -1.748785 -0.054359 -1.033610 -0.129079 1.653812 0.928695 -1.172270 0.486627 -0.019880 -0.111378 -0.437311 1.284269 -0.069255 -1.335289 -1.319913 -0.035875 -0.869061 -2.134685 0.385500 1.829430 0.371401 -0.362229 1.888770 -0.630379 0.173607 -0.136362 0.450250 -0.141483 0.200930 -1.754633 -0.476055 -0.266175 -0.188664 -0.500135 1.121266 -0.394497 -0.139994 -0.423697 0.190290 -0.572376 -0.375019 -0.210088 0.484841 0.707872 -1.700909 1.327949 0.842642 -0.007785 -0.377126 -1.563404 2.146070 0.146229 -0.443976 -0.876051 -0.220869 0.538810 0.398863 1.748010 -0.369311 -1.675143 -0.003432 -0.492425 0.187755 0.492163 -0.938629 -1.037755 0.080770 -0.002701 -1.007847 0.853987 -0.164478 -0.586833 -1.293584 -0.256036 0.437317 1.393137 0.208788 -0.394750 0.331242 -0.772671 0.340594 1.592066 -0.301789 -0.844044 0.021706 0.296460 -1.231358 0.160473 -0.245541 -0.196629 -0.438995 -0.481516 1.152915 -0.220597 -1.095774 -1.095240 0.150008 1.577137 -1.289475 1.372407 0.317459 0.410006 0.312145 -0.186980 1.864612 -0.169926 -1.451632 -1.194584 -0.135702 0.778528 -2.139501 -0.234931 -1.039731 -0.838129 -1.151880 -0.200349 -0.185952 -0.072594 2.106698 0.339477 0.774952 -1.687562 0.381897 . x o - x o o - o - o x x o x x x o o o | x o o - - x x x o x - x - o - x - o o | x x x x o x x x o - o x o - o x x o o x x x x x x o o x x - - x x x x x o x o | x x x o - - o - o o x o o x o - o x - x o x x o x x o x o o - - - x o o o o o o o x o | x o x x x x o o - o x - o o - o x x | x x | o x x o x x x x o o x o - o | | x | x o x x o - - - o x o o - - - | o o | x o | o o o x o o x x x - x o x x | x o x x x x o o x x x o o - - x x - x x o x o x x x o o o x o x - x o x - o o | o | x o o o o | | o o o x - x x o x | o | x o x o x | o o o o o o x o - o o x o o o | x x o | | x x o o o o x x - - o o | o x | x x o o o | | o | o - x x o | o x o o x o o o o x x x o x o o x - x o | o x x o x o o o o x | o o o x x x o x | x | x | x | o x | o o o o | x o x o | | o o | | | | o | o o o | x x x o x . The error in solving: 6.500470e-16 The error in solving: 1.143466e-15 The error in solving: 6.741539e-16 The error in solving: 6.074703e-16 The error in solving: 6.206335e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a standard normal distribution with a dense diagonal and a density of 0.250000 [ 2.138076 0.000000 -0.180298 1.821863 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.448410 0.000000 0.000000 -1.052589 0.000000 0.000000 0.000000 0.000000 0.000000 -0.644959 -1.852477 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.288760 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.875646 -1.410557 -0.626807 0.000000 0.643820 1.441206 0.000000 0.000000 0.000000 0.754276 0.000000 0.000000 0.000000 -1.962696 0.000000 0.000000 0.000000 0.863826 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.685179 -0.413134 -0.708276 0.000000 0.331426 0.000000 0.000000 0.000000 0.000000 0.858488 0.000000 0.000000 0.527381 -1.119121 0.000000 0.000000 0.140637 1.975826 0.000000 0.000000 0.000000 0.000000 1.686513 -0.266826 0.000000 0.000000 0.661313 1.874211 -0.417080 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.514577 0.000000 0.000000 0.000000 -0.289988 0.000000 0.000000 0.663001 0.000000 0.000000 -0.474877 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.318115 0.000000 0.000000 0.000000 0.000000 0.000000 -1.510998 0.006051 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.081792 0.000000 0.000000 -0.428003 -0.803112 0.000000 0.000000 0.000000 0.000000 0.000000 0.194430 -0.754846 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.331789 0.000000 0.000000 0.000000 0.000000 -1.686938 -1.004958 -0.624216 0.000000 0.000000 0.000000 0.000000 -1.225140 0.000000 -0.657117 0.000000 0.989762 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.337219 0.898645 0.000000 0.000000 -1.605362 0.000000 0.000000 -0.115924 0.000000 0.000000 0.000000 1.262165 0.000000 0.000000 -0.745768 0.315860 0.000000 0.000000 -0.098393 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.258885 0.000000 0.000000 0.000000 1.133335 0.000000 0.000000 -0.131276 0.000000 0.000000 0.000000 -0.306298 0.000000 0.000000 0.000000 0.000000 -0.679309 0.000000 0.000000 0.410074 0.000000 0.000000 0.179738 0.000000 0.000000 0.000000 0.000000 1.647947 -0.604863 0.000000 0.000000 0.000000 -0.273055 0.000000 0.000000 -0.816687 -0.680785 -0.317455 0.000000 0.000000 -0.441327 0.000000 0.000000 0.229565 0.000000 0.000000 0.000000 0.000000 0.000000 -0.148764 0.000000 0.000000 0.000000 -0.432317 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.211513 0.000000 0.000000 1.271525 0.000000 0.000000 0.740043 1.354041 0.322962 1.053723 0.000000 0.000000 0.000000 0.000000 0.000000 -0.239396 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.603373 0.000000 0.000000 -0.049475 0.000000 0.000000 0.000000 0.000000 0.000000 -1.802711 0.000000 0.000000 0.000000 0.316148 0.000000 0.000000 0.000000 0.000000 1.083111 0.000000 -1.802864 -0.761161 2.002161 -0.349819 0.726659 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.560631 0.000000 -0.286471 0.000000 0.000000 -0.573147 -0.178421 0.000000 0.000000 0.000000 0.000000 -0.925158 0.000000 0.000000 0.000000 -0.506232 -1.445674 0.000000 0.000000 0.000000 0.000000 0.000000 -2.054087 0.000000 -0.074051 0.000000 0.000000 -1.434517 -0.674152 -0.085820 0.000000 -0.695598 -0.423931 0.000000 0.000000 0.000000 -0.097734 -1.545025 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.011588 0.000000 -0.530265 0.000000 0.000000 0.000000 0.000000 -1.034901 -0.137444 1.723165 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.800336 0.000000 0.000000 0.448354 0.000000 0.000000 0.000000 0.000000 0.758384 0.000000 0.000000 -0.503529]; Dimension: 20 x 20 Off-diagonal entries: 96 (max 380) Diagonal entries: 2.138076 -1.852477 0.643820 -0.413134 1.686513 0.663001 -1.510998 -0.754846 -0.657117 1.262165 -0.131276 -0.604863 -0.148764 1.053723 -0.049475 0.726659 -0.925158 -0.423931 1.723165 -0.503529 Row indices: 0 4 8 13 21 26 28 32 36 42 47 51 57 61 67 68 75 79 87 93 96 Column indices: 2 3 11 14 0 8 18 19 0 3 7 11 15 2 4 6 11 14 15 18 19 5 8 9 10 18 2 8 0 7 16 19 0 6 14 19 0 1 6 10 18 19 2 5 12 13 16 3 7 14 19 2 5 10 15 18 19 0 3 6 16 4 7 10 11 12 19 11 0 4 9 11 12 13 14 5 7 10 11 0 1 7 9 12 13 14 16 1 2 9 11 16 17 8 11 16 Off-diagonal values: -0.180298 1.821863 0.448410 -1.052589 -0.644959 1.288760 0.875646 -1.410557 -0.626807 1.441206 0.754276 -1.962696 0.863826 0.685179 -0.708276 0.331426 0.858488 0.527381 -1.119121 0.140637 1.975826 -0.266826 0.661313 1.874211 -0.417080 0.514577 -0.289988 -0.474877 0.318115 0.006051 -1.081792 -0.428003 -0.803112 0.194430 -0.331789 -1.686938 -1.004958 -0.624216 -1.225140 0.989762 1.337219 0.898645 -1.605362 -0.115924 -0.745768 0.315860 -0.098393 -2.258885 1.133335 -0.306298 -0.679309 0.410074 0.179738 1.647947 -0.273055 -0.816687 -0.680785 -0.317455 -0.441327 0.229565 -0.432317 -0.211513 1.271525 0.740043 1.354041 0.322962 -0.239396 0.603373 -1.802711 0.316148 1.083111 -1.802864 -0.761161 2.002161 -0.349819 -1.560631 -0.286471 -0.573147 -0.178421 -0.506232 -1.445674 -2.054087 -0.074051 -1.434517 -0.674152 -0.085820 -0.695598 -0.097734 -1.545025 1.011588 -0.530265 -1.034901 -0.137444 -1.800336 0.448354 0.758384 x - o x - - - - - - - x - - o - - - - - o o - - - - - - x - - - - - - - - - x o o | x x - - - x - - - o - - - x - - - - | | x o o - x - - - - x - - x o - - x x | | | | x o - - x x o - - - - - - - x - | | o | | x - - o - - - - - - - - - - - x | | | | | o x - - - - - - - - o - - o o | | | | | x o - - - - - - o - - - - o o o | | | | o | o - x - - - - - - - x x | | o | | o | | | x - - o x - - o - - - | | | o | | | x | | o - - - o - - - - o | | x | | x | | | | x o - - - o - - o o o | | o | | x | | | | | o - - - o - - - | | | | o | | x | | x x x x - - - - - o | | | | | | | | | | | x | | o - - - - - o | | | x | | | | x | o o x o x - - - - | | | | | o | o | | o o | | | | o - - - o o | | | | | o | o | | o o o | o o - - | o o | | | | | | x | o | | | | o o x - | | | | | | | | o | | x | | | | x | | o The error in solving: 3.743508e-16 The error in solving: 5.317656e-16 The error in solving: 8.120581e-16 The error in solving: 9.006674e-16 The error in solving: 4.795632e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a standard normal distribution with a dense diagonal and a density of 0.500000 [ 1.971604 -0.152090 0.075639 0.000000 -1.819645 0.000000 -0.111352 0.000000 0.000000 0.467347 0.236113 0.000000 -0.511201 0.000000 -0.413986 0.000000 0.657081 1.025689 0.000000 0.000000 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13 15 16 17 19 2 6 8 12 13 16 17 0 1 4 8 9 11 12 15 17 2 3 4 5 8 9 10 16 17 0 1 2 3 4 8 10 11 12 13 14 16 17 0 1 2 3 4 5 7 11 14 15 17 19 0 1 2 3 5 7 8 10 11 12 16 17 18 19 2 4 5 9 11 14 17 0 1 2 3 4 6 7 9 13 15 18 19 3 4 5 8 10 11 15 16 17 18 2 3 5 7 8 10 11 15 17 18 0 4 5 10 12 13 15 17 5 6 8 9 11 13 17 19 4 7 8 9 10 14 15 19 1 2 3 7 8 9 11 12 13 15 18 19 1 5 7 9 10 11 16 19 0 1 2 3 5 6 7 9 10 11 13 18 Off-diagonal values: -0.152090 0.075639 -1.819645 -0.111352 0.467347 0.236113 -0.511201 -0.413986 0.657081 1.025689 0.370519 0.768901 -1.466692 -1.154561 -1.342894 -1.283234 1.957913 0.760204 0.100310 0.005645 0.829226 0.383756 -0.938861 1.237160 -1.186649 -0.403127 0.371023 0.046250 -0.418371 -0.039350 0.243655 1.787915 -0.975750 -0.838989 0.000426 0.352716 0.238418 -1.668770 -0.067864 0.012809 -0.926714 -0.355091 1.659379 -0.260587 0.422400 0.317862 -1.773084 -0.586046 -0.568279 -0.239951 0.042492 -0.888733 -0.332828 -1.852073 1.535685 1.334515 -0.978120 -0.377908 -0.688097 1.332240 -1.575795 1.143003 0.497008 2.393458 -1.002000 0.226634 0.402699 -0.187845 -0.490695 -0.599937 1.540859 -0.696597 -0.365631 0.214877 0.955230 1.252989 -0.779087 1.251681 1.930054 -2.127517 -0.535529 -0.387826 -0.819759 0.782925 -0.251375 -0.557064 -1.249818 -0.427071 0.307806 -0.534874 -0.597636 1.251095 -1.455141 -1.673197 0.572580 -0.204669 -0.125491 -0.744938 1.842966 -1.581930 -0.914510 1.574317 0.156354 1.936884 -0.896143 1.045611 0.836426 -0.397756 0.282979 0.272898 -1.053178 -0.634078 -0.210874 1.192890 -0.546170 -1.317876 0.982632 -0.181538 -1.301430 0.721005 0.500964 0.195544 0.542403 -0.824831 1.804992 0.207629 -0.590787 0.307130 0.404203 -1.770531 -0.581919 0.817010 -1.303512 -1.197844 -0.556381 -0.726686 -0.818392 0.990632 -1.985075 1.100346 0.152531 1.191409 -0.327648 1.041273 -0.289489 0.351541 -0.544208 -1.018567 2.045718 1.692684 2.451713 0.121378 -0.182600 1.554392 -1.564228 -0.101809 0.381621 -0.352446 0.155912 -1.067321 1.549008 -0.099606 -0.265601 0.617168 -1.495136 0.141603 -0.351644 0.095281 0.974353 -0.995074 -0.345750 1.098741 -0.312797 0.807254 -0.356722 -1.125768 -0.455150 -0.101892 0.683242 2.127641 -1.240594 -1.182324 -1.353854 -0.651801 0.487880 -0.761525 -1.008579 0.022350 -1.019446 1.346607 -0.048325 -0.514688 0.457512 0.483621 -0.114159 -0.412066 -0.752830 -1.303291 0.578491 -0.791269 -0.038575 0.918186 0.046829 1.151849 0.587475 x o x - o - o - - x x - o - o - x x - - | x x x - o o o - o - x x x - x x x o - x | x o o x x - - - o - o x x - o - - - o x | o x - - x o o x - o o - x o x - x | | o | x - o - o - - - o x - - o o - - o x | | x x - - o o - o x - - o - x - - | | x x o x x - x o o - - - - - o x - - o o x x x | | x o - x x o o o - o x - - o o o o x o | o o - - x - - o o - x - o o o x o | o | x x x x o x - - - x o x x | | o | o o | | | x o o - - o - - x - - o o x x x | x o | x | x - x - o - - x x | | | o o x | | o | o o x - - o o x o - | | x x | x | o x | o x | o - o - o x - x | | | x x | | | | o | x o x o - x - - | | | | | o x | o x | o | o | o - x - o | | | | x | | o x x o | | | o x o - - o | x o o | | | o o x | x o o | o | o o x | o | | | o | x | o x o | | | | o | x x x o o o | o x o | o x x | x | | | | x o The error in solving: 4.435061e-16 The error in solving: 5.585810e-16 The error in solving: 7.179324e-16 The error in solving: 7.048017e-16 The error in solving: 4.726604e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a standard normal distribution with a dense diagonal and a density of 0.750000 [ -0.065498 0.000000 0.348015 -0.686946 0.000000 0.491377 0.000000 0.339786 1.790577 -0.334992 0.000000 1.469040 0.000000 0.124054 -2.105043 0.000000 -0.950688 0.517906 0.000000 1.987953 -0.108244 -0.504867 -0.702534 0.232555 0.000000 -1.487488 0.536836 -1.810339 0.928269 0.490172 -0.561696 0.000000 0.000000 0.113480 -1.630733 0.000000 1.686578 1.410499 0.884247 -1.943098 0.000000 -0.717482 -0.904779 0.084046 -0.314785 -1.317211 -0.443979 0.713444 0.935073 -0.217567 0.000000 0.557552 -0.011668 1.385525 -0.923571 -0.804534 0.591814 -1.477212 -0.850107 0.951411 -0.223826 0.194571 -0.306811 2.092068 0.000000 -1.259120 -0.286034 -0.814786 0.930081 0.000000 0.620043 -0.696222 1.217495 -0.564406 -0.639083 0.552807 0.046738 0.728387 0.000000 0.000000 -0.774987 -0.445570 0.046160 1.048137 -0.274718 -1.825069 0.875927 0.000000 0.442286 0.975760 1.348430 -0.720194 0.000000 -0.458080 0.851135 0.000785 0.000000 0.000000 0.000000 0.000000 0.798658 -0.814601 0.000000 1.022874 0.000000 -0.662662 0.925132 0.000000 -1.752970 1.323072 0.328724 0.519461 -0.767773 -1.761101 0.000000 -0.341028 -0.442495 1.510517 0.440117 -0.220950 0.577284 0.654854 0.745240 1.001667 -0.380842 0.000000 1.166961 1.546782 0.788115 0.000000 -0.574485 0.040836 2.221289 0.422443 0.000000 0.179893 -1.579314 0.000000 -1.130095 1.079970 0.000000 -1.673178 -0.253056 -1.722953 0.000000 -0.186535 0.061499 -1.384418 -0.112332 0.065599 1.841232 0.479422 -0.628177 0.614493 -1.638112 -0.855586 -0.175687 -0.972944 0.473034 0.990690 -1.505481 0.654882 1.266351 0.000000 1.837380 1.616025 0.556110 -1.313659 1.133211 -0.970046 1.654441 1.627962 -0.466807 -0.650799 0.000000 0.900402 -1.302201 -0.138462 -0.766420 -1.727632 -1.022085 0.163294 0.000000 0.003372 -0.499836 0.000000 0.237079 0.000000 -0.513863 -0.327842 0.427270 0.000000 0.104425 -2.036219 -0.378861 0.000000 1.584413 0.000000 0.000000 0.123349 -0.162666 0.017194 2.235921 1.151253 0.263697 -0.514731 0.615684 0.000000 -0.040555 0.000000 -0.860736 0.418687 -2.169307 -1.106282 0.000000 -2.250718 -0.155955 0.000000 -0.603917 1.425058 -1.240379 0.662990 0.000000 -1.009514 1.210139 -0.023229 0.583214 -0.165630 0.000000 0.965446 1.806872 -0.075594 0.256172 0.013946 -0.438029 0.000000 1.522404 0.000000 0.446721 -1.478401 0.000000 -0.691431 0.267319 -1.114500 0.000000 -1.367989 0.339483 0.307173 0.048204 0.520095 -0.367550 -0.687016 0.640589 0.000000 0.000000 1.165695 -0.087789 0.000000 0.000000 2.055121 -0.034037 -0.677677 -0.387264 0.762185 -1.960756 -2.170452 -0.567450 0.000000 0.145832 0.000000 0.000000 0.000000 -0.370371 -1.163585 0.000000 -0.379397 1.777704 -0.265910 0.266553 -2.382477 0.000000 0.000000 0.000000 0.000000 -0.545300 -0.943241 0.190449 -0.282746 -1.765781 -0.440368 1.069122 1.114086 -1.202142 -0.665445 -0.590770 0.000000 0.533000 0.000000 -1.173515 0.511175 1.229689 0.000000 0.000000 -0.813363 -0.687043 -0.954206 1.452229 -0.239033 -0.922842 0.446369 0.948762 -0.023516 0.000000 0.000000 0.000000 -0.245602 0.000000 0.000000 -0.168505 -0.043006 -1.178572 0.000000 0.000000 -0.018761 0.704931 -0.295420 0.000000 -2.160026 -0.376254 0.000000 -1.564582 -0.322143 -0.750515 -1.379782 0.878538 -0.284333 -0.153255 -0.748352 -0.563985 0.000000 0.687020 -1.614141 -1.847002 0.450984 0.455589 0.701693 0.476971 0.000000 0.000000 -0.692407 0.000000 -0.414396 -2.996268 0.000000 -1.841940 -0.959557 1.001506 0.998153 0.000000 0.690876 0.000000 -0.973244 -0.048641 -0.083754 -1.035665 -0.176053 0.000000 -0.802306 1.275975 -0.309348 0.000000 1.029264 -0.545315 0.866866 0.000000 -0.188525 0.566446 1.729943 -1.341417 0.000000 -0.421812 -0.485937 1.612829 0.236394 0.000000 -0.821243 -0.449033 -2.178699 0.323203 0.000000 0.200379 -0.050806 0.295438 -0.238681 -0.447916 0.000000 -0.823712 0.271253 0.000000 1.889259]; Dimension: 20 x 20 Off-diagonal entries: 287 (max 380) Diagonal entries: -0.065498 -0.504867 -0.904779 2.092068 -0.274718 -0.662662 1.166961 -1.384418 1.133211 -0.327842 -0.860736 -0.075594 0.640589 -1.163585 -0.590770 -0.245602 -0.153255 0.998153 -1.341417 1.889259 Row indices: 0 12 27 44 59 72 87 102 119 136 148 163 178 191 205 218 230 244 258 272 287 Column indices: 2 3 5 7 8 9 11 13 14 16 17 19 0 2 3 5 6 7 8 9 10 13 14 16 17 18 19 1 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 0 1 2 5 6 7 8 10 11 12 13 14 15 16 17 0 1 2 3 5 6 8 9 10 11 13 14 15 0 1 3 6 8 9 10 11 12 13 15 16 17 18 19 0 1 2 3 4 7 8 10 11 12 13 15 16 18 19 1 2 3 5 6 8 9 10 11 12 13 14 15 16 17 18 19 0 1 2 4 5 6 7 9 10 11 12 13 15 16 17 18 19 0 1 3 4 6 8 10 12 13 14 16 19 0 1 2 3 4 5 6 8 11 12 13 15 16 18 19 0 1 3 4 5 6 7 9 10 12 13 14 16 18 19 1 2 3 5 6 7 8 9 10 11 15 16 19 0 1 2 3 4 5 6 8 12 15 16 17 18 19 4 5 6 7 8 9 10 11 12 13 16 18 19 0 3 4 5 6 7 8 9 10 11 18 19 0 3 4 5 7 8 10 11 12 13 14 15 17 18 0 1 2 3 4 5 6 9 11 12 14 15 16 19 1 2 3 4 5 7 8 9 11 12 13 15 16 17 0 1 2 3 5 6 7 8 10 11 12 13 14 16 17 Off-diagonal values: 0.348015 -0.686946 0.491377 0.339786 1.790577 -0.334992 1.469040 0.124054 -2.105043 -0.950688 0.517906 1.987953 -0.108244 -0.702534 0.232555 -1.487488 0.536836 -1.810339 0.928269 0.490172 -0.561696 0.113480 -1.630733 1.686578 1.410499 0.884247 -1.943098 -0.717482 0.084046 -0.314785 -1.317211 -0.443979 0.713444 0.935073 -0.217567 0.557552 -0.011668 1.385525 -0.923571 -0.804534 0.591814 -1.477212 -0.850107 0.951411 -0.223826 0.194571 -0.306811 -1.259120 -0.286034 -0.814786 0.930081 0.620043 -0.696222 1.217495 -0.564406 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1.275975 -0.309348 1.029264 -0.545315 0.866866 -0.188525 0.566446 1.729943 -0.421812 -0.485937 1.612829 0.236394 -0.821243 -0.449033 -2.178699 0.323203 0.200379 -0.050806 0.295438 -0.238681 -0.447916 -0.823712 0.271253 o - x o - x - x x o - x - x o - o x - x o o o x - o x o x x o - - x o - x x x o | o o x o o o x x o - x o x o o x o o x o x o x - o o o x - x o x o o x x x - - o o x x o o x - x x x o - o x x - - - - x o | x | o x - o x x x o o - o o x x o x x x x o | x x x - o x x x - x o - o x | o o o | o x o o x x x o x o o o o x x o x x | x x x o x o x x o o - x o o o o o x | x o | x | o o x - x o o - x - - x o x x x x o x | o | o x o o - o o - o x o x | o x o x o | x x o x x o - x - x o | o x o | o x x x x o o x - - x o - - x o o o x o o o | x | | | o o - o x o x o | | | | o o x o o o x x o o o - x - o x x | | o o o x o o x x o | | | o - - o o o | | o x o | o o | o o o o x o o o o - x o o x x x x | | o | o o | o o x x - x | o o o o o | o x o | x o x | o x x o - o o x x | o o o x | x o x o o | o x | x The error in solving: 7.596108e-16 The error in solving: 3.914262e-16 The error in solving: 7.824122e-16 The error in solving: 3.762391e-16 The error in solving: 4.050793e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a standard normal distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 -0.005680 0.000000 0.533088 0.000000 0.000000 0.000000 0.000000 0.000000 0.719262 0.000000 0.000000 0.000000 0.000000 0.000000 0.395775 -0.461677 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.651666 0.000000 0.000000 0.000000 0.000000 0.000000 0.592397 0.000000 0.000000 0.000000 0.000000 0.001748 0.000000 0.387661 0.000000 0.000000 0.000000 0.000000 -0.754139 0.000000 0.000000 0.000000 -0.582565 0.000000 -1.012492 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.720216 0.000000 0.000000 0.000000 0.000000 1.396025 0.000000 0.000000 0.000000 -1.368847 0.000000 -0.624797 0.000000 0.000000 0.000000 0.000000 0.000000 -1.012147 0.000000 1.302353 0.000000 0.000000 0.000000 0.000000 0.000000 0.005838 0.000000 0.000000 -0.159500 0.000000 -0.326010 0.000000 0.000000 0.000000 0.000000 0.000000 1.031537 0.000000 -0.725025 0.000000 0.637413 1.762058 0.000000 0.000000 -0.195266 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.747856 0.000000 0.000000 1.039512 0.000000 -0.079352 0.000000 0.000000 0.331441 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.301899 0.280518 1.821919 0.837788 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.177912 0.387056 0.000000 0.000000 -0.949875 0.000000 0.000000 0.788611 0.000000 -0.898187 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 88 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 4 8 12 17 19 23 25 32 37 40 43 49 57 60 65 70 75 79 85 88 Column indices: 5 7 13 19 0 8 14 19 1 6 10 12 4 6 7 10 11 8 11 3 10 14 19 0 18 0 2 10 12 13 14 16 6 10 11 13 19 10 16 18 2 6 9 0 1 8 9 13 14 2 4 5 7 9 14 15 17 4 8 11 2 4 9 13 15 1 3 9 12 14 0 2 4 5 8 7 10 12 15 2 3 4 5 16 17 0 3 5 Off-diagonal values: -0.005680 0.533088 0.719262 0.395775 -0.461677 -1.651666 0.592397 0.001748 0.387661 -0.754139 -0.582565 -1.012492 -0.709803 0.329341 -0.677955 0.962346 -0.344851 -0.922310 0.628397 0.211993 2.639319 -1.307539 0.787612 -0.823800 -0.838386 -0.356262 0.354878 1.245473 -0.767805 1.345136 0.681239 -0.749437 0.024332 1.585045 -1.715085 0.924321 1.562203 0.397981 -0.906906 2.512866 1.262635 -0.766039 -3.017663 -1.748464 0.947391 -1.423641 -0.937317 -0.537189 0.914721 -0.634989 1.635491 -2.027271 -0.766274 0.239470 -0.138257 -1.219553 -0.643192 0.661092 0.157940 1.506182 0.107604 0.720216 1.396025 -1.368847 -0.624797 -1.012147 1.302353 0.005838 -0.159500 -0.326010 1.031537 -0.725025 0.637413 1.762058 -0.195266 -0.747856 1.039512 -0.079352 0.331441 -0.301899 0.280518 1.821919 0.837788 1.177912 0.387056 -0.949875 0.788611 -0.898187 . - - - - o - x - - - - - x - - - - - x o . - - - - - - o - - - - - x - - - - x | x . - - - o - - - o - o - - - - - - - | | | . o - x o - - x o - - - - - - - - | | | | . - - - o - - x - - - - - - - - | | | x | . - - - - x - - - o - - - - x o | | | | | . - - - - - - - - - - - o - o | x | | | | . - - x - o x x - o - - - | | | | | | x | . - x o - x - - - - - x | | | | | | | | | . x - - - - - o - x - | | x | | | o | | o . - - - - - - - - - o x | | | | | | o o | . - o x - - - - - | | o | x o | o | x | | . - o o - o - - | | | | x | | | x | | x | . - - - - - - | | x | x | | | | x | | | o . o - - - - | o | x | | | | | x | | o | o . - - - - x | o | x x | | o | | | | | | | . - - - | | | | | | | o | | x | o | | x | . - - | | o x x x | | | | | | | | | | x x . - o | | x | o | | | | | | | | | | | | | . The error in solving: 4.711244e-16 The error in solving: 5.005632e-16 The error in solving: 3.586811e-16 The error in solving: 7.820044e-16 The error in solving: 6.980403e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a standard normal distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.225114 0.000000 0.000000 1.067372 0.773545 -0.134368 1.923968 0.000000 0.057295 -1.364858 -0.030422 0.012379 -0.017507 -0.971752 -0.478395 0.000000 0.000000 0.890792 0.000000 0.000000 0.000000 0.000000 0.248797 0.000000 0.000000 0.761277 1.380616 0.000000 -0.477170 -0.062334 0.400754 0.968586 0.000000 0.156612 0.000000 0.000000 -0.536243 1.206704 0.042927 0.064844 0.957812 0.000000 -0.707486 1.068992 1.609339 0.000000 -1.036428 0.000000 0.000000 -0.572162 0.000000 -0.116754 -0.385369 0.000000 0.000000 0.151197 0.000000 0.086829 0.000000 0.000000 0.980591 -1.065637 0.000000 -0.237375 0.000000 -0.549530 0.258917 0.000000 0.380918 -0.018440 0.000000 -0.682561 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.729340 0.637589 -0.839027 0.540524 0.816275 0.000000 -0.035198 0.000000 0.030768 0.000000 0.000000 0.000000 0.000000 -0.363432 0.656963 0.000000 0.000000 0.803452 0.061466 0.000000 -0.214987 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.995537 0.000000 0.000000 0.748340 0.000000 -0.558329 0.383011 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.139251 0.321689 0.000000 0.000000 -1.146022 0.000000 0.000000 -0.529163 0.000000 0.000000 0.000000 0.000000 -0.146345 -1.420389 0.394795 0.000000 -0.674429 0.000000 -0.542032 0.000000 1.406501 0.000000 0.000000 0.699967 0.000000 0.489768 -1.252012 0.000000 1.293149 0.000000 -0.428666 0.000000 -1.532448 0.000000 2.452068 0.000000 0.635659 -0.179554 -1.945813 0.000000 0.130265 0.000000 0.000000 0.000000 -2.609396 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.112028 1.040020 -0.749244 0.618951 0.000000 0.667155 0.000000 -0.238186 0.167128 -1.117430 0.000000 0.000000 -0.670374 0.000000 0.000000 0.000000 0.000000 0.346066 -0.051353 0.000000 0.000000 1.284348 0.000000 -0.844894 -0.292091 0.000000 0.000000 -0.911315 0.000000 0.000000 0.000000 -0.472972 0.819768 1.089759 0.000000 2.309861 0.000000 -0.484551 0.000000 0.464812 -0.628050 0.781953 0.478840 -0.836959 -0.080516 0.928114 0.537975 0.000000 0.398974 0.000000 1.785503 0.000000 -0.764894 -2.251040 1.322354 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.319592 0.000000 0.000000 0.000000 -2.301473 -0.959299 0.000000 0.000000 0.491393 0.834140 0.000000 0.000000 0.016436 0.000000 1.168770 0.000000 0.000000 0.000000 -0.066747 1.077885 0.000000 -0.446982 0.000000 0.000000 0.661372 0.000000 -0.140614 0.000000 0.000000 0.195675 0.000000 0.000000 0.000000 0.000000 0.000000 -2.460823 -0.211115 0.000000 0.000000 0.000000 0.000000 -0.707199 0.000000 -0.360032 -1.008795 0.000000 0.000000 1.606780 0.238852 0.000000 0.298304 0.000000 0.421320 -1.317024 0.000000 1.338429 0.501482 -0.397580 0.000000 -0.186665 0.000000 0.000000 -1.195577 0.652220 0.000000 0.000000 0.000000 0.000000 1.109106 -0.606042 0.826640 1.229397 0.000000 0.000000 0.000000 -0.046835 0.000000 0.000000 0.000000 0.000000 -0.356412 0.000000 0.000000 -0.726316 -0.864453 -1.023377 1.026195 0.000000 -0.417117 2.269729 0.000000 -0.131659 2.506513 -1.699792 0.000000 0.293400 -0.188549 -1.735554 0.000000 -0.828888 0.000000 0.000000 0.207415 0.000000 0.000000 -0.523059 -0.349952 0.000000 0.000000 -1.902925 0.000000 -0.572521 -0.062846 -0.255653 0.000000 -1.340076 0.000000 -1.263256 0.614791 -2.039430 0.000000 0.000000 0.000000 0.552528 0.000000 0.000000 0.000000 0.252770 0.974666 0.000000 0.245270 -0.124725 -1.900985 0.000000 0.000000 -0.311567 1.006599 0.000000 -0.150110 0.000000 0.912848 0.199453 0.000000 0.000000 0.000000 0.000000 0.000000 -0.955410 0.000000 0.000000 -0.389935 -0.282413 0.000000 -0.077222 0.000000 0.000000 0.000000 -0.070248 0.000000 -2.665469 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 190 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 13 24 35 44 55 59 67 77 86 95 108 115 124 131 143 150 163 174 184 190 Column indices: 1 4 5 6 7 9 10 11 12 13 14 15 18 3 6 7 9 10 11 12 14 17 18 19 0 1 3 4 5 7 10 12 13 16 18 1 2 4 6 7 9 10 12 19 0 1 2 3 5 7 12 13 16 17 19 7 10 12 13 3 4 7 10 15 16 17 19 1 3 6 8 9 11 13 15 17 19 0 1 3 7 14 15 16 17 19 1 2 3 6 11 12 15 17 18 1 5 6 7 9 11 13 14 15 16 17 18 19 0 2 4 6 7 8 16 0 1 4 5 8 10 14 15 17 0 2 5 11 12 17 19 0 3 4 6 8 9 11 12 13 15 18 19 4 5 6 7 11 16 19 0 1 2 4 5 7 8 9 11 12 13 15 18 1 2 5 7 8 9 11 13 14 15 19 3 4 6 7 8 11 12 14 16 17 3 6 7 9 13 15 Off-diagonal values: 0.225114 1.067372 0.773545 -0.134368 1.923968 0.057295 -1.364858 -0.030422 0.012379 -0.017507 -0.971752 -0.478395 0.890792 0.248797 0.761277 1.380616 -0.477170 -0.062334 0.400754 0.968586 0.156612 -0.536243 1.206704 0.042927 0.064844 0.957812 -0.707486 1.068992 1.609339 -1.036428 -0.572162 -0.116754 -0.385369 0.151197 0.086829 0.980591 -1.065637 -0.237375 -0.549530 0.258917 0.380918 -0.018440 -0.682561 0.729340 0.637589 -0.839027 0.540524 0.816275 -0.035198 0.030768 -0.363432 0.656963 0.803452 0.061466 -0.214987 1.995537 0.748340 -0.558329 0.383011 0.139251 0.321689 -1.146022 -0.529163 -0.146345 -1.420389 0.394795 -0.674429 -0.542032 1.406501 0.699967 0.489768 -1.252012 1.293149 -0.428666 -1.532448 2.452068 0.635659 -0.179554 -1.945813 0.130265 -2.609396 -0.112028 1.040020 -0.749244 0.618951 0.667155 -0.238186 0.167128 -1.117430 -0.670374 0.346066 -0.051353 1.284348 -0.844894 -0.292091 -0.911315 -0.472972 0.819768 1.089759 2.309861 -0.484551 0.464812 -0.628050 0.781953 0.478840 -0.836959 -0.080516 0.928114 0.537975 0.398974 1.785503 -0.764894 -2.251040 1.322354 -0.319592 -2.301473 -0.959299 0.491393 0.834140 0.016436 1.168770 -0.066747 1.077885 -0.446982 0.661372 -0.140614 0.195675 -2.460823 -0.211115 -0.707199 -0.360032 -1.008795 1.606780 0.238852 0.298304 0.421320 -1.317024 1.338429 0.501482 -0.397580 -0.186665 -1.195577 0.652220 1.109106 -0.606042 0.826640 1.229397 -0.046835 -0.356412 -0.726316 -0.864453 -1.023377 1.026195 -0.417117 2.269729 -0.131659 2.506513 -1.699792 0.293400 -0.188549 -1.735554 -0.828888 0.207415 -0.523059 -0.349952 -1.902925 -0.572521 -0.062846 -0.255653 -1.340076 -1.263256 0.614791 -2.039430 0.552528 0.252770 0.974666 0.245270 -0.124725 -1.900985 -0.311567 1.006599 -0.150110 0.912848 0.199453 -0.955410 -0.389935 -0.282413 -0.077222 -0.070248 -2.665469 . x - - x x o x - x o o x o o o - - x - | . - x - - x x - o o x x - x - - o x x x x . o x x - o - - o - o o - - x - x - | x o . o - o x - x o - o - - - - - - x x o x x . o - x - - - - o x - - x x - o | | | | | . - x - - x - o x - - - - - - | | | x x | . o - - o - - - - o o x - o | o | x | | x . x o - x - o - o - x - x o o | x | | | o . - - - - - o x o x - x | o x o | | o | | . - x o - - x - o o - | o | | | o x x | x . o - x o x x o o x x | x | x | o o x | | . - - - - o - - - o o | | x x | | x | x | . - o x - o - - x | o | | x | | | | | o o . - - - o - o o | | x x | x | x o | x x o . o - - o x | | | | x o x x | | | o | | | . o - - o o o x | o x | o x o | x o o | o . - x - | o o | | o | o o o | o | o x o | . - x | | | x x | x o o | | o x | o | x x . - | | | o | | o o | o | | | o | o | | | . The error in solving: 6.762485e-16 The error in solving: 2.822220e-16 The error in solving: 6.784876e-16 The error in solving: 5.690766e-16 The error in solving: 6.090065e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A matrix using a standard normal distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 -0.900448 0.667900 0.100357 0.354353 0.000000 -0.289258 -0.407960 -0.551104 0.304697 0.899455 0.846574 0.691452 -0.172875 0.000000 -0.822321 -0.471127 -0.136624 -1.605849 -0.675452 0.000000 -0.834026 0.000000 -0.130688 0.000000 -0.104759 -0.952696 0.000000 0.383020 0.783677 0.235350 -0.245700 1.804867 0.834232 -0.316215 -1.644950 0.000000 -1.660099 0.912421 -0.847828 -2.047754 0.000000 0.993004 0.000000 0.000000 -0.109606 0.804220 0.000000 -1.555840 0.000000 0.834326 0.000000 0.000000 -1.334227 0.687775 0.873001 1.232175 -0.245219 0.000000 0.202881 -0.180962 0.000000 0.000000 0.000000 0.312849 0.000000 0.467781 0.000000 -0.366004 -0.174846 1.341725 0.482003 3.022659 0.000000 0.000000 0.000000 0.000000 -0.677064 0.378567 1.599525 -1.280674 -0.179515 0.517281 0.000000 0.476464 0.690992 -0.141609 -0.692642 0.000000 1.256813 -1.813998 -2.340402 0.897876 0.080464 1.003874 -1.357267 -0.510068 -0.997860 1.027875 -0.080953 0.904516 -3.064064 -0.547626 1.275956 0.000000 1.303623 0.000000 -0.094126 0.154473 0.157768 0.000000 -0.364276 1.501832 -1.192134 -0.820151 -1.596516 -1.088233 -0.605811 0.785519 -2.055544 0.000000 1.027154 0.000000 -0.784713 0.000000 0.000000 0.000000 0.261399 0.000000 0.093985 -0.507958 0.851768 0.000000 1.065365 0.000000 -1.851915 -0.575081 0.115015 0.431679 0.477865 -1.355519 1.309416 -0.045332 0.908451 1.885918 0.000000 0.000000 1.704500 -0.556585 -0.442446 0.000000 -0.321578 -0.321434 0.000000 -0.452574 -0.123277 1.998678 -0.018983 -0.654550 -0.122510 0.412066 0.444584 0.000000 0.265980 0.000000 -0.698059 0.000000 0.000000 -0.511983 -1.405430 -1.012430 0.000000 2.619409 0.391716 0.744555 1.589418 0.000000 0.251051 -0.077780 0.021221 2.195241 0.000000 0.000000 -0.087574 0.000000 0.781530 0.191582 0.000000 0.000000 1.425380 1.121128 0.494684 0.000000 -2.568693 0.000000 -0.894047 0.065203 0.696431 0.243111 -0.742558 0.486557 0.000000 -0.181199 -0.620105 0.000000 -0.126329 -0.160422 0.000000 -0.362537 0.000000 -1.113289 0.000000 -1.559364 -0.281374 -1.487159 -0.950086 -1.185923 -0.780840 -0.543416 0.000000 0.000000 0.020420 0.000000 0.625001 1.152257 0.213324 2.452340 -1.127177 -0.003579 0.000000 0.000000 -0.913662 -0.844761 -1.223403 1.063192 -2.198891 0.695915 0.428820 0.828921 -1.091646 -0.422424 0.652656 0.000000 -2.429613 -1.184030 0.091422 -0.587243 0.000000 -0.731719 -0.055869 -1.721319 0.000000 0.550823 -0.938762 1.776347 0.363675 0.000000 0.000000 -0.382067 1.610590 0.000000 -0.354983 -0.028296 0.403506 1.454283 -1.163304 0.000000 0.000000 0.000000 0.837174 0.000000 -1.021717 0.000000 1.781268 0.489737 0.000000 -0.751233 -0.851684 -1.112690 0.777156 -2.173499 -1.053933 -0.427066 0.000000 -2.835942 -0.197649 -1.002646 0.000000 0.225031 -0.132023 -0.725087 0.000000 -0.261685 0.000000 -0.080496 1.097932 0.000000 0.835989 -0.451882 0.000000 -0.852985 -0.212941 -0.151793 -0.144566 -0.930200 -0.757683 1.119671 0.000000 0.000000 0.200915 0.000000 -0.209859 -0.193258 1.172156 0.000000 0.000000 -1.507781 0.000000 1.468908 -0.647619 0.230976 1.310413 -2.730212 -0.484510 1.448525 -0.437070 -0.586316 2.313506 -1.617406 1.424212 -0.638321 -1.431616 0.000000 1.247676 0.000000 0.000000 0.000000 0.000000 0.000000 -0.246440 -0.456548 0.912968 -0.863313 0.000000 0.868041 0.000000 0.000000 -1.194155 2.481189 0.000000 -0.690212 0.125600 -0.846623 0.108334 -1.253927 1.502764 0.000000 0.305099 -0.734026 0.000000 -0.174437 0.933714 0.199224 0.000000 0.405521 0.530343 0.000000 0.982354 -1.678261 0.330006 -1.048618 0.000000 0.209078 -0.008863 -0.342763 0.000000 -0.530788 0.000000 -1.549363 0.000000 0.000000 1.190282 -0.043599 0.000000 0.529956 -0.305978 -0.478659 -0.451596 -0.805254 0.000000 0.000000 0.000000 -0.471292 -0.375379 -1.750594 -0.465746 0.577158 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 285 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 16 31 43 54 72 89 101 117 131 144 159 174 189 202 217 230 244 259 273 285 Column indices: 2 3 4 5 7 8 9 10 11 12 13 14 16 17 18 19 0 2 4 6 7 9 10 11 12 13 14 15 16 18 19 0 1 3 6 7 9 11 14 15 16 17 18 0 1 5 7 9 10 11 12 13 18 19 0 1 2 3 5 6 7 8 10 11 12 13 14 15 16 17 18 19 0 1 2 3 4 6 8 9 10 12 13 14 15 16 17 18 19 0 2 4 8 10 11 12 14 16 17 18 19 0 1 2 3 4 5 8 9 10 12 13 15 16 17 18 19 0 1 2 4 6 9 10 11 13 14 15 16 18 19 0 1 4 6 7 10 11 12 14 16 17 18 19 0 1 3 4 6 7 9 11 13 14 15 16 17 18 19 2 4 5 6 7 8 9 12 13 14 15 16 17 18 19 0 1 2 4 5 6 7 9 10 11 13 14 15 16 19 0 2 3 4 5 6 10 12 14 15 17 18 19 0 1 2 3 5 6 7 9 10 11 13 15 16 18 19 1 2 3 4 5 6 7 10 12 13 14 17 19 0 1 2 3 4 5 6 7 8 9 10 11 12 14 0 1 2 3 5 8 9 11 12 13 14 15 16 18 19 1 2 3 5 6 8 9 10 11 13 14 15 17 19 2 3 5 6 7 8 9 13 14 15 16 17 Off-diagonal values: -0.900448 0.667900 0.100357 0.354353 -0.289258 -0.407960 -0.551104 0.304697 0.899455 0.846574 0.691452 -0.172875 -0.822321 -0.471127 -0.136624 -1.605849 -0.675452 -0.834026 -0.130688 -0.104759 -0.952696 0.383020 0.783677 0.235350 -0.245700 1.804867 0.834232 -0.316215 -1.644950 -1.660099 0.912421 -0.847828 -2.047754 0.993004 -0.109606 0.804220 -1.555840 0.834326 -1.334227 0.687775 0.873001 1.232175 -0.245219 0.202881 -0.180962 0.312849 0.467781 -0.366004 -0.174846 1.341725 0.482003 3.022659 -0.677064 0.378567 1.599525 -1.280674 -0.179515 0.517281 0.476464 0.690992 -0.141609 -0.692642 1.256813 -1.813998 -2.340402 0.897876 0.080464 1.003874 -1.357267 -0.510068 -0.997860 1.027875 -0.080953 0.904516 -3.064064 -0.547626 1.275956 1.303623 -0.094126 0.154473 0.157768 -0.364276 1.501832 -1.192134 -0.820151 -1.596516 -1.088233 -0.605811 0.785519 -2.055544 1.027154 -0.784713 0.261399 0.093985 -0.507958 0.851768 1.065365 -1.851915 -0.575081 0.115015 0.431679 0.477865 -1.355519 1.309416 -0.045332 0.908451 1.885918 1.704500 -0.556585 -0.442446 -0.321578 -0.321434 -0.452574 -0.123277 1.998678 -0.018983 -0.654550 -0.122510 0.412066 0.444584 0.265980 -0.698059 -0.511983 -1.405430 -1.012430 2.619409 0.391716 0.744555 1.589418 0.251051 -0.077780 0.021221 2.195241 -0.087574 0.781530 0.191582 1.425380 1.121128 0.494684 -2.568693 -0.894047 0.065203 0.696431 0.243111 -0.742558 0.486557 -0.181199 -0.620105 -0.126329 -0.160422 -0.362537 -1.113289 -1.559364 -0.281374 -1.487159 -0.950086 -1.185923 -0.780840 -0.543416 0.020420 0.625001 1.152257 0.213324 2.452340 -1.127177 -0.003579 -0.913662 -0.844761 -1.223403 1.063192 -2.198891 0.695915 0.428820 0.828921 -1.091646 -0.422424 0.652656 -2.429613 -1.184030 0.091422 -0.587243 -0.731719 -0.055869 -1.721319 0.550823 -0.938762 1.776347 0.363675 -0.382067 1.610590 -0.354983 -0.028296 0.403506 1.454283 -1.163304 0.837174 -1.021717 1.781268 0.489737 -0.751233 -0.851684 -1.112690 0.777156 -2.173499 -1.053933 -0.427066 -2.835942 -0.197649 -1.002646 0.225031 -0.132023 -0.725087 -0.261685 -0.080496 1.097932 0.835989 -0.451882 -0.852985 -0.212941 -0.151793 -0.144566 -0.930200 -0.757683 1.119671 0.200915 -0.209859 -0.193258 1.172156 -1.507781 1.468908 -0.647619 0.230976 1.310413 -2.730212 -0.484510 1.448525 -0.437070 -0.586316 2.313506 -1.617406 1.424212 -0.638321 -1.431616 1.247676 -0.246440 -0.456548 0.912968 -0.863313 0.868041 -1.194155 2.481189 -0.690212 0.125600 -0.846623 0.108334 -1.253927 1.502764 0.305099 -0.734026 -0.174437 0.933714 0.199224 0.405521 0.530343 0.982354 -1.678261 0.330006 -1.048618 0.209078 -0.008863 -0.342763 -0.530788 -1.549363 1.190282 -0.043599 0.529956 -0.305978 -0.478659 -0.451596 -0.805254 -0.471292 -0.375379 -1.750594 -0.465746 0.577158 . - o x x x - o o o x x x x o - o o o o o . o - o - o o - x x x o x x o o - o x o o . x - - o x - o - x - - o x x x o - x o | . - x - x - o o x x x - - - - o x x o o x . x x o o - x o o x x x o o o x o x o o x . x - o x x - o x o o o o o x o | x | o | . - x - x o x - x - o o x x x o x o x x | . x o o - o o - o o x o o o x x | x | o | . o o o - x x x x - x o x x | | o | x x | . x x x - o - o x x x o x | o o | o o | o . o - o o o o o o o | | x | x x x x o o | . o o o x o x x x o o x | o o x o | o o o . x o x x - - o x | o o x x o | | | x | o . x x - o o o x o o o | o o o | x o o | o . o x - x o | o o o o o o x | | x | o o x . - o - x o x x o o x o o x o x o o | x | . - - - o o x o | x | | o x | o x o x o x . x o | o x x | x x | x o x o | x o o | o . o | | x o | x o o o o | | | o o o o x | . The error in solving: 5.779962e-16 The error in solving: 5.826011e-16 The error in solving: 4.579670e-16 The error in solving: 5.240588e-16 The error in solving: 8.261656e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.792980 0.000000 0.621286 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.805281 0.000000 0.000000 0.000000 0.342532 0.128834 0.000000 0.000000 0.791435 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.225398 0.000000 0.000000 0.083758 0.000000 0.000000 0.000000 0.000000 0.004200 0.000000 0.939181 0.000000 0.000000 0.104662 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.713766 0.247496 0.000000 0.922367 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.898666 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.044994 0.000000 0.000000 0.000000 0.310595 0.150437 0.000000 0.000000 0.000000 0.000000 0.000000 0.487607 0.157682 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.505994 0.373876 0.000000 0.596363 0.000000 0.235445 0.000000 0.000000 0.000000 0.000000 0.000000 0.309690 0.304795 0.000000 0.896589 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.363702 0.000000 0.000000 0.313450 0.000000 0.000000 0.000000 0.000000 0.000000 0.052423 0.000000 0.000000 0.358914 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.036574 0.000000 0.733012 0.000000 0.000000 0.038562 0.716797 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.991402 0.104148 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.293039 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.530122 0.020186 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.226434 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.102016 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.145277 0.564490 0.323079 0.000000 0.164580 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.085237 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.568411 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.461493 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 43 (max 380) Diagonal entries: 0.000000 0.000000 0.225398 0.713766 0.000000 0.505994 0.000000 0.363702 0.036574 0.000000 0.000000 0.000000 0.000000 0.145277 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 3 6 10 13 18 24 24 27 30 33 35 37 37 40 41 42 43 43 43 43 Column indices: 7 9 18 2 3 6 5 10 12 15 4 6 15 6 10 11 17 18 6 8 10 16 17 19 10 16 19 10 13 14 10 11 18 14 15 12 19 14 15 17 16 16 19 Off-diagonal values: 0.792980 0.621286 0.805281 0.342532 0.128834 0.791435 0.083758 0.004200 0.939181 0.104662 0.247496 0.922367 0.898666 0.044994 0.310595 0.150437 0.487607 0.157682 0.373876 0.596363 0.235445 0.309690 0.304795 0.896589 0.313450 0.052423 0.358914 0.733012 0.038562 0.716797 0.991402 0.104148 0.293039 0.530122 0.020186 0.226434 0.102016 0.564490 0.323079 0.164580 0.085237 0.568411 0.461493 . - - - - - - x - x - - - - - - - - x - | . x x - - x - - - - - - - - - - - - - | | x - - x - - - - x - x - - x - - - - | | | x x - x - - - - - - - - x - - - - | | | | . - x - - - x x - - - - - x x - | | | | | x x - x - x - - - - - x x - x | | | | | | . - - - - - - - - - - - - - | | | | | | | x - - x - - - - - x - - x | | | | | | | | x - x - - x x - - - - - | | | | | | | | | . x x - - - - - - x - | | | | | | | | | | . - - - x x - - - - | | | | | | | | | | | . x - - - - - - x | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | x x x - x - - | | | | | | | | | | | | | | . - x - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | | . - - x | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.355139e-16 The error in solving: 5.721958e-17 The error in solving: 1.734723e-18 The error in solving: 3.155481e-16 The error in solving: 2.775558e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.709399 0.408024 0.082195 0.382119 0.325540 0.631045 0.000000 0.000000 0.397885 0.000000 0.000000 0.000000 0.865415 0.347418 0.000000 0.604113 0.243137 0.098219 0.000000 0.000000 0.000000 0.488806 0.000000 0.000000 0.587207 0.000000 0.000000 0.816120 0.333158 0.913219 0.872957 0.000000 0.000000 0.610336 0.000000 0.821748 0.000000 0.000000 0.487253 0.000000 0.000000 0.727064 0.000000 0.990828 0.346892 0.000000 0.000000 0.172439 0.000000 0.000000 0.110373 0.000000 0.561562 0.532746 0.252246 0.000000 0.276663 0.094447 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.969208 0.000000 0.639362 0.000000 0.000000 0.706007 0.000000 0.000000 0.000000 0.000000 0.613330 0.775962 0.487050 0.205271 0.831221 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.821032 0.513157 0.082331 0.437267 0.000000 0.972911 0.497382 0.000000 0.725603 0.429791 0.069932 0.000000 0.656630 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.599602 0.905978 0.996062 0.000000 0.991213 0.000000 0.000000 0.000000 0.176334 0.967992 0.000000 0.594741 0.000000 0.157127 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.215986 0.497725 0.000000 0.864591 0.000000 0.000000 0.304668 0.805653 0.000000 0.000000 0.360712 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.288129 0.610456 0.988306 0.403598 0.563455 0.079659 0.348581 0.555216 0.729107 0.000000 0.938737 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.674076 0.000000 0.000000 0.000000 0.427853 0.284930 0.000000 0.000000 0.203376 0.742559 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.489187 0.000000 0.000000 0.876264 0.000000 0.103012 0.000000 0.000000 0.000000 0.503232 0.239169 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.132318 0.492673 0.409732 0.000000 0.231762 0.000000 0.602979 0.611698 0.000000 0.629439 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.917396 0.889013 0.000000 0.000000 0.984964 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.277539 0.378507 0.109091 0.248362 0.000000 0.000000 0.177920 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.020908 0.956038 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.260580 0.000000 0.568126 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.524609 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.254281 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.905496 0.979919 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 101 (max 380) Diagonal entries: 0.000000 0.000000 0.727064 0.000000 0.000000 0.000000 0.000000 0.000000 0.674076 0.489187 0.132318 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.905496 0.000000 0.000000 Row indices: 0 12 21 30 38 48 56 62 72 76 80 86 89 94 96 98 99 100 101 101 101 Column indices: 1 2 3 4 5 6 9 13 14 16 17 18 2 5 8 9 10 11 14 16 19 4 5 8 11 13 14 15 17 18 5 7 10 15 16 17 18 19 7 8 9 10 12 13 15 16 17 19 6 7 8 10 14 15 17 19 9 10 12 15 16 19 8 9 10 11 12 13 14 15 16 18 12 13 16 17 12 14 18 19 11 12 14 16 17 19 15 16 19 13 14 15 16 19 16 17 15 17 18 17 18 Off-diagonal values: 0.709399 0.408024 0.082195 0.382119 0.325540 0.631045 0.397885 0.865415 0.347418 0.604113 0.243137 0.098219 0.488806 0.587207 0.816120 0.333158 0.913219 0.872957 0.610336 0.821748 0.487253 0.990828 0.346892 0.172439 0.110373 0.561562 0.532746 0.252246 0.276663 0.094447 0.969208 0.639362 0.706007 0.613330 0.775962 0.487050 0.205271 0.831221 0.821032 0.513157 0.082331 0.437267 0.972911 0.497382 0.725603 0.429791 0.069932 0.656630 0.599602 0.905978 0.996062 0.991213 0.176334 0.967992 0.594741 0.157127 0.215986 0.497725 0.864591 0.304668 0.805653 0.360712 0.288129 0.610456 0.988306 0.403598 0.563455 0.079659 0.348581 0.555216 0.729107 0.938737 0.427853 0.284930 0.203376 0.742559 0.876264 0.103012 0.503232 0.239169 0.492673 0.409732 0.231762 0.602979 0.611698 0.629439 0.917396 0.889013 0.984964 0.277539 0.378507 0.109091 0.248362 0.177920 0.020908 0.956038 0.260580 0.568126 0.524609 0.254281 0.979919 . x x x x x x - - x - - - x x - x x x - | . x - - x - - x x x x - - x - x - - x | | x - x x - - x - - x - x x x - x x - | | | . - x - x - - x - - - - x x x x x | | | | . - - x x x x - x x - x x x - x | | | | | . x x x - x - - - x x - x - x | | | | | | . - - x x - x - - x x - - x | | | | | | | . x x x x x x x x x - x - | | | | | | | | x - - - x x - - x x - - | | | | | | | | | x - - x - x - - - x x | | | | | | | | | | x x x - x - x x - x | | | | | | | | | | | . - - - x x - - x | | | | | | | | | | | | . x x x x - - x | | | | | | | | | | | | | . - - x x - - | | | | | | | | | | | | | | . x - x - - | | | | | | | | | | | | | | | . - - x - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.792851e-16 The error in solving: 1.964148e-16 The error in solving: 2.562698e-16 The error in solving: 2.020636e-16 The error in solving: 2.220717e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.750000 [ 0.343502 0.414985 0.000000 0.419823 0.000000 0.014257 0.395359 0.336783 0.263405 0.435776 0.387776 0.478293 0.375005 0.050782 0.213205 0.291717 0.000000 0.663147 0.586634 0.619738 0.000000 0.640511 0.239746 0.127560 0.169006 0.508261 0.335676 0.076435 0.634592 0.217490 0.847092 0.181848 0.000000 0.787115 0.000000 0.000000 0.478284 0.000000 0.000000 0.640631 0.000000 0.000000 0.409029 0.652289 0.814884 0.388073 0.000000 0.282811 0.167288 0.000000 0.814913 0.117045 0.910496 0.102001 0.311777 0.606663 0.385091 0.851331 0.000000 0.535119 0.000000 0.000000 0.000000 0.399778 0.000000 0.082969 0.207610 0.182983 0.452586 0.806772 0.000000 0.391660 0.061809 0.395450 0.793759 0.000000 0.001698 0.454921 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.614519 0.000000 0.661275 0.162917 0.145422 0.000000 0.473835 0.150790 0.836909 0.000000 0.000000 0.693782 0.142313 0.378218 0.052654 0.458682 0.000000 0.000000 0.000000 0.000000 0.000000 0.066591 0.904609 0.000000 0.000000 0.720483 0.713982 0.507151 0.991168 0.353041 0.000000 0.000000 0.000000 0.000000 0.607830 0.195522 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.417236 0.421499 0.982376 0.089283 0.000000 0.000000 0.527646 0.192607 0.899283 0.707001 0.186975 0.000000 0.864909 0.895906 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.876651 0.839884 0.000000 0.000000 0.000000 0.081611 0.650635 0.031862 0.121175 0.000000 0.778483 0.517017 0.554179 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.509109 0.000000 0.963490 0.683410 0.356811 0.147717 0.632933 0.155115 0.000000 0.000000 0.018398 0.384324 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.187729 0.156530 0.000000 0.000000 0.257648 0.368607 0.522639 0.000000 0.253934 0.595510 0.591369 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.147465 0.789642 0.752292 0.493863 0.567567 0.000000 0.968455 0.646378 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.991455 0.050901 0.000000 0.271130 0.946045 0.923543 0.444878 0.361752 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.936351 0.610203 0.000000 0.323096 0.000000 0.604132 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.566798 0.000000 0.000000 0.969602 0.828225 0.953188 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.798300 0.652227 0.047905 0.559509 0.865930 0.563783 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.326643 0.005893 0.700753 0.647616 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.109292 0.197312 0.542835 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.660811 0.960770 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.958759 0.354280 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.838276]; Dimension: 20 x 20 Off-diagonal entries: 142 (max 380) Diagonal entries: 0.343502 0.640511 0.409029 0.399778 0.614519 0.066591 0.417236 0.876651 0.509109 0.187729 0.000000 0.000000 0.000000 0.566798 0.798300 0.000000 0.000000 0.000000 0.958759 0.838276 Row indices: 0 16 29 43 54 65 73 83 91 99 106 113 120 124 127 132 136 139 141 142 142 Column indices: 1 3 5 6 7 8 9 10 11 12 13 14 15 17 18 19 2 3 4 5 6 7 8 9 10 11 13 16 19 3 4 5 7 8 10 11 12 13 14 15 16 17 19 5 6 7 8 9 11 12 13 14 16 17 6 7 8 10 11 12 15 16 17 18 19 6 9 10 11 12 13 18 19 7 8 9 12 13 14 15 16 18 19 8 12 13 14 15 17 18 19 10 11 12 13 14 15 18 19 10 13 14 15 17 18 19 11 12 13 14 15 17 18 12 13 15 16 17 18 19 13 14 16 18 16 17 18 15 16 17 18 19 16 17 18 19 17 18 19 18 19 19 Off-diagonal values: 0.414985 0.419823 0.014257 0.395359 0.336783 0.263405 0.435776 0.387776 0.478293 0.375005 0.050782 0.213205 0.291717 0.663147 0.586634 0.619738 0.239746 0.127560 0.169006 0.508261 0.335676 0.076435 0.634592 0.217490 0.847092 0.181848 0.787115 0.478284 0.640631 0.652289 0.814884 0.388073 0.282811 0.167288 0.814913 0.117045 0.910496 0.102001 0.311777 0.606663 0.385091 0.851331 0.535119 0.082969 0.207610 0.182983 0.452586 0.806772 0.391660 0.061809 0.395450 0.793759 0.001698 0.454921 0.661275 0.162917 0.145422 0.473835 0.150790 0.836909 0.693782 0.142313 0.378218 0.052654 0.458682 0.904609 0.720483 0.713982 0.507151 0.991168 0.353041 0.607830 0.195522 0.421499 0.982376 0.089283 0.527646 0.192607 0.899283 0.707001 0.186975 0.864909 0.895906 0.839884 0.081611 0.650635 0.031862 0.121175 0.778483 0.517017 0.554179 0.963490 0.683410 0.356811 0.147717 0.632933 0.155115 0.018398 0.384324 0.156530 0.257648 0.368607 0.522639 0.253934 0.595510 0.591369 0.147465 0.789642 0.752292 0.493863 0.567567 0.968455 0.646378 0.991455 0.050901 0.271130 0.946045 0.923543 0.444878 0.361752 0.936351 0.610203 0.323096 0.604132 0.969602 0.828225 0.953188 0.652227 0.047905 0.559509 0.865930 0.563783 0.326643 0.005893 0.700753 0.647616 0.109292 0.197312 0.542835 0.660811 0.960770 0.354280 x x - x - x x x x x x x x x x x - x x x | x x x x x x x x x x x - x - - x - - x | | x x x x - x x - x x x x x x x x - x | | | x - x x x x x - x x x x - x x - - | | | | x - x x x - x x x - - x x x x x | | | | | x x - - x x x x x - - - - x x | | | | | | x x x x - - x x x x x - x x | | | | | | | x x - - - x x x x - x x x | | | | | | | | x - x x x x x x - - x x | | | | | | | | | x x - - x x x - x x x | | | | | | | | | | . x x x x x - x x - | | | | | | | | | | | . x x - x x x x x | | | | | | | | | | | | . x x - x - x - | | | | | | | | | | | | | x - - x x x - | | | | | | | | | | | | | | x x x x x x | | | | | | | | | | | | | | | . x x x x | | | | | | | | | | | | | | | | . x x x | | | | | | | | | | | | | | | | | . x x | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | | x The error in solving: 2.001483e-16 The error in solving: 1.996666e-16 The error in solving: 2.288783e-16 The error in solving: 2.242092e-16 The error in solving: 2.676651e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.481189 0.078451 0.000000 0.962170 0.881181 0.000000 0.448590 0.000000 0.970474 0.000000 0.000000 0.626462 0.000000 0.000000 0.408831 0.588909 0.000000 0.000000 0.000000 0.000000 0.000000 0.489763 0.000000 0.000000 0.178449 0.000000 0.000000 0.369751 0.874832 0.886178 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.439340 0.000000 0.000000 0.000000 0.000000 0.000000 0.180746 0.000000 0.000000 0.000000 0.000000 0.000000 0.535266 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.366731 0.000000 0.000000 0.000000 0.000000 0.705456 0.000000 0.085730 0.000000 0.074565 0.000000 0.790474 0.000000 0.000000 0.000000 0.000000 0.219087 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.909338 0.000000 0.000000 0.116314 0.000000 0.000000 0.000000 0.695163 0.000000 0.000000 0.000000 0.000000 0.176896 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.730661 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.151862 0.581422 0.597577 0.000000 0.636289 0.978093 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.456627 0.000000 0.064314 0.000000 0.000000 0.000000 0.000000 0.000000 0.496466 0.731938 0.000000 0.000000 0.487868 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.294715 0.000000 0.624633 0.000000 0.000000 0.000000 0.000000 0.093312 0.355819 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.889490 0.000000 0.000000 0.000000 0.000000 0.062529 0.140135 0.000000 0.072115 0.000000 0.826332 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.516064 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.444340 0.150349 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.454882 0.000000 0.000000 0.000000 0.000000 0.992764 0.000000 0.655561 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.809482 0.049984 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.455144 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.178056 0.238848 0.000000 0.000000 0.227258 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.670350 0.000000 0.557511 0.727814 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.397542 0.000000 0.000000 0.000000 0.000000 0.933526 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.309575 0.000000 0.000000 0.000000 0.647442 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.653780 0.970433 0.732644 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.672473 0.749199 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.330760 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.842413]; Dimension: 20 x 20 Off-diagonal entries: 53 (max 380) Diagonal entries: 0.481189 0.489763 0.180746 0.705456 0.909338 0.730661 0.456627 0.294715 0.889490 0.516064 0.454882 0.809482 0.178056 0.670350 0.397542 0.309575 0.653780 0.672473 0.330760 0.842413 Row indices: 0 8 13 15 19 22 27 31 34 38 40 42 44 46 48 49 50 52 53 53 53 Column indices: 1 3 4 6 8 11 14 15 4 7 8 9 16 8 18 5 7 9 14 7 11 16 12 13 14 16 17 8 14 15 18 9 14 15 13 14 16 18 16 17 15 17 12 19 13 16 15 16 19 19 17 18 18 Off-diagonal values: 0.078451 0.962170 0.881181 0.448590 0.970474 0.626462 0.408831 0.588909 0.178449 0.369751 0.874832 0.886178 0.439340 0.535266 0.366731 0.085730 0.074565 0.790474 0.219087 0.116314 0.695163 0.176896 0.151862 0.581422 0.597577 0.636289 0.978093 0.064314 0.496466 0.731938 0.487868 0.624633 0.093312 0.355819 0.062529 0.140135 0.072115 0.826332 0.444340 0.150349 0.992764 0.655561 0.049984 0.455144 0.238848 0.227258 0.557511 0.727814 0.933526 0.647442 0.970433 0.732644 0.749199 x x - x x - x - x - - x - - x x - - - - | x - - x - - x x x - - - - - - x - - - | | x - - - - - x - - - - - - - - - x - | | | x - x - x - x - - - - x - - - - - | | | | x - - x - - - x - - - - x - - - | | | | | x - - - - - - x x x - x x - - | | | | | | x - x - - - - - x x - - x - | | | | | | | x - x - - - - x x - - - - | | | | | | | | x - - - - x x - x - x - | | | | | | | | | x - - - - - - x x - - | | | | | | | | | | x - - - - x - x - - | | | | | | | | | | | x x - - - - - - x | | | | | | | | | | | | x x - - x - - - | | | | | | | | | | | | | x - x x - - - | | | | | | | | | | | | | | x - - - - x | | | | | | | | | | | | | | | x - - - x | | | | | | | | | | | | | | | | x x x - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | x The error in solving: 3.342214e-16 The error in solving: 1.271920e-16 The error in solving: 2.748538e-16 The error in solving: 1.927964e-16 The error in solving: 2.775558e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.210900 0.512629 0.974828 0.000000 0.561680 0.709985 0.000000 0.386773 0.000000 0.000000 0.000000 0.000000 0.000000 0.495071 0.000000 0.481722 0.000000 0.426315 0.000000 0.380047 0.000000 0.370344 0.000000 0.000000 0.026253 0.000000 0.751531 0.000000 0.000000 0.000000 0.000000 0.608996 0.000000 0.792869 0.130803 0.000000 0.185294 0.000000 0.000000 0.529324 0.000000 0.000000 0.612302 0.000000 0.435502 0.000000 0.000000 0.307911 0.106920 0.000000 0.000000 0.000000 0.718077 0.218073 0.000000 0.999841 0.000000 0.000000 0.000000 0.282685 0.000000 0.000000 0.000000 0.275058 0.000000 0.000000 0.098526 0.000000 0.238658 0.000000 0.333717 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.560993 0.000000 0.366111 0.000000 0.000000 0.000000 0.000000 0.345132 0.631216 0.000000 0.000000 0.139815 0.000000 0.851158 0.013868 0.000000 0.382585 0.173441 0.600015 0.269720 0.531545 0.000000 0.318604 0.000000 0.000000 0.000000 0.000000 0.000000 0.304465 0.369979 0.724101 0.000000 0.000000 0.735699 0.000000 0.000000 0.136495 0.151500 0.000000 0.916886 0.000000 0.831682 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.296735 0.076616 0.000000 0.591015 0.871302 0.000000 0.670700 0.420902 0.328704 0.227194 0.433543 0.777297 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.135236 0.379099 0.127801 0.378706 0.879383 0.049632 0.000000 0.378014 0.053266 0.000000 0.628445 0.000000 0.036305 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.694821 0.000000 0.000000 0.000000 0.298989 0.851828 0.000000 0.000000 0.000000 0.506598 0.554167 0.503373 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.292075 0.000000 0.494479 0.701743 0.673149 0.000000 0.049366 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.047946 0.000000 0.000000 0.000000 0.317533 0.000000 0.000000 0.000000 0.861296 0.961166 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.174386 0.000000 0.922567 0.366316 0.000000 0.326942 0.000000 0.000000 0.704802 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.071684 0.000000 0.086361 0.000000 0.508596 0.025592 0.856618 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.595910 0.000000 0.301110 0.987928 0.000000 0.000000 0.047254 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.858876 0.000000 0.589317 0.739616 0.904638 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.972219 0.161960 0.000000 0.472139 0.144253 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.179902 0.741729 0.223217 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.692835 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.725819 0.960028 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.067739]; Dimension: 20 x 20 Off-diagonal entries: 95 (max 380) Diagonal entries: 0.210900 0.370344 0.612302 0.275058 0.345132 0.304465 0.296735 0.135236 0.694821 0.292075 0.047946 0.174386 0.071684 0.595910 0.858876 0.972219 0.179902 0.692835 0.725819 0.067739 Row indices: 0 9 16 23 28 38 45 54 63 68 72 75 79 83 86 89 92 94 94 95 95 Column indices: 1 2 4 5 7 13 15 17 19 4 6 11 13 14 16 19 4 7 8 12 13 15 19 6 8 10 17 19 5 8 10 11 13 14 15 16 17 19 6 7 10 13 14 16 18 7 9 10 12 13 14 15 16 17 8 9 10 11 12 14 15 17 19 12 13 17 18 19 11 12 13 15 14 18 19 13 14 16 19 14 16 17 18 15 16 19 16 17 18 16 18 19 17 18 19 Off-diagonal values: 0.512629 0.974828 0.561680 0.709985 0.386773 0.495071 0.481722 0.426315 0.380047 0.026253 0.751531 0.608996 0.792869 0.130803 0.185294 0.529324 0.435502 0.307911 0.106920 0.718077 0.218073 0.999841 0.282685 0.098526 0.238658 0.333717 0.560993 0.366111 0.631216 0.139815 0.851158 0.013868 0.382585 0.173441 0.600015 0.269720 0.531545 0.318604 0.369979 0.724101 0.735699 0.136495 0.151500 0.916886 0.831682 0.076616 0.591015 0.871302 0.670700 0.420902 0.328704 0.227194 0.433543 0.777297 0.379099 0.127801 0.378706 0.879383 0.049632 0.378014 0.053266 0.628445 0.036305 0.298989 0.851828 0.506598 0.554167 0.503373 0.494479 0.701743 0.673149 0.049366 0.317533 0.861296 0.961166 0.922567 0.366316 0.326942 0.704802 0.086361 0.508596 0.025592 0.856618 0.301110 0.987928 0.047254 0.589317 0.739616 0.904638 0.161960 0.472139 0.144253 0.741729 0.223217 0.960028 x x x - x x - x - - - - - x - x - x - x | x - - x - x - - - - x - x x - x - - x | | x - x - - x x - - - x x - x - - - x | | | x - - x - x - x - - - - - - x - x | | | | x x - - x - x x - x x x x x - x | | | | | x x x - - x - - x x - x - x - | | | | | | x x - x x - x x x x x x - - | | | | | | | x x x x x x - x x - x - x | | | | | | | | x - - - x x - - - x x x | | | | | | | | | x - x x x - x - - - - | | | | | | | | | | x - - - x - - - x x | | | | | | | | | | | x - x x - x - - x | | | | | | | | | | | | x - x - x x x - | | | | | | | | | | | | | x - x x - - x | | | | | | | | | | | | | | x - x x x - | | | | | | | | | | | | | | | x x - x x | | | | | | | | | | | | | | | | x x x - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | | x The error in solving: 2.483504e-16 The error in solving: 3.248707e-16 The error in solving: 6.798700e-17 The error in solving: 2.722038e-16 The error in solving: 3.510833e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.772466 0.475293 0.680084 0.718043 0.683329 0.726463 0.927564 0.201178 0.000000 0.000000 0.401381 0.678282 0.007690 0.000000 0.247653 0.032421 0.379647 0.775099 0.541882 0.249298 0.000000 0.462381 0.301954 0.000000 0.744536 0.977093 0.054192 0.000000 0.000000 0.000000 0.005500 0.699318 0.200575 0.719039 0.834926 0.338689 0.352186 0.501912 0.422668 0.032610 0.000000 0.000000 0.734043 0.053872 0.539667 0.370359 0.652631 0.000000 0.397099 0.228522 0.668190 0.000000 0.526161 0.600316 0.884099 0.815124 0.103567 0.750929 0.572166 0.324107 0.000000 0.000000 0.000000 0.545106 0.759916 0.430901 0.527126 0.290017 0.458586 0.985567 0.950667 0.502610 0.863247 0.552897 0.828163 0.284355 0.000000 0.022283 0.969327 0.377131 0.000000 0.000000 0.000000 0.000000 0.670369 0.839403 0.000000 0.778312 0.000000 0.921945 0.577193 0.267441 0.667079 0.449188 0.079620 0.355246 0.835643 0.000000 0.096816 0.135242 0.000000 0.000000 0.000000 0.000000 0.000000 0.133305 0.695999 0.000000 0.354251 0.000000 0.509037 0.841957 0.390380 0.000000 0.272381 0.471967 0.745684 0.410283 0.560620 0.595513 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.014399 0.309790 0.200253 0.000000 0.000000 0.075665 0.000000 0.512977 0.000000 0.319755 0.701217 0.253430 0.585261 0.726138 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.735432 0.268533 0.000000 0.869820 0.768840 0.468174 0.464824 0.000000 0.000000 0.298084 0.616359 0.000000 0.011149 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.173736 0.562283 0.575445 0.000000 0.000000 0.126014 0.643254 0.526658 0.895029 0.318056 0.070667 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.473397 0.135828 0.768521 0.872798 0.000000 0.074876 0.249347 0.417878 0.000000 0.870939 0.114667 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.170376 0.638166 0.028746 0.513977 0.000000 0.146759 0.723282 0.558529 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.556350 0.005827 0.774729 0.643549 0.778168 0.000000 0.343434 0.891059 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.783930 0.033693 0.728858 0.981964 0.151267 0.032469 0.383281 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.324631 0.450871 0.864948 0.665650 0.388695 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.619233 0.739336 0.639360 0.000000 0.935870 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.268867 0.591554 0.269874 0.000000 0.236817 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.109407 0.474237 0.832247 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.889904 0.011304 0.712879 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.320070 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.356896]; Dimension: 20 x 20 Off-diagonal entries: 148 (max 380) Diagonal entries: 0.772466 0.462381 0.734043 0.545106 0.670369 0.133305 0.014399 0.735432 0.173736 0.473397 0.170376 0.556350 0.783930 0.324631 0.619233 0.268867 0.109407 0.889904 0.320070 0.356896 Row indices: 0 16 30 45 60 72 83 92 100 108 116 122 128 134 138 141 144 146 148 148 148 Column indices: 1 2 3 4 5 6 7 10 11 12 14 15 16 17 18 19 2 4 5 6 10 11 12 13 14 15 16 17 18 19 3 4 5 6 8 9 10 12 13 14 15 16 17 18 19 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 5 7 9 10 11 12 13 14 15 16 18 19 6 8 10 11 12 14 15 16 17 18 19 7 8 11 13 15 16 17 18 19 8 10 11 12 13 16 17 19 9 10 13 14 15 16 17 18 10 11 12 14 15 16 18 19 11 12 13 15 16 17 12 13 14 15 17 18 13 14 15 16 17 18 14 15 16 17 15 16 18 16 17 19 17 18 18 19 Off-diagonal values: 0.475293 0.680084 0.718043 0.683329 0.726463 0.927564 0.201178 0.401381 0.678282 0.007690 0.247653 0.032421 0.379647 0.775099 0.541882 0.249298 0.301954 0.744536 0.977093 0.054192 0.005500 0.699318 0.200575 0.719039 0.834926 0.338689 0.352186 0.501912 0.422668 0.032610 0.053872 0.539667 0.370359 0.652631 0.397099 0.228522 0.668190 0.526161 0.600316 0.884099 0.815124 0.103567 0.750929 0.572166 0.324107 0.759916 0.430901 0.527126 0.290017 0.458586 0.985567 0.950667 0.502610 0.863247 0.552897 0.828163 0.284355 0.022283 0.969327 0.377131 0.839403 0.778312 0.921945 0.577193 0.267441 0.667079 0.449188 0.079620 0.355246 0.835643 0.096816 0.135242 0.695999 0.354251 0.509037 0.841957 0.390380 0.272381 0.471967 0.745684 0.410283 0.560620 0.595513 0.309790 0.200253 0.075665 0.512977 0.319755 0.701217 0.253430 0.585261 0.726138 0.268533 0.869820 0.768840 0.468174 0.464824 0.298084 0.616359 0.011149 0.562283 0.575445 0.126014 0.643254 0.526658 0.895029 0.318056 0.070667 0.135828 0.768521 0.872798 0.074876 0.249347 0.417878 0.870939 0.114667 0.638166 0.028746 0.513977 0.146759 0.723282 0.558529 0.005827 0.774729 0.643549 0.778168 0.343434 0.891059 0.033693 0.728858 0.981964 0.151267 0.032469 0.383281 0.450871 0.864948 0.665650 0.388695 0.739336 0.639360 0.935870 0.591554 0.269874 0.236817 0.474237 0.832247 0.011304 0.712879 x x x x x x x x - - x x x - x x x x x x | x x - x x x - - - x x x x x x x x x x | | x x x x x - x x x - x x x x x x x x | | | x x x x x x x x x x x x x - x x x | | | | x x - x - x x x x x x x x - x x | | | | | x x - x - x x x - x x x x x x | | | | | | x x x - - x - x - x x x x x | | | | | | | x x - x x x x - - x x - x | | | | | | | | x x x - - x x x x x x - | | | | | | | | | x x x x - x x x - x x | | | | | | | | | | x x x x - x x x - - | | | | | | | | | | | x x x x x - x x - | | | | | | | | | | | | x x x x x x x - | | | | | | | | | | | | | x x x x x - - | | | | | | | | | | | | | | x x x - x - | | | | | | | | | | | | | | | x x x - x | | | | | | | | | | | | | | | | x x x - | | | | | | | | | | | | | | | | | x x x | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | x The error in solving: 2.118352e-16 The error in solving: 2.221530e-16 The error in solving: 4.611103e-16 The error in solving: 4.200754e-16 The error in solving: 3.421937e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.982996 0.000000 0.641837 0.428548 0.000000 0.000000 0.000000 0.961909 0.000000 0.000000 0.000000 0.000000 0.000000 0.760819 0.000000 0.146957 0.000000 0.000000 0.000000 0.000000 0.000000 0.065624 0.000000 0.000000 0.000000 0.509676 0.000000 0.657051 0.000000 0.000000 0.000000 0.172416 0.000000 0.618632 0.791275 0.000000 0.000000 0.000000 0.000000 0.000000 0.600172 0.000000 0.565340 0.389699 0.982585 0.000000 0.000000 0.000000 0.019523 0.885758 0.000000 0.000000 0.000000 0.295126 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.749404 0.000000 0.000000 0.000000 0.044096 0.000000 0.000000 0.000000 0.000000 0.000000 0.699541 0.170111 0.000000 0.441144 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.901130 0.000000 0.230308 0.955080 0.000000 0.000000 0.000000 0.000000 0.954415 0.000000 0.000000 0.117489 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.609388 0.000000 0.000000 0.455642 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.688347 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.126011 0.000000 0.484623 0.000000 0.197533 0.331031 0.000000 0.000000 0.000000 0.981608 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.022211 0.417498 0.000000 0.000000 0.000000 0.976449 0.871994 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.098095 0.438655 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.412448 0.000000 0.000000 0.000000 0.000000 0.246885 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.711437 0.311991 0.269022 0.000000 0.000000 0.058256 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.894673 0.773560 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.566596 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.181589 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 53 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 6 12 19 24 29 31 32 37 41 43 45 45 49 49 51 52 52 53 53 53 Column indices: 4 6 7 11 17 19 5 9 11 15 17 18 4 6 7 8 12 13 17 4 8 14 15 17 6 8 9 14 17 8 11 9 10 12 14 15 19 12 13 17 18 17 18 14 19 13 14 15 18 15 16 17 19 Off-diagonal values: 0.982996 0.641837 0.428548 0.961909 0.760819 0.146957 0.065624 0.509676 0.657051 0.172416 0.618632 0.791275 0.600172 0.565340 0.389699 0.982585 0.019523 0.885758 0.295126 0.749404 0.044096 0.699541 0.170111 0.441144 0.901130 0.230308 0.955080 0.954415 0.117489 0.609388 0.455642 0.688347 0.126011 0.484623 0.197533 0.331031 0.981608 0.022211 0.417498 0.976449 0.871994 0.098095 0.438655 0.412448 0.246885 0.711437 0.311991 0.269022 0.058256 0.894673 0.773560 0.566596 0.181589 . - - - x - x x - - - x - - - - - x - x | . - - - x - - - x - x - - - x - x x - | | . - x - x x x - - - x x - - - x - - | | | . x - - - x - - - - - x x - x - - | | | | . - x - x x - - - - x - - x - - | | | | | . - - x - - x - - - - - - - - | | | | | | . - - x - - - - - - - - - - | | | | | | | . - - x - x - x x - - - x | | | | | | | | . - - - x x - - - x x - | | | | | | | | | . - - - - - - - x x - | | | | | | | | | | . - - - x - - - - x | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . x x x - - x - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . x x - - - | | | | | | | | | | | | | | | . - x - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - x | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 3.845925e-16 The error in solving: 1.366804e-16 The error in solving: 2.258341e-16 The error in solving: 3.983675e-16 The error in solving: 3.929063e-17 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.808747 0.155864 0.000000 0.256228 0.739838 0.000000 0.000000 0.080082 0.252255 0.126994 0.000000 0.884843 0.000000 0.000000 0.647977 0.000000 0.000454 0.588047 0.000000 0.000000 0.000000 0.000000 0.000000 0.198538 0.471491 0.573825 0.442008 0.000000 0.000000 0.000000 0.663377 0.000000 0.000000 0.663960 0.000000 0.000000 0.000000 0.247878 0.000000 0.000000 0.000000 0.000000 0.996512 0.000000 0.000000 0.092597 0.000000 0.115969 0.674129 0.000000 0.000000 0.000000 0.304716 0.000000 0.219141 0.266591 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.675493 0.502777 0.076088 0.493539 0.000000 0.001086 0.000000 0.190742 0.779145 0.000000 0.000000 0.664944 0.696249 0.578830 0.000000 0.954044 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.251290 0.423471 0.103766 0.000000 0.000000 0.000000 0.692524 0.000000 0.674307 0.000000 0.534950 0.921707 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.703958 0.000000 0.234269 0.000000 0.151904 0.098329 0.000000 0.645913 0.502438 0.000000 0.418424 0.476711 0.311177 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.274422 0.216610 0.000000 0.698449 0.000000 0.000000 0.000000 0.000000 0.000000 0.398854 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.556015 0.000000 0.912929 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.483731 0.000000 0.457400 0.075213 0.378193 0.640958 0.000000 0.897204 0.000000 0.000000 0.708490 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.439087 0.345650 0.000000 0.553928 0.000000 0.000000 0.000000 0.109895 0.000000 0.376660 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.676015 0.000000 0.630206 0.000000 0.000000 0.000000 0.000000 0.101765 0.595019 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.031083 0.729903 0.772344 0.811669 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.708885 0.000000 0.752485 0.000000 0.222728 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.213758 0.000000 0.000000 0.799333 0.530757 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.565446 0.000000 0.783838 0.982743 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.260965 0.000000 0.363058 0.203890 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.685413 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 91 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 11 18 25 36 43 52 56 58 65 70 74 78 81 84 87 90 91 91 91 91 Column indices: 2 3 5 6 9 10 11 13 16 18 19 5 6 7 8 12 15 19 4 7 9 10 14 16 17 4 5 6 7 9 11 12 15 16 17 19 8 9 10 14 16 18 19 7 9 11 12 14 15 17 18 19 7 8 10 16 16 18 9 11 12 13 14 16 19 10 11 13 17 19 11 13 18 19 16 17 18 19 14 16 18 15 18 19 15 17 18 16 18 19 17 Off-diagonal values: 0.808747 0.155864 0.256228 0.739838 0.080082 0.252255 0.126994 0.884843 0.647977 0.000454 0.588047 0.198538 0.471491 0.573825 0.442008 0.663377 0.663960 0.247878 0.996512 0.092597 0.115969 0.674129 0.304716 0.219141 0.266591 0.675493 0.502777 0.076088 0.493539 0.001086 0.190742 0.779145 0.664944 0.696249 0.578830 0.954044 0.251290 0.423471 0.103766 0.692524 0.674307 0.534950 0.921707 0.703958 0.234269 0.151904 0.098329 0.645913 0.502438 0.418424 0.476711 0.311177 0.274422 0.216610 0.698449 0.398854 0.556015 0.912929 0.483731 0.457400 0.075213 0.378193 0.640958 0.897204 0.708490 0.439087 0.345650 0.553928 0.109895 0.376660 0.676015 0.630206 0.101765 0.595019 0.031083 0.729903 0.772344 0.811669 0.708885 0.752485 0.222728 0.213758 0.799333 0.530757 0.565446 0.783838 0.982743 0.260965 0.363058 0.203890 0.685413 . - x x - x x - - x x x - x - - x - x x | . - - - x x x x - - - x - - x - - - x | | . - x - - x - x x - - - x - x x - - | | | . x x x x - x - x x - - x x x - x | | | | . - - - x x x - - - x - x - x x | | | | | . - x - x - x x - x x - x x x | | | | | | . x x - x - - - - - x - - - | | | | | | | . - - - - - - - - x - x - | | | | | | | | . x - x x x x - x - - x | | | | | | | | | . x x - x - - - x - x | | | | | | | | | | . x - x - - - - x x | | | | | | | | | | | . - - - - x x x x | | | | | | | | | | | | . - x - x - x - | | | | | | | | | | | | | . - x - - x x | | | | | | | | | | | | | | . x - x x - | | | | | | | | | | | | | | | . x - x x | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.570092e-16 The error in solving: 4.163336e-16 The error in solving: 1.777224e-16 The error in solving: 4.966159e-16 The error in solving: 1.271920e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.251714 0.000000 0.286959 0.000000 0.604253 0.789303 0.400069 0.275444 0.288236 0.000000 0.000000 0.202862 0.007712 0.797037 0.908918 0.337846 0.744463 0.000000 0.000000 0.000000 0.000000 0.606795 0.225541 0.172125 0.804449 0.285531 0.186234 0.715261 0.867806 0.000000 0.463887 0.603869 0.000000 0.233329 0.075730 0.286600 0.522743 0.000000 0.168602 0.000000 0.000000 0.000000 0.043280 0.000000 0.000000 0.100145 0.000000 0.864152 0.679542 0.000000 0.174666 0.425822 0.591623 0.000000 0.165265 0.534008 0.000000 0.996395 0.917856 0.000000 0.000000 0.000000 0.000000 0.166075 0.000000 0.243582 0.553313 0.760144 0.965244 0.734523 0.058587 0.323825 0.254403 0.000000 0.156788 0.000000 0.420814 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.815446 0.087428 0.031246 0.149864 0.664249 0.716714 0.143817 0.413080 0.062449 0.549916 0.087265 0.000000 0.000000 0.298983 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.088739 0.000000 0.692551 0.617603 0.357569 0.000000 0.091689 0.000000 0.423989 0.000000 0.000000 0.000000 0.062411 0.815802 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.173230 0.659946 0.429915 0.000000 0.820194 0.327593 0.001801 0.053661 0.554864 0.998742 0.610098 0.597436 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.157783 0.000000 0.052917 0.741482 0.238101 0.000000 0.460858 0.516545 0.576742 0.552411 0.842050 0.083747 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.882110 0.000000 0.524309 0.924214 0.345469 0.000000 0.745138 0.169073 0.000000 0.466307 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.675078 0.837524 0.056059 0.331197 0.171300 0.884571 0.000000 0.277014 0.989126 0.544742 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.135591 0.829702 0.060340 0.000000 0.883219 0.000000 0.000000 0.503761 0.832573 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.955692 0.525771 0.000000 0.017723 0.319151 0.021680 0.174533 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.118303 0.908399 0.344158 0.000000 0.225012 0.922254 0.821166 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.301158 0.000000 0.734968 0.000000 0.364374 0.255597 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.492267 0.433327 0.884031 0.000000 0.548346 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.949461 0.047154 0.532356 0.816816 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.029277 0.796537 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.776321 0.161376 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.926946 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 142 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 13 28 39 50 62 70 81 91 98 107 113 119 125 129 133 137 139 141 142 142 Column indices: 1 3 5 6 7 8 9 12 13 14 15 16 17 2 3 4 5 6 7 8 9 11 12 14 15 16 17 19 3 6 8 9 11 12 13 15 16 18 19 4 6 7 8 9 10 11 12 13 15 17 6 7 8 9 10 11 12 13 14 15 16 19 6 8 9 10 12 14 18 19 8 9 10 12 13 14 15 16 17 18 19 8 10 11 12 14 15 16 17 18 19 9 11 12 13 15 16 18 10 11 12 13 14 15 17 18 19 11 12 13 15 18 19 12 13 15 16 17 18 13 14 15 17 18 19 14 16 18 19 15 16 17 19 16 17 18 19 17 18 18 19 19 Off-diagonal values: 0.251714 0.286959 0.604253 0.789303 0.400069 0.275444 0.288236 0.202862 0.007712 0.797037 0.908918 0.337846 0.744463 0.606795 0.225541 0.172125 0.804449 0.285531 0.186234 0.715261 0.867806 0.463887 0.603869 0.233329 0.075730 0.286600 0.522743 0.168602 0.043280 0.100145 0.864152 0.679542 0.174666 0.425822 0.591623 0.165265 0.534008 0.996395 0.917856 0.166075 0.243582 0.553313 0.760144 0.965244 0.734523 0.058587 0.323825 0.254403 0.156788 0.420814 0.815446 0.087428 0.031246 0.149864 0.664249 0.716714 0.143817 0.413080 0.062449 0.549916 0.087265 0.298983 0.088739 0.692551 0.617603 0.357569 0.091689 0.423989 0.062411 0.815802 0.173230 0.659946 0.429915 0.820194 0.327593 0.001801 0.053661 0.554864 0.998742 0.610098 0.597436 0.157783 0.052917 0.741482 0.238101 0.460858 0.516545 0.576742 0.552411 0.842050 0.083747 0.882110 0.524309 0.924214 0.345469 0.745138 0.169073 0.466307 0.675078 0.837524 0.056059 0.331197 0.171300 0.884571 0.277014 0.989126 0.544742 0.135591 0.829702 0.060340 0.883219 0.503761 0.832573 0.955692 0.525771 0.017723 0.319151 0.021680 0.174533 0.118303 0.908399 0.344158 0.225012 0.922254 0.821166 0.301158 0.734968 0.364374 0.255597 0.492267 0.433327 0.884031 0.548346 0.949461 0.047154 0.532356 0.816816 0.029277 0.796537 0.776321 0.161376 0.926946 . x - x - x x x x x - - x x x x x x - - | . x x x x x x x x - x x - x x x x - x | | . x - - x - x x - x x x - x x - x x | | | . x - x x x x x x x x - x - x - - | | | | . - x x x x x x x x x x x - - x | | | | | . x - x x x - x - x - - - x x | | | | | | . - x x x - x x x x x x x x | | | | | | | . x - x x x - x x x x x x | | | | | | | | . x - x x x - x x - x - | | | | | | | | | . x x x x x x - x x x | | | | | | | | | | . x x x - x - - x x | | | | | | | | | | | . x x - x x x x - | | | | | | | | | | | | . x x x - x x x | | | | | | | | | | | | | . x - x - x x | | | | | | | | | | | | | | . x x x - x | | | | | | | | | | | | | | | . x x x x | | | | | | | | | | | | | | | | . x x - | | | | | | | | | | | | | | | | | . x x | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | | . The error in solving: 2.789401e-16 The error in solving: 3.188873e-16 The error in solving: 2.779025e-16 The error in solving: 2.775558e-16 The error in solving: 2.482534e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.250000 [ -0.302982 0.035130 0.000000 0.000000 0.000000 0.841450 0.000000 0.000000 -0.939709 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.645089 0.248172 0.000000 0.000000 -0.949462 0.000000 0.000000 0.000000 0.000000 0.398588 0.000000 0.000000 0.000000 0.000000 0.502165 -0.367340 0.212318 0.000000 0.728293 0.273981 -0.800428 0.000000 0.930587 0.000000 0.000000 0.218933 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.346390 0.000000 0.000000 0.000000 0.000000 0.915184 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.182377 0.000000 -0.659231 0.000000 0.000000 0.000000 0.000000 0.823063 -0.893155 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.397183 -0.832732 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.299496 0.912613 0.000000 0.000000 0.809725 -0.551165 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.149248 0.000000 0.000000 0.000000 0.000000 -0.951356 0.000000 0.000000 0.000000 0.000000 0.000000 0.806177 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.750892 -0.394433 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.670015 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.429720 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.190258 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.715452 0.000000 -0.119464 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.496754 0.000000 0.000000 0.000000 0.290150 -0.545877 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.128732 0.431494 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.540105 0.629947 -0.238468 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.739527 -0.506442 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.912522 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.060462 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.186895 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 46 (max 380) Diagonal entries: -0.302982 -0.949462 0.218933 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.912522 0.000000 -0.186895 0.000000 Row indices: 0 5 13 15 19 21 25 28 28 31 32 33 35 38 40 43 45 45 46 46 46 Column indices: 1 5 8 17 18 6 11 12 13 15 16 17 19 10 15 11 13 18 19 18 19 11 12 15 16 7 12 18 10 11 18 15 19 12 14 13 17 18 15 16 16 17 18 17 18 18 Off-diagonal values: 0.035130 0.841450 -0.939709 -0.645089 0.248172 0.398588 0.502165 -0.367340 0.212318 0.728293 0.273981 -0.800428 0.930587 0.346390 0.915184 -0.182377 -0.659231 0.823063 -0.893155 -0.397183 -0.832732 -0.299496 0.912613 0.809725 -0.551165 -0.149248 -0.951356 0.806177 -0.750892 -0.394433 -0.670015 -0.429720 0.190258 -0.715452 -0.119464 0.496754 0.290150 -0.545877 0.128732 0.431494 -0.540105 0.629947 -0.238468 -0.739527 -0.506442 -0.060462 o x - - - x - - o - - - - - - - - o x - | o - - - - x - - - - x o x - x x o - x | | x - - - - - - - x - - - - x - - - - | | | . - - - - - - - o - o - - - - x o | | | | . - - - - - - - - - - - - - o o | | | | | . - - - - - o x - - x o - - - | | | | | | . o - - - - o - - - - - x - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - o o - - - - - - o - | | | | | | | | | . - - - - - o - - - - | | | | | | | | | | . - - - - - - - - x | | | | | | | | | | | . o - o - - - - - | | | | | | | | | | | | . x - - - x o - | | | | | | | | | | | | | . - x x - - - | | | | | | | | | | | | | | . - o x o - | | | | | | | | | | | | | | | . - o o - | | | | | | | | | | | | | | | | o - - - | | | | | | | | | | | | | | | | | . o - | | | | | | | | | | | | | | | | | | o - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.237726e-16 The error in solving: 7.850462e-17 The error in solving: 2.482534e-16 The error in solving: 2.498002e-16 The error in solving: 3.336446e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.500000 [ -0.514459 0.532304 0.000000 0.506128 0.000000 0.000000 -0.338813 0.239826 0.000000 0.860537 -0.717809 0.908361 0.591489 0.000000 -0.841999 0.565135 0.000000 0.000000 0.157305 -0.148299 0.000000 0.000000 0.923736 0.000000 0.245038 0.000000 0.000000 0.994486 0.000000 0.000000 0.000000 0.000000 0.000000 -0.030646 0.552943 0.000000 0.000000 0.000000 -0.962603 0.000000 0.000000 0.000000 0.926840 0.000000 0.756434 0.611667 0.000000 0.000000 0.000000 -0.065112 -0.846881 0.806293 0.000000 0.000000 -0.115596 0.000000 0.366218 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.138286 0.000000 -0.187891 0.000000 0.000000 -0.121326 0.000000 0.000000 0.274023 0.000000 0.000000 0.000000 0.000000 0.255073 -0.824956 -0.404318 0.000000 0.000000 0.000000 0.000000 -0.191723 0.000000 0.000000 0.000000 -0.493641 0.000000 -0.794092 -0.536704 0.470374 0.000000 -0.376992 -0.291794 0.000000 0.000000 0.851125 0.372777 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.411569 0.000000 0.000000 -0.973612 -0.196170 0.000000 -0.080354 -0.298244 -0.769316 0.000000 -0.594942 -0.047588 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.892292 0.000000 -0.484770 0.545570 0.419368 0.000000 -0.579570 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.515987 0.722747 -0.610313 0.000000 0.000000 0.686584 0.000000 0.000000 0.000000 0.975983 0.000000 0.767469 0.003951 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.855800 0.331615 0.790519 0.000000 0.405460 -0.181106 0.000000 0.341803 0.408510 -0.363990 0.000000 -0.825000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.626365 0.573086 0.000000 0.000000 -0.005352 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.153722 0.042628 0.447406 0.000000 0.000000 0.000000 0.000000 -0.702473 -0.296742 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.292418 0.467268 0.000000 -0.729335 0.000000 -0.736317 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.559724 0.000000 0.000000 0.139756 0.000000 -0.973316 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.167927 0.000000 -0.874778 0.000000 0.000000 0.152263 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.347811 -0.248010 0.419194 0.448028 0.934486 -0.272017 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.430868 0.928354 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.584866 0.454190 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.596163 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.920908]; Dimension: 20 x 20 Off-diagonal entries: 93 (max 380) Diagonal entries: -0.514459 0.000000 0.926840 0.000000 -0.191723 0.000000 0.000000 -0.515987 0.855800 0.000000 0.000000 0.000000 0.559724 0.000000 0.347811 0.000000 0.000000 0.000000 0.596163 -0.920908 Row indices: 0 12 18 25 32 40 48 53 59 67 70 75 79 81 84 89 91 93 93 93 93 Column indices: 1 3 6 7 9 10 11 12 14 15 18 19 2 4 7 13 14 18 4 5 9 10 11 14 16 4 6 9 12 17 18 19 8 10 11 12 14 15 18 19 8 11 12 14 15 16 18 19 13 15 16 17 19 8 9 12 16 18 19 9 10 12 13 15 16 17 19 13 14 17 11 12 13 18 19 14 15 17 19 15 17 14 16 19 15 16 17 18 19 18 19 18 19 Off-diagonal values: 0.532304 0.506128 -0.338813 0.239826 0.860537 -0.717809 0.908361 0.591489 -0.841999 0.565135 0.157305 -0.148299 0.923736 0.245038 0.994486 -0.030646 0.552943 -0.962603 0.756434 0.611667 -0.065112 -0.846881 0.806293 -0.115596 0.366218 0.138286 -0.187891 -0.121326 0.274023 0.255073 -0.824956 -0.404318 -0.493641 -0.794092 -0.536704 0.470374 -0.376992 -0.291794 0.851125 0.372777 0.411569 -0.973612 -0.196170 -0.080354 -0.298244 -0.769316 -0.594942 -0.047588 0.892292 -0.484770 0.545570 0.419368 -0.579570 0.722747 -0.610313 0.686584 0.975983 0.767469 0.003951 0.331615 0.790519 0.405460 -0.181106 0.341803 0.408510 -0.363990 -0.825000 0.626365 0.573086 -0.005352 0.153722 0.042628 0.447406 -0.702473 -0.296742 0.292418 0.467268 -0.729335 -0.736317 0.139756 -0.973316 0.167927 -0.874778 0.152263 -0.248010 0.419194 0.448028 0.934486 -0.272017 -0.430868 0.928354 0.584866 0.454190 o x - x - - o x - x o x x - o x - - x o | . x - x - - x - - - - - o x - - - o - | | x - x x - - - o o x - - o - x - - - | | | . x - o - - o - - x - - - - x o o | | | | o - - - o - o o x - o o - - x x | | | | | . - - x - - o o - o o o - o o | | | | | | . - - - - - - x - o x x - o | | | | | | | o x o - - x - - - x - x x | | | | | | | | x x x - x o - x x o - o | | | | | | | | | . - - - x x - - o - - | | | | | | | | | | . x x x - - - - o o | | | | | | | | | | | . - - x x - o - o | | | | | | | | | | | | x - - x - o - - | | | | | | | | | | | | | . x - o - - x | | | | | | | | | | | | | | x o x x x o | | | | | | | | | | | | | | | . - - o x | | | | | | | | | | | | | | | | . - x x | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | o The error in solving: 2.498243e-16 The error in solving: 1.001343e-16 The error in solving: 1.665335e-16 The error in solving: 1.570092e-16 The error in solving: 1.947840e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.750000 [ 0.560799 0.000000 -0.693022 0.347493 -0.790387 0.041268 -0.712923 0.000000 0.005740 0.826715 0.940754 -0.198098 0.360654 0.000000 0.340186 -0.387668 0.169613 -0.557899 -0.482529 -0.996862 0.000000 0.378700 -0.258317 -0.345266 0.000000 -0.602810 0.000000 0.370150 0.000000 0.000000 0.617777 0.000000 0.990103 0.132205 -0.186032 0.876377 0.542895 0.000000 0.970627 0.826984 0.000000 0.000000 0.014844 -0.247903 0.000000 -0.940464 0.571114 0.765103 0.023078 0.000000 0.000000 0.414579 0.330653 0.468562 -0.335954 -0.974142 -0.106432 -0.942095 0.000000 -0.819578 0.000000 0.000000 0.000000 0.000000 0.000000 -0.395041 -0.789025 0.000000 -0.976960 -0.641468 0.578822 -0.073404 0.000000 -0.513128 -0.705703 0.620450 0.000000 0.000000 -0.814953 0.805457 0.000000 0.000000 0.000000 0.000000 0.985121 -0.365056 0.000000 -0.803069 0.118220 0.278276 -0.286832 0.297042 0.000000 -0.597666 0.082831 0.138056 -0.947196 0.000000 -0.706353 0.236846 0.000000 0.000000 0.000000 0.000000 0.000000 0.300112 -0.960168 -0.075343 0.992433 0.786374 0.000000 -0.559135 0.617193 -0.869340 -0.205081 0.000000 -0.865364 -0.913630 0.136274 -0.234555 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.602463 0.000000 0.000000 0.000000 -0.695151 0.000000 -0.808376 -0.400248 -0.043497 0.000000 -0.759871 -0.044312 -0.517406 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.909821 -0.397690 -0.895628 0.000000 -0.548753 -0.757001 0.000000 -0.252324 -0.233986 -0.628727 0.473152 0.000000 -0.807008 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.307108 0.000000 -0.570438 0.940047 -0.664175 0.749203 -0.043245 -0.864285 -0.501283 0.803394 0.602650 -0.321384 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.934662 0.043832 0.199218 0.656082 0.911804 -0.774466 -0.972957 0.578335 0.000000 -0.494250 -0.100580 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.967118 -0.404901 0.051058 -0.339606 -0.406630 0.256647 0.601886 -0.061619 0.000000 -0.013887 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.680612 -0.370243 0.000000 -0.940365 0.549247 0.000000 0.000000 -0.362146 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.346387 -0.701319 0.054312 -0.100407 -0.983919 0.161934 -0.540591 0.456700 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.218405 0.000000 0.233753 0.261276 0.478148 0.920538 0.120970 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.669994 -0.238262 0.000000 0.851048 0.460549 -0.261181 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.158811 0.688823 -0.629089 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.961848 -0.764795 0.287776 0.411817 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.952740 0.911503 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.678955 0.806143 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.452025]; Dimension: 20 x 20 Off-diagonal entries: 148 (max 380) Diagonal entries: 0.560799 0.378700 0.014844 0.000000 0.985121 0.300112 0.000000 -0.909821 0.307108 -0.934662 -0.967118 0.000000 0.346387 0.218405 0.669994 0.158811 -0.961848 0.952740 -0.678955 -0.452025 Row indices: 0 16 28 41 52 64 76 84 93 103 112 120 125 132 137 141 143 146 147 148 148 Column indices: 2 3 4 5 6 8 9 10 11 12 14 15 16 17 18 19 2 3 5 7 10 12 13 14 15 16 18 19 3 5 6 7 8 11 12 13 14 15 16 17 19 5 6 8 9 10 11 13 14 15 18 19 5 7 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0.136274 -0.234555 -0.602463 -0.695151 -0.808376 -0.400248 -0.043497 -0.759871 -0.044312 -0.517406 -0.397690 -0.895628 -0.548753 -0.757001 -0.252324 -0.233986 -0.628727 0.473152 -0.807008 -0.570438 0.940047 -0.664175 0.749203 -0.043245 -0.864285 -0.501283 0.803394 0.602650 -0.321384 0.043832 0.199218 0.656082 0.911804 -0.774466 -0.972957 0.578335 -0.494250 -0.100580 -0.404901 0.051058 -0.339606 -0.406630 0.256647 0.601886 -0.061619 -0.013887 -0.680612 -0.370243 -0.940365 0.549247 -0.362146 -0.701319 0.054312 -0.100407 -0.983919 0.161934 -0.540591 0.456700 0.233753 0.261276 0.478148 0.920538 0.120970 -0.238262 0.851048 0.460549 -0.261181 0.688823 -0.629089 -0.764795 0.287776 0.411817 0.911503 0.806143 x - o x o x o - x x x o x - x o x o o o | x o o - o - x - - x - x x o x x - x x | | x o - o x x x - - x x x o o o o - o | | | . - o o - o o x o - o o x - - o x | | | | x o - o x x o x - o x x o - o x | | | | | x o o x x - o x o o - o o x o | | | | | | . o - - - o - o o o - o o o | | | | | | | o o o - o o - o o o x - o | | | | | | | | x - o x o x o o o x x o | | | | | | | | | o x x x x o o x - o o | | | | | | | | | | o o x o o x x o - o | | | | | | | | | | | . o o - o x - - o | | | | | | | | | | | | x o x o o x o x | | | | | | | | | | | | | x - x x x x x | | | | | | | | | | | | | | x o - x x o | | | | | | | | | | | | | | | x x o - - | | | | | | | | | | | | | | | | o o x x | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | o x | | | | | | | | | | | | | | | | | | | o The error in solving: 1.118997e-16 The error in solving: 1.712375e-16 The error in solving: 1.756788e-16 The error in solving: 2.077037e-16 The error in solving: 2.789401e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.250000 [ -0.166593 -0.705501 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.810981 0.000000 -0.116795 0.000000 0.000000 0.000000 -0.529798 0.000000 0.000000 -0.054545 -0.933917 0.000000 -0.919242 0.000000 0.723244 -0.843932 0.000000 0.000000 0.000000 0.978295 0.000000 0.000000 0.806199 0.000000 0.595023 0.892184 -0.144034 0.000000 0.000000 0.000000 0.032828 0.000000 0.006321 0.000000 0.000000 0.000000 0.536510 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.116968 0.000000 0.000000 0.000000 0.000000 0.063348 0.446864 0.000000 0.000000 0.000000 0.585556 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.662872 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.653076 0.000000 -0.719261 0.000000 0.216250 0.754073 0.000000 0.000000 0.000000 0.000000 0.000000 -0.748690 0.000000 0.007203 0.000000 -0.282501 0.000000 0.000000 0.000000 0.000000 0.000000 -0.445205 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.677597 -0.839266 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.508499 0.000000 -0.579132 0.000000 -0.403491 0.230729 -0.339502 0.996774 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.776135 0.000000 0.000000 0.698113 0.331002 -0.958084 0.000000 0.472971 0.874243 0.000000 0.713666 0.572516 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.593795 0.000000 0.000000 0.000000 0.000000 -0.849908 0.000000 0.000000 -0.530277 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.876554 0.000000 -0.999590 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.095492 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.091277 0.641955 -0.791169 -0.775823 0.263394 0.000000 0.000000 0.000000 0.178455 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.298450 0.000000 0.000000 -0.078373 0.000000 0.846589 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.674579 0.000000 0.000000 0.000000 0.610963 0.000000 0.436193 0.162251 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.543658 0.000000 0.000000 0.000000 0.000000 -0.061347 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.422794 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.061903 0.000000 0.006189 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.005575 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.891079 0.000000 0.826503 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.586808 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.543538]; Dimension: 20 x 20 Off-diagonal entries: 56 (max 380) Diagonal entries: -0.166593 -0.054545 0.032828 0.063348 0.653076 -0.445205 -0.508499 0.776135 0.593795 0.876554 -0.091277 0.298450 -0.674579 -0.543658 0.422794 -0.061903 -0.005575 0.891079 -0.586808 -0.543538 Row indices: 0 4 13 16 19 25 27 32 39 41 43 48 50 53 54 54 55 55 56 56 56 Column indices: 1 12 14 18 2 4 6 7 11 14 16 17 18 4 8 18 4 8 16 6 8 9 15 17 19 14 15 8 10 11 12 13 10 11 12 14 15 17 18 13 16 11 18 11 12 13 14 18 14 16 16 18 19 18 17 19 Off-diagonal values: -0.705501 0.810981 -0.116795 -0.529798 -0.933917 -0.919242 0.723244 -0.843932 0.978295 0.806199 0.595023 0.892184 -0.144034 0.006321 0.536510 -0.116968 0.446864 0.585556 0.662872 -0.719261 0.216250 0.754073 -0.748690 0.007203 -0.282501 -0.677597 -0.839266 -0.579132 -0.403491 0.230729 -0.339502 0.996774 0.698113 0.331002 -0.958084 0.472971 0.874243 0.713666 0.572516 -0.849908 -0.530277 -0.999590 -0.095492 0.641955 -0.791169 -0.775823 0.263394 0.178455 -0.078373 0.846589 0.610963 0.436193 0.162251 -0.061347 0.006189 0.826503 o o - - - - - - - - - - x - o - - - o - | o o - o - x o - - - x - - x - x x o - | | x - x - - - x - - - - - - - - - o - | | | x x - - - x - - - - - - - x - - - | | | | x - o - x x - - - - - o - x - o | | | | | o - - - - - - - - o o - - - - | | | | | | o - o - o x o x - - - - - - | | | | | | | x - - x x o - x x - x x - | | | | | | | | x - - - - o - - o - - - | | | | | | | | | x - o - - - - - - o - | | | | | | | | | | o x o o x - - - x - | | | | | | | | | | | x - - o - x - - - | | | | | | | | | | | | o - - - x - x x | | | | | | | | | | | | | o - - - - o - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | o - x - - | | | | | | | | | | | | | | | | o - - - | | | | | | | | | | | | | | | | | x - x | | | | | | | | | | | | | | | | | | o - | | | | | | | | | | | | | | | | | | | o The error in solving: 1.000742e-16 The error in solving: 2.719480e-16 The error in solving: 3.200929e-16 The error in solving: 2.937374e-16 The error in solving: 2.779025e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.089917 0.889202 -0.721483 0.813297 -0.764410 -0.644631 -0.219220 0.000000 0.000000 0.103790 -0.667726 0.000000 0.000000 -0.853213 0.228177 -0.216288 0.000000 0.964513 -0.527008 0.000000 0.000000 0.263915 -0.706413 0.965219 0.882795 0.760592 0.196101 0.000000 0.000000 0.000000 0.885921 0.082613 0.327308 0.857770 0.521503 0.192255 0.000000 0.000000 0.263009 0.000000 0.000000 0.000000 0.350464 -0.146056 0.000000 0.000000 0.000000 0.000000 -0.406976 -0.661971 0.000000 0.000000 0.000000 -0.493945 -0.114337 0.000000 0.000000 0.000000 0.000000 0.982922 0.000000 0.000000 0.000000 0.719806 0.000000 -0.409056 0.000000 0.338639 0.000000 0.000000 0.000000 0.221911 0.000000 -0.421737 0.000000 0.974479 -0.985850 -0.201750 -0.781246 0.000000 0.000000 0.000000 0.000000 0.000000 0.472432 0.000000 0.000000 0.786533 -0.789822 -0.818923 0.767556 -0.932858 0.419181 0.990623 -0.434823 0.000000 0.000000 -0.646016 0.000000 -0.909279 0.000000 0.000000 0.000000 0.000000 0.000000 0.533019 0.000000 0.000000 0.000000 -0.091888 0.000000 -0.645260 0.081717 0.677247 0.000000 0.000000 0.374628 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.241890 0.000000 0.915656 0.000000 -0.097447 0.000000 -0.163869 -0.232034 0.642467 -0.986539 -0.488175 -0.653003 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.104859 0.000000 -0.791862 0.000000 0.000000 0.000000 0.916168 0.000000 -0.562045 0.742977 0.000000 -0.718402 -0.238858 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.853227 -0.083192 0.740775 0.000000 -0.409351 0.647584 0.114656 0.000000 0.420339 0.000000 -0.235704 0.056205 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.125725 0.000000 0.052049 0.299900 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.740813 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.465250 -0.863767 0.891546 0.472785 0.201565 0.000000 0.000000 0.000000 0.907405 0.529646 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.458695 0.000000 -0.762635 0.453473 -0.930176 0.000000 0.860638 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.390324 0.090818 0.000000 0.000000 -0.792488 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.688507 0.494608 0.629085 0.023610 0.000000 0.610622 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.307131 0.245507 0.935513 0.952966 -0.902182 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.074132 0.000000 0.620655 0.000000 -0.837641 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.197192 0.134063 0.000000 -0.657415 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.274038 0.279518 -0.721632 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.629823 -0.024672 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.886699]; Dimension: 20 x 20 Off-diagonal entries: 106 (max 380) Diagonal entries: 0.089917 0.263915 0.350464 0.719806 0.472432 0.533019 0.241890 -0.104859 -0.853227 0.125725 -0.465250 -0.458695 0.390324 -0.688507 0.307131 0.074132 0.197192 0.274038 0.629823 -0.886699 Row indices: 0 13 25 31 39 49 54 62 68 76 79 85 89 91 95 99 101 103 105 106 106 Column indices: 1 2 3 4 5 6 9 10 13 14 15 17 18 2 3 4 5 6 10 11 12 13 14 15 18 3 8 9 13 14 19 5 7 11 13 15 16 17 18 7 8 9 10 11 12 13 14 17 19 9 11 12 13 16 8 10 12 13 14 15 16 17 9 13 15 16 18 19 9 10 12 13 14 16 18 19 11 12 19 11 12 13 14 18 19 13 14 15 17 13 16 14 15 16 18 15 16 17 18 17 19 17 19 18 19 19 Off-diagonal values: 0.889202 -0.721483 0.813297 -0.764410 -0.644631 -0.219220 0.103790 -0.667726 -0.853213 0.228177 -0.216288 0.964513 -0.527008 -0.706413 0.965219 0.882795 0.760592 0.196101 0.885921 0.082613 0.327308 0.857770 0.521503 0.192255 0.263009 -0.146056 -0.406976 -0.661971 -0.493945 -0.114337 0.982922 -0.409056 0.338639 0.221911 -0.421737 0.974479 -0.985850 -0.201750 -0.781246 0.786533 -0.789822 -0.818923 0.767556 -0.932858 0.419181 0.990623 -0.434823 -0.646016 -0.909279 -0.091888 -0.645260 0.081717 0.677247 0.374628 0.915656 -0.097447 -0.163869 -0.232034 0.642467 -0.986539 -0.488175 -0.653003 -0.791862 0.916168 -0.562045 0.742977 -0.718402 -0.238858 -0.083192 0.740775 -0.409351 0.647584 0.114656 0.420339 -0.235704 0.056205 0.052049 0.299900 0.740813 -0.863767 0.891546 0.472785 0.201565 0.907405 0.529646 -0.762635 0.453473 -0.930176 0.860638 0.090818 -0.792488 0.494608 0.629085 0.023610 0.610622 0.245507 0.935513 0.952966 -0.902182 0.620655 -0.837641 0.134063 -0.657415 0.279518 -0.721632 -0.024672 x x o x o o o - - x o - - o x o - x o - | x o x x x x - - - x x x x x x - - x - | | x o - - - - o o - - - o o - - - - x | | | x - o - x - - - x - o - x o o o - | | | | x - - x o o x o x x o - - o - o | | | | | x - - - o - o x x - - x - - - | | | | | | x - x - o - o o x o o o - - | | | | | | | o - o - - - x - o x - o o | | | | | | | | o o x - o x x - x - o x | | | | | | | | | x - x x - - - - - - x | | | | | | | | | | o o x x x - - - x x | | | | | | | | | | | o - o x o - x - - | | | | | | | | | | | | x x - - o - - - | | | | | | | | | | | | | o x x x - x - | | | | | | | | | | | | | | x x x x o - | | | | | | | | | | | | | | | x - x - o | | | | | | | | | | | | | | | | x x - o | | | | | | | | | | | | | | | | | x x o | | | | | | | | | | | | | | | | | | x o | | | | | | | | | | | | | | | | | | | o The error in solving: 2.289835e-16 The error in solving: 1.189772e-16 The error in solving: 2.110382e-17 The error in solving: 1.570188e-16 The error in solving: 2.312068e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.249682 0.578271 0.019181 0.253390 0.000000 -0.335177 -0.070372 0.332389 -0.490351 0.221855 0.667668 0.000000 -0.282536 0.000000 0.999989 -0.921964 0.042230 0.901747 0.000000 0.189520 0.000000 0.277940 0.059753 -0.166254 0.000000 0.000000 0.000000 0.000000 -0.516478 -0.984696 -0.500055 0.398418 0.512100 0.276362 0.113291 0.954792 0.707088 0.086308 0.101608 -0.290221 0.000000 0.000000 0.987413 -0.511328 0.215620 0.340644 0.000000 0.097592 -0.904428 0.365841 -0.642188 0.193206 -0.299223 -0.166437 0.747530 0.000000 0.000000 -0.802474 0.911141 -0.659112 0.000000 0.000000 0.000000 0.310493 0.000000 0.436379 -0.022259 -0.964457 -0.475835 -0.610343 -0.905481 -0.080799 0.000000 0.492374 -0.953412 -0.049586 0.000000 0.973115 0.858102 0.000000 0.000000 0.000000 0.000000 0.000000 0.955574 0.000000 0.324411 -0.641520 0.105345 0.000000 0.000000 -0.135759 -0.446940 0.757921 0.000000 0.532620 -0.790576 -0.698531 -0.556772 0.396271 0.000000 0.000000 0.000000 0.000000 0.000000 -0.491248 -0.798334 0.000000 -0.974158 -0.414603 0.368422 0.248516 0.170928 -0.516324 -0.133941 -0.829325 0.956640 0.859159 -0.843981 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.419400 -0.920243 0.000000 0.000000 -0.344193 0.000000 0.267679 -0.917980 0.480546 -0.723163 -0.494664 0.049486 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.146023 -0.487934 0.596033 -0.122571 0.000000 -0.933896 0.517436 0.000000 -0.886009 0.035431 0.290257 0.107729 0.590639 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.709131 0.000000 0.994689 0.567137 0.598589 0.000000 0.476607 0.578805 -0.084575 -0.818733 -0.122720 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.667222 0.554125 -0.831507 -0.873896 0.000000 0.008995 -0.117530 -0.461891 -0.272658 0.000000 -0.553583 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.430528 0.761156 -0.818023 0.000000 -0.701037 0.000000 -0.896613 0.000000 0.000000 -0.169063 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.156935 -0.433848 0.000000 0.000000 0.513555 -0.795739 0.000000 0.000000 -0.943449 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.023543 -0.184753 0.121709 0.000000 -0.966247 -0.258975 0.823902 0.968689 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.296802 0.634442 0.321447 0.734819 -0.028299 0.905332 -0.109095 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.180232 0.505279 0.966022 0.000000 -0.857847 -0.652134 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.249040 0.131238 0.000000 0.126467 0.164283 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.999455 0.317754 0.871740 -0.863709 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.827995 0.379648 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.835260 -0.709158 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.818041]; Dimension: 20 x 20 Off-diagonal entries: 145 (max 380) Diagonal entries: 0.249682 0.277940 0.987413 0.310493 0.955574 -0.491248 -0.419400 0.146023 -0.709131 0.667222 -0.430528 0.156935 -0.023543 0.296802 -0.180232 -0.249040 0.999455 -0.827995 0.835260 0.818041 Row indices: 0 15 29 43 55 66 78 86 96 104 112 117 121 127 133 137 140 143 144 145 145 Column indices: 1 2 3 5 6 7 8 9 10 12 14 15 16 17 19 2 3 8 9 10 11 12 13 14 15 16 17 18 19 3 4 5 7 8 9 10 11 12 13 14 17 18 19 5 6 7 8 9 10 11 13 14 15 17 18 6 7 8 11 12 13 15 16 17 18 19 6 8 9 10 11 12 13 14 15 16 17 18 7 10 12 13 14 15 16 17 8 9 10 12 13 15 16 17 18 19 10 11 12 14 15 16 17 18 10 11 12 14 15 16 17 19 11 12 14 16 19 12 15 16 19 13 14 16 17 18 19 14 15 16 17 18 19 15 16 18 19 16 18 19 17 18 19 18 19 Off-diagonal values: 0.578271 0.019181 0.253390 -0.335177 -0.070372 0.332389 -0.490351 0.221855 0.667668 -0.282536 0.999989 -0.921964 0.042230 0.901747 0.189520 0.059753 -0.166254 -0.516478 -0.984696 -0.500055 0.398418 0.512100 0.276362 0.113291 0.954792 0.707088 0.086308 0.101608 -0.290221 -0.511328 0.215620 0.340644 0.097592 -0.904428 0.365841 -0.642188 0.193206 -0.299223 -0.166437 0.747530 -0.802474 0.911141 -0.659112 0.436379 -0.022259 -0.964457 -0.475835 -0.610343 -0.905481 -0.080799 0.492374 -0.953412 -0.049586 0.973115 0.858102 0.324411 -0.641520 0.105345 -0.135759 -0.446940 0.757921 0.532620 -0.790576 -0.698531 -0.556772 0.396271 -0.798334 -0.974158 -0.414603 0.368422 0.248516 0.170928 -0.516324 -0.133941 -0.829325 0.956640 0.859159 -0.843981 -0.920243 -0.344193 0.267679 -0.917980 0.480546 -0.723163 -0.494664 0.049486 -0.487934 0.596033 -0.122571 -0.933896 0.517436 -0.886009 0.035431 0.290257 0.107729 0.590639 0.994689 0.567137 0.598589 0.476607 0.578805 -0.084575 -0.818733 -0.122720 0.554125 -0.831507 -0.873896 0.008995 -0.117530 -0.461891 -0.272658 -0.553583 0.761156 -0.818023 -0.701037 -0.896613 -0.169063 -0.433848 0.513555 -0.795739 -0.943449 -0.184753 0.121709 -0.966247 -0.258975 0.823902 0.968689 0.634442 0.321447 0.734819 -0.028299 0.905332 -0.109095 0.505279 0.966022 -0.857847 -0.652134 0.131238 0.126467 0.164283 0.317754 0.871740 -0.863709 0.379648 -0.709158 x x x x - o o x o x x - o - x o x x - x | x x o - - - - o o o x x x x x x x x o | | x o x x - x o x o x o o x - - o x o | | | x - x o o o o o o - x o o - x x - | | | | x - x o x - - o o x - x o o o x | | | | | o o - o o x x x o o o x x o - | | | | | | o o - - o - x o x o o x - - | | | | | | | x o x o - o x - o x x x x | | | | | | | | o - x x x - x x o o o - | | | | | | | | | x x o o - x o o o - o | | | | | | | | | | o x o - o - o - - o | | | | | | | | | | | x o - - x o - - o | | | | | | | | | | | | o o x - o o x x | | | | | | | | | | | | | x x x x o x o | | | | | | | | | | | | | | o x x - o o | | | | | | | | | | | | | | | o x - x x | | | | | | | | | | | | | | | | x x x o | | | | | | | | | | | | | | | | | o x - | | | | | | | | | | | | | | | | | | x o | | | | | | | | | | | | | | | | | | | x The error in solving: 3.565268e-16 The error in solving: 2.847484e-16 The error in solving: 1.782634e-16 The error in solving: 3.231618e-16 The error in solving: 5.911107e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.362466 0.000000 0.000000 0.785038 -0.087752 0.000000 0.000000 -0.493419 0.000000 0.000000 0.552736 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.230059 0.416832 0.360414 0.136315 0.000000 -0.377389 0.000000 0.000000 0.000000 0.000000 0.838366 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.410751 0.000000 0.000000 0.728050 0.000000 0.000000 0.000000 -0.260738 0.000000 -0.091076 -0.940793 0.135290 0.000000 0.000000 0.000000 0.000000 -0.414615 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.733001 0.000000 0.000000 0.000000 0.000000 0.275612 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.678302 0.934932 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.070020 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.938770 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.528093 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.663913 0.000000 0.000000 0.000000 0.000000 0.053870 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.480535 -0.359990 0.424519 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.838249 -0.796272 -0.673579 0.000000 0.000000 0.000000 0.288884 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.133157 0.000000 0.000000 0.000000 0.000000 0.000000 -0.385831 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.627343 0.000000 0.000000 0.122010 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.363060 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.888150 0.000000 0.490703 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.493872 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.327771 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.859890 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.113698 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.610998 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 46 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 5 11 18 20 23 25 27 30 34 36 38 39 41 42 43 44 44 45 46 46 Column indices: 1 4 5 8 11 3 4 5 6 8 13 3 6 10 12 13 14 19 14 19 7 8 19 9 17 8 13 9 10 11 10 11 12 16 11 17 12 15 16 16 18 19 19 19 18 19 Off-diagonal values: 0.362466 0.785038 -0.087752 -0.493419 0.552736 0.230059 0.416832 0.360414 0.136315 -0.377389 0.838366 0.410751 0.728050 -0.260738 -0.091076 -0.940793 0.135290 -0.414615 -0.733001 0.275612 -0.678302 0.934932 0.070020 0.938770 0.528093 -0.663913 0.053870 -0.480535 -0.359990 0.424519 0.838249 -0.796272 -0.673579 0.288884 0.133157 -0.385831 -0.627343 0.122010 -0.363060 0.888150 0.490703 0.493872 0.327771 0.859890 -0.113698 0.610998 . x - - x o - - o - - x - - - - - - - - | . - x x x x - o - - - - x - - - - - - | | . x - - x - - - o - o o x - - - - o | | | . - - - - - - - - - - o - - - - x | | | | . - - o x - - - - - - - - - - x | | | | | . - - - x - - - - - - - x - - | | | | | | . - o - - - - x - - - - - - | | | | | | | . - o o x - - - - - - - - | | | | | | | | . - x o o - - - x - - - | | | | | | | | | . - x - - - - - o - - | | | | | | | | | | . - o - - x - - - - | | | | | | | | | | | . - - - - o - - - | | | | | | | | | | | | . - - - x - x - | | | | | | | | | | | | | . - - - - - x | | | | | | | | | | | | | | . - - - - x | | | | | | | | | | | | | | | . - - - x | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . o - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | | . The error in solving: 1.570092e-16 The error in solving: 2.322263e-16 The error in solving: 1.241267e-16 The error in solving: 1.241267e-16 The error in solving: 1.430490e-17 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.480129 0.458571 0.748535 0.000000 0.000000 0.720704 0.000000 -0.147648 0.672302 0.000000 0.000000 0.420924 0.000000 0.194284 -0.519091 0.000000 0.000000 0.598162 0.000000 0.000000 0.000000 0.000000 0.000000 -0.500339 -0.538176 0.624489 0.000000 -0.974478 0.371696 -0.584297 -0.129572 -0.478824 0.000000 0.000000 0.000000 0.000000 -0.883748 -0.567374 0.000000 0.000000 0.000000 0.000000 0.694820 0.000000 0.000000 0.000000 -0.545346 0.000000 0.555036 -0.279647 0.450308 0.000000 0.000000 -0.563653 0.000000 0.000000 0.000000 0.074338 0.000000 0.000000 0.000000 0.000000 -0.494988 0.000000 0.813726 0.999329 -0.720912 -0.135630 -0.290437 -0.453194 -0.695188 -0.511918 -0.810850 0.860973 -0.595064 0.000000 0.000000 0.183465 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.967408 0.000000 0.030867 0.183701 -0.022933 0.000000 0.000000 0.000000 0.000000 -0.108635 0.000000 -0.440487 0.602275 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.457992 0.857824 0.260347 0.000000 0.000000 0.000000 0.000000 0.000000 0.636282 0.000000 0.131025 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.297124 0.422097 0.546653 0.000000 0.000000 0.000000 0.000000 0.000000 0.337685 0.000000 0.000000 0.192223 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.871365 0.000000 -0.834048 -0.976205 0.000000 0.498937 0.285349 0.000000 -0.312291 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.523568 0.000000 0.000000 -0.770620 0.268501 0.000000 -0.953601 0.000000 0.231010 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.447842 0.000000 0.399143 0.676513 0.000000 0.000000 -0.798373 -0.747869 0.000000 0.069901 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.194912 -0.101387 0.000000 0.782130 0.525990 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.623931 0.000000 -0.537460 -0.747662 0.000000 0.447109 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.720480 0.000000 0.129062 -0.468129 -0.533378 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.389409 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.297181 0.000000 0.913424 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.793761 -0.865138 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.015202 0.647856 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.862097 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 94 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 10 20 27 40 47 52 57 63 68 74 78 82 86 87 89 91 93 94 94 94 Column indices: 2 3 4 7 9 10 13 15 16 19 5 6 7 9 10 11 12 13 18 19 4 8 10 11 12 15 19 4 6 7 8 9 10 11 12 13 14 15 16 19 6 8 9 10 15 17 18 6 7 8 14 16 7 8 9 15 18 10 12 13 15 16 18 9 12 13 15 17 10 12 13 16 17 19 13 14 16 17 14 16 17 19 14 16 17 18 17 16 18 18 19 17 18 19 Off-diagonal values: 0.480129 0.458571 0.748535 0.720704 -0.147648 0.672302 0.420924 0.194284 -0.519091 0.598162 -0.500339 -0.538176 0.624489 -0.974478 0.371696 -0.584297 -0.129572 -0.478824 -0.883748 -0.567374 0.694820 -0.545346 0.555036 -0.279647 0.450308 -0.563653 0.074338 -0.494988 0.813726 0.999329 -0.720912 -0.135630 -0.290437 -0.453194 -0.695188 -0.511918 -0.810850 0.860973 -0.595064 0.183465 -0.967408 0.030867 0.183701 -0.022933 -0.108635 -0.440487 0.602275 0.457992 0.857824 0.260347 0.636282 0.131025 -0.297124 0.422097 0.546653 0.337685 0.192223 0.871365 -0.834048 -0.976205 0.498937 0.285349 -0.312291 -0.523568 -0.770620 0.268501 -0.953601 0.231010 -0.447842 0.399143 0.676513 -0.798373 -0.747869 0.069901 -0.194912 -0.101387 0.782130 0.525990 -0.623931 -0.537460 -0.747662 0.447109 0.720480 0.129062 -0.468129 -0.533378 0.389409 -0.297181 0.913424 0.793761 -0.865138 0.015202 0.647856 0.862097 . - x x x - - x - o x - - x - x o - - x | . - - - o o x - o x o o o - - - - o o | | . - x - - - o - x o x - - o - - - x | | | . o - x x o o o o o o o x o - - x | | | | . - o - x x o - - - - o - o x - | | | | | . x x x - - - - - x - x - - - | | | | | | . o x x - - - - - x - - x - | | | | | | | . - - x - o o - x x - o - | | | | | | | | . o - - o x - o - x - - | | | | | | | | | . o - x x - - o o - x | | | | | | | | | | . - - o o - x x - - | | | | | | | | | | | . - - o - o o - x | | | | | | | | | | | | . - x - x o o - | | | | | | | | | | | | | . - - - x - - | | | | | | | | | | | | | | . - o - x - | | | | | | | | | | | | | | | . - - x o | | | | | | | | | | | | | | | | . x x - | | | | | | | | | | | | | | | | | . - x | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.719480e-16 The error in solving: 3.200929e-16 The error in solving: 1.571625e-16 The error in solving: 3.103168e-17 The error in solving: 2.545038e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.894830 0.000000 -0.481200 -0.204049 0.000000 -0.387954 0.000000 0.533738 0.000000 0.210731 0.163759 0.000000 -0.515280 -0.163607 0.878317 -0.583417 0.744476 0.000000 0.074558 0.000000 0.000000 -0.651456 0.419448 -0.096887 -0.161648 0.000000 -0.469471 0.000000 0.000000 0.000000 0.000000 -0.999513 0.000000 0.000000 0.000000 0.000000 -0.261746 -0.294895 0.000000 0.000000 0.000000 0.000000 0.000000 -0.854906 -0.034397 0.354606 0.633608 0.850508 0.618588 -0.667683 0.000000 0.459646 0.236169 0.000000 0.071528 0.220090 -0.446836 0.236861 0.705571 0.000000 0.000000 0.000000 0.000000 -0.680075 0.000000 -0.307597 0.583908 0.000000 -0.807406 -0.941631 0.057749 -0.634550 0.809720 0.000000 0.000000 0.763667 -0.912951 0.123190 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.797228 0.235357 -0.170507 0.000000 -0.123010 0.294275 0.291923 -0.895225 0.000000 0.933579 0.170804 -0.934138 0.077933 0.000000 -0.444803 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.526533 0.490856 -0.744563 -0.257991 0.000000 0.000000 -0.339625 0.705574 0.269992 -0.587997 -0.833580 0.000000 -0.980018 0.137511 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.038312 -0.585451 -0.128037 0.397793 0.000000 -0.600722 -0.244052 0.533082 -0.884025 0.715258 0.000000 0.578989 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.320168 0.917716 0.000000 -0.085069 0.982146 -0.891583 0.687079 -0.981177 0.416791 -0.531333 0.288684 0.174002 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.753204 0.000000 0.776826 -0.394446 0.201341 0.000000 0.807131 0.890172 0.467850 0.260234 0.470417 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.597502 0.977180 -0.471788 0.851022 -0.955420 0.628701 -0.414595 0.552828 0.343453 0.015723 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.470698 0.000000 0.796050 0.786847 0.023796 0.000000 -0.674855 -0.689155 0.659430 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.834729 0.697776 0.184624 -0.519853 0.000000 0.731147 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.104081 -0.199661 -0.260300 0.120239 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.043210 0.662739 -0.929656 -0.909489 -0.081609 -0.866091 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.644974 0.000000 0.240186 -0.840908 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.421380 0.159841 -0.269298 -0.158339 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.746446 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.608912 0.519389 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.400934 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 142 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 13 21 35 46 58 69 79 90 99 109 116 121 125 131 134 138 139 141 142 142 Column indices: 1 3 4 6 8 10 11 13 14 15 16 17 19 2 3 4 5 7 12 17 18 4 5 6 7 8 9 10 12 13 15 16 17 18 19 4 6 7 9 10 11 12 13 16 17 18 5 6 7 9 10 11 12 14 15 16 17 19 6 7 8 9 12 13 14 15 16 18 19 8 9 10 11 13 14 15 16 17 19 8 9 11 12 13 14 15 16 17 18 19 9 11 12 13 15 16 17 18 19 10 11 12 13 14 15 16 17 18 19 11 13 14 15 17 18 19 13 14 15 16 18 13 14 15 16 14 15 16 17 18 19 15 17 18 16 17 18 19 19 18 19 19 Off-diagonal values: 0.894830 -0.481200 -0.204049 -0.387954 0.533738 0.210731 0.163759 -0.515280 -0.163607 0.878317 -0.583417 0.744476 0.074558 -0.651456 0.419448 -0.096887 -0.161648 -0.469471 -0.999513 -0.261746 -0.294895 -0.854906 -0.034397 0.354606 0.633608 0.850508 0.618588 -0.667683 0.459646 0.236169 0.071528 0.220090 -0.446836 0.236861 0.705571 -0.680075 -0.307597 0.583908 -0.807406 -0.941631 0.057749 -0.634550 0.809720 0.763667 -0.912951 0.123190 -0.797228 0.235357 -0.170507 -0.123010 0.294275 0.291923 -0.895225 0.933579 0.170804 -0.934138 0.077933 -0.444803 0.526533 0.490856 -0.744563 -0.257991 -0.339625 0.705574 0.269992 -0.587997 -0.833580 -0.980018 0.137511 -0.038312 -0.585451 -0.128037 0.397793 -0.600722 -0.244052 0.533082 -0.884025 0.715258 0.578989 0.320168 0.917716 -0.085069 0.982146 -0.891583 0.687079 -0.981177 0.416791 -0.531333 0.288684 0.174002 -0.753204 0.776826 -0.394446 0.201341 0.807131 0.890172 0.467850 0.260234 0.470417 0.597502 0.977180 -0.471788 0.851022 -0.955420 0.628701 -0.414595 0.552828 0.343453 0.015723 0.470698 0.796050 0.786847 0.023796 -0.674855 -0.689155 0.659430 -0.834729 0.697776 0.184624 -0.519853 0.731147 0.104081 -0.199661 -0.260300 0.120239 0.043210 0.662739 -0.929656 -0.909489 -0.081609 -0.866091 -0.644974 0.240186 -0.840908 0.421380 0.159841 -0.269298 -0.158339 0.746446 -0.608912 0.519389 0.400934 . x - o o - o - x - x x - o o x o x - x | . o x o o - o - - - - o - - - - o o - | | . - o o x x x x o - x x - x x o x x | | | . o - o x - o o x o x - - x o x - | | | | . o x o - o x x o - x x o x - o | | | | | . x x o o - - o x x o o - o x | | | | | | . - o o o x - o o x o x - x | | | | | | | . x x - o x o x o x o x x | | | | | | | | . o - x o x - x x x x x | | | | | | | | | . x x o x o x o x x x | | | | | | | | | | . x - x x x - o o x | | | | | | | | | | | . - o x x o - x - | | | | | | | | | | | | . x o o x - - - | | | | | | | | | | | | | . x x o o o o | | | | | | | | | | | | | | . o - x o - | | | | | | | | | | | | | | | . x x o o | | | | | | | | | | | | | | | | . - - x | | | | | | | | | | | | | | | | | . o x | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | | . The error in solving: 3.511519e-16 The error in solving: 1.249001e-16 The error in solving: 2.953720e-16 The error in solving: 3.379462e-16 The error in solving: 4.577567e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a standard normal distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.997187 0.352223 0.000000 0.000000 0.000000 0.482820 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.282208 0.000000 0.000000 0.138510 0.000000 -0.922068 0.000000 -0.526339 0.000000 0.000000 0.000000 0.000000 0.000000 -0.563333 0.000000 0.000000 1.075560 0.000000 0.000000 0.000000 0.000000 1.034128 0.284680 0.000000 0.000000 0.553600 0.000000 0.000000 1.339416 0.000000 0.000000 0.000000 0.000000 0.000000 -1.043103 0.105796 0.000000 0.000000 0.771178 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.819710]; Dimension: 20 x 20 Off-diagonal entries: 46 (max 380) Diagonal entries: 0.000000 0.282208 1.034128 0.000000 0.000000 -1.034883 0.000000 -1.664037 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.410192 0.000000 0.000000 0.000000 0.000000 0.819710 Row indices: 0 3 8 14 16 17 21 26 28 30 32 34 38 41 43 43 43 44 45 46 46 Column indices: 9 10 14 4 6 8 14 17 3 6 9 15 16 19 6 13 6 7 9 13 15 8 11 14 15 18 10 12 12 13 10 12 11 16 12 13 15 18 15 17 19 14 18 18 18 19 Off-diagonal values: 0.997187 0.352223 0.482820 0.138510 -0.922068 -0.526339 -0.563333 1.075560 0.284680 0.553600 1.339416 -1.043103 0.105796 0.771178 1.493295 -1.880037 0.609746 0.830307 -0.897341 0.008676 -0.552596 2.181504 0.506579 -2.184366 1.502343 -1.573114 -0.750687 -2.950696 0.633007 0.084998 -0.438703 -1.352627 1.109122 -0.079714 -1.651654 -1.602761 0.230928 1.351809 1.714780 -0.907911 0.027476 1.451499 -0.872879 0.628320 0.286626 -1.256391 . - - - - - - - - x x - - - x - - - - - | x - - x - o - o - - - - - o - - x - - | | x x - - x - - x - - - - - o x - - x | | | . - - x - - - - - - o - - - - - - | | | | . - x - - - - - - - - - - - - - | | | | | o - x - o - - - x - o - - - - | | | | | | . - x - - x - - o x - - o - | | | | | | | o - - o - o - - - - - - - | | | | | | | | . - - - x x - - - - - - | | | | | | | | | . o - o - - - - - - - | | | | | | | | | | . x - - - - o - - - | | | | | | | | | | | . o o - x - - x - | | | | | | | | | | | | . - - x - o - x | | | | | | | | | | | | | . x - - - o - | | | | | | | | | | | | | | o - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - x - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | | | . o | | | | | | | | | | | | | | | | | | | x The error in solving: 3.723963e-16 The error in solving: 7.881069e-17 The error in solving: 2.558938e-16 The error in solving: 2.548155e-16 The error in solving: 5.551115e-17 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a standard normal distribution with a random diagonal and a density of 0.500000 [ -0.577001 -0.115501 0.000000 0.000000 0.000000 0.010814 0.000000 0.000000 3.259730 0.358299 0.000000 0.000000 -0.209031 -0.590144 0.000000 0.000000 0.000000 -1.535193 0.000000 0.000000 0.000000 3.247686 0.256629 -0.108406 0.000000 0.743724 0.064165 0.000000 0.767051 -0.191851 0.000000 0.000000 0.000000 0.000000 0.939444 0.000000 0.000000 0.000000 0.584250 0.886624 0.000000 0.000000 -0.929509 0.000000 0.000000 0.000000 0.953871 0.000000 0.000000 0.000000 0.621618 0.000000 0.656216 -0.555688 -1.265874 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.372830 0.000000 0.000000 -0.920294 0.000000 0.000000 0.000000 -0.565426 0.000000 -0.618808 0.000000 0.000000 0.000000 0.000000 0.285702 1.257788 0.006762 0.000000 0.000000 0.000000 0.000000 0.000000 -0.199858 0.000000 0.000000 -0.409964 0.000000 0.233403 2.042913 -0.481561 0.000000 -0.686151 0.697426 0.000000 0.000000 0.000000 0.461234 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.414114 -1.276501 1.205495 0.000000 0.000000 -0.088074 0.000000 0.000000 -1.250761 0.000000 -2.079526 -0.265162 -1.039982 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.098673 0.000000 -0.571016 0.000000 0.000000 -0.365857 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.179129 0.521383 0.000000 0.000000 0.159116 -0.429737 0.000000 0.000000 -1.462390 0.893205 -0.556752 0.655426 -0.367728 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.515885 -0.782223 0.000000 -0.401965 0.000000 -0.100624 0.000000 0.000000 0.000000 0.000000 0.000000 1.776287 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.233895 -1.030194 1.336944 0.669591 0.000000 0.000000 0.269642 0.000000 -0.552302 -0.370412 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.520494 0.650494 0.000000 -0.071603 -0.152077 0.899679 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.248285 0.000000 0.495044 0.000000 0.617496 0.000000 0.000000 -1.109440 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.534384 0.469420 -0.768544 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.121578 -1.075114 1.742208 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.504355 -0.586103 -0.578023 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.517987 0.000000 0.000000 2.052252 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.483593 0.113127 2.109303 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.008035 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 86 (max 380) Diagonal entries: -0.577001 3.247686 -0.929509 -0.372830 0.000000 0.000000 0.000000 -1.179129 -0.515885 0.233895 0.520494 1.248285 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 7 16 21 27 35 43 46 54 58 64 68 71 74 77 80 82 85 85 86 86 Column indices: 1 5 8 9 12 13 17 2 3 5 6 8 9 14 18 19 6 10 12 13 14 6 10 12 17 18 19 5 8 10 11 12 14 15 19 7 8 9 12 15 17 18 19 10 12 15 8 11 12 15 16 17 18 19 9 11 13 19 10 11 12 15 17 18 11 13 14 15 13 15 18 15 16 17 15 16 17 15 16 17 16 19 17 18 19 19 Off-diagonal values: -0.115501 0.010814 3.259730 0.358299 -0.209031 -0.590144 -1.535193 0.256629 -0.108406 0.743724 0.064165 0.767051 -0.191851 0.939444 0.584250 0.886624 0.953871 0.621618 0.656216 -0.555688 -1.265874 -0.920294 -0.565426 -0.618808 0.285702 1.257788 0.006762 -0.199858 -0.409964 0.233403 2.042913 -0.481561 -0.686151 0.697426 0.461234 0.414114 -1.276501 1.205495 -0.088074 -1.250761 -2.079526 -0.265162 -1.039982 -0.098673 -0.571016 -0.365857 0.521383 0.159116 -0.429737 -1.462390 0.893205 -0.556752 0.655426 -0.367728 -0.782223 -0.401965 -0.100624 1.776287 -1.030194 1.336944 0.669591 0.269642 -0.552302 -0.370412 0.650494 -0.071603 -0.152077 0.899679 0.495044 0.617496 -1.109440 0.534384 0.469420 -0.768544 2.121578 -1.075114 1.742208 0.504355 -0.586103 -0.578023 0.517987 2.052252 0.483593 0.113127 2.109303 0.008035 o o - - - x - - x x - - o o - - - o - - | x x o - x x - x o - - - - x - - - x x | | o - - - x - - - x - x o o - - - - - | | | o - - o - - - o - o - - - - x x x | | | | . o - - o - x x o - o x - - - x | | | | | . - x o x - - o - - o - o o o | | | | | | . - - - o - o - - o - - - - | | | | | | | o x - - x o - - o x o x o | | | | | | | | o o - o - o - - - - - x | | | | | | | | | x o x x - - x - o o - | | | | | | | | | | x x - o o x - - - - | | | | | | | | | | | x - x - x - - o - | | | | | | | | | | | | . - - x x o - - | | | | | | | | | | | | | . - x o x - - | | | | | | | | | | | | | | . x o o - - | | | | | | | | | | | | | | | . x - - x | | | | | | | | | | | | | | | | . x x x | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | | . The error in solving: 2.559878e-16 The error in solving: 5.561947e-17 The error in solving: 3.258511e-16 The error in solving: 3.521788e-16 The error in solving: 2.747662e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a standard normal distribution with a random diagonal and a density of 0.750000 [ -0.684614 0.994073 0.270363 0.058687 0.000000 0.643091 -0.876280 0.572993 0.836081 0.000000 0.000000 1.027951 1.681599 0.152328 0.000000 0.000000 0.140577 0.000000 -0.911685 0.919447 0.000000 -0.470611 -0.521117 -2.353657 0.000000 -0.159141 -1.022116 1.504135 0.000000 -0.025398 -1.431586 -1.745840 -1.466829 0.989067 -0.000344 0.000000 -0.565590 0.482986 -0.847634 -0.085155 0.000000 0.000000 0.000000 -0.388585 0.683017 0.003527 1.624171 0.721680 0.787090 0.531531 0.000000 -1.045591 0.303172 0.000000 -1.573884 0.704383 0.000000 -1.271428 1.294689 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.212104 -0.644532 -0.087170 0.000000 -0.780450 1.288094 -0.416916 0.000000 -2.021500 -0.375965 0.526767 0.919330 0.000000 -0.893773 0.640901 0.000000 0.000000 0.000000 0.000000 0.772907 -0.035069 -0.401064 -0.025818 0.765101 -0.088713 0.142394 0.013704 -0.237539 0.031763 0.533491 0.000000 -0.941572 0.000000 0.000000 -1.588789 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.145207 -0.776486 -0.881435 -0.376789 1.055036 0.242378 0.000000 0.007360 0.000000 1.064398 0.313203 0.000000 1.219819 1.307188 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.436348 -0.760380 0.626032 0.000000 0.000000 -0.503897 0.283935 0.000000 -1.592116 0.000000 -0.394683 0.000000 1.424216 0.863275 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.418049 1.450292 -1.660473 -0.156757 0.000000 -1.345034 0.000000 -0.953674 0.000000 0.000000 -0.274800 -1.543129 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.442213 -1.370036 1.469431 0.925900 0.000000 0.000000 0.000000 0.668348 0.034348 0.109446 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.015439 0.000000 0.000000 -1.861132 0.884864 1.218266 -0.437844 0.000000 0.221445 0.000000 -0.070128 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.537369 -1.861812 -1.525805 1.364426 -1.017277 0.000000 -0.919597 1.901553 1.139086 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.211009 0.000000 2.241378 -0.973371 -2.035210 -0.335489 2.028624 0.000000 2.836833 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.710105 0.140409 0.000000 0.000000 0.264812 0.000000 1.143824 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.841720 -0.355491 0.000000 0.000000 0.000000 0.000000 -1.038287 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.686163 0.000000 0.000000 -0.068278 -0.365130 0.852913 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.857786 -0.167444 0.818998 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.169082 -0.272503 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.459373 0.000000 0.242561 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.026626 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.056399]; Dimension: 20 x 20 Off-diagonal entries: 134 (max 380) Diagonal entries: -0.684614 -0.470611 0.000000 0.000000 0.772907 0.000000 -0.436348 0.000000 0.000000 0.015439 0.000000 -0.211009 0.000000 -0.841720 -1.686163 -0.857786 0.000000 -1.459373 0.000000 0.056399 Row indices: 0 13 28 41 53 65 76 84 92 99 105 113 119 123 125 128 130 132 133 134 134 Column indices: 1 2 3 5 6 7 8 11 12 13 16 18 19 2 3 5 6 7 9 10 11 12 13 14 16 17 18 19 3 4 5 6 7 8 9 11 12 14 15 17 18 5 6 7 9 10 11 13 14 15 16 18 19 5 6 7 8 9 10 11 12 13 14 16 19 6 7 8 9 10 11 13 15 16 18 19 7 8 11 12 14 16 18 19 8 9 10 11 13 15 18 19 10 11 12 13 17 18 19 12 13 14 15 17 19 11 12 13 14 15 17 18 19 13 14 15 16 17 19 13 14 17 19 14 19 17 18 19 16 17 17 18 19 19 Off-diagonal values: 0.994073 0.270363 0.058687 0.643091 -0.876280 0.572993 0.836081 1.027951 1.681599 0.152328 0.140577 -0.911685 0.919447 -0.521117 -2.353657 -0.159141 -1.022116 1.504135 -0.025398 -1.431586 -1.745840 -1.466829 0.989067 -0.000344 -0.565590 0.482986 -0.847634 -0.085155 -0.388585 0.683017 0.003527 1.624171 0.721680 0.787090 0.531531 -1.045591 0.303172 -1.573884 0.704383 -1.271428 1.294689 0.212104 -0.644532 -0.087170 -0.780450 1.288094 -0.416916 -2.021500 -0.375965 0.526767 0.919330 -0.893773 0.640901 -0.035069 -0.401064 -0.025818 0.765101 -0.088713 0.142394 0.013704 -0.237539 0.031763 0.533491 -0.941572 -1.588789 0.145207 -0.776486 -0.881435 -0.376789 1.055036 0.242378 0.007360 1.064398 0.313203 1.219819 1.307188 -0.760380 0.626032 -0.503897 0.283935 -1.592116 -0.394683 1.424216 0.863275 -0.418049 1.450292 -1.660473 -0.156757 -1.345034 -0.953674 -0.274800 -1.543129 -1.442213 -1.370036 1.469431 0.925900 0.668348 0.034348 0.109446 -1.861132 0.884864 1.218266 -0.437844 0.221445 -0.070128 -0.537369 -1.861812 -1.525805 1.364426 -1.017277 -0.919597 1.901553 1.139086 2.241378 -0.973371 -2.035210 -0.335489 2.028624 2.836833 -0.710105 0.140409 0.264812 1.143824 -0.355491 -1.038287 -0.068278 -0.365130 0.852913 -0.167444 0.818998 -2.169082 -0.272503 0.242561 -0.026626 o x x x - x o x x - - x x x - - x - o x | o o o - o o x - o o o o x o - o x o o | | . o x x x x x x - o x - o x - o x - | | | . - x o o - o x o - o o x x - o x | | | | x o o o x o x x o x x - o - - o | | | | | . x o o o x x - x - x x - x x | | | | | | o o x - - o x - o - o - x x | | | | | | | . o x o o - o - o - - o o | | | | | | | | . - o o x x - - - x x x | | | | | | | | | x - - o x x o - x - o | | | | | | | | | | . o o o x o - o x x | | | | | | | | | | | o - x o o o x - x | | | | | | | | | | | | . o x - - x - x | | | | | | | | | | | | | o o - - - - o | | | | | | | | | | | | | | o - - o o x | | | | | | | | | | | | | | | o o x - - | | | | | | | | | | | | | | | | . o o - | | | | | | | | | | | | | | | | | o - x | | | | | | | | | | | | | | | | | | . o | | | | | | | | | | | | | | | | | | | x The error in solving: 1.040834e-16 The error in solving: 3.806285e-16 The error in solving: 1.691956e-16 The error in solving: 1.571625e-16 The error in solving: 2.723019e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a standard normal distribution with a dense diagonal and a density of 0.250000 [ -1.624866 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.442360 0.000000 0.000000 0.000000 0.000000 0.000000 -0.614009 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.928202 0.000000 0.000000 -0.833822 0.000000 0.000000 0.000000 0.000000 0.000000 -0.176039 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.359420 0.000000 0.000000 0.000000 0.185345 0.000000 -0.076504 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.856138 0.000000 0.000000 0.000000 0.000000 -1.837480 0.000000 0.000000 0.000000 0.000000 0.000000 2.610065 0.000000 0.721943 0.190684 0.000000 0.000000 0.000000 0.000000 0.000000 -2.899672 0.000000 0.000000 0.000000 0.000000 0.000000 0.310083 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.246654 0.000000 0.000000 0.000000 0.000000 0.586123 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.303419 -2.618763 0.000000 0.000000 0.049509 0.000000 0.000000 0.000000 -0.031969 0.000000 0.000000 0.000000 0.000000 0.000000 -0.925021 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.298635 0.000000 0.000000 0.000000 0.000000 0.000000 -0.207386 0.000000 0.000000 1.209258 -0.602196 -0.065689 0.171578 -0.962409 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.766734 0.000000 0.000000 0.000000 0.000000 0.597102 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.370925 0.000000 0.121135 0.000000 0.000000 0.688937 0.000000 0.000000 -1.398749 0.874405 0.000000 -0.898368 0.000000 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20 x 20 Off-diagonal entries: 41 (max 380) Diagonal entries: -1.624866 -0.928202 0.185345 -1.837480 0.310083 -0.303419 -0.298635 -0.766734 0.370925 1.597787 -0.315154 0.002734 -0.339598 -0.647792 1.925786 -0.689962 -0.802190 -1.180731 -1.051431 -0.868387 Row indices: 0 2 5 7 11 13 17 23 24 29 30 30 32 36 39 39 40 41 41 41 41 Column indices: 8 14 4 10 18 4 18 9 11 12 18 13 18 6 9 13 19 12 15 16 17 18 19 12 10 13 16 17 19 12 13 18 14 16 18 19 14 17 18 17 17 Off-diagonal values: 0.442360 -0.614009 -0.833822 -0.176039 -0.359420 -0.076504 -0.856138 2.610065 0.721943 0.190684 -2.899672 -1.246654 0.586123 -2.618763 0.049509 -0.031969 -0.925021 -0.207386 1.209258 -0.602196 -0.065689 0.171578 -0.962409 0.597102 0.121135 0.688937 -1.398749 0.874405 -0.898368 1.251591 -0.404956 1.005702 1.818220 0.131158 -1.022906 -0.135765 0.978211 -0.772139 -2.310415 1.187926 0.266705 o - - - - - - - x - - - - - o - - - - - | o - - o - - - - - o - - - - - - - o - | | x - o - - - - - - - - - - - - - o - | | | o - - - - - x - x x - - - - - o - | | | | x - - - - - - - - o - - - - x - | | | | | o o - - x - - - o - - - - - o | | | | | | o - - - - - o - - x o o x o | | | | | | | o - - - - x - - - - - - - | | | | | | | | x - x - - x - - o x - o | | | | | | | | | x - - x - - - - - - - | | | | | | | | | | o - - - - - - - - - | | | | | | | | | | | x - o - - - - x - | | | | | | | | | | | | o - x - x - o o | | | | | | | | | | | | | o x - - o o - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | o - x - - | | | | | | | | | | | | | | | | o x - - | | | | | | | | | | | | | | | | | o - - | | | | | | | | | | | | | | | | | | o - | | | | | | | | | | | | | | | | | | | o The error in solving: 6.206335e-17 The error in solving: 2.482777e-16 The error in solving: 2.237726e-16 The error in solving: 1.594436e-16 The error in solving: 2.543841e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a standard normal distribution with a dense diagonal and a density of 0.500000 [ 1.394528 -0.033686 -0.475127 0.000000 -0.835122 1.316795 -0.179050 3.201992 0.000000 -0.187567 0.609489 0.000000 0.584493 1.061428 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.450671 -0.384561 -1.035514 -0.132037 -1.463970 0.000000 -1.295146 -1.838255 0.400283 0.000000 0.534810 1.091997 0.237190 -0.457158 0.000000 0.000000 0.552505 0.000000 -0.704078 0.000000 0.000000 1.735984 0.000000 0.155859 0.000000 -1.313418 1.878282 0.000000 0.380620 -0.321323 0.000000 0.000000 0.599729 0.000000 0.813475 -0.549779 -1.031313 0.252772 1.140512 0.000000 0.000000 0.000000 -0.861254 1.561835 -0.468173 0.854258 0.000000 0.000000 0.083238 -0.332496 1.077663 0.017171 0.818215 -2.475376 -0.158064 -0.377286 0.000000 -0.165512 0.000000 0.000000 0.000000 0.000000 0.000000 0.207239 0.000000 0.000000 0.000000 1.728957 0.043515 0.000000 0.000000 0.000000 -1.139077 0.000000 0.121040 -0.806348 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.622455 0.000000 1.485057 0.000000 1.585439 0.000000 0.000000 -1.518597 0.000000 1.356464 1.261910 0.000000 -0.402922 1.021518 -0.867170 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.575917 -1.184841 0.000000 1.218329 0.000000 0.000000 0.000000 0.000000 1.432039 0.000000 0.000000 0.000000 0.449052 -1.206442 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.565961 -1.532664 -0.325702 -0.002155 -1.119363 1.177421 0.000000 0.000000 0.000000 0.000000 0.000000 0.265906 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.002459 0.000000 0.614146 -0.500057 -1.008277 -1.781868 0.000000 -0.153484 0.118881 -2.512056 0.000000 1.951533 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.033161 0.000000 0.000000 0.000000 0.499420 -0.817710 0.000000 -0.149255 0.000000 -0.285028 0.251681 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.912126 0.000000 0.000000 0.382154 0.000000 0.000000 0.000000 0.000000 0.000000 -2.692560 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.233071 0.000000 -1.544285 0.227284 -0.160716 -0.975301 1.040260 0.132796 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.961247 -0.525015 0.064669 -1.763143 1.403595 0.011211 0.000000 2.850105 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.407924 1.598289 0.000000 0.000000 0.303813 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.558944 -0.077369 0.897111 -0.064852 0.000000 0.837351 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.086800 0.000000 0.299706 -0.425311 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.337991 -0.066226 0.039623 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.822899 -0.017242 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.136047 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.703512]; Dimension: 20 x 20 Off-diagonal entries: 108 (max 380) Diagonal entries: 1.394528 0.450671 1.735984 -0.861254 0.207239 -0.622455 -0.575917 -0.565961 0.002459 -2.033161 -0.912126 1.233071 1.961247 -1.407924 1.558944 -1.086800 0.337991 -0.822899 -1.136047 -0.703512 Row indices: 0 10 23 34 46 51 59 64 70 78 83 85 91 97 99 103 105 107 108 108 108 Column indices: 1 2 4 5 6 7 9 10 12 13 2 3 4 5 7 8 9 11 12 13 14 17 19 4 6 7 9 10 13 15 16 17 18 19 4 5 6 9 10 11 12 13 14 15 16 18 8 9 13 15 16 7 9 12 14 15 17 18 19 7 9 14 18 19 8 9 10 11 12 18 10 11 12 13 15 16 17 19 13 14 16 18 19 13 19 13 14 15 16 17 18 13 14 15 16 17 19 14 17 15 16 17 19 17 18 17 18 18 Off-diagonal values: -0.033686 -0.475127 -0.835122 1.316795 -0.179050 3.201992 -0.187567 0.609489 0.584493 1.061428 -0.384561 -1.035514 -0.132037 -1.463970 -1.295146 -1.838255 0.400283 0.534810 1.091997 0.237190 -0.457158 0.552505 -0.704078 0.155859 -1.313418 1.878282 0.380620 -0.321323 0.599729 0.813475 -0.549779 -1.031313 0.252772 1.140512 1.561835 -0.468173 0.854258 0.083238 -0.332496 1.077663 0.017171 0.818215 -2.475376 -0.158064 -0.377286 -0.165512 1.728957 0.043515 -1.139077 0.121040 -0.806348 1.485057 1.585439 -1.518597 1.356464 1.261910 -0.402922 1.021518 -0.867170 -1.184841 1.218329 1.432039 0.449052 -1.206442 -1.532664 -0.325702 -0.002155 -1.119363 1.177421 0.265906 0.614146 -0.500057 -1.008277 -1.781868 -0.153484 0.118881 -2.512056 1.951533 0.499420 -0.817710 -0.149255 -0.285028 0.251681 0.382154 -2.692560 -1.544285 0.227284 -0.160716 -0.975301 1.040260 0.132796 -0.525015 0.064669 -1.763143 1.403595 0.011211 2.850105 1.598289 0.303813 -0.077369 0.897111 -0.064852 0.837351 0.299706 -0.425311 -0.066226 0.039623 -0.017242 x o o - o x o x - o x - x x - - - - - - | x o o o o - o o x - x x x o - - x - o | | x - x - o x - x o - - x - x o o x x | | | o x o x - - x o x x x o o o - o - | | | | x - - - x x - - - o - x o - - - | | | | | o - x - x - - o - x x - o x o | | | | | | o o - x - - - - x - - - x o | | | | | | | o o o o o x - - - - - x - | | | | | | | | x - x o o o - o x o - x | | | | | | | | | o - - - x o - o - o x | | | | | | | | | | o - - x - - - - - o | | | | | | | | | | | x - o x o o x x - | | | | | | | | | | | | x o x o x x - x | | | | | | | | | | | | | o x - - x - - | | | | | | | | | | | | | | x o x o - x | | | | | | | | | | | | | | | o - x o - | | | | | | | | | | | | | | | | x o x - | | | | | | | | | | | | | | | | | o o - | | | | | | | | | | | | | | | | | | o - | | | | | | | | | | | | | | | | | | | o The error in solving: 3.284267e-16 The error in solving: 4.974998e-16 The error in solving: 5.551115e-17 The error in solving: 3.388000e-16 The error in solving: 4.335560e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a standard normal distribution with a dense diagonal and a density of 0.750000 [ -0.955443 0.017692 -2.158096 1.195207 0.613882 -0.983471 -0.149231 0.000000 0.000000 -0.195690 -0.702249 -0.151282 0.000000 -0.981587 -2.008980 -0.726246 -0.754969 0.000000 -0.774709 -0.177567 0.000000 -1.802166 0.000000 0.000000 1.220094 0.101486 0.000000 0.116701 -0.812579 0.125241 -0.111481 -0.035177 1.375496 -1.204361 0.000000 -0.515415 0.102536 -0.791283 -0.472222 1.551729 0.000000 0.000000 0.213597 0.000000 0.000000 -0.121464 -0.221604 -0.015397 0.176813 -0.881651 -0.107746 0.000000 0.308070 0.000000 -1.103035 0.000000 0.500312 0.406590 1.817882 -1.295068 0.000000 0.000000 0.000000 -0.919193 1.192594 -1.756889 -1.099516 0.489118 -0.434376 -1.246531 0.033372 0.000000 0.328534 0.108677 -1.407627 -1.154824 -0.860665 -1.738520 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.729751 0.174516 -0.265574 -0.699547 0.000000 0.000000 -0.380396 -0.069350 -0.154929 0.539479 0.752120 0.279695 -0.058451 -0.929923 -0.483294 0.315037 0.000000 0.000000 0.000000 0.000000 0.000000 0.611178 1.572630 -0.383932 0.000000 0.123649 1.086156 -0.178577 1.679267 -1.024850 0.000000 0.914112 -1.592953 -0.432161 0.000000 0.226914 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.264872 1.113550 0.053993 -1.616360 -0.020696 0.000000 0.109293 -0.553156 0.109082 0.278340 -0.358103 0.174301 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.031970 -2.280111 -0.954870 -0.693948 0.000000 1.176087 1.473804 -0.114772 -0.671282 -1.366494 -0.716856 0.000000 -0.934937 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.801209 -0.376474 -1.473377 -0.963480 0.189789 -1.848543 0.825418 -1.125346 0.000000 0.000000 0.531985 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.258384 1.096853 -1.152718 0.000000 -0.365583 -0.286751 -0.656660 -1.192804 0.090495 -0.960910 -0.649339 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.373414 -0.068926 1.978930 -0.105485 1.112224 -0.224204 0.000000 0.253575 -1.832582 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.556802 -0.301944 0.031568 -0.072324 -0.349826 -0.451537 -0.445314 0.000000 -0.430891 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.640997 0.186602 0.000000 -0.770109 -0.275483 -1.098810 0.954926 1.984220 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.491874 0.000000 0.000000 -1.278490 0.000000 -0.161417 0.418393 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.844855 -0.008624 0.222355 -1.019837 1.185512 -0.354072 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.865305 0.000000 -0.736278 -0.925898 -1.502446 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.263969 0.000000 0.922611 -2.613798 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.426419 -0.823397 -1.041523 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.470410 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.631374]; Dimension: 20 x 20 Off-diagonal entries: 150 (max 380) Diagonal entries: -0.955443 -1.802166 0.213597 -0.919193 0.729751 0.611178 0.264872 0.031970 1.801209 -0.258384 -0.373414 0.556802 -0.640997 1.491874 0.844855 0.865305 -1.263969 1.426419 0.470410 -0.631374 Row indices: 0 15 29 41 54 67 78 88 98 106 115 122 129 135 138 143 146 148 150 150 150 Column indices: 1 2 3 4 5 6 9 10 11 13 14 15 16 18 19 4 5 7 8 9 10 11 12 13 15 16 17 18 19 5 6 7 8 9 10 12 14 16 17 18 19 4 5 6 7 8 9 10 12 13 14 15 16 17 5 6 7 10 11 12 13 14 15 16 17 18 19 6 7 9 10 11 12 13 15 16 17 19 7 8 9 10 12 13 14 15 16 17 8 9 10 12 13 14 15 16 17 19 9 10 11 12 13 14 15 18 10 11 13 14 15 16 17 18 19 11 12 13 14 15 17 18 12 13 14 15 16 17 19 13 15 16 17 18 19 16 18 19 15 16 17 18 19 17 18 19 18 19 18 19 Off-diagonal values: 0.017692 -2.158096 1.195207 0.613882 -0.983471 -0.149231 -0.195690 -0.702249 -0.151282 -0.981587 -2.008980 -0.726246 -0.754969 -0.774709 -0.177567 1.220094 0.101486 0.116701 -0.812579 0.125241 -0.111481 -0.035177 1.375496 -1.204361 -0.515415 0.102536 -0.791283 -0.472222 1.551729 -0.121464 -0.221604 -0.015397 0.176813 -0.881651 -0.107746 0.308070 -1.103035 0.500312 0.406590 1.817882 -1.295068 1.192594 -1.756889 -1.099516 0.489118 -0.434376 -1.246531 0.033372 0.328534 0.108677 -1.407627 -1.154824 -0.860665 -1.738520 0.174516 -0.265574 -0.699547 -0.380396 -0.069350 -0.154929 0.539479 0.752120 0.279695 -0.058451 -0.929923 -0.483294 0.315037 1.572630 -0.383932 0.123649 1.086156 -0.178577 1.679267 -1.024850 0.914112 -1.592953 -0.432161 0.226914 1.113550 0.053993 -1.616360 -0.020696 0.109293 -0.553156 0.109082 0.278340 -0.358103 0.174301 -2.280111 -0.954870 -0.693948 1.176087 1.473804 -0.114772 -0.671282 -1.366494 -0.716856 -0.934937 -0.376474 -1.473377 -0.963480 0.189789 -1.848543 0.825418 -1.125346 0.531985 1.096853 -1.152718 -0.365583 -0.286751 -0.656660 -1.192804 0.090495 -0.960910 -0.649339 -0.068926 1.978930 -0.105485 1.112224 -0.224204 0.253575 -1.832582 -0.301944 0.031568 -0.072324 -0.349826 -0.451537 -0.445314 -0.430891 0.186602 -0.770109 -0.275483 -1.098810 0.954926 1.984220 -1.278490 -0.161417 0.418393 -0.008624 0.222355 -1.019837 1.185512 -0.354072 -0.736278 -0.925898 -1.502446 0.922611 -2.613798 -0.823397 -1.041523 o x o x x o o - - o o o - o o o o - o o | o - - x x - x o x o o x o - o x o o x | | x - - o o o x o o - x - o - x x x o | | | o x o o x o o x - x x o o o o - - | | | | x x o o - - o o o x x x o o o x | | | | | x x o - x x o x o - x o o - x | | | | | | x x x o o - x o x x o x - - | | | | | | | x o o o - x x o o o o - o | | | | | | | | x o o o x o x o - - x - | | | | | | | | | o x o - o o o o x o o | | | | | | | | | | o o x o x o - x o - | | | | | | | | | | | x o x o o o o - o | | | | | | | | | | | | o x - o o o x x | | | | | | | | | | | | | x - - o - o x | | | | | | | | | | | | | | x o x o x o | | | | | | | | | | | | | | | x - o o o | | | | | | | | | | | | | | | | o - x o | | | | | | | | | | | | | | | | | x o o | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | o The error in solving: 1.526951e-16 The error in solving: 2.733607e-16 The error in solving: 4.082170e-16 The error in solving: 6.901322e-16 The error in solving: 4.203294e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a standard normal distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 -1.456013 0.651144 0.000000 -0.520046 0.000000 0.000000 0.000000 0.000000 -0.619674 0.000000 0.000000 2.178938 0.000000 0.000000 0.000000 0.173522 0.434634 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.695670 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.334899 0.444851 -0.359604 -0.185416 0.000000 0.000000 0.682920 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.100087 -0.351990 0.000000 0.000000 0.000000 0.000000 -0.907384 0.789159 0.000000 0.000000 0.000000 0.000000 0.000000 -0.062826 0.000000 0.000000 0.000000 0.000000 -0.563137 0.000000 -0.975849 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.040399 0.000000 -1.092157 -0.242459 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.136075 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.747679 0.000000 0.912339 0.000000 0.000000 1.559659 0.000000 0.000000 -2.770091 0.589146 1.551264 0.038130 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.512127 0.564162 0.000000 0.000000 0.000000 0.000000 1.350790 0.370343 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.320869 0.000000 0.000000 0.000000 0.000000 0.000000 -1.591001 -0.452171 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.098196 0.000000 0.000000 0.000000 0.989488 0.000000 0.000000 0.000000 1.321020 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.923846 0.000000 0.000000 0.368038 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.124676 1.407188 0.000000 0.000000 0.000000 0.445713 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.576479 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.155702 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.391074 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 49 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 7 13 15 20 24 31 35 38 41 43 43 46 47 47 48 49 49 49 49 49 Column indices: 2 3 5 10 13 17 18 6 13 14 15 16 19 18 19 4 5 11 16 18 5 7 8 18 6 8 11 14 15 16 17 8 9 14 15 9 15 16 11 15 19 15 18 12 13 17 19 17 17 Off-diagonal values: -1.456013 0.651144 -0.520046 -0.619674 2.178938 0.173522 0.434634 -0.695670 -2.334899 0.444851 -0.359604 -0.185416 0.682920 2.100087 -0.351990 -0.907384 0.789159 -0.062826 -0.563137 -0.975849 -1.040399 -1.092157 -0.242459 -0.136075 -0.747679 0.912339 1.559659 -2.770091 0.589146 1.551264 0.038130 0.512127 0.564162 1.350790 0.370343 -1.320869 -1.591001 -0.452171 0.098196 0.989488 1.321020 -0.923846 0.368038 1.124676 1.407188 0.445713 -0.576479 -0.155702 0.391074 . - o x - o - - - - o - - x - - - x x - | . - - - - o - - - - - - o x o o - - x | | . - - - - - - - - - - - - - - - x o | | | . o x - - - - - o - - - - o - o - | | | | . o - o o - - - - - - - - - o - | | | | | . o - x - - x - - o x x x - - | | | | | | . - x x - - - - x x - - - - | | | | | | | . - o - - - - - o o - - - | | | | | | | | . - - x - - - x - - - x | | | | | | | | | . - - - - - o - - x - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . x x - - - x - - | | | | | | | | | | | | . - - - - - - o | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - o - - | | | | | | | | | | | | | | | . - x - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 4.041273e-16 The error in solving: 3.015027e-16 The error in solving: 2.001558e-16 The error in solving: 3.597534e-16 The error in solving: 3.122502e-17 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a standard normal distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.304351 -0.270477 -1.030313 0.000000 0.731304 0.134484 -1.488570 -0.275229 0.000000 0.000000 -1.302772 0.000000 0.000000 0.878455 0.000000 0.447015 0.100303 1.571706 0.000000 0.000000 -0.558954 0.000000 0.000000 -0.709192 0.000000 2.463582 0.000000 0.081204 -1.056195 0.000000 1.560047 1.506909 0.000000 0.000000 0.000000 -0.673641 0.000000 0.802806 0.000000 0.000000 0.000000 0.000000 0.000000 1.438733 0.000000 0.000000 0.000000 -0.518454 0.599821 -0.171863 -1.436104 -0.095225 0.000000 0.000000 -0.519979 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.538165 -0.546053 0.475933 0.000000 0.791235 0.000000 1.038244 -0.082287 0.000000 0.130510 -0.333925 -0.003684 1.103906 0.615853 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.391201 0.000000 -0.316295 0.358178 0.000000 0.000000 0.000000 0.000000 0.000000 0.442682 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.566905 1.278425 -0.052872 1.366570 0.000000 0.000000 0.014194 0.000000 -0.799267 -0.316171 0.000000 0.000000 0.000000 2.160535 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.261624 0.340288 1.314595 0.000000 0.000000 0.000000 0.433197 0.000000 -0.133032 0.369619 0.590894 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.602362 -0.346703 0.000000 0.000000 0.616526 0.000000 0.000000 0.000000 0.000000 0.015181 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.428210 0.000000 -0.426302 0.000000 0.000000 -0.897967 0.000000 0.000000 0.000000 -0.039741 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.220862 0.000000 0.000000 0.000000 -0.099375 0.000000 0.000000 0.000000 -0.752443 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.561883 0.407752 0.195409 0.000000 0.000000 -1.146366 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.775572 0.000000 1.371611 1.187697 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.612018 0.000000 0.000000 0.000000 0.000000 0.000000 -1.988276 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.473290 0.000000 -1.592584 2.053741 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.658563 -0.282109 0.000000 0.516525 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.152267 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.082725 1.074631 0.094226 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.539339 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 89 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 12 21 28 39 43 51 58 62 66 69 73 76 78 81 84 85 88 89 89 89 Column indices: 2 3 4 6 7 8 9 12 15 17 18 19 2 5 7 9 10 12 13 17 19 5 9 10 11 12 13 16 5 6 7 9 11 12 14 15 16 17 18 6 8 9 15 6 7 8 9 12 14 15 19 8 9 10 14 16 17 18 9 10 13 18 9 11 14 18 11 15 19 11 12 13 16 13 15 16 13 19 16 18 19 16 17 19 16 17 18 19 18 Off-diagonal values: 0.304351 -0.270477 -1.030313 0.731304 0.134484 -1.488570 -0.275229 -1.302772 0.878455 0.447015 0.100303 1.571706 -0.558954 -0.709192 2.463582 0.081204 -1.056195 1.560047 1.506909 -0.673641 0.802806 1.438733 -0.518454 0.599821 -0.171863 -1.436104 -0.095225 -0.519979 -0.538165 -0.546053 0.475933 0.791235 1.038244 -0.082287 0.130510 -0.333925 -0.003684 1.103906 0.615853 1.391201 -0.316295 0.358178 0.442682 0.566905 1.278425 -0.052872 1.366570 0.014194 -0.799267 -0.316171 2.160535 2.261624 0.340288 1.314595 0.433197 -0.133032 0.369619 0.590894 -0.602362 -0.346703 0.616526 0.015181 0.428210 -0.426302 -0.897967 -0.039741 -0.220862 -0.099375 -0.752443 0.561883 0.407752 0.195409 -1.146366 0.775572 1.371611 1.187697 -0.612018 -1.988276 0.473290 -1.592584 2.053741 -0.658563 -0.282109 0.516525 1.152267 1.082725 1.074631 0.094226 0.539339 . - x o o - x x o o - - o - - x - x x x | . o - - o - x - x o - x x - - - o - x | | . - - x - - - o x o o o - - o - - - | | | . - o o x - x - x o - x o o x x - | | | | . - x - o x - - - - - x - - - - | | | | | . x x o x - - x - o o - - - x | | | | | | . - x x x - - - x - o x x - | | | | | | | . - o o - - x - - - - x - | | | | | | | | . x - o - - o - - - o - | | | | | | | | | . - o - - - o - - - o | | | | | | | | | | . x x x - - o - - - | | | | | | | | | | | . - x - x x - - - | | | | | | | | | | | | . o - - - - - o | | | | | | | | | | | | | . - - x - o x | | | | | | | | | | | | | | . - o o - x | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | | . x x x | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.371437e-16 The error in solving: 2.775558e-16 The error in solving: 1.312900e-16 The error in solving: 2.559878e-16 The error in solving: 2.491247e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A upper-triangular matrix using a standard normal distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.599736 -0.107529 1.091314 -0.165287 1.916546 1.173987 0.477503 0.000000 -0.634888 0.000000 -0.138544 0.543449 0.737811 0.000000 0.176519 0.292550 0.000000 -0.101539 0.000000 0.000000 0.000000 0.116831 0.000000 -0.757138 0.955231 2.265025 0.000000 0.000000 0.738151 0.000000 1.300168 -0.353330 0.655658 0.804566 -1.098178 0.000000 0.000000 -2.029867 -1.188284 0.000000 0.000000 0.000000 -0.211257 0.381318 -0.850151 -0.239182 0.000000 0.000000 0.000000 1.112135 0.000000 0.835251 0.384624 1.958711 -0.467794 0.346202 -0.696321 -0.745540 0.000000 0.000000 0.000000 0.000000 0.000000 -0.920592 -0.292753 1.219892 0.582041 0.473452 0.000000 0.000000 1.074064 -1.072831 -0.032699 -3.867626 0.448651 1.096654 0.000000 1.810299 0.239686 0.000000 0.000000 0.000000 0.000000 0.000000 0.960420 -1.479312 0.694609 -1.622875 -0.904797 0.000000 0.034071 -0.935498 0.489064 -0.822511 -2.201884 0.000000 0.363567 0.679541 -0.152120 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.606689 2.544288 -0.567149 0.370870 0.000000 0.805939 0.000000 0.010088 -0.235900 1.212087 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.699285 -2.127894 0.683256 0.000000 -0.858846 -0.348990 1.526699 1.165526 0.000000 0.794924 1.745689 -0.834744 0.113682 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.127429 -0.374789 0.002776 0.155867 1.415114 -0.377469 -1.330850 -0.128133 -0.268648 0.000000 0.000000 -0.883076 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.457296 0.000000 -1.591921 -1.164508 -1.065135 -1.607148 0.000000 -0.532934 1.542267 -2.185155 -0.655124 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.967365 0.632520 0.000000 0.000000 0.190485 0.000000 -0.359933 1.686219 0.000000 1.256366 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.057539 0.000000 1.495074 -1.780880 -0.964872 0.537411 0.000000 -1.279094 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.189387 -0.773833 0.772966 0.575556 1.092547 1.008182 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.099708 -0.320612 -2.503711 0.000000 0.829558 0.394678 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.032503 -0.589001 1.762723 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.117791 -0.060533 0.000000 -0.491526 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.277631 0.297997 0.000000 0.103380 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.766146 -2.092294 0.657410 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.570772 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.796288 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 139 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 14 26 38 51 64 72 83 93 102 108 114 120 125 128 131 134 137 138 139 139 Column indices: 1 2 3 4 5 6 7 9 11 12 13 15 16 18 2 4 5 6 9 11 12 13 14 15 18 19 3 4 5 6 10 12 13 14 15 16 17 18 4 5 6 7 8 11 12 13 14 15 16 18 19 5 6 7 8 9 11 12 13 14 15 17 18 19 10 11 12 13 15 17 18 19 7 8 9 11 12 13 14 16 17 18 19 8 9 10 11 12 13 14 15 16 19 9 11 12 13 14 16 17 18 19 10 11 14 16 17 19 12 14 15 16 17 19 14 15 16 17 18 19 13 14 15 17 18 17 18 19 16 17 19 16 17 19 17 18 19 19 19 Off-diagonal values: 0.599736 -0.107529 1.091314 -0.165287 1.916546 1.173987 0.477503 -0.634888 -0.138544 0.543449 0.737811 0.176519 0.292550 -0.101539 0.116831 -0.757138 0.955231 2.265025 0.738151 1.300168 -0.353330 0.655658 0.804566 -1.098178 -2.029867 -1.188284 -0.211257 0.381318 -0.850151 -0.239182 1.112135 0.835251 0.384624 1.958711 -0.467794 0.346202 -0.696321 -0.745540 -0.920592 -0.292753 1.219892 0.582041 0.473452 1.074064 -1.072831 -0.032699 -3.867626 0.448651 1.096654 1.810299 0.239686 0.960420 -1.479312 0.694609 -1.622875 -0.904797 0.034071 -0.935498 0.489064 -0.822511 -2.201884 0.363567 0.679541 -0.152120 0.606689 2.544288 -0.567149 0.370870 0.805939 0.010088 -0.235900 1.212087 0.699285 -2.127894 0.683256 -0.858846 -0.348990 1.526699 1.165526 0.794924 1.745689 -0.834744 0.113682 -1.127429 -0.374789 0.002776 0.155867 1.415114 -0.377469 -1.330850 -0.128133 -0.268648 -0.883076 -1.457296 -1.591921 -1.164508 -1.065135 -1.607148 -0.532934 1.542267 -2.185155 -0.655124 0.967365 0.632520 0.190485 -0.359933 1.686219 1.256366 0.057539 1.495074 -1.780880 -0.964872 0.537411 -1.279094 0.189387 -0.773833 0.772966 0.575556 1.092547 1.008182 1.099708 -0.320612 -2.503711 0.829558 0.394678 -0.032503 -0.589001 1.762723 0.117791 -0.060533 -0.491526 0.277631 0.297997 0.103380 0.766146 -2.092294 0.657410 -0.570772 -0.796288 . x o x o x x x - o - o x x - x x - o - | . x - o x x - - x - x o x x o - - o o | | . o x o o - - - x - x x x o x o o - | | | . o o x x x - - x o o o x x - x x | | | | . x o x o o - x o x o o - x x o | | | | | . - - - - x x o x - x - x o x | | | | | | . x o x - o o x x - x x o x | | | | | | | . o o x x x o o o o - - o | | | | | | | | . o - o o o o - o x o o | | | | | | | | | . x x - - x - o x - x | | | | | | | | | | . - x - x o o x - o | | | | | | | | | | | . - - x o x x x x | | | | | | | | | | | | . x o o - x x - | | | | | | | | | | | | | . - - - o o x | | | | | | | | | | | | | | . - x o - o | | | | | | | | | | | | | | | . x x - x | | | | | | | | | | | | | | | | . x o x | | | | | | | | | | | | | | | | | . - o | | | | | | | | | | | | | | | | | | . o | | | | | | | | | | | | | | | | | | | . The error in solving: 4.017973e-16 The error in solving: 6.853804e-17 The error in solving: 3.188873e-16 The error in solving: 3.353719e-16 The error in solving: 3.692639e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.689170 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.765042 0.000000 0.558172 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.735430 0.077755 0.636798 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.130010 0.155055 0.990993 0.168216 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.892689 0.000000 0.589719 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.669924 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.594032 0.000000 0.128590 0.067774 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.677500 0.000000 0.000000 0.000000 0.000000 0.000000 0.979935 0.000000 0.000000 0.710073 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.577306 0.000000 0.000000 0.000000 0.000000 0.766700 0.957652 0.000000 0.018118 0.148519 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.008860 0.000000 0.541462 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.907118 0.000000 0.208165 0.000000 0.000000 0.350203 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.597457 0.000000 0.000000 0.000000 0.000000 0.719930 0.000000 0.000000 0.116105 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.913794 0.000000 0.007500 0.677610 0.000000 0.000000 0.846903 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.523679 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.518331 0.080682 0.240944 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.717697 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.971670 0.000000 0.000000 0.389400 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.743248 0.000000 0.926996 0.000000 0.000000 0.000000 0.000000 0.871851 0.000000 0.000000 0.000000 0.000000 0.000000 0.995281 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.919641 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.476996 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 45 (max 380) Diagonal entries: 0.000000 0.000000 0.558172 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.710073 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.389400 0.995281 0.000000 0.000000 Row indices: 0 0 1 2 2 5 9 11 12 15 17 22 24 27 30 34 38 40 43 44 45 Column indices: 0 0 1 2 3 0 1 2 3 3 5 2 1 3 4 0 6 0 5 6 8 9 4 6 2 4 7 4 9 12 3 5 6 9 0 7 8 9 1 13 4 6 11 9 16 Off-diagonal values: 0.689170 0.765042 0.735430 0.077755 0.636798 0.130010 0.155055 0.990993 0.168216 0.892689 0.589719 0.669924 0.594032 0.128590 0.067774 0.677500 0.979935 0.577306 0.766700 0.957652 0.018118 0.148519 0.008860 0.541462 0.907118 0.208165 0.350203 0.597457 0.719930 0.116105 0.913794 0.007500 0.677610 0.846903 0.523679 0.518331 0.080682 0.240944 0.717697 0.971670 0.743248 0.926996 0.871851 0.919641 0.476996 . - - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - x | x - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | x x x . - - - - - - - - - - - - - - - x x x x | . - - - - - - - - - - - - - - | | | x | x . - - - - - - - - - - - - - | | x | | | | . - - - - - - - - - - - - | x | x x | | | . - - - - - - - - - - - x | | | | | x | | x - - - - - - - - - - x | | | | x x | x x . - - - - - - - - - | | | | x | x | | | | . - - - - - - - - | | x | x | | x | | | | . - - - - - - - | | | | x | | | | x | | x . - - - - - - | | | x | x x | | x | | | | . - - - - - x | | | | | | x x x | | | | | . - - - - | x | | | | | | | | | | | x | | x - - - | | | | x | x | | | | x | | | | | x - - | | | | | | | | | x | | | | | | | | . - | | | | | | | | | | | | | | | | x | | . The error in solving: 6.206335e-17 The error in solving: 2.785298e-16 The error in solving: 2.789617e-16 The error in solving: 6.943229e-17 The error in solving: 3.156160e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.065506 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.520888 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.226790 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.067732 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.991374 0.000000 0.000000 0.000000 0.000000 0.352357 0.070326 0.000000 0.197700 0.000000 0.035809 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.648012 0.000000 0.000000 0.723054 0.000000 0.000000 0.932106 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.692022 0.000000 0.000000 0.202117 0.367090 0.413756 0.547649 0.650290 0.000000 0.000000 0.106769 0.000000 0.529915 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.500477 0.623928 0.323099 0.000000 0.000000 0.000000 0.000000 0.664956 0.000000 0.217538 0.603024 0.852672 0.187620 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.212617 0.608631 0.886869 0.000000 0.000000 0.509186 0.035008 0.000000 0.000000 0.000000 0.448936 0.991492 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.634521 0.728868 0.000000 0.000000 0.000000 0.419056 0.432610 0.000000 0.219840 0.000000 0.254883 0.904634 0.553334 0.487023 0.000000 0.669099 0.000000 0.000000 0.000000 0.000000 0.634797 0.000000 0.581056 0.000000 0.184766 0.000000 0.000000 0.000000 0.000000 0.000000 0.497369 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.163391 0.801701 0.000000 0.000000 0.000000 0.601981 0.918903 0.000000 0.000000 0.074622 0.542277 0.000000 0.558993 0.000000 0.056499 0.000000 0.000000 0.000000 0.377078 0.923442 0.000000 0.000000 0.996596 0.000000 0.073465 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.544021 0.000000 0.000000 0.875857 0.793164 0.000000 0.110660 0.000000 0.000000 0.564516 0.000000 0.000000 0.057372 0.000000 0.000000 0.749293 0.994326 0.000000 0.000000 0.000000 0.623530 0.484053 0.000000 0.399129 0.000000 0.270043]; Dimension: 20 x 20 Off-diagonal entries: 80 (max 380) Diagonal entries: 0.000000 0.065506 0.000000 0.000000 0.940571 0.890672 0.000000 0.000000 0.000000 0.067732 0.035809 0.000000 0.529915 0.187620 0.000000 0.669099 0.000000 0.000000 0.793164 0.270043 Row indices: 0 0 0 0 1 3 6 9 13 16 17 21 24 31 38 45 54 58 66 72 80 Column indices: 2 1 3 1 2 4 2 3 4 1 3 4 5 2 4 5 1 0 5 6 8 3 6 9 0 3 4 5 6 7 10 1 2 3 8 10 11 12 0 1 2 5 6 10 11 0 1 5 6 8 10 11 12 13 0 2 4 10 2 3 7 8 11 12 14 16 0 1 4 6 14 17 0 3 6 9 10 14 15 17 Off-diagonal values: 0.520888 0.260672 0.743620 0.868283 0.376374 0.546209 0.524082 0.856936 0.715492 0.689972 0.882407 0.661698 0.940074 0.479400 0.861130 0.249031 0.226790 0.991374 0.352357 0.070326 0.197700 0.648012 0.723054 0.932106 0.692022 0.202117 0.367090 0.413756 0.547649 0.650290 0.106769 0.500477 0.623928 0.323099 0.664956 0.217538 0.603024 0.852672 0.212617 0.608631 0.886869 0.509186 0.035008 0.448936 0.991492 0.634521 0.728868 0.419056 0.432610 0.219840 0.254883 0.904634 0.553334 0.487023 0.634797 0.581056 0.184766 0.497369 0.163391 0.801701 0.601981 0.918903 0.074622 0.542277 0.558993 0.056499 0.377078 0.923442 0.996596 0.073465 0.544021 0.875857 0.110660 0.564516 0.057372 0.749293 0.994326 0.623530 0.484053 0.399129 . - - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | x | x x - - - - - - - - - - - - - - - | x x | x x - - - - - - - - - - - - - - | | x x x | . - - - - - - - - - - - - - | x | x x x | . - - - - - - - - - - - - | | x | x x | | . - - - - - - - - - - - | x | | | | | | | x - - - - - - - - - - x | | | | x x | x | x - - - - - - - - - | | | x | | x | | x | . - - - - - - - - x | | x x x x x | | x | x - - - - - - - | x x x | | | | x | x x x x - - - - - - x x x | | x x | | | x x | | . - - - - - x x | | | x x | x | x x x x | x - - - - x | x | x | | | | | x | | | | | . - - - | | x x | | | x x | | x x | x | x . - - x x | | x | x | | | | | | | x | | x x - x | | x | | x | | x x | | | x x | x | x The error in solving: 3.122502e-17 The error in solving: 1.256687e-16 The error in solving: 1.594436e-16 The error in solving: 3.295792e-16 The error in solving: 2.224779e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.750000 [ 0.209587 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.304125 0.419432 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.299750 0.719869 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.849670 0.000000 0.460390 0.950293 0.000000 0.350121 0.523239 0.613715 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 138 (max 380) Diagonal entries: 0.209587 0.419432 0.000000 0.463926 0.988642 0.000000 0.523445 0.000000 0.000000 0.000000 0.730398 0.334120 0.002684 0.496039 0.000000 0.604474 0.019632 0.973072 0.997732 0.000000 Row indices: 0 0 1 3 5 8 13 17 23 30 38 45 56 62 72 81 92 103 113 128 138 Column indices: 0 0 1 0 2 0 2 3 0 1 2 3 4 0 1 3 5 0 1 2 3 5 6 0 1 2 3 4 5 6 1 2 3 4 5 6 7 8 0 1 3 4 7 8 9 0 1 2 3 4 5 6 7 8 9 10 0 1 4 5 6 11 0 1 2 3 4 7 8 9 10 12 0 2 3 4 5 6 7 10 11 0 1 2 6 7 8 9 10 12 13 14 1 2 3 4 6 8 10 11 13 14 15 1 3 5 6 8 9 10 11 15 16 0 1 2 3 4 5 6 7 8 9 10 13 14 15 17 1 2 5 6 9 11 12 14 15 16 Off-diagonal values: 0.304125 0.299750 0.719869 0.574602 0.770507 0.423264 0.308223 0.568422 0.854040 0.068177 0.269292 0.452834 0.917759 0.935115 0.267105 0.513803 0.737942 0.068056 0.988145 0.981000 0.006469 0.986451 0.765178 0.161444 0.853747 0.358488 0.125843 0.461025 0.549056 0.559664 0.781684 0.917480 0.704423 0.778779 0.959973 0.552377 0.990537 0.502099 0.881069 0.654534 0.309383 0.867781 0.828458 0.951618 0.556986 0.065321 0.521230 0.625850 0.167298 0.059206 0.056867 0.813511 0.257503 0.688924 0.607339 0.569347 0.624231 0.372362 0.915936 0.585775 0.609568 0.072550 0.292310 0.524689 0.470471 0.584025 0.343009 0.226334 0.958392 0.546725 0.543018 0.324817 0.893106 0.602550 0.431547 0.576044 0.202247 0.608164 0.653904 0.472434 0.728462 0.800469 0.653077 0.765256 0.953543 0.282120 0.663581 0.982896 0.093665 0.550909 0.229699 0.089934 0.173619 0.421886 0.589820 0.248772 0.489977 0.087354 0.840620 0.216695 0.618854 0.220470 0.786436 0.556199 0.294963 0.075098 0.265740 0.417775 0.483825 0.058317 0.340484 0.883604 0.723106 0.714166 0.770861 0.782467 0.179859 0.097724 0.724026 0.400232 0.510483 0.669736 0.901422 0.470723 0.099514 0.053060 0.452918 0.974708 0.294728 0.271701 0.503749 0.282593 0.849670 0.460390 0.950293 0.350121 0.523239 0.613715 x - - - - - - - - - - - - - - - - - - - x x - - - - - - - - - - - - - - - - - - x x . - - - - - - - - - - - - - - - - - x | x x - - - - - - - - - - - - - - - - x | x x x - - - - - - - - - - - - - - - x x x x x . - - - - - - - - - - - - - - x x | x | x x - - - - - - - - - - - - - x x x x | x x . - - - - - - - - - - - - x x x x x x x | . - - - - - - - - - - - | x x x x x x x x . - - - - - - - - - - x x | x x | | x x x x - - - - - - - - - x x x x x x x x x x x x - - - - - - - - x x | | x x x | | | | x x - - - - - - - x x x x x | | x x x x | x x - - - - - - x | x x x x x x | | x x | | . - - - - - x x x | | | x x x x x | x x x x - - - - | x x x x | x | x | x x | x x x x - - - | x | x | x x | x x x x | | | x x x - - x x x x x x x x x x x | | x x x | x x - | x x | | x x | | x | x x | x x x | | . The error in solving: 1.241267e-16 The error in solving: 2.573946e-16 The error in solving: 4.710277e-16 The error in solving: 3.695287e-16 The error in solving: 2.803605e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.521384 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.773390 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.360743 0.000000 0.335657 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.144022 0.000000 0.000000 0.809287 0.000000 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0.000000 0.762868]; Dimension: 20 x 20 Off-diagonal entries: 55 (max 380) Diagonal entries: 0.521384 0.773390 0.335657 0.809287 0.731918 0.866456 0.498537 0.188280 0.406960 0.376822 0.120369 0.937842 0.823340 0.462802 0.622333 0.328397 0.570551 0.744277 0.741204 0.762868 Row indices: 0 0 0 1 2 3 4 5 8 10 12 19 25 27 30 35 38 42 44 50 55 Column indices: 0 0 2 4 5 0 3 5 0 2 1 6 2 3 5 6 7 8 9 2 4 5 6 8 9 5 9 2 3 7 2 3 5 11 13 2 8 10 0 4 5 14 4 14 1 5 7 8 14 15 0 3 6 8 11 Off-diagonal values: 0.360743 0.144022 0.493083 0.902280 0.513957 0.662447 0.139318 0.331507 0.157920 0.803827 0.970467 0.913579 0.255776 0.926662 0.213676 0.853784 0.506802 0.439932 0.204984 0.841401 0.545829 0.946338 0.496087 0.022096 0.469987 0.237167 0.038284 0.061077 0.443088 0.601066 0.613971 0.953709 0.664838 0.305121 0.701071 0.432719 0.116859 0.728996 0.259865 0.047728 0.728177 0.960180 0.219024 0.280645 0.024404 0.413577 0.010763 0.556547 0.833395 0.480251 0.156274 0.502418 0.657372 0.716180 0.462445 x - - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - x | x - - - - - - - - - - - - - - - - - x | | x - - - - - - - - - - - - - - - - | | x | x - - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - x | | x | x | x - - - - - - - - - - - - x | x | | | | | x - - - - - - - - - - - | x | | | | x | | x - - - - - - - - - - | | x x | x x x x x x - - - - - - - - - | | x | x x x | x x | x - - - - - - - - | | | | | x | | | x | | x - - - - - - - | | x x | | | x | | | | | x - - - - - - | | x x | x | | | | | x | x x - - - - - | | x | | | | | x | x | | | | x - - - - x | | | x x | | | | | | | | x | x - - - | | | | x | | | | | | | | | x | | x - - | x | | | x | x x | | | | | x x | | x - x | | x | | x | x | | x | | | | | | | x The error in solving: 1.243205e-16 The error in solving: 3.204687e-16 The error in solving: 6.359601e-17 The error in solving: 1.712463e-16 The error in solving: 2.483761e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.156683 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.478417 0.500608 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.579572 0.211642 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.977646 0.312028 0.000000 0.109859 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.148354 0.893146 0.412768 0.000000 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0.000000 0.182783 0.000000 0.652537 0.000000 0.000000 0.000000 0.270718 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.065988 0.000000 0.340532 0.000000 0.000000 0.000000 0.515140 0.000000 0.662805 0.000000 0.676084 0.000000 0.382675 0.000000 0.483166 0.000000 0.000000 0.000000 0.323665 0.966710 0.984140 0.000000 0.000000 0.927389 0.000000 0.596901 0.377870 0.152746 0.425921 0.771699 0.736760 0.000000 0.000000 0.000000 0.000000 0.813907 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.336587 0.000000 0.687038 0.000000 0.000000 0.794245 0.146041 0.061674 0.009408 0.000000 0.606241 0.097699 0.629533 0.106158 0.847583 0.000000 0.000000 0.000000 0.667887 0.794879 0.000000 0.000000 0.330411 0.000000 0.685636 0.685402 0.000000 0.235197 0.120385 0.881444 0.000000 0.000000 0.000000 0.978780 0.000000 0.134204]; Dimension: 20 x 20 Off-diagonal entries: 99 (max 380) Diagonal entries: 0.156683 0.500608 0.211642 0.109859 0.412768 0.741693 0.951063 0.608966 0.966610 0.925027 0.028337 0.516300 0.273316 0.103333 0.209497 0.270718 0.483166 0.813907 0.847583 0.134204 Row indices: 0 0 1 2 4 6 8 12 16 20 27 31 39 44 51 58 64 70 80 90 99 Column indices: 0 1 0 1 2 3 0 1 1 2 4 5 0 2 4 5 0 1 3 4 0 1 3 4 5 6 7 0 3 5 8 1 2 3 4 6 7 8 9 0 2 4 7 11 0 1 5 7 8 10 12 2 5 6 9 10 11 12 1 3 5 7 9 11 2 4 8 10 12 14 0 1 2 5 7 8 9 10 11 12 4 6 9 10 11 12 14 15 16 17 2 3 6 8 9 11 12 13 17 Off-diagonal values: 0.478417 0.579572 0.977646 0.312028 0.148354 0.893146 0.065192 0.330899 0.968328 0.099233 0.430595 0.985404 0.134647 0.449010 0.289041 0.802956 0.894354 0.610345 0.957255 0.043826 0.510446 0.268806 0.347791 0.084588 0.464220 0.236740 0.815859 0.784347 0.920710 0.156565 0.023817 0.937384 0.830714 0.502839 0.206109 0.961587 0.075461 0.808163 0.691839 0.649925 0.287293 0.519248 0.330766 0.180192 0.894650 0.201533 0.993503 0.312704 0.072593 0.541202 0.899837 0.437277 0.562051 0.957582 0.087612 0.240119 0.275780 0.828411 0.236614 0.658660 0.930511 0.921514 0.182783 0.652537 0.065988 0.340532 0.515140 0.662805 0.676084 0.382675 0.323665 0.966710 0.984140 0.927389 0.596901 0.377870 0.152746 0.425921 0.771699 0.736760 0.336587 0.687038 0.794245 0.146041 0.061674 0.009408 0.606241 0.097699 0.629533 0.106158 0.667887 0.794879 0.330411 0.685636 0.685402 0.235197 0.120385 0.881444 0.978780 x - - - - - - - - - - - - - - - - - - - x x - - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - x x | x - - - - - - - - - - - - - - - - | | x x x - - - - - - - - - - - - - - - x x | | | x - - - - - - - - - - - - - - | x x | x x x - - - - - - - - - - - - - x | x | x x | x - - - - - - - - - - - - x x | x x | | | x - - - - - - - - - - - x x | x x x x x | x - - - - - - - - - - x | | x | x | | x | x - - - - - - - - - | x x x x | x x x x | x - - - - - - - - x | x | x | | x | | | x x - - - - - - - x x | | | x | x x | x | x x - - - - - - | | x | | x x | | x x x x | x - - - - - | x | x | x | x | x | x | | | x - - - - | | x | x | | | x | x | x | x | x - - - x x x | | x | x x x x x x | | | | x - - | | | | x | x | | x x x x | x x x x x - | | x x | | x | x x | x x x | | | x | x The error in solving: 2.560172e-16 The error in solving: 4.712321e-16 The error in solving: 2.618686e-16 The error in solving: 3.250975e-16 The error in solving: 3.192080e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.277015 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.218837 0.499909 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.537316 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.203562 0.412046 0.786781 0.955538 0.983394 0.241186 0.525564 0.092876 x - - - - - - - - - - - - - - - - - - - x x - - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | x x x - - - - - - - - - - - - - - - - | x x | x - - - - - - - - - - - - - - - x x | x | x - - - - - - - - - - - - - - | x x | x x x - - - - - - - - - - - - - x | x x x | x x - - - - - - - - - - - - | x | x | x | x x - - - - - - - - - - - | x x x | x x x x x - - - - - - - - - - x x x x x x x x x | x - - - - - - - - - x x x x | x x x x x x x - - - - - - - - x x x x x x x x x x | x x - - - - - - - x x x | x | | x x | x | x x - - - - - - | x x x x x | x | | | x x x x - - - - - | x x | x x x x x x x | x x x x - - - - x x x x | | x x x x x x x x x x x - - - x | x x | x x | x x x x | x x x | x - - x x x | | | x x x x x | x | x x | x x - x | x x x | x x x | x x x x x | x x x x The error in solving: 2.838169e-16 The error in solving: 1.778578e-16 The error in solving: 3.046799e-16 The error in solving: 1.279469e-16 The error in solving: 2.127425e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000024 0.918324 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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| | | | | | . - - - - - - - - - - - x x x | | | x | | . - - - - - - - - - - | | | | | | | | x | . - - - - - - - - - x | | | x | | | | | | . - - - - - - - - x | | | | | | | | | | x . - - - - - - - x | | | | | | | | x | | x . - - - - - - | | | | | | | | | | x x | | . - - - - - | | | x | x | | | x | | | x x . - - - - x | | | x | | | | | | | x x | x . - - - | | | | | | x | | | | | | x | | | . - - | | | | | x | | | | | x | | | | | | . - | x | | | | | x | | | | | | | | | | x . The error in solving: 1.271987e-16 The error in solving: 3.868394e-16 The error in solving: 2.498002e-16 The error in solving: 8.326673e-17 The error in solving: 3.331437e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.456344 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.700314 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.440524 0.993996 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.141024 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.333530 0.477010 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.997810 0.246401 0.000000 0.687846 0.355582 0.731635 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.361423 0.000000 0.000000 0.973155 0.000000 0.458727 0.872555 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.140495 0.636949 0.000000 0.000000 0.913157 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.827109 0.000000 0.512064 0.000000 0.651245 0.007418 0.000000 0.000000 0.101650 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.359085 0.000000 0.039364 0.478819 0.000000 0.000000 0.613816 0.143484 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.618686 0.000000 0.857239 0.201390 0.340920 0.613149 0.424546 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.935234 0.000000 0.482190 0.000000 0.000000 0.000000 0.292291 0.989539 0.262642 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.522691 0.712154 0.111106 0.000000 0.097957 0.868612 0.207561 0.828186 0.000000 0.229026 0.182651 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.127999 0.000000 0.000000 0.432115 0.000000 0.000000 0.000000 0.000000 0.342105 0.173814 0.536823 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.590600 0.322166 0.167746 0.073217 0.000000 0.600803 0.000000 0.000000 0.000000 0.000000 0.294508 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.524779 0.582489 0.565481 0.706387 0.677192 0.000000 0.000000 0.428979 0.225576 0.282191 0.419745 0.000000 0.000000 0.025030 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.724347 0.000000 0.093667 0.827855 0.000000 0.609847 0.000000 0.000000 0.000000 0.000000 0.736511 0.502904 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.074537 0.716342 0.636346 0.581108 0.000000 0.654092 0.000000 0.000000 0.000000 0.000000 0.278408 0.000000 0.000000 0.577264 0.000000 0.545425 0.000000 0.000000 0.000000 0.000000 0.387101 0.026706 0.723876 0.331540 0.708485 0.125685 0.000000 0.000000 0.000000 0.880168 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 91 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 2 4 5 7 12 16 19 24 29 35 40 49 54 60 70 76 82 91 Column indices: 0 0 0 1 0 3 4 0 1 3 4 5 0 3 5 6 1 2 5 0 2 4 5 8 1 3 4 7 8 2 4 5 6 7 8 2 4 8 9 10 0 1 2 4 5 6 7 9 10 1 4 9 10 11 3 4 5 6 8 13 0 1 2 3 4 7 8 9 10 13 4 6 7 9 14 15 7 8 9 10 12 17 0 2 7 8 9 10 11 12 16 Off-diagonal values: 0.456344 0.700314 0.440524 0.993996 0.141024 0.333530 0.477010 0.997810 0.246401 0.687846 0.355582 0.731635 0.361423 0.973155 0.458727 0.872555 0.140495 0.636949 0.913157 0.827109 0.512064 0.651245 0.007418 0.101650 0.359085 0.039364 0.478819 0.613816 0.143484 0.618686 0.857239 0.201390 0.340920 0.613149 0.424546 0.935234 0.482190 0.292291 0.989539 0.262642 0.522691 0.712154 0.111106 0.097957 0.868612 0.207561 0.828186 0.229026 0.182651 0.127999 0.432115 0.342105 0.173814 0.536823 0.590600 0.322166 0.167746 0.073217 0.600803 0.294508 0.524779 0.582489 0.565481 0.706387 0.677192 0.428979 0.225576 0.282191 0.419745 0.025030 0.724347 0.093667 0.827855 0.609847 0.736511 0.502904 0.074537 0.716342 0.636346 0.581108 0.654092 0.278408 0.577264 0.545425 0.387101 0.026706 0.723876 0.331540 0.708485 0.125685 0.880168 . - - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - x | . - - - - - - - - - - - - - - - - - x x | . - - - - - - - - - - - - - - - - x | | | . - - - - - - - - - - - - - - - | | | x x . - - - - - - - - - - - - - - x x | x x x . - - - - - - - - - - - - - x | | x | x x . - - - - - - - - - - - - | x x | | x | | . - - - - - - - - - - - x | x | x x | | x . - - - - - - - - - - | x | x x | | x x | . - - - - - - - - - | | x | x x x x x | | . - - - - - - - - | | x | x | | | x x x | . - - - - - - - x x x | x x x x | x x | | . - - - - - - | x | | x | | | | x x x | | . - - - - - | | | x x x x | x | | | | x | . - - - - x x x x x | | x x x x | | x | | . - - - | | | | x | x x | x | | | | x x | . - - | | | | | | | x x x x | x | | | | x . - x | x | | | | x x x x x x | | | x | | . The error in solving: 1.570092e-16 The error in solving: 2.559878e-16 The error in solving: 1.738882e-16 The error in solving: 3.816392e-16 The error in solving: 2.006289e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.220862 0.256294 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.872116 0.000000 0.723286 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.370440 0.937336 0.000000 0.441444 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.640631 0.237405 0.000000 0.168840 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.293876 0.000000 0.198495 0.885619 0.562498 0.127262 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.406123 0.462660 0.398319 0.408834 0.308649 0.000000 0.902710 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.482335 0.188336 0.328389 0.000000 0.000000 0.081656 0.609811 0.025893 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.671931 0.000000 0.000000 0.500147 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.316364 0.662730 0.012837 0.773909 0.170019 0.000000 0.574542 0.651318 0.549955 0.931917 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.323772 0.715827 0.381582 0.000000 0.348214 0.000000 0.594968 0.358264 0.000000 0.793060 0.870710 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.761480 0.000000 0.488365 0.717798 0.201677 0.876542 0.677819 0.000000 0.063191 0.928379 0.000000 0.008354 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.249443 0.844154 0.563888 0.627495 0.000000 0.660058 0.616696 0.000000 0.809324 0.557678 0.000000 0.683900 0.127233 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.550120 0.711354 0.108946 0.071732 0.423296 0.814137 0.064659 0.733012 0.875732 0.000000 0.220036 0.936324 0.367155 0.246340 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.774851 0.646622 0.000000 0.177160 0.778461 0.989144 0.000000 0.958056 0.854058 0.929156 0.778445 0.000000 0.512477 0.898039 0.167937 0.000000 0.000000 0.000000 0.000000 0.000000 0.284848 0.321686 0.427520 0.921510 0.000582 0.555484 0.087280 0.098655 0.000000 0.076298 0.747149 0.835563 0.913247 0.000000 0.269571 0.000000 0.000000 0.000000 0.000000 0.000000 0.449093 0.000000 0.834732 0.936050 0.000000 0.009009 0.579380 0.892778 0.846839 0.244445 0.009726 0.724627 0.000000 0.000000 0.994792 0.316654 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.170538 0.599880 0.465404 0.252195 0.000000 0.138253 0.184035 0.324169 0.685816 0.039949 0.321529 0.213174 0.407342 0.294218 0.457239 0.888432 0.000000 0.000000 0.329041 0.935007 0.795865 0.000000 0.423540 0.000000 0.000000 0.495269 0.533622 0.328850 0.722635 0.084929 0.762319 0.921915 0.959671 0.035000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 143 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 2 4 7 10 15 21 27 29 38 46 55 65 78 90 103 115 130 143 Column indices: 0 1 0 2 0 1 3 0 1 3 0 2 3 4 5 0 1 2 3 4 6 0 1 2 5 6 7 1 4 0 1 2 3 4 6 7 8 9 0 1 2 4 6 7 9 10 0 2 3 4 5 6 8 9 11 0 1 2 3 5 6 8 9 11 12 0 1 2 3 4 5 6 7 8 10 11 12 13 0 1 3 4 5 7 8 9 10 12 13 14 0 1 2 3 4 5 6 7 9 10 11 12 14 0 2 3 5 6 7 8 9 10 11 14 15 2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 0 1 2 4 7 8 9 10 11 12 13 14 15 Off-diagonal values: 0.220862 0.256294 0.872116 0.723286 0.370440 0.937336 0.441444 0.640631 0.237405 0.168840 0.293876 0.198495 0.885619 0.562498 0.127262 0.406123 0.462660 0.398319 0.408834 0.308649 0.902710 0.482335 0.188336 0.328389 0.081656 0.609811 0.025893 0.671931 0.500147 0.316364 0.662730 0.012837 0.773909 0.170019 0.574542 0.651318 0.549955 0.931917 0.323772 0.715827 0.381582 0.348214 0.594968 0.358264 0.793060 0.870710 0.761480 0.488365 0.717798 0.201677 0.876542 0.677819 0.063191 0.928379 0.008354 0.249443 0.844154 0.563888 0.627495 0.660058 0.616696 0.809324 0.557678 0.683900 0.127233 0.550120 0.711354 0.108946 0.071732 0.423296 0.814137 0.064659 0.733012 0.875732 0.220036 0.936324 0.367155 0.246340 0.774851 0.646622 0.177160 0.778461 0.989144 0.958056 0.854058 0.929156 0.778445 0.512477 0.898039 0.167937 0.284848 0.321686 0.427520 0.921510 0.000582 0.555484 0.087280 0.098655 0.076298 0.747149 0.835563 0.913247 0.269571 0.449093 0.834732 0.936050 0.009009 0.579380 0.892778 0.846839 0.244445 0.009726 0.724627 0.994792 0.316654 0.170538 0.599880 0.465404 0.252195 0.138253 0.184035 0.324169 0.685816 0.039949 0.321529 0.213174 0.407342 0.294218 0.457239 0.888432 0.329041 0.935007 0.795865 0.423540 0.495269 0.533622 0.328850 0.722635 0.084929 0.762319 0.921915 0.959671 0.035000 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - x x . - - - - - - - - - - - - - - - - - x | x . - - - - - - - - - - - - - - - - x x | x . - - - - - - - - - - - - - - - x x | x | . - - - - - - - - - - - - - - x | x x x x . - - - - - - - - - - - - - x x x x x | x . - - - - - - - - - - - - x x x | | x x x . - - - - - - - - - - - | x | | x | | | | . - - - - - - - - - - x x x x x | x x x x . - - - - - - - - - x x x | x | x x | x x . - - - - - - - - x | x x x x x | x x | x . - - - - - - - x x x x | x x | x x | x x . - - - - - - x x x x x x x x x | x x x x . - - - - - x x | x x x | x x x x | x x x . - - - - x x x x x x x x | x x x x | x | . - - - x | x x | x x x x x x x | | x x | . - - | | x x x x | x x x x x x x x x x x . - x x x | x | | x x x x x x x x x | | | . The error in solving: 1.416962e-16 The error in solving: 3.093844e-16 The error in solving: 1.570092e-16 The error in solving: 4.710277e-16 The error in solving: 2.897767e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.250000 [ -0.136777 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.021712 0.000000 0.962044 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.164658 0.000000 0.013344 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.615138 0.000000 0.000000 -0.707801 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.242876 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.796984 0.000000 0.657104 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.939386 0.214444 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.311744 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.345467 0.004417 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.564742 -0.029911 -0.575510 -0.445179 0.000000 0.000000 0.000000 0.473364 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.999156 0.000000 0.000000 0.000000 0.000000 0.000000 0.852824 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.226965 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.225368 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.806811 0.000000 -0.575625 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.250738 0.000000 0.000000 0.000000 0.799841 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.444274 0.071641 0.507712 0.000000 0.000000 -0.729653 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.923824 0.000000 0.000000 0.086387 0.000000 0.402756 0.000000 0.000000 0.000000 0.758582 0.000000 0.000000 0.000000 -0.721557 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.727196 0.000000 0.000000 0.510007 0.000000 0.000000 0.711204 0.000000 -0.358130 0.000000 0.830369 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.794035 0.000000 -0.854449 0.000000 0.000000 0.000000 -0.062936 0.000000 0.000000 -0.491411 0.271052 -0.224719 -0.884946 0.000000 0.000000 0.000000 -0.604718 0.000000 0.000000 0.000000 -0.826082 -0.568829 0.000000 0.000000 0.000000 -0.799532 0.000000 0.000000 0.000000 -0.810876 0.000000 0.000000 0.000000 0.000000 -0.340291 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 53 (max 380) Diagonal entries: -0.136777 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.799841 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 2 4 6 7 9 11 12 14 19 21 23 26 30 35 40 47 53 Column indices: 0 2 0 2 0 3 5 1 3 4 5 0 4 5 2 3 4 5 9 3 9 3 10 0 2 10 1 2 3 6 0 3 5 9 13 5 8 11 13 15 4 6 10 13 14 15 16 0 4 5 9 13 18 Off-diagonal values: -0.021712 0.962044 -0.164658 0.013344 -0.615138 -0.707801 -0.242876 0.796984 0.657104 -0.939386 0.214444 0.311744 0.345467 0.004417 0.564742 -0.029911 -0.575510 -0.445179 0.473364 -0.999156 0.852824 -0.226965 0.225368 -0.806811 -0.575625 0.250738 -0.444274 0.071641 0.507712 -0.729653 -0.923824 0.086387 0.402756 0.758582 -0.721557 0.727196 0.510007 0.711204 -0.358130 0.830369 0.794035 -0.854449 -0.062936 -0.491411 0.271052 -0.224719 -0.884946 -0.604718 -0.826082 -0.568829 -0.799532 -0.810876 -0.340291 o - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - o | x . - - - - - - - - - - - - - - - - o | x | . - - - - - - - - - - - - - - - o | | o | . - - - - - - - - - - - - - - | | | | | o . - - - - - - - - - - - - - | x | x | | | . - - - - - - - - - - - - | | | | o x | | . - - - - - - - - - - - x | | | | | | | | . - - - - - - - - - - | | | | x x | | | | . - - - - - - - - - | | x o o o | | | x | . - - - - - - - - | | | o | | | | | x | | . - - - - - - - | | | o | | | | | | x | | . - - - - - - o | o | | | | | | | x | | | x - - - - - | o x x | | o | | | | | | | | . - - - - o | | x | x | | | x | | | o | | . - - - | | | | | x | | x | | x | o | x | . - - | | | | x | o | | | o | | o x o o | . - o | | | o o | | | o | | | o | | | | o . The error in solving: 2.081668e-16 The error in solving: 2.603704e-16 The error in solving: 3.383022e-16 The error in solving: 1.977585e-16 The error in solving: 2.543841e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.668147 -0.166186 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.978579 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.668709 0.000000 0.174527 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.074994 0.000000 0.538450 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.664161 0.000000 0.000000 -0.492426 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.033039 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.599156 -0.739416 0.183761 -0.962742 -0.589272 0.000000 0.000000 0.919818 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.537569 0.000000 0.000000 -0.849864 0.000000 0.000000 0.903376 0.508092 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.060384 0.000000 0.000000 0.000000 -0.841531 0.000000 -0.827491 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.006195 -0.944519 0.000000 0.443293 0.000000 -0.966293 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.536896 -0.937574 0.000000 0.000000 0.545825 0.000000 0.000000 -0.107652 0.000000 0.329216 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.427606 -0.578358 0.000000 0.117182 0.000000 -0.214025 0.000000 0.000000 0.500300 0.000000 -0.466854 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.990686 0.831421 -0.119355 0.000000 0.536377 -0.599655 -0.362514 -0.196832 0.000000 0.000000 0.000000 -0.816693 0.000000 0.884874 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.402572 -0.189743 0.000000 0.000000 0.000000 0.000000 -0.971701 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.980207 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.142048 -0.897605 0.000000 0.000000 0.000000 -0.775660 0.743377 0.720611 0.000000 -0.701675 0.644487 -0.387868 0.243336 0.000000 0.000000 0.000000 0.000000 0.000000 0.980584 0.000000 0.250058 0.949273 0.000000 -0.379018 0.000000 0.000000 0.000000 0.000000 0.665279 0.377867 -0.490757 0.000000 -0.283611 -0.579987 0.000000 0.000000 0.000000 0.000000 -0.519200 0.000000 0.083516 0.000000 0.000000 -0.005628 0.000000 0.000000 0.000000 0.000000 0.415479 -0.851141 0.961775 -0.966190 -0.338317 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.820722 0.000000 0.000000 0.000000 -0.017242 0.000000 0.804601 0.000000 0.000000 0.701783 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.529873 -0.776378 0.000000 0.000000 0.271977 0.271709 0.000000 0.000000 0.000000 -0.308071 0.000000 0.000000 0.379094 0.823018 0.491388 0.000000 0.000000 0.464940 0.584258 0.000000]; 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The error in solving: 3.632165e-16 The error in solving: 2.562698e-16 The error in solving: 2.484715e-16 The error in solving: 1.279469e-16 The error in solving: 2.721526e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.750000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.876250 -0.493377 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.501687 -0.432549 -0.464923 0.006216 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.715886 0.704534 -0.297362 -0.333362 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.673776 -0.304549 -0.740365 0.000000 0.171423 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.237069 0.597640 0.005790 -0.320455 0.000000 -0.807383 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.972295 0.710033 -0.200854 0.000000 0.000000 -0.280136 0.000000 0.462789 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.518465 -0.351514 -0.591537 -0.107014 0.408003 0.092211 -0.819428 0.152598 0.412426 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.354875 -0.386259 0.000000 -0.683427 0.000000 0.000000 0.000000 0.000000 -0.175197 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.542266 0.702634 -0.170742 0.143673 -0.196334 0.394569 0.000000 0.914171 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.428947 0.000000 -0.609676 0.149807 -0.316179 0.708931 0.567874 0.000000 -0.138651 0.151798 -0.905660 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.346503 0.000000 0.000000 -0.975160 0.315584 -0.851500 0.636324 -0.740060 -0.432690 0.469283 0.899692 0.000000 -0.991281 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.828256 -0.105734 0.000000 0.269288 -0.449801 0.000000 0.000000 -0.715665 -0.668178 0.000000 -0.734514 0.842036 0.927412 0.534259 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.500423 0.846384 -0.938527 -0.719423 0.512947 -0.153758 0.484790 0.000000 0.276610 0.730114 0.000000 0.000000 -0.162442 0.000000 0.027879 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.855150 0.694257 -0.407688 -0.168482 0.000000 0.716256 -0.995111 -0.620332 -0.193994 0.000000 0.777038 -0.605115 0.011764 -0.622372 0.000000 0.000000 0.000000 0.000000 0.000000 0.908748 -0.342881 -0.972249 0.082196 0.000000 0.095086 0.549243 -0.267864 0.927646 -0.500644 0.878203 -0.936886 -0.493865 0.197592 0.731660 0.631793 -0.462306 0.000000 0.000000 0.000000 0.648187 -0.292671 0.729530 0.630499 0.008926 -0.382423 0.461457 -0.956559 -0.556830 -0.625122 -0.734817 0.976427 -0.601657 0.000000 -0.027956 0.000000 -0.493783 0.000000 0.000000 0.000000 0.000000 0.434314 0.333244 0.000000 0.077751 0.764403 0.336387 -0.639988 -0.696243 0.000000 0.000000 -0.076891 -0.843725 0.937709 0.000000 -0.810465 0.626345 -0.304398 -0.514107 0.000000 0.127940 -0.252074 -0.315597 0.000000 0.787406 -0.014040 -0.081456 -0.274109 -0.794291 -0.507310 0.976009 -0.792317 0.899816 0.000000 0.000000 -0.249982 0.296213 -0.457945 0.250224 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 148 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.006216 -0.333362 0.000000 0.000000 0.462789 0.412426 0.000000 0.000000 0.000000 -0.991281 0.534259 0.027879 0.000000 -0.462306 0.000000 -0.514107 0.000000 Row indices: 0 0 0 2 5 8 12 17 21 29 33 40 49 58 67 77 89 104 119 132 148 Column indices: 0 1 0 1 2 1 2 3 0 1 2 4 0 1 2 3 5 0 1 2 5 0 1 2 3 4 5 6 7 0 1 3 8 2 3 4 5 6 7 9 0 2 3 4 5 6 8 9 10 0 3 4 5 6 7 8 9 10 0 1 3 4 7 8 10 11 12 0 1 2 3 4 5 6 8 9 12 1 2 3 4 6 7 8 9 11 12 13 14 0 1 2 3 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 8 9 10 11 12 14 16 1 2 4 5 6 7 8 11 12 13 15 16 17 0 1 2 4 5 6 7 8 9 10 11 12 15 16 17 18 Off-diagonal values: -0.876250 -0.493377 0.501687 -0.432549 -0.464923 -0.715886 0.704534 -0.297362 0.673776 -0.304549 -0.740365 0.171423 -0.237069 0.597640 0.005790 -0.320455 -0.807383 -0.972295 0.710033 -0.200854 -0.280136 0.518465 -0.351514 -0.591537 -0.107014 0.408003 0.092211 -0.819428 0.152598 0.354875 -0.386259 -0.683427 -0.175197 0.542266 0.702634 -0.170742 0.143673 -0.196334 0.394569 0.914171 -0.428947 -0.609676 0.149807 -0.316179 0.708931 0.567874 -0.138651 0.151798 -0.905660 -0.346503 -0.975160 0.315584 -0.851500 0.636324 -0.740060 -0.432690 0.469283 0.899692 0.828256 -0.105734 0.269288 -0.449801 -0.715665 -0.668178 -0.734514 0.842036 0.927412 -0.500423 0.846384 -0.938527 -0.719423 0.512947 -0.153758 0.484790 0.276610 0.730114 -0.162442 0.855150 0.694257 -0.407688 -0.168482 0.716256 -0.995111 -0.620332 -0.193994 0.777038 -0.605115 0.011764 -0.622372 0.908748 -0.342881 -0.972249 0.082196 0.095086 0.549243 -0.267864 0.927646 -0.500644 0.878203 -0.936886 -0.493865 0.197592 0.731660 0.631793 0.648187 -0.292671 0.729530 0.630499 0.008926 -0.382423 0.461457 -0.956559 -0.556830 -0.625122 -0.734817 0.976427 -0.601657 -0.027956 -0.493783 0.434314 0.333244 0.077751 0.764403 0.336387 -0.639988 -0.696243 -0.076891 -0.843725 0.937709 -0.810465 0.626345 -0.304398 0.127940 -0.252074 -0.315597 0.787406 -0.014040 -0.081456 -0.274109 -0.794291 -0.507310 0.976009 -0.792317 0.899816 -0.249982 0.296213 -0.457945 0.250224 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - o o . - - - - - - - - - - - - - - - - - x o o x - - - - - - - - - - - - - - - - | o x o o - - - - - - - - - - - - - - - x o o | x . - - - - - - - - - - - - - - o x x o | o . - - - - - - - - - - - - - o x o | | o | x - - - - - - - - - - - - x o o o x x o x x - - - - - - - - - - - x o | o | | | | o . - - - - - - - - - - | | x x o x o x | x . - - - - - - - - - o | o x o x x | o x o . - - - - - - - - o | | o x o x o o x x | o - - - - - - - x o | x o | | o o | o x x x - - - - - - o x o o x o x | x x | | o | x - - - - - | x x o o | x o o o | x o x o . - - - - x o o x | x x o x o x o o x x x o - - - x o x x x o x o o o o x o | o | o . - - | x x | x x x o o | | o o x | o x o o - x o o | x o o o o o x o x | | o x o x . The error in solving: 3.331076e-16 The error in solving: 2.343097e-16 The error in solving: 7.972182e-17 The error in solving: 2.501854e-16 The error in solving: 1.600465e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.250000 [ -0.535984 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.391401 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.411225 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.688700 0.975414 0.264866 0.000000 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- - - - - - - - - - - - | | | | | o o - - - - - - - - - - - - - | | | | o | | x - - - - - - - - - - - - | o | | | x | | x - - - - - - - - - - - | | | x | | o | x x - - - - - - - - - - | | | | | | | | | | o - - - - - - - - - | | | x | | | | | | | x - - - - - - - - | | x | | | | | | | o | o - - - - - - - | | | | | | | | | | | | | o - - - - - - | | o | o | | x | | | | o | x - - - - - x | | | | | x | x | x | x | | x - - - - | | | | | | | | x o | | | o | | o - - - | | | o o o | | x | | | | | | | | x - - | | | | | | | | | | x | | | | | | | o - | | x | | | o | | | | | | | | | | | | o The error in solving: 2.355139e-16 The error in solving: 2.558938e-16 The error in solving: 1.110765e-16 The error in solving: 8.326673e-17 The error in solving: 2.289835e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.500000 [ 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Column indices: 0 1 1 2 0 4 0 2 5 6 1 2 3 6 7 0 1 3 6 7 8 1 5 6 8 4 8 0 1 3 4 5 8 10 1 6 7 8 12 0 1 3 4 5 9 10 0 2 3 4 6 8 10 14 1 4 6 7 8 11 12 13 14 6 8 9 10 12 14 16 2 3 4 6 8 10 11 13 14 15 16 1 5 7 8 10 11 12 15 16 18 Off-diagonal values: 0.948745 -0.761936 -0.562935 0.737515 -0.562886 0.098128 0.872100 -0.703159 -0.676499 0.809285 0.657249 -0.490215 0.059566 -0.704145 0.515064 0.738624 -0.295990 -0.131640 -0.493952 -0.896790 0.386611 0.104608 -0.081285 -0.306353 0.519260 0.629709 -0.125107 0.540567 0.967774 -0.891575 0.707319 0.342646 0.511502 -0.617112 0.861652 0.760353 -0.369437 0.662666 -0.006588 -0.822884 0.063038 0.125778 -0.642384 0.148297 -0.483995 -0.185248 0.341950 -0.006709 -0.012432 0.903527 0.941088 0.997722 -0.346344 -0.216605 -0.926923 -0.973223 -0.349402 0.111022 -0.663849 0.100965 0.127449 -0.818799 -0.552842 0.424723 0.177478 0.891255 0.272946 0.115048 -0.881540 -0.594795 0.112383 -0.692106 0.925810 0.722616 -0.217743 0.918109 0.627413 0.764482 0.577587 -0.066449 0.289713 -0.310735 -0.271185 -0.130134 0.447725 -0.557716 0.515380 0.079780 0.139896 0.264597 -0.437047 o - - - - - - - - - - - - - - - - - - - x o - - - - - - - - - - - - - - - - - - | | o - - - - - - - - - - - - - - - - - | o | o - - - - - - - - - - - - - - - - | o | | o - - - - - - - - - - - - - - - | | x | | x - - - - - - - - - - - - - - o | | | x | o - - - - - - - - - - - - - x | o | | o x o - - - - - - - - - - - - | x o x | | o x o - - - - - - - - - - - x o | o | | o o x x - - - - - - - - - - | x | | | o o | x | x - - - - - - - - - | | | | x | | | o | | o - - - - - - - - x x | o x x | | x | o | o - - - - - - - | x | | | | x o x | | | o x - - - - - - o x | x o x | | | o o | | | o - - - - - x | o o x | x | x | o | | | o o - - - - | o | | o | o x o | | x x o o | o - - - | | | | | | x | x x x | x | o | o x - - | | x o x | x | o | x x | x x o x | o - | o | | | o | o x | o x x | | x x | o x The error in solving: 1.144392e-16 The error in solving: 1.600465e-16 The error in solving: 2.574881e-16 The error in solving: 2.483504e-16 The error in solving: 5.034884e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.750000 [ -0.875942 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.433130 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.582770 -0.934867 0.885213 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.407750 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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Dimension: 20 x 20 Off-diagonal entries: 130 (max 380) Diagonal entries: -0.875942 0.433130 0.885213 -0.407750 0.936276 -0.189658 0.707985 0.898284 -0.060993 -0.832467 -0.544948 0.669787 -0.273242 -0.036102 0.683952 0.080144 0.547224 0.895490 -0.849273 -0.529255 Row indices: 0 0 0 2 2 5 8 13 17 23 29 35 43 53 63 72 80 94 104 119 130 Column indices: 0 1 0 2 3 0 1 3 1 2 3 4 5 0 3 5 6 1 2 3 4 5 7 0 1 2 5 6 8 1 3 5 7 8 9 2 3 4 5 6 8 9 10 1 2 3 5 6 7 8 9 10 11 0 1 2 5 6 7 8 10 11 12 0 1 2 5 6 8 9 10 13 0 1 4 5 6 8 10 11 0 1 2 3 4 5 6 7 8 9 10 12 13 15 0 1 2 3 4 5 9 12 14 15 0 1 4 5 6 7 8 9 10 11 12 13 14 15 16 2 3 4 5 7 8 9 10 12 13 17 Off-diagonal values: 0.582770 -0.934867 0.657153 -0.177135 -0.066284 -0.516852 -0.664695 0.240848 -0.627105 -0.303531 0.311444 0.249245 0.787920 -0.250195 -0.712814 0.751484 -0.436149 0.334947 0.038897 -0.192018 0.090861 -0.152814 -0.936495 0.453478 0.938664 -0.168274 0.202424 -0.144903 0.459701 0.790033 -0.659667 -0.871200 0.571508 0.514460 0.193008 0.573616 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- | | | o - - - - - - - - - - - - - - - - x | o o x - - - - - - - - - - - - - - - o o | x | o - - - - - - - - - - - - - - | o o x x x x - - - - - - - - - - - - - o | | o | x o x - - - - - - - - - - - - | x x o x o | o o - - - - - - - - - - - x x o | | x o | x o - - - - - - - - - - | x | o | o | x x x o - - - - - - - - - | | x x x o x | x o x x - - - - - - - - | x x o | x x o x o x o o - - - - - - - x x x | | x o o o | x x o o - - - - - - o o o | | x o | x x x | | o x - - - - - x x | | x o o | o | x o | | | x - - - - x x o x x o o x o o x | x x | x x - - - x x x o x x | | | o | | x | o o | x - - x x | | o x x x x o o x o x o x x | o - | | x o o x | x x o x | x x | | | o | o The error in solving: 1.277704e-16 The error in solving: 2.081668e-16 The error in solving: 2.084814e-16 The error in solving: 2.618456e-16 The error in solving: 2.603704e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular 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- - - - - - x x | | o | | | | . - - - - - - - - - - | | | | o o | | | | . - - - - - - - - - | x | | o x o | | | | . - - - - - - - - x | x o o x | | | | x | . - - - - - - - | | | | | | | | | | | | o . - - - - - - o | | | | | | | o | x | | | . - - - - - | | o x | | | | o | o | x | | . - - - - | | | x | | | | | | | | | | o | . - - - x o | x | x o | | | | | | | o x | . - - | x | o | | | | | x | | | | | | | | . - | | | o | | | | | | | | | | | | | | | . The error in solving: 0.000000e+00 The error in solving: 2.419675e-16 The error in solving: 1.144392e-16 The error in solving: 2.292987e-16 The error in solving: 2.221530e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.016720 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.602961 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.592666 -0.041327 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.086912 -0.921154 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.784290 -0.867885 -0.092047 0.000000 -0.192077 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.899778 0.000000 -0.129089 0.000000 0.779100 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.308302 0.000000 0.850237 0.445756 -0.386985 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.975022 0.887380 0.000000 0.000000 0.000000 0.337482 0.993804 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.850769 -0.296776 -0.539919 0.000000 0.000000 0.000000 -0.451106 0.131812 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.434394 0.000000 0.587439 0.000000 0.434525 0.000000 0.801609 -0.833322 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.727363 0.000000 -0.693533 0.707405 0.000000 -0.096746 0.556958 0.000000 0.000000 -0.199877 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.421193 -0.389212 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.268929 0.351255 -0.177401 0.824659 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.439631 0.000000 -0.902152 -0.093855 0.000000 -0.760450 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.267164 -0.269589 -0.209136 0.430119 0.000000 0.919850 0.000000 0.000000 0.548227 -0.589938 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.709254 -0.581805 0.000000 0.599631 0.000000 0.000000 0.000000 -0.197369 0.000000 0.643800 0.000000 -0.123209 0.000000 -0.569266 0.724098 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.428273 -0.324337 0.000000 -0.575674 0.000000 0.000000 0.000000 0.659665 0.415952 0.516187 0.000000 -0.662627 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.440734 -0.007549 0.000000 0.640851 0.000000 0.000000 -0.813246 -0.709970 0.000000 0.537415 0.518142 -0.590992 0.000000 0.000000 -0.333258 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.620605 0.000000 -0.266562 0.971194 -0.443195 0.018510 0.000000 -0.703922 -0.221397 0.000000 0.000000 0.000000 0.000000 -0.638648 0.000000 0.000000 0.000000 0.000000 -0.279796 0.000000 0.000000 0.000000 -0.059487 0.000000 -0.315262 0.000000 0.325834 -0.006060 0.178687 -0.435557 0.000000 -0.382125 0.000000 0.000000 0.832052 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 95 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 2 4 6 10 13 17 21 26 31 37 43 47 54 62 69 78 86 95 Column indices: 0 0 1 2 1 2 0 1 2 4 1 3 5 0 2 3 4 1 2 6 7 1 2 3 7 8 1 3 5 7 8 1 3 4 6 7 10 0 1 8 9 10 11 4 6 7 9 4 5 6 7 9 12 13 0 1 3 7 9 11 13 14 2 3 5 9 10 11 13 0 1 3 6 7 9 10 11 14 4 6 7 8 9 11 12 17 2 6 8 10 11 12 13 15 18 Off-diagonal values: -0.016720 0.602961 0.592666 -0.041327 -0.086912 -0.921154 -0.784290 -0.867885 -0.092047 -0.192077 -0.899778 -0.129089 0.779100 0.308302 0.850237 0.445756 -0.386985 0.975022 0.887380 0.337482 0.993804 0.850769 -0.296776 -0.539919 -0.451106 0.131812 0.434394 0.587439 0.434525 0.801609 -0.833322 -0.727363 -0.693533 0.707405 -0.096746 0.556958 -0.199877 -0.421193 -0.389212 0.268929 0.351255 -0.177401 0.824659 0.439631 -0.902152 -0.093855 -0.760450 0.267164 -0.269589 -0.209136 0.430119 0.919850 0.548227 -0.589938 0.709254 -0.581805 0.599631 -0.197369 0.643800 -0.123209 -0.569266 0.724098 -0.428273 -0.324337 -0.575674 0.659665 0.415952 0.516187 -0.662627 -0.440734 -0.007549 0.640851 -0.813246 -0.709970 0.537415 0.518142 -0.590992 -0.333258 -0.620605 -0.266562 0.971194 -0.443195 0.018510 -0.703922 -0.221397 -0.638648 -0.279796 -0.059487 -0.315262 0.325834 -0.006060 0.178687 -0.435557 -0.382125 0.832052 . - - - - - - - - - - - - - - - - - - - o . - - - - - - - - - - - - - - - - - - x | . - - - - - - - - - - - - - - - - - | x o . - - - - - - - - - - - - - - - - | o o | . - - - - - - - - - - - - - - - o o o | o . - - - - - - - - - - - - - - | o | o | x . - - - - - - - - - - - - - x | x x o | | . - - - - - - - - - - - - | x x | | | x x . - - - - - - - - - - - | x o o | | | o x . - - - - - - - - - - | x | x | x | x o | . - - - - - - - - - | o | o x | o x | | o . - - - - - - - - o o | | | | | | x x o x . - - - - - - - | | | | x | o o | o | | | . - - - - - - | | | | x o o x | x | | x o . - - - - - x o | x | | | o | x | o | o x . - - - - | | o o | o | | | x x x | o | | . - - - o o | x | | o o | x x o | | o | | . - - | | | | o | o x o x | o o | | | | o . - | | o | | | o | o | x o x o | o | | x . The error in solving: 1.666780e-16 The error in solving: 4.577567e-16 The error in solving: 9.614813e-17 The error in solving: 2.861821e-16 The error in solving: 1.594436e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.285411 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.787792 0.764265 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.896836 0.975738 0.206907 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.363648 -0.536521 0.220131 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.281246 0.836787 -0.026226 0.889688 -0.761504 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.920335 0.036142 0.000000 -0.207826 0.331725 -0.812810 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.450028 -0.597832 0.309210 0.000000 -0.734947 0.000000 -0.925980 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.927245 -0.738157 0.409332 0.000000 -0.331224 0.466823 -0.002580 -0.692295 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.260750 -0.273708 0.636406 0.976583 0.230954 0.000000 0.655495 0.546637 -0.794898 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.967587 0.761149 0.000000 0.257162 0.321418 0.000000 -0.505699 -0.522851 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.149144 0.000000 0.000000 0.235966 0.000000 0.440229 0.000000 0.000000 0.499305 -0.829448 0.589092 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.043268 -0.075919 -0.389189 -0.657978 0.641422 -0.449597 -0.668015 -0.820927 0.734463 0.448759 -0.941317 -0.851703 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.967214 0.490992 -0.184124 0.440845 -0.598593 0.000000 0.423883 -0.310119 0.000000 -0.940371 0.000000 -0.211006 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.111274 -0.567871 -0.611173 -0.880353 -0.847262 0.709995 0.000000 0.738219 -0.229165 0.000000 0.000000 0.496828 0.093438 0.817985 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.716157 0.000000 0.985229 0.000000 0.790554 -0.102568 0.000000 0.746730 0.000000 -0.844510 -0.646421 -0.651733 0.000000 0.806892 -0.236690 0.000000 0.000000 0.000000 0.000000 0.000000 0.759724 0.402775 0.697490 -0.854962 0.921551 -0.271427 0.000000 0.562485 0.676121 0.000000 0.000000 0.000000 -0.712804 0.603866 0.974292 0.000000 0.000000 0.000000 0.000000 0.000000 0.630010 0.000000 0.000000 0.000000 0.475488 0.000000 0.000000 0.000000 0.732383 0.000000 0.286439 0.245409 0.905363 0.540694 0.675393 -0.310622 -0.686969 0.000000 0.000000 0.000000 -0.156617 0.613095 0.000000 -0.954330 -0.292691 0.615527 -0.766041 -0.076172 0.000000 0.590566 -0.201103 0.000000 -0.749856 0.611234 -0.317070 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.465015 -0.108286 0.140990 0.200950 0.000000 0.911135 0.987870 0.110035 0.795847 -0.158097 0.457126 0.413222 0.000000 0.759352 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 138 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 3 6 9 14 19 24 31 39 45 51 63 72 83 93 104 114 126 138 Column indices: 0 0 1 0 1 2 0 1 2 0 1 2 3 4 0 1 3 4 5 0 1 2 4 6 0 1 2 4 5 6 7 0 1 2 3 4 6 7 8 0 1 3 4 6 7 0 3 5 8 9 10 0 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 7 8 10 12 0 1 2 3 4 5 7 8 11 12 13 0 2 4 5 7 9 10 11 13 14 0 1 2 3 4 5 7 8 12 13 14 0 4 8 10 11 12 13 14 15 16 0 1 3 4 5 6 7 9 10 12 13 14 4 5 6 7 9 10 11 12 13 14 15 17 Off-diagonal values: 0.285411 0.787792 0.764265 -0.896836 0.975738 0.206907 0.363648 -0.536521 0.220131 0.281246 0.836787 -0.026226 0.889688 -0.761504 0.920335 0.036142 -0.207826 0.331725 -0.812810 0.450028 -0.597832 0.309210 -0.734947 -0.925980 0.927245 -0.738157 0.409332 -0.331224 0.466823 -0.002580 -0.692295 0.260750 -0.273708 0.636406 0.976583 0.230954 0.655495 0.546637 -0.794898 0.967587 0.761149 0.257162 0.321418 -0.505699 -0.522851 -0.149144 0.235966 0.440229 0.499305 -0.829448 0.589092 -0.043268 -0.075919 -0.389189 -0.657978 0.641422 -0.449597 -0.668015 -0.820927 0.734463 0.448759 -0.941317 -0.851703 -0.967214 0.490992 -0.184124 0.440845 -0.598593 0.423883 -0.310119 -0.940371 -0.211006 -0.111274 -0.567871 -0.611173 -0.880353 -0.847262 0.709995 0.738219 -0.229165 0.496828 0.093438 0.817985 0.716157 0.985229 0.790554 -0.102568 0.746730 -0.844510 -0.646421 -0.651733 0.806892 -0.236690 0.759724 0.402775 0.697490 -0.854962 0.921551 -0.271427 0.562485 0.676121 -0.712804 0.603866 0.974292 0.630010 0.475488 0.732383 0.286439 0.245409 0.905363 0.540694 0.675393 -0.310622 -0.686969 -0.156617 0.613095 -0.954330 -0.292691 0.615527 -0.766041 -0.076172 0.590566 -0.201103 -0.749856 0.611234 -0.317070 0.465015 -0.108286 0.140990 0.200950 0.911135 0.987870 0.110035 0.795847 -0.158097 0.457126 0.413222 0.759352 . - - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - x x . - - - - - - - - - - - - - - - - - o x x . - - - - - - - - - - - - - - - - x o x | . - - - - - - - - - - - - - - - x x o x o . - - - - - - - - - - - - - - x x | o x o . - - - - - - - - - - - - - x o x | o | o . - - - - - - - - - - - - x o x | o x o o . - - - - - - - - - - - x o x x x | x x o . - - - - - - - - - - x x | x x | o o | | . - - - - - - - - - o | | x | x | | x o x . - - - - - - - - o o o o x o o o x x o o . - - - - - - - | o x o x o | x o | o | o . - - - - - - o o o o o x | x o | | x x x . - - - - - x | x | x o | x | o o o | x o . - - - - x x x o x o | x x | | | o x x | . - - - x | | | x | | | x | x x x x x o o . - - o x | o o x o o | x o | o x o | | | . - | | | | x o x x | x x x x o x x | x | . The error in solving: 4.041273e-16 The error in solving: 1.010318e-16 The error in solving: 1.600465e-16 The error in solving: 1.665335e-16 The error in solving: 6.877911e-17 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a standard normal distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.526700 -1.130378 0.709534 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.186348 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.915245 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.092728 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.471115 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.393511 0.000000 -1.130892 0.000000 0.000000 0.000000 0.620842 -0.810284 0.888738 0.000000 0.401715 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.357880 1.403918 0.000000 0.000000 0.000000 -0.921854 0.000000 0.000000 0.000000 0.139297 0.000000 2.806461 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.612418 -0.716360 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.578682 0.000000 0.000000 0.338269 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.690057 1.080493 0.000000 0.000000 0.000000 0.000000 0.087791 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.574287 0.000000 0.000000 0.000000 -0.101309 0.000000 0.000000 0.000000 0.000000 -1.237439 0.136750 -0.584179 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.733107 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.119093 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.416504 0.000000 0.000000 -1.151346 0.000000 0.000000 0.000000 0.345711 -1.460561 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.328409 0.927600 0.000000 0.000000 0.000000 0.965353 0.969301 0.000000 0.000000 0.355275 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.313577 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.355293 1.320534 0.000000 0.000000 0.000000 1.571386 0.000000 0.216761 0.000000 0.000000 0.000000 0.000000 0.534719 0.000000 -0.833678 0.000000 0.000000 -2.112435 0.000000 0.000000 -0.372313 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.370852 -1.290204 0.000000 0.000000 -0.892648 0.063949 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 49 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.092728 0.000000 0.401715 2.806461 0.000000 0.000000 0.000000 0.000000 0.927600 0.000000 -0.833678 0.000000 Row indices: 0 0 0 0 0 0 3 4 5 5 6 11 15 19 22 27 29 34 38 43 49 Column indices: 0 1 2 4 4 3 0 2 6 7 8 0 1 5 9 0 1 8 11 2 3 8 1 5 10 11 12 3 13 0 3 7 8 15 0 1 4 16 4 5 9 11 16 1 4 12 13 16 17 Off-diagonal values: 0.526700 -1.130378 0.709534 -1.186348 -0.915245 0.471115 1.393511 -1.130892 0.620842 -0.810284 0.888738 -0.357880 1.403918 -0.921854 0.139297 -0.612418 -0.716360 0.578682 0.338269 -1.690057 1.080493 0.087791 -0.574287 -0.101309 -1.237439 0.136750 -0.584179 1.733107 -0.119093 -0.416504 -1.151346 0.345711 -1.460561 0.328409 0.965353 0.969301 0.355275 2.313577 -0.355293 1.320534 1.571386 0.216761 0.534719 -2.112435 -0.372313 -0.370852 -1.290204 -0.892648 0.063949 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - x o x | | . - - - - - - - - - - - - - - | | | | o | . - - - - - - - - - - - - - | | | | o | | . - - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | x | | | | | . - - - - - - - - - - x | o | | | x o x | x - - - - - - - - - o x | | | o | | | x | x - - - - - - - - o o | | | | | | x | | x . - - - - - - - | | o x | | | | x | | | | . - - - - - - | o | | | o | | | | o x o | . - - - - - | | | x | | | | | | | | | o | . - - - - o | | o | | | x o | | | | | | x x - - - x x | | x | | | | | | | | | | | x . - - | | | | o x | | | x | x | | | | x | o - | o | | o | | | | | | | o o | | o x | . The error in solving: 1.867065e-16 The error in solving: 4.264457e-16 The error in solving: 1.618507e-16 The error in solving: 3.236829e-16 The error in solving: 2.995803e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a standard normal distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.033697 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.130211 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.228808 0.246403 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.193403 0.000000 0.302037 0.225381 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.151489 0.948037 -0.551512 1.432849 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.809732 0.000000 -0.970434 0.000000 0.000000 1.647314 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.277773 0.000000 -0.305403 0.000000 -0.218844 1.751676 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.850308 0.000000 0.000000 0.674615 -0.030810 0.808870 1.029455 -1.132286 0.592523 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.333509 -0.096096 0.000000 0.493172 0.000000 -1.203514 -1.378189 0.000000 0.000000 0.705882 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.574706 0.000000 -1.206836 0.000000 0.000000 0.926540 0.367782 -0.575567 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.547844 0.579707 -0.323492 0.000000 0.000000 0.000000 0.000000 0.142927 -0.217257 0.731540 0.512315 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.421762 0.000000 -0.563926 -1.283074 0.000000 0.000000 0.000000 -0.085252 -0.076533 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.136281 0.711727 0.000000 0.000000 0.000000 1.380613 0.000000 0.000000 -0.575296 0.000000 0.000000 -0.439816 0.048391 -0.285618 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.284582 0.000000 -0.015585 0.000000 0.604998 0.000000 -1.362802 0.000000 0.519866 0.000000 0.000000 0.000000 1.161906 1.570033 -0.665096 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.040218 0.000000 0.000000 0.266239 -0.467322 0.000000 1.067489 -0.661594 0.532061 0.000000 0.000000 -0.955156 0.000000 0.928283 0.000000 0.000000 0.000000 0.000000 -0.045193 0.000000 0.364719 0.109038 0.000000 0.000000 0.000000 0.304736 0.060503 0.095169 0.000000 -1.117838 0.000000 0.000000 0.000000 0.000000 -0.156427 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.858795 0.000000 0.000000 -0.582083 2.773900 0.000000 -0.239658 -2.416071 -0.580502 -0.475755 0.000000 1.425755 0.000000 0.000000 0.766483 0.000000 0.000000 0.000000 -0.170959 -1.148609 1.442133 0.000000 0.000000 0.000000 0.000000 -1.103526 -0.588496 0.000000 0.111333 0.000000 0.033505 0.097864 1.386225 -1.526669 0.000000 0.191904 0.000000 0.000000 -1.735370 0.571608 0.000000 -0.752774 0.000000 0.041840 0.000000 0.000000 0.000000 1.166584 0.483905 0.000000 -0.232973 0.178662 -0.469955 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 96 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.246403 0.225381 0.000000 0.000000 1.751676 0.592523 0.705882 0.000000 0.512315 0.000000 -0.285618 -0.665096 0.928283 -0.156427 0.766483 0.191904 0.000000 Row indices: 0 0 1 2 3 5 9 12 15 21 26 31 37 42 48 55 62 69 77 87 96 Column indices: 0 1 2 1 3 1 2 3 4 0 2 5 2 4 6 0 3 4 5 6 7 0 1 3 5 6 1 3 6 7 8 1 2 3 8 9 10 3 5 6 10 11 0 1 5 8 11 12 0 2 4 6 8 12 13 2 5 6 8 9 10 13 0 2 3 7 8 9 11 3 6 7 9 10 11 12 14 1 2 3 8 9 11 13 14 15 16 1 2 4 6 10 11 13 14 15 Off-diagonal values: -2.033697 0.130211 0.228808 1.193403 0.302037 -0.151489 0.948037 -0.551512 1.432849 -0.809732 -0.970434 1.647314 2.277773 -0.305403 -0.218844 0.850308 0.674615 -0.030810 0.808870 1.029455 -1.132286 1.333509 -0.096096 0.493172 -1.203514 -1.378189 0.574706 -1.206836 0.926540 0.367782 -0.575567 -0.547844 0.579707 -0.323492 0.142927 -0.217257 0.731540 -1.421762 -0.563926 -1.283074 -0.085252 -0.076533 -0.136281 0.711727 1.380613 -0.575296 -0.439816 0.048391 2.284582 -0.015585 0.604998 -1.362802 0.519866 1.161906 1.570033 -0.040218 0.266239 -0.467322 1.067489 -0.661594 0.532061 -0.955156 -0.045193 0.364719 0.109038 0.304736 0.060503 0.095169 -1.117838 -0.858795 -0.582083 2.773900 -0.239658 -2.416071 -0.580502 -0.475755 1.425755 -0.170959 -1.148609 1.442133 -1.103526 -0.588496 0.111333 0.033505 0.097864 1.386225 -1.526669 -1.735370 0.571608 -0.752774 0.041840 1.166584 0.483905 -0.232973 0.178662 -0.469955 . - - - - - - - - - - - - - - - - - - - o . - - - - - - - - - - - - - - - - - - | x . - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | x | x x - - - - - - - - - - - - - - - | o x o x . - - - - - - - - - - - - - - o | o | | x . - - - - - - - - - - - - - | | x | o | o x - - - - - - - - - - - - x | | x o x x o x - - - - - - - - - - - x o | x | o o | | x - - - - - - - - - - | x | o | | x x o | . - - - - - - - - - | o x o | | | | x o x x - - - - - - - - | | | o | o o | | | o o . - - - - - - - o x | | | x | | o | | o x o - - - - - - x | o | x | o | x | | | x x o - - - - - | | o | | x o | x o x | | o | x - - - - o | x x | | | x x x | o | | | | o - - - | | | o | | o x | o o o o | x | | x - - | o o x | | | | o o | x | x x x o | x - | o x | o | x | | | x x | o x o | | | . The error in solving: 9.614813e-17 The error in solving: 1.782634e-16 The error in solving: 3.330669e-16 The error in solving: 1.481742e-16 The error in solving: 1.694000e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a standard normal distribution with a random diagonal and a density of 0.750000 [ -0.707417 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.526246 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.226180 1.309251 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.046687 -1.519082 0.000000 -0.276959 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1.072967 0.608318 1.416278 -0.382783 0.000000 -0.047028 -0.327623 0.000000 -0.481391 0.044505]; Dimension: 20 x 20 Off-diagonal entries: 136 (max 380) Diagonal entries: -0.707417 0.526246 0.000000 -0.276959 0.443503 -0.147778 0.623041 -0.648711 -0.744402 0.000000 0.000000 1.267766 0.000000 0.668957 0.000000 0.738796 0.000000 0.000000 1.355338 0.044505 Row indices: 0 0 0 2 4 8 12 16 23 28 36 42 47 56 67 75 86 96 108 122 136 Column indices: 0 1 0 1 0 1 2 3 1 2 3 4 1 2 3 4 0 1 2 3 4 5 6 0 2 4 6 7 0 1 2 3 4 5 7 8 1 2 4 5 8 9 0 1 3 7 10 1 2 3 4 5 7 9 10 11 0 1 3 4 5 7 8 9 10 11 12 0 2 5 6 7 8 11 13 1 3 5 6 7 8 9 10 12 13 14 0 2 3 4 5 6 7 9 12 13 0 1 3 4 5 8 10 11 13 14 15 16 0 2 4 6 7 8 9 11 12 13 14 15 16 17 2 3 5 6 7 8 9 10 11 12 13 15 16 18 Off-diagonal values: -0.226180 1.309251 0.046687 -1.519082 -0.691166 1.141152 -0.648722 0.203136 0.263029 -1.160712 -0.241632 1.412951 1.576171 0.032350 0.222656 -0.719717 -0.326197 -0.658850 -0.497554 -0.591388 -0.913287 -0.667633 -0.994597 -0.335605 0.910124 -0.043132 0.390412 -1.048723 0.646277 -0.307118 -0.626315 1.117196 1.351681 -0.768840 0.101408 -0.638104 0.854017 1.710050 0.735199 0.641271 0.397900 -0.093558 -0.698135 0.702746 -1.540587 -0.456992 1.456313 1.309589 -1.091170 0.593292 -0.295284 1.540095 -0.414253 -2.632103 -0.828980 0.295044 0.031528 1.360241 -0.280285 1.753299 -2.124446 0.508172 -1.088251 0.364157 0.212509 1.659803 -1.528495 1.013546 -0.242059 1.158540 -0.836440 1.492504 0.000822 0.771850 -0.299489 -0.659110 0.142865 1.286478 0.810931 0.277353 -0.779728 -0.395685 0.135903 1.341692 0.393652 -0.848035 -0.617153 -0.836328 2.301658 0.804068 0.984703 -1.083536 -0.673135 0.162967 0.511124 0.470414 0.850900 0.297559 -0.850360 -0.381935 -0.932149 0.256724 0.633557 -1.746564 -0.489998 0.719539 -1.836437 0.860897 2.403999 -0.731499 0.541413 -0.342508 -0.365024 1.585015 1.281179 -2.105817 -0.243667 0.558911 -0.581999 0.505258 -2.085895 0.736151 1.347059 0.177661 0.927618 -0.381581 0.348106 -0.146049 0.005923 1.072967 0.608318 1.416278 -0.382783 -0.047028 -0.327623 -0.481391 o - - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - o x . - - - - - - - - - - - - - - - - - x o | o - - - - - - - - - - - - - - - - o x o x x - - - - - - - - - - - - - - - | x o o x o - - - - - - - - - - - - - - | x x x o | x - - - - - - - - - - - - - o o o o o o o o - - - - - - - - - - - - o | x | o | x o o - - - - - - - - - - - x o o x x o | x o . - - - - - - - - - - | x x | x x | | x o . - - - - - - - - - o x | o | | | o | | x x - - - - - - - - | x o x o x | o | o o x . - - - - - - - x x | o x o | x o x x x o x - - - - - - x | o | | x o x x | | x | o . - - - - - | o | x | x x x o o x | x x o x - - - - o | o x x x o o | x | | x x | | . - - - x x | o o o | | x | x o | o x o x . - - x | o | x | o o x x | o o x o x o x x - | | x x | x o x o x x x x o | o o | o x The error in solving: 4.176363e-16 The error in solving: 3.236829e-16 The error in solving: 4.169115e-16 The error in solving: 4.005521e-16 The error in solving: 1.882475e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a standard normal distribution with a dense diagonal and a density of 0.250000 [ -0.536218 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.291826 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.218664 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.132214 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.003301 0.880042 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.624404 0.859400 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.194548 0.000000 0.000000 0.000000 0.000000 1.782766 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.337312 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.224308 0.000000 0.000000 0.000000 0.000000 0.000000 1.195774 1.543851 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.224587 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.338383 0.396376 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0.000000 0.000000 0.000000 1.549225 0.000000 0.000000 0.634682 0.000000 0.000000 0.000000 0.000000 -0.016071 0.000000 0.029211 0.000000 0.000000 0.393676 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.027528 0.000000 -0.545690 0.000000 0.299449 0.000000 0.000000 0.000000 -0.242845 -0.896907 0.000000 1.071771 0.000000 0.000000 0.000000 0.036550 0.000000 0.000000 0.000000 0.000000 0.000000 -0.825675 0.000000 0.000000 0.000000 -0.321534 1.139973 0.000000 0.000000 0.000000 0.000000 0.000000 -0.967216 0.000000 0.000000 0.453929 -0.858330 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.299821 0.000000 0.000000 0.000000 0.000000 0.000000 -0.092910 -0.601064 0.000000 0.000000 0.000000 0.000000 0.000000 -0.213496 0.778874 0.000000 -0.435040 0.000000 0.000000 0.000000 0.000000 -0.574459]; Dimension: 20 x 20 Off-diagonal entries: 46 (max 380) Diagonal entries: -0.536218 -0.291826 -1.218664 0.132214 0.880042 0.859400 1.782766 -1.337312 1.543851 0.396376 -0.075964 -1.381699 -1.754678 -0.762014 0.104055 0.393676 1.071771 -0.967216 0.299821 -0.574459 Row indices: 0 0 0 0 0 1 2 3 3 5 7 9 14 15 21 26 30 35 39 41 46 Column indices: 3 4 1 1 7 1 8 0 3 2 3 7 9 10 10 1 3 5 6 8 11 3 7 11 12 13 2 5 10 12 5 7 9 13 14 0 6 10 11 0 1 4 5 11 12 14 Off-diagonal values: 1.003301 1.624404 1.194548 -1.224308 1.195774 2.224587 -1.338383 0.272029 -1.526677 -1.029593 0.185705 0.867860 0.772867 -0.442376 0.899422 -0.586606 -1.339597 -0.596810 -0.207539 0.726505 -1.316397 -1.736263 0.162829 0.956971 1.409469 0.390949 1.549225 0.634682 -0.016071 0.029211 -1.027528 -0.545690 0.299449 -0.242845 -0.896907 0.036550 -0.825675 -0.321534 1.139973 0.453929 -0.858330 -0.092910 -0.601064 -0.213496 0.778874 -0.435040 o - - - - - - - - - - - - - - - - - - - | o - - - - - - - - - - - - - - - - - - | | o - - - - - - - - - - - - - - - - - | | | x - - - - - - - - - - - - - - - - | | | x x - - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | x | | | | x - - - - - - - - - - - - - | | | | | | | o - - - - - - - - - - - - | o | | | | | x x - - - - - - - - - - - | x | | | | | | o x - - - - - - - - - - x | | o | | | | | | o - - - - - - - - - | | o x | | | x | x o o - - - - - - - - | | | | | | | | | | x | o - - - - - - - | o | o | o o | x | | o | o - - - - - - | | | o | | | x | | | x x x x - - - - - | | x | | x | | | | o | x | | x - - - - | | | | | o | o | x | | | o o | x - - - x | | | | | o | | | o x | | | | | o - - x o | | | | | | | | | | | | | | | | x - | | | | o o | | | | | o x | o | | | | o The error in solving: 1.666780e-16 The error in solving: 2.543841e-16 The error in solving: 9.714451e-17 The error in solving: 2.543841e-16 The error in solving: 1.366804e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a standard normal distribution with a dense diagonal and a density of 0.500000 [ 0.363984 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.786492 2.495392 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.993131 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.119379 0.000000 0.000000 0.662526 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.838529 0.000000 1.749658 1.513489 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.342938 0.000000 0.205830 1.631754 0.562860 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.902361 1.264878 0.648224 1.732879 0.000000 -0.032952 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.804028 0.000000 -0.527607 0.270051 -0.374469 -0.846666 -0.679392 -0.176832 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.963075 0.000000 0.000000 0.000000 0.286445 0.000000 0.000000 -2.247312 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.659722 0.488675 0.150669 0.150739 0.000000 0.868866 0.000000 0.611073 -1.304770 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.080925 0.000000 0.000000 0.000000 0.000000 -1.245589 0.000000 0.000000 0.000000 -0.404124 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.271937 0.000000 0.000000 0.000000 0.904259 0.800436 -0.212268 0.000000 0.000000 1.257197 -0.453460 0.230759 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.574053 0.000000 0.000000 0.269020 1.321738 0.486575 -0.220580 -0.403519 0.586743 0.000000 -1.227501 0.000000 0.943572 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.626171 0.000000 -0.306232 0.000000 -0.760968 0.000000 0.023567 0.015891 0.536344 0.000000 -1.111443 -0.806988 0.765582 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.259205 0.000000 0.721816 0.000000 0.405242 1.637853 -1.458844 0.000000 0.000000 -0.268644 0.000000 0.000000 0.000000 -1.227627 0.000000 0.000000 0.000000 0.000000 0.000000 1.850578 0.000000 1.197569 0.000000 -0.436269 0.000000 0.000000 -0.163197 1.550194 0.651789 2.616455 2.104779 0.012920 0.000000 -0.209551 -0.240799 0.000000 0.000000 0.000000 0.000000 -0.153029 0.000000 0.611014 1.515983 0.000000 -0.671854 0.000000 0.000000 -1.156896 0.000000 -0.267878 0.000000 0.932906 0.000000 0.984665 0.000000 -0.723997 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.417869 0.000000 -2.034449 0.000000 0.000000 0.669505 -0.656956 0.000000 -0.655620 0.000000 0.000000 -1.579332 0.725960 0.000000 0.000000 0.000000 0.000000 1.848939 -0.011566 0.000000 0.000000 0.745544 1.225155 0.849323 0.000000 0.181688 0.000000 -2.091652 0.000000 0.459153 0.480962 -0.871944 1.012115 0.650791 0.000000 -0.374103 1.196472 0.693103 0.614561 0.000000 0.000000 0.000000 -1.109212 0.000000 0.000000 0.000000 0.000000 -1.357511 0.000000 1.009555 0.000000 0.000000 -0.733219 -0.221563 -0.176295]; Dimension: 20 x 20 Off-diagonal entries: 99 (max 380) Diagonal entries: 0.363984 2.495392 0.993131 0.662526 1.513489 0.562860 -0.032952 -0.176832 -2.247312 -1.304770 -0.404124 0.230759 0.943572 0.765582 -1.227627 -0.240799 -0.723997 0.725960 0.650791 -0.176295 Row indices: 0 0 1 1 2 4 7 11 17 19 25 27 33 41 49 55 65 73 79 90 99 Column indices: 0 0 1 3 1 3 4 1 2 3 4 0 2 3 4 5 6 1 5 1 2 3 4 6 8 1 6 0 4 5 6 9 10 0 3 4 5 6 7 8 10 1 3 5 7 8 9 11 12 1 3 5 6 7 10 0 2 4 7 8 9 10 11 12 14 0 2 3 5 8 10 12 14 5 7 10 11 13 16 2 3 6 7 8 10 12 14 15 16 17 0 1 2 3 7 12 14 17 18 Off-diagonal values: 0.786492 -1.119379 0.838529 1.749658 -0.342938 0.205830 1.631754 0.902361 1.264878 0.648224 1.732879 -0.804028 -0.527607 0.270051 -0.374469 -0.846666 -0.679392 -1.963075 0.286445 -1.659722 0.488675 0.150669 0.150739 0.868866 0.611073 -1.080925 -1.245589 -0.271937 0.904259 0.800436 -0.212268 1.257197 -0.453460 -0.574053 0.269020 1.321738 0.486575 -0.220580 -0.403519 0.586743 -1.227501 -0.626171 -0.306232 -0.760968 0.023567 0.015891 0.536344 -1.111443 -0.806988 1.259205 0.721816 0.405242 1.637853 -1.458844 -0.268644 1.850578 1.197569 -0.436269 -0.163197 1.550194 0.651789 2.616455 2.104779 0.012920 -0.209551 -0.153029 0.611014 1.515983 -0.671854 -1.156896 -0.267878 0.932906 0.984665 0.417869 -2.034449 0.669505 -0.656956 -0.655620 -1.579332 1.848939 -0.011566 0.745544 1.225155 0.849323 0.181688 -2.091652 0.459153 0.480962 -0.871944 1.012115 -0.374103 1.196472 0.693103 0.614561 -1.109212 -1.357511 1.009555 -0.733219 -0.221563 x - - - - - - - - - - - - - - - - - - - x x - - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - o | | x - - - - - - - - - - - - - - - - | x | x x - - - - - - - - - - - - - - - | o | x x x - - - - - - - - - - - - - - | x x x x | o - - - - - - - - - - - - - o | o x o o o o - - - - - - - - - - - - | o | | | x | | o - - - - - - - - - - - | o x x x | x | x o - - - - - - - - - - | o | | | | o | | | o - - - - - - - - - o | | | x x o | | x o x - - - - - - - - o | | x x x o o x | o | x - - - - - - - | o | o | o | x x x | o o x - - - - - - | x | x | x x o | | o | | | o - - - - - x | x | o | | o x x x x x | o o - - - - o | x x | o | | o | o | x | x | o - - - | | | | | x | o | | x o | o | | o x - - | | x o | | x x x | x | o | x x o x x - o x x x | | | o | | | | o | x | | o o o The error in solving: 2.541000e-16 The error in solving: 3.342394e-16 The error in solving: 3.513575e-16 The error in solving: 2.785960e-16 The error in solving: 6.425880e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a standard normal distribution with a dense diagonal and a density of 0.750000 [ 0.580216 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.190141 -0.410222 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.081036 0.379804 -0.528656 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.446553 0.392629 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.358130 0.078708 0.000000 0.345674 0.446294 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.829300 -0.508042 -0.666403 0.000000 -1.451144 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.444354 0.000000 0.000000 1.095054 -1.652853 1.328843 1.271191 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.560428 0.000000 0.184581 -2.003647 -1.632967 0.000000 -0.515158 0.610444 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.064900 1.311335 -0.268949 0.831188 1.394770 0.284471 -2.495385 -1.217663 -0.382950 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.254778 0.000000 -1.253405 0.000000 1.329120 -0.183432 -1.763095 2.512912 1.846096 -0.822358 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.056241 0.000000 0.000000 -1.393372 0.061764 0.000000 0.000000 -0.865544 1.323202 0.441075 -0.417591 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.764824 -1.472766 0.617018 0.000000 0.041721 -1.411356 0.459604 0.205946 0.000000 -0.046480 -0.412420 0.304219 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.752638 1.023266 0.737928 -0.698822 0.223117 1.276920 -1.131865 1.993292 0.427429 -1.198569 0.943920 -1.456268 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.504595 -1.172587 -0.423316 -0.677134 0.000000 0.000000 -0.007524 0.000000 -0.276618 1.242012 -1.758911 0.000000 1.529449 -2.973791 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.502031 -0.304544 0.000000 0.229982 -1.719733 0.000000 0.006876 0.306370 -0.379059 0.000000 0.737290 0.000000 -0.983018 0.002631 0.689064 0.000000 0.000000 0.000000 0.000000 0.000000 -0.850336 0.000000 -0.619346 0.881238 -1.870682 0.064241 2.468860 0.000000 -1.290728 0.000000 -0.095462 0.000000 -0.366067 0.018147 -0.404350 -0.800012 0.000000 0.000000 0.000000 0.000000 -0.334424 0.000000 1.159402 -0.130127 0.342771 0.000000 0.058862 0.000000 0.000000 0.000000 0.372913 -0.502952 0.606226 -0.368623 0.000000 0.427873 2.861867 0.000000 0.000000 0.000000 0.346445 0.642535 0.429784 0.441945 1.119458 0.020080 1.373065 -1.865218 0.000000 2.619182 -0.616496 -2.093247 0.872093 0.271755 1.126732 0.000000 -1.306460 0.216147 0.000000 0.000000 0.000000 0.000000 0.000000 0.632191 0.000000 0.414255 -0.543889 0.282336 0.000000 -0.802708 -0.709330 -0.634196 1.459334 0.842758 -0.107543 0.000000 0.656368 0.000000 -1.183297 0.000000 0.811562 -0.108013 -0.802305 1.157684 -0.548925 -0.145344 1.630067 1.888203 -1.724405 0.000000 0.811408 0.298847 0.615862 0.000000 -0.353852 0.421364 1.272678 0.000000 0.726155 -0.384269]; Dimension: 20 x 20 Off-diagonal entries: 142 (max 380) Diagonal entries: 0.580216 -0.410222 -0.528656 0.392629 0.446294 -1.451144 1.271191 0.610444 -0.382950 -0.822358 -0.417591 0.304219 -1.456268 -2.973791 0.689064 -0.800012 2.861867 0.216147 -1.183297 -0.384269 Row indices: 0 0 1 3 4 7 10 14 19 27 34 40 49 60 69 79 90 100 115 126 142 Column indices: 0 0 1 2 0 1 3 1 2 3 0 3 4 5 0 2 3 4 6 0 1 2 3 4 5 6 7 0 2 4 5 6 7 8 0 3 4 7 8 9 0 1 2 4 5 6 7 9 10 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 6 8 9 10 12 0 1 3 4 6 7 8 10 12 13 0 2 3 4 5 6 8 10 12 13 14 0 2 3 4 6 10 11 12 13 15 0 1 2 3 4 5 6 7 9 10 11 12 13 14 16 3 5 6 7 9 10 11 12 13 14 16 0 1 2 3 4 5 6 7 8 10 11 12 14 15 16 18 Off-diagonal values: 0.190141 1.081036 0.379804 -0.446553 1.358130 0.078708 0.345674 -1.829300 -0.508042 -0.666403 -0.444354 1.095054 -1.652853 1.328843 -0.560428 0.184581 -2.003647 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1.459334 0.842758 -0.107543 0.656368 0.811562 -0.108013 -0.802305 1.157684 -0.548925 -0.145344 1.630067 1.888203 -1.724405 0.811408 0.298847 0.615862 -0.353852 0.421364 1.272678 0.726155 x - - - - - - - - - - - - - - - - - - - x o - - - - - - - - - - - - - - - - - - x x o - - - - - - - - - - - - - - - - - | | o x - - - - - - - - - - - - - - - - x x | x x - - - - - - - - - - - - - - - | o o o | o - - - - - - - - - - - - - - o | | x o x x - - - - - - - - - - - - - o | x o o | o x - - - - - - - - - - - - o x o x x x o o o - - - - - - - - - - - o | o | x o o x x o - - - - - - - - - - x | | o x | | o x x o - - - - - - - - - x o x | x o x x | o o x - - - - - - - - | o x x o x x o x x o x o - - - - - - - x o o o | | o | o x o | x o - - - - - - o o | x o | x x o | x | o x x - - - - - o | o x o x x | o | o | o x o o - - - - o | x o x | x | | | x o x o | x x - - - x x x x x x x o | x o o x x x | o x - - | | | x | x o x | o o o x x o | x | o - x o o x o o x x o | x x x | o x x | x o The error in solving: 2.821153e-16 The error in solving: 1.688306e-16 The error in solving: 8.326673e-17 The error in solving: 3.815761e-16 The error in solving: 3.368045e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a standard normal distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.954134 -1.670957 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.393688 -0.750721 -0.201355 -0.113991 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.441065 0.000000 0.000000 0.000000 1.843689 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.217471 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.940292 0.000000 0.000000 0.000000 -0.465163 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.111855 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.744601 0.000000 0.000000 0.167593 0.000000 0.000000 0.000000 0.000000 0.000000 -0.971898 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.198701 -0.063436 0.000000 0.000000 0.000000 0.000000 1.020356 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.066198 0.000000 0.000000 0.000000 0.000000 0.000000 0.992089 0.000000 0.000000 1.540667 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.160305 0.000000 0.000000 0.000000 0.000000 0.000000 0.102426 0.000000 0.000000 0.000000 0.000000 0.091955 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.081458 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.259234 0.000000 0.000000 1.366074 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.075151 0.000000 0.000000 0.000000 -1.785072 0.000000 1.314925 0.000000 -0.669362 -0.522281 0.000000 0.000000 -0.056863 0.000000 0.000000 0.411954 0.000000 0.000000 0.000000 0.000000 1.470510 0.840450 0.000000 0.000000 0.000000 0.000000 0.000000 0.939391 0.372515 0.000000 -0.451700 0.000000 0.000000 0.000000 0.000000 0.000000 -0.769929 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.358617 0.000000 0.000000 0.050916 0.000000 0.000000 0.000000 1.045621 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 43 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 2 6 6 6 8 9 11 12 15 18 21 24 25 27 34 40 43 Column indices: 0 1 0 1 2 3 0 4 7 3 7 0 1 4 10 3 4 9 2 8 11 2 8 13 7 2 5 1 5 7 9 10 13 16 1 2 8 9 11 17 11 14 18 Off-diagonal values: -0.954134 -1.670957 1.393688 -0.750721 -0.201355 -0.113991 -0.441065 1.843689 0.217471 0.940292 -0.465163 0.111855 1.744601 0.167593 -0.971898 0.198701 -0.063436 1.020356 -1.066198 0.992089 1.540667 0.160305 0.102426 0.091955 0.081458 -1.259234 1.366074 2.075151 -1.785072 1.314925 -0.669362 -0.522281 -0.056863 0.411954 1.470510 0.840450 0.939391 0.372515 -0.451700 -0.769929 -1.358617 0.050916 1.045621 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - o o | . - - - - - - - - - - - - - - - - x o o o . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - o | | | x | | . - - - - - - - - - - - - | | | | | | | x . - - - - - - - - - - - | | | x | | | o | . - - - - - - - - - - x | | | | | | | | | . - - - - - - - - - | x | | x | | | | | o . - - - - - - - - | | | x o | | | | x | | . - - - - - - - | | o | | | | | x | | x | . - - - - - - | | x | | | | | x | | | | x . - - - - - | | | | | | | x | | | | | | | . - - - - | | o | | x | | | | | | | | | | . - - - | x | | | o | x | o o | | o | | x . - - | x x | | | | | x x | o | | | | | o . - | | | | | | | | | | | o | | x | | | x . The error in solving: 3.421937e-16 The error in solving: 3.345094e-16 The error in solving: 2.547623e-16 The error in solving: 3.565437e-16 The error in solving: 9.054510e-17 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a standard normal distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.020152 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.937559 0.000000 -0.648318 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.666438 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.162541 -0.349018 -0.607391 -0.355789 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.479364 1.112509 0.092818 -0.768964 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.966904 -0.176234 0.016885 0.000000 1.003778 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.490160 0.000000 -1.055022 0.739883 0.000000 -1.423407 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.034970 -1.005249 -0.471743 0.000000 0.000000 -0.288449 0.000000 0.000000 -1.376965 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.759460 1.043147 0.000000 0.000000 0.000000 0.000000 0.000000 1.086289 0.000000 0.659288 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.079302 -0.431803 0.234373 0.000000 1.966342 0.000000 -1.259293 0.354252 -1.597007 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.107314 0.000000 -0.903925 -0.379667 -0.662523 -0.435675 0.000000 0.000000 0.359165 0.363815 0.992092 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.728734 0.000000 0.147318 0.000000 2.570752 -1.335597 0.574914 0.000000 0.000000 0.168803 1.680230 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.375276 0.000000 -0.161180 -0.674526 0.000000 -0.598331 0.000000 0.000000 1.845043 -0.431830 -0.883624 1.088774 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.481294 0.000000 1.186092 0.706412 0.492813 0.000000 0.000000 0.000000 -1.932315 0.000000 0.000000 0.000000 0.622607 0.140437 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.282588 0.000000 0.000000 -0.215148 -1.125064 -0.657839 0.140606 -0.906547 -0.602328 0.000000 0.440075 2.315901 0.637079 0.393731 0.569628 0.000000 0.000000 0.000000 0.000000 0.000000 -0.280856 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.912662 0.000000 -1.186556 0.247811 0.523553 -1.412888 2.323138 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.073994 0.132193 0.000000 -0.073145 -0.220238 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.528699 0.000000 0.000000 0.000000 -0.026385 0.000000 0.000000 0.000000 0.791391 0.000000 0.313252 0.000000 -0.838300 0.000000 0.710983 -0.470721 0.917158 0.000000 1.304851 -1.000185 0.756871 0.000000 -0.894015 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 101 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 1 3 4 8 12 16 20 25 29 36 44 51 59 66 78 85 91 101 Column indices: 1 0 2 2 1 2 3 4 1 2 3 4 1 2 3 5 2 4 5 7 0 1 2 5 8 0 1 7 9 1 2 3 5 7 8 9 1 3 4 5 6 9 10 11 0 2 4 5 6 9 10 1 3 4 6 9 10 11 12 0 2 3 4 8 12 13 0 3 4 5 6 7 8 10 11 12 13 14 0 7 9 10 11 12 13 1 2 4 5 13 17 1 3 5 7 8 9 11 12 13 15 Off-diagonal values: -0.020152 0.937559 -0.648318 0.666438 -1.162541 -0.349018 -0.607391 -0.355789 -0.479364 1.112509 0.092818 -0.768964 -0.966904 -0.176234 0.016885 1.003778 0.490160 -1.055022 0.739883 -1.423407 -1.034970 -1.005249 -0.471743 -0.288449 -1.376965 0.759460 1.043147 1.086289 0.659288 0.079302 -0.431803 0.234373 1.966342 -1.259293 0.354252 -1.597007 0.107314 -0.903925 -0.379667 -0.662523 -0.435675 0.359165 0.363815 0.992092 -0.728734 0.147318 2.570752 -1.335597 0.574914 0.168803 1.680230 0.375276 -0.161180 -0.674526 -0.598331 1.845043 -0.431830 -0.883624 1.088774 0.481294 1.186092 0.706412 0.492813 -1.932315 0.622607 0.140437 -0.282588 -0.215148 -1.125064 -0.657839 0.140606 -0.906547 -0.602328 0.440075 2.315901 0.637079 0.393731 0.569628 -0.280856 0.912662 -1.186556 0.247811 0.523553 -1.412888 2.323138 -0.073994 0.132193 -0.073145 -0.220238 1.528699 -0.026385 0.791391 0.313252 -0.838300 0.710983 -0.470721 0.917158 1.304851 -1.000185 0.756871 -0.894015 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | o . - - - - - - - - - - - - - - - - - x | o . - - - - - - - - - - - - - - - - | | x | . - - - - - - - - - - - - - - - | o o o o . - - - - - - - - - - - - - - | o x x o | . - - - - - - - - - - - - - | o o x | x | . - - - - - - - - - - - - | | x | o x | o . - - - - - - - - - - - o o o | | o | | o . - - - - - - - - - - x x | | | | | x | x . - - - - - - - - - | x o x | x | o x o | . - - - - - - - - | x | o o o o | | x x x . - - - - - - - o | x | x o x | | x x | | . - - - - - - | x | o o | o | | x o o x | . - - - - - x | x x x | | | o | | | x x | . - - - - o | | o o o x o o | x x x x x | . - - - o | | | | | | x | o x x o x | | | . - - | o x | o o | | | | | | | x | | | o . - | x | x | o | x o x | x o x | o | | | . The error in solving: 2.776425e-16 The error in solving: 5.580528e-16 The error in solving: 1.688306e-16 The error in solving: 1.581574e-16 The error in solving: 6.216025e-17 - MATRIX ------------------------------------------------------------------------------------------------------------------ A lower-triangular matrix using a standard normal distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.696528 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.162965 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.266540 -0.194712 -1.079541 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.450755 -0.474685 0.802067 -1.509931 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.289204 0.433759 0.042304 -1.079376 -0.776086 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.249619 -0.144639 0.748204 0.000000 -1.353664 -0.306693 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.590974 -0.900049 -0.691418 0.174134 -0.129465 -0.165648 1.112822 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.127253 1.010133 -0.428052 -0.651172 -1.409194 0.701389 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.303375 -0.414804 0.000000 1.135748 -1.013783 2.459103 -0.937048 0.009310 0.349663 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.013959 -0.034006 0.127083 -1.191359 -1.714564 0.020057 0.951740 -0.651781 0.763268 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.326608 1.097461 0.000000 0.000000 -0.283438 -0.348867 0.619883 0.606385 1.143873 1.625122 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.304489 -0.415810 -0.127394 0.679870 -0.339846 0.000000 0.069802 -0.555188 -0.220015 -1.105821 -1.485961 0.819054 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.242071 1.770957 1.012663 0.000000 0.466479 0.352377 0.000000 0.000000 -0.469222 0.000000 -0.834827 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.754013 0.000000 -0.681405 -1.790425 0.798031 -0.605487 0.722119 0.357960 1.786577 0.306083 0.000000 0.275171 0.886183 -0.605414 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.035130 0.000000 1.668932 1.002509 0.000000 0.288959 0.000000 0.042044 -1.512800 -0.511944 2.066252 -0.063291 -0.778745 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.216900 -0.044765 -0.780904 0.000000 0.000000 0.008935 -0.422635 0.637179 0.052800 1.024567 1.523449 -0.851494 -0.453198 -1.952815 -0.098482 0.000000 0.000000 0.000000 0.000000 -0.205295 0.000000 0.000107 0.000000 0.523566 -1.480276 -0.119954 0.863069 -0.355221 0.367598 0.850111 -1.180322 -1.679773 1.353750 1.082844 -0.338624 1.694597 0.000000 0.000000 0.000000 0.000000 -0.323276 0.447059 -0.381378 0.000000 0.000000 -0.431445 0.000000 -0.146342 0.000000 2.371202 0.000000 1.950877 -0.211260 -1.119880 0.000000 -1.592525 -0.824823 0.000000 0.000000 0.000000 -0.323952 0.000000 -0.187582 -0.759223 -0.462040 -1.724736 -2.845648 0.163816 1.075062 -0.883960 0.000000 -0.147646 -0.871878 -1.448865 -0.078474 -1.505373 0.000000 0.993189 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 151 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 2 5 9 14 19 26 32 40 49 57 68 75 87 97 110 125 136 151 Column indices: 0 1 0 1 2 0 1 2 3 0 1 2 3 4 0 1 2 4 5 0 1 2 3 4 5 6 0 1 2 3 4 5 0 1 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 1 2 5 6 7 8 9 10 0 1 2 3 4 6 7 8 9 10 11 0 1 2 4 5 8 10 0 2 3 4 5 6 7 8 9 11 12 13 1 3 4 6 8 9 10 11 12 13 1 2 3 6 7 8 9 10 11 12 13 14 15 0 2 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 6 8 10 12 13 14 16 17 1 3 4 5 6 7 8 9 10 12 13 14 15 16 18 Off-diagonal values: 0.696528 -0.162965 -0.266540 -0.194712 -1.079541 0.450755 -0.474685 0.802067 -1.509931 -0.289204 0.433759 0.042304 -1.079376 -0.776086 1.249619 -0.144639 0.748204 -1.353664 -0.306693 -0.590974 -0.900049 -0.691418 0.174134 -0.129465 -0.165648 1.112822 1.127253 1.010133 -0.428052 -0.651172 -1.409194 0.701389 -0.303375 -0.414804 1.135748 -1.013783 2.459103 -0.937048 0.009310 0.349663 -0.013959 -0.034006 0.127083 -1.191359 -1.714564 0.020057 0.951740 -0.651781 0.763268 -0.326608 1.097461 -0.283438 -0.348867 0.619883 0.606385 1.143873 1.625122 -1.304489 -0.415810 -0.127394 0.679870 -0.339846 0.069802 -0.555188 -0.220015 -1.105821 -1.485961 0.819054 0.242071 1.770957 1.012663 0.466479 0.352377 -0.469222 -0.834827 0.754013 -0.681405 -1.790425 0.798031 -0.605487 0.722119 0.357960 1.786577 0.306083 0.275171 0.886183 -0.605414 -0.035130 1.668932 1.002509 0.288959 0.042044 -1.512800 -0.511944 2.066252 -0.063291 -0.778745 1.216900 -0.044765 -0.780904 0.008935 -0.422635 0.637179 0.052800 1.024567 1.523449 -0.851494 -0.453198 -1.952815 -0.098482 -0.205295 0.000107 0.523566 -1.480276 -0.119954 0.863069 -0.355221 0.367598 0.850111 -1.180322 -1.679773 1.353750 1.082844 -0.338624 1.694597 -0.323276 0.447059 -0.381378 -0.431445 -0.146342 2.371202 1.950877 -0.211260 -1.119880 -1.592525 -0.824823 -0.323952 -0.187582 -0.759223 -0.462040 -1.724736 -2.845648 0.163816 1.075062 -0.883960 -0.147646 -0.871878 -1.448865 -0.078474 -1.505373 0.993189 . - - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | o . - - - - - - - - - - - - - - - - - o o o . - - - - - - - - - - - - - - - - x o x o . - - - - - - - - - - - - - - - o x x o o . - - - - - - - - - - - - - - x o x | o o . - - - - - - - - - - - - - o o o x o o x . - - - - - - - - - - - - x x o o o x | | . - - - - - - - - - - - o o | x o x o x x . - - - - - - - - - - o o x o o x x o x | . - - - - - - - - - | o x | | o o x x x x . - - - - - - - - o o o x o | x o o o o x . - - - - - - - x x x | x x | | o | o | | . - - - - - - x | o o x o x x x x | x x o . - - - - - | o | x x | x | x o o x o o | . - - - - | x o o | | x o x x x x o o o o . - - - o | x | x o o x o x x o o x x o x . - - | o x o | | o | o | x | x o o | o o . - | o | o o o o o x x o | o o o o o | x . The error in solving: 4.163336e-16 The error in solving: 2.420670e-16 The error in solving: 1.672547e-16 The error in solving: 3.600251e-16 The error in solving: 4.129079e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.250000 [ 0.802156 0.406609 0.000000 0.401799 0.285350 0.000000 0.000000 0.000000 0.795446 0.000000 0.000000 0.000000 0.743826 0.000000 0.000000 0.625122 0.000000 0.000000 0.664065 0.235622 0.406609 0.348851 0.000000 0.000000 0.000000 0.000000 0.000000 0.955469 0.000000 0.000000 0.000000 0.000000 0.000000 0.656455 0.000000 0.000000 0.000000 0.000000 0.130703 0.000000 0.000000 0.000000 0.000000 0.179764 0.658673 0.000000 0.000000 0.000000 0.955645 0.983996 0.721683 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.133686 0.000000 0.000000 0.401799 0.000000 0.179764 0.000000 0.000000 0.000000 0.269373 0.000000 0.000000 0.495089 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.656758 0.000000 0.000000 0.285350 0.000000 0.658673 0.000000 0.000000 0.000000 0.000000 0.000000 0.030007 0.000000 0.871485 0.000000 0.000000 0.000000 0.000000 0.000000 0.703635 0.978458 0.690416 0.779453 0.000000 0.000000 0.000000 0.000000 0.000000 0.562279 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.645896 0.000000 0.000000 0.000000 0.000000 0.000000 0.731081 0.000000 0.000000 0.000000 0.000000 0.269373 0.000000 0.000000 0.000000 0.390159 0.000000 0.142613 0.728783 0.000000 0.000000 0.000000 0.000000 0.511675 0.000000 0.272255 0.700013 0.000000 0.000000 0.955469 0.000000 0.000000 0.000000 0.000000 0.390159 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.968093 0.000000 0.431480 0.000000 0.000000 0.795446 0.000000 0.955645 0.000000 0.030007 0.000000 0.000000 0.000000 0.000000 0.414347 0.000000 0.000000 0.973337 0.889213 0.163780 0.979207 0.449329 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0.629156]; Dimension: 20 x 20 Off-diagonal entries: 136 (max 380) Diagonal entries: 0.802156 0.348851 0.000000 0.000000 0.000000 0.562279 0.000000 0.000000 0.000000 0.628969 0.000000 0.000000 0.030873 0.000000 0.000000 0.000000 0.000000 0.000000 0.698076 0.629156 Row indices: 0 8 12 18 23 31 33 40 44 55 64 72 78 85 90 96 103 109 117 127 136 Column indices: 1 3 4 8 12 15 18 19 0 7 13 18 3 4 8 9 10 17 0 2 6 9 17 0 2 8 10 16 17 18 19 12 18 3 7 9 10 15 17 18 1 6 15 17 0 2 4 9 12 13 14 15 16 18 19 2 3 6 8 10 12 14 15 19 2 4 6 9 11 14 16 19 10 12 13 14 15 19 0 5 8 9 11 14 18 1 8 11 18 19 8 9 10 11 12 16 0 6 7 8 9 11 16 4 8 10 14 15 17 2 3 4 6 7 16 18 19 0 1 4 5 6 8 12 13 17 19 0 4 8 9 10 11 13 17 18 Off-diagonal values: 0.406609 0.401799 0.285350 0.795446 0.743826 0.625122 0.664065 0.235622 0.406609 0.955469 0.656455 0.130703 0.179764 0.658673 0.955645 0.983996 0.721683 0.133686 0.401799 0.179764 0.269373 0.495089 0.656758 0.285350 0.658673 0.030007 0.871485 0.703635 0.978458 0.690416 0.779453 0.645896 0.731081 0.269373 0.390159 0.142613 0.728783 0.511675 0.272255 0.700013 0.955469 0.390159 0.968093 0.431480 0.795446 0.955645 0.030007 0.414347 0.973337 0.889213 0.163780 0.979207 0.449329 0.196037 0.781740 0.983996 0.495089 0.142613 0.414347 0.563892 0.703394 0.531786 0.170540 0.889872 0.721683 0.871485 0.728783 0.563892 0.618805 0.076339 0.318404 0.658742 0.618805 0.896172 0.194828 0.550729 0.914700 0.798423 0.743826 0.645896 0.973337 0.703394 0.896172 0.237288 0.181196 0.656455 0.889213 0.194828 0.777651 0.522447 0.163780 0.531786 0.076339 0.550729 0.237288 0.990151 0.625122 0.511675 0.968093 0.979207 0.170540 0.914700 0.880784 0.703635 0.449329 0.318404 0.990151 0.880784 0.236954 0.133686 0.656758 0.978458 0.272255 0.431480 0.236954 0.169120 0.998086 0.664065 0.130703 0.690416 0.731081 0.700013 0.196037 0.181196 0.777651 0.169120 0.128883 0.235622 0.779453 0.781740 0.889872 0.658742 0.798423 0.522447 0.998086 0.128883 x x - x x - - - x - - - x - - x - - x x x x - - - - - x - - - - - x - - - - x - | | . x x - - - x x x - - - - - - x - - x | x . - - x - - x - - - - - - - x - - x | x | . - - - x - x - - - - - x x x x | | | | | x - - - - - - x - - - - - x - | | | x | | . x - x x - - - - x - x x - | x | | | | x . - - - - - - - x - x - - x | x | x | | | . x - - x x x x x - x x | | x x | | x | x x x - x - x x - - - x | | x | x | x | | x . x - - x - x - - x | | | | | | | | | | x . x x x x - - - x x | | | | x | | x x | x x - x - - - x - | x | | | | | | x | | x | . - - - - x x | | | | | | | | x x x x x | . - x - - - x | | | | | x x x x | x | | | . x - - - | | | | x | | | x | x | | | x x . x - - | | x x x | x x | | | | | | | | x . x x x x | | x x x | x | | | x x | | | x x x x | | | x | | | x x x x | x | | | x x x The error in solving: 4.619448e-16 The error in solving: 5.150814e-16 The error in solving: 6.963570e-16 The error in solving: 6.222702e-16 The error in solving: 8.420970e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.500000 [ 0.844851 0.025236 0.000000 0.323826 0.000000 0.930058 0.000000 0.027633 0.000000 0.000000 0.329695 0.000000 0.765434 0.592450 0.000000 0.289654 0.563290 0.000000 0.000000 0.487101 0.025236 0.518266 0.297391 0.000000 0.000000 0.961794 0.979233 0.000000 0.723339 0.576657 0.025736 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.620804 0.130078 0.000000 0.297391 0.616230 0.592280 0.425547 0.138663 0.657795 0.919768 0.191379 0.000000 0.000000 0.901246 0.000000 0.000000 0.000000 0.000000 0.383045 0.346684 0.008729 0.000000 0.323826 0.000000 0.592280 0.000000 0.931195 0.027892 0.734893 0.500453 0.545633 0.249606 0.614675 0.000000 0.000000 0.983882 0.400465 0.490220 0.866103 0.000000 0.778386 0.000000 0.000000 0.000000 0.425547 0.931195 0.000000 0.009408 0.000000 0.000000 0.812762 0.000000 0.052811 0.000000 0.000000 0.000000 0.554822 0.208178 0.692429 0.000000 0.949744 0.000000 0.930058 0.961794 0.138663 0.027892 0.009408 0.609119 0.397756 0.499479 0.116652 0.000000 0.375447 0.000000 0.146541 0.749183 0.000000 0.124096 0.000000 0.000000 0.486065 0.000000 0.000000 0.979233 0.657795 0.734893 0.000000 0.397756 0.000000 0.032425 0.000000 0.741793 0.000000 0.001211 0.585273 0.000000 0.000000 0.565000 0.861744 0.504404 0.787449 0.732888 0.027633 0.000000 0.919768 0.500453 0.000000 0.499479 0.032425 0.376311 0.000000 0.010730 0.416899 0.767497 0.000000 0.000000 0.000000 0.000000 0.672253 0.000000 0.000000 0.000000 0.000000 0.723339 0.191379 0.545633 0.812762 0.116652 0.000000 0.000000 0.901898 0.882265 0.938610 0.000000 0.000000 0.927213 0.000000 0.430415 0.981298 0.000000 0.745601 0.413716 0.000000 0.576657 0.000000 0.249606 0.000000 0.000000 0.741793 0.010730 0.882265 0.822559 0.913114 0.000000 0.000000 0.000000 0.060063 0.000000 0.000000 0.142288 0.000000 0.000000 0.329695 0.025736 0.000000 0.614675 0.052811 0.375447 0.000000 0.416899 0.938610 0.913114 0.132238 0.000000 0.172564 0.000000 0.000000 0.000000 0.262460 0.723295 0.896987 0.176148 0.000000 0.000000 0.901246 0.000000 0.000000 0.000000 0.001211 0.767497 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.927040 0.000000 0.765434 0.000000 0.000000 0.000000 0.000000 0.146541 0.585273 0.000000 0.000000 0.000000 0.172564 0.000000 0.000000 0.156226 0.000000 0.055463 0.000000 0.000000 0.000000 0.000000 0.592450 0.000000 0.000000 0.983882 0.000000 0.749183 0.000000 0.000000 0.927213 0.000000 0.000000 0.000000 0.156226 0.290182 0.000000 0.000000 0.000000 0.000000 0.167450 0.292429 0.000000 0.000000 0.000000 0.400465 0.554822 0.000000 0.000000 0.000000 0.000000 0.060063 0.000000 0.000000 0.000000 0.000000 0.000000 0.731071 0.511743 0.000000 0.556510 0.425618 0.289654 0.000000 0.000000 0.490220 0.208178 0.124096 0.565000 0.000000 0.430415 0.000000 0.000000 0.000000 0.055463 0.000000 0.731071 0.130763 0.496319 0.000000 0.000000 0.446431 0.563290 0.000000 0.383045 0.866103 0.692429 0.000000 0.861744 0.672253 0.981298 0.000000 0.262460 0.000000 0.000000 0.000000 0.511743 0.496319 0.000000 0.198321 0.000000 0.461541 0.000000 0.000000 0.346684 0.000000 0.000000 0.000000 0.504404 0.000000 0.000000 0.142288 0.723295 0.000000 0.000000 0.000000 0.000000 0.000000 0.198321 0.016453 0.379342 0.000000 0.000000 0.620804 0.008729 0.778386 0.949744 0.486065 0.787449 0.000000 0.745601 0.000000 0.896987 0.927040 0.000000 0.167450 0.556510 0.000000 0.000000 0.379342 0.489906 0.767691 0.487101 0.130078 0.000000 0.000000 0.000000 0.000000 0.732888 0.000000 0.413716 0.000000 0.176148 0.000000 0.000000 0.292429 0.425618 0.446431 0.461541 0.000000 0.767691 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 196 (max 380) Diagonal entries: 0.844851 0.518266 0.616230 0.000000 0.000000 0.609119 0.000000 0.376311 0.901898 0.822559 0.132238 0.000000 0.000000 0.290182 0.000000 0.130763 0.000000 0.016453 0.489906 0.000000 Row indices: 0 10 19 30 44 53 66 79 88 100 108 121 125 131 138 145 155 167 173 186 196 Column indices: 1 3 5 7 10 12 13 15 16 19 0 2 5 6 8 9 10 18 19 1 3 4 5 6 7 8 11 16 17 18 0 2 4 5 6 7 8 9 10 13 14 15 16 18 2 3 5 8 10 14 15 16 18 0 1 2 3 4 6 7 8 10 12 13 15 18 1 2 3 5 7 9 11 12 15 16 17 18 19 0 2 3 5 6 9 10 11 16 1 2 3 4 5 9 10 13 15 16 18 19 1 3 6 7 8 10 14 17 0 1 3 4 5 7 8 9 12 16 17 18 19 2 6 7 18 0 5 6 10 13 15 0 3 5 8 12 18 19 3 4 9 15 16 18 19 0 3 4 5 6 8 12 14 16 19 0 2 3 4 6 7 8 10 14 15 17 19 2 6 9 10 16 18 1 2 3 4 5 6 8 10 11 13 14 17 19 0 1 6 8 10 13 14 15 16 18 Off-diagonal values: 0.025236 0.323826 0.930058 0.027633 0.329695 0.765434 0.592450 0.289654 0.563290 0.487101 0.025236 0.297391 0.961794 0.979233 0.723339 0.576657 0.025736 0.620804 0.130078 0.297391 0.592280 0.425547 0.138663 0.657795 0.919768 0.191379 0.901246 0.383045 0.346684 0.008729 0.323826 0.592280 0.931195 0.027892 0.734893 0.500453 0.545633 0.249606 0.614675 0.983882 0.400465 0.490220 0.866103 0.778386 0.425547 0.931195 0.009408 0.812762 0.052811 0.554822 0.208178 0.692429 0.949744 0.930058 0.961794 0.138663 0.027892 0.009408 0.397756 0.499479 0.116652 0.375447 0.146541 0.749183 0.124096 0.486065 0.979233 0.657795 0.734893 0.397756 0.032425 0.741793 0.001211 0.585273 0.565000 0.861744 0.504404 0.787449 0.732888 0.027633 0.919768 0.500453 0.499479 0.032425 0.010730 0.416899 0.767497 0.672253 0.723339 0.191379 0.545633 0.812762 0.116652 0.882265 0.938610 0.927213 0.430415 0.981298 0.745601 0.413716 0.576657 0.249606 0.741793 0.010730 0.882265 0.913114 0.060063 0.142288 0.329695 0.025736 0.614675 0.052811 0.375447 0.416899 0.938610 0.913114 0.172564 0.262460 0.723295 0.896987 0.176148 0.901246 0.001211 0.767497 0.927040 0.765434 0.146541 0.585273 0.172564 0.156226 0.055463 0.592450 0.983882 0.749183 0.927213 0.156226 0.167450 0.292429 0.400465 0.554822 0.060063 0.731071 0.511743 0.556510 0.425618 0.289654 0.490220 0.208178 0.124096 0.565000 0.430415 0.055463 0.731071 0.496319 0.446431 0.563290 0.383045 0.866103 0.692429 0.861744 0.672253 0.981298 0.262460 0.511743 0.496319 0.198321 0.461541 0.346684 0.504404 0.142288 0.723295 0.198321 0.379342 0.620804 0.008729 0.778386 0.949744 0.486065 0.787449 0.745601 0.896987 0.927040 0.167450 0.556510 0.379342 0.767691 0.487101 0.130078 0.732888 0.413716 0.176148 0.292429 0.425618 0.446431 0.461541 0.767691 x x - x - x - x - - x - x x - x x - - x x x x - - x x - x x x - - - - - - - x x | x x x x x x x x - - x - - - - x x x - x | x . x x x x x x x - - x x x x - x - | | x x . x - - x - x - - - x x x - x - x x x x x x x x x - x - x x - x - - x - | x x x | x . x - x - x x - - x x x x x x | x x | x x x - x x x - - - - x - - - | x x x x x | | x x x - - x - x x - x x | x | x | | x x x x x - - - x - - x - - x x | x x x | x x x x - x - - - x x x x | | x | | | x x | | | . - - - - - - x - x | | | | x x | | | x | . x - x - - - - x | | x | x | | x | | | x x - - - - x x | | | x x | | | | x | | | | . x x - x x x | | x x x x | x | | | x | x x x - - x x | x x x | x x x | x | | | x x . x - x | | x | | | x | | x x | | | | | x x x - | x x x x x x | x | x x | x x | | x x x x x | | | | x | x | x | | x x x x | x . The error in solving: 5.863263e-16 The error in solving: 5.965835e-16 The error in solving: 4.615799e-16 The error in solving: 4.755674e-16 The error in solving: 5.417672e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.750000 [ 0.633305 0.736834 0.663921 0.667568 0.691195 0.227082 0.726637 0.000000 0.000000 0.326779 0.392612 0.000000 0.815249 0.000000 0.321911 0.000000 0.849977 0.000000 0.825748 0.317655 0.736834 0.920197 0.726329 0.117318 0.000000 0.402293 0.515330 0.341074 0.000000 0.608973 0.713245 0.720423 0.143049 0.705496 0.977034 0.340492 0.000000 0.086214 0.165977 0.183717 0.663921 0.726329 0.274081 0.994969 0.996898 0.961757 0.230256 0.869484 0.650317 0.256155 0.781529 0.000000 0.946634 0.280651 0.036285 0.000000 0.326887 0.210791 0.000000 0.373678 0.667568 0.117318 0.994969 0.823060 0.992606 0.977424 0.000000 0.697229 0.442651 0.131339 0.587646 0.632936 0.000000 0.330643 0.576133 0.756100 0.714345 0.000000 0.809754 0.000000 0.691195 0.000000 0.996898 0.992606 0.876297 0.613030 0.352356 0.000000 0.725430 0.417807 0.043999 0.000000 0.553189 0.000000 0.713136 0.445278 0.000000 0.862667 0.496706 0.353963 0.227082 0.402293 0.961757 0.977424 0.613030 0.358527 0.997425 0.799193 0.113644 0.429595 0.193540 0.916336 0.017177 0.000000 0.767209 0.123744 0.525867 0.000000 0.622282 0.126222 0.726637 0.515330 0.230256 0.000000 0.352356 0.997425 0.000000 0.000000 0.000000 0.800361 0.167115 0.000000 0.126790 0.333209 0.000000 0.774050 0.000000 0.121552 0.634172 0.705042 0.000000 0.341074 0.869484 0.697229 0.000000 0.799193 0.000000 0.156882 0.000000 0.589086 0.208159 0.649992 0.105828 0.653614 0.043011 0.046175 0.108019 0.361203 0.000000 0.690582 0.000000 0.000000 0.650317 0.442651 0.725430 0.113644 0.000000 0.000000 0.747538 0.406315 0.608354 0.738323 0.320245 0.475635 0.000000 0.192416 0.136015 0.000000 0.296604 0.000000 0.326779 0.608973 0.256155 0.131339 0.417807 0.429595 0.800361 0.589086 0.406315 0.219386 0.000000 0.769330 0.490522 0.015072 0.687206 0.201554 0.360956 0.595592 0.000000 0.771325 0.392612 0.713245 0.781529 0.587646 0.043999 0.193540 0.167115 0.208159 0.608354 0.000000 0.040115 0.313952 0.803860 0.350604 0.209710 0.000000 0.000000 0.000000 0.054273 0.000000 0.000000 0.720423 0.000000 0.632936 0.000000 0.916336 0.000000 0.649992 0.738323 0.769330 0.313952 0.000000 0.000000 0.456797 0.000000 0.000000 0.459567 0.702692 0.834847 0.566993 0.815249 0.143049 0.946634 0.000000 0.553189 0.017177 0.126790 0.105828 0.320245 0.490522 0.803860 0.000000 0.885998 0.700699 0.000000 0.325184 0.000000 0.586642 0.000000 0.000000 0.000000 0.705496 0.280651 0.330643 0.000000 0.000000 0.333209 0.653614 0.475635 0.015072 0.350604 0.456797 0.700699 0.020845 0.501279 0.409193 0.000000 0.000000 0.000000 0.073307 0.321911 0.977034 0.036285 0.576133 0.713136 0.767209 0.000000 0.043011 0.000000 0.687206 0.209710 0.000000 0.000000 0.501279 0.094777 0.671465 0.000000 0.000000 0.553751 0.760697 0.000000 0.340492 0.000000 0.756100 0.445278 0.123744 0.774050 0.046175 0.192416 0.201554 0.000000 0.000000 0.325184 0.409193 0.671465 0.935058 0.833253 0.704880 0.020376 0.585574 0.849977 0.000000 0.326887 0.714345 0.000000 0.525867 0.000000 0.108019 0.136015 0.360956 0.000000 0.459567 0.000000 0.000000 0.000000 0.833253 0.557256 0.274330 0.775872 0.000000 0.000000 0.086214 0.210791 0.000000 0.862667 0.000000 0.121552 0.361203 0.000000 0.595592 0.000000 0.702692 0.586642 0.000000 0.000000 0.704880 0.274330 0.220118 0.939145 0.529371 0.825748 0.165977 0.000000 0.809754 0.496706 0.622282 0.634172 0.000000 0.296604 0.000000 0.054273 0.834847 0.000000 0.000000 0.553751 0.020376 0.775872 0.939145 0.614059 0.283969 0.317655 0.183717 0.373678 0.000000 0.353963 0.126222 0.705042 0.690582 0.000000 0.771325 0.000000 0.566993 0.000000 0.073307 0.760697 0.585574 0.000000 0.529371 0.283969 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 278 (max 380) Diagonal entries: 0.633305 0.920197 0.274081 0.823060 0.876297 0.358527 0.000000 0.156882 0.747538 0.219386 0.040115 0.000000 0.885998 0.020845 0.094777 0.935058 0.557256 0.220118 0.614059 0.000000 Row indices: 0 13 29 45 60 74 91 104 118 130 147 161 173 186 199 212 227 238 250 264 278 Column indices: 1 2 3 4 5 6 9 10 12 14 16 18 19 0 2 3 5 6 7 9 10 11 12 13 14 15 17 18 19 0 1 3 4 5 6 7 8 9 10 12 13 14 16 17 19 0 1 2 4 5 7 8 9 10 11 13 14 15 16 18 0 2 3 5 6 8 9 10 12 14 15 17 18 19 0 1 2 3 4 6 7 8 9 10 11 12 14 15 16 18 19 0 1 2 4 5 9 10 12 13 15 17 18 19 1 2 3 5 9 10 11 12 13 14 15 16 17 19 2 3 4 5 9 10 11 12 13 15 16 18 0 1 2 3 4 5 6 7 8 11 12 13 14 15 16 17 19 0 1 2 3 4 5 6 7 8 11 12 13 14 18 1 3 5 7 8 9 10 13 16 17 18 19 0 1 2 4 5 6 7 8 9 10 13 15 17 1 2 3 6 7 8 9 10 11 12 14 15 19 0 1 2 3 4 5 7 9 10 13 15 18 19 1 3 4 5 6 7 8 9 12 13 14 16 17 18 19 0 2 3 5 7 8 9 11 15 17 18 1 2 4 6 7 9 11 12 15 16 18 19 0 1 3 4 5 6 8 10 11 14 15 16 17 19 0 1 2 4 5 6 7 9 11 13 14 15 17 18 Off-diagonal values: 0.736834 0.663921 0.667568 0.691195 0.227082 0.726637 0.326779 0.392612 0.815249 0.321911 0.849977 0.825748 0.317655 0.736834 0.726329 0.117318 0.402293 0.515330 0.341074 0.608973 0.713245 0.720423 0.143049 0.705496 0.977034 0.340492 0.086214 0.165977 0.183717 0.663921 0.726329 0.994969 0.996898 0.961757 0.230256 0.869484 0.650317 0.256155 0.781529 0.946634 0.280651 0.036285 0.326887 0.210791 0.373678 0.667568 0.117318 0.994969 0.992606 0.977424 0.697229 0.442651 0.131339 0.587646 0.632936 0.330643 0.576133 0.756100 0.714345 0.809754 0.691195 0.996898 0.992606 0.613030 0.352356 0.725430 0.417807 0.043999 0.553189 0.713136 0.445278 0.862667 0.496706 0.353963 0.227082 0.402293 0.961757 0.977424 0.613030 0.997425 0.799193 0.113644 0.429595 0.193540 0.916336 0.017177 0.767209 0.123744 0.525867 0.622282 0.126222 0.726637 0.515330 0.230256 0.352356 0.997425 0.800361 0.167115 0.126790 0.333209 0.774050 0.121552 0.634172 0.705042 0.341074 0.869484 0.697229 0.799193 0.589086 0.208159 0.649992 0.105828 0.653614 0.043011 0.046175 0.108019 0.361203 0.690582 0.650317 0.442651 0.725430 0.113644 0.406315 0.608354 0.738323 0.320245 0.475635 0.192416 0.136015 0.296604 0.326779 0.608973 0.256155 0.131339 0.417807 0.429595 0.800361 0.589086 0.406315 0.769330 0.490522 0.015072 0.687206 0.201554 0.360956 0.595592 0.771325 0.392612 0.713245 0.781529 0.587646 0.043999 0.193540 0.167115 0.208159 0.608354 0.313952 0.803860 0.350604 0.209710 0.054273 0.720423 0.632936 0.916336 0.649992 0.738323 0.769330 0.313952 0.456797 0.459567 0.702692 0.834847 0.566993 0.815249 0.143049 0.946634 0.553189 0.017177 0.126790 0.105828 0.320245 0.490522 0.803860 0.700699 0.325184 0.586642 0.705496 0.280651 0.330643 0.333209 0.653614 0.475635 0.015072 0.350604 0.456797 0.700699 0.501279 0.409193 0.073307 0.321911 0.977034 0.036285 0.576133 0.713136 0.767209 0.043011 0.687206 0.209710 0.501279 0.671465 0.553751 0.760697 0.340492 0.756100 0.445278 0.123744 0.774050 0.046175 0.192416 0.201554 0.325184 0.409193 0.671465 0.833253 0.704880 0.020376 0.585574 0.849977 0.326887 0.714345 0.525867 0.108019 0.136015 0.360956 0.459567 0.833253 0.274330 0.775872 0.086214 0.210791 0.862667 0.121552 0.361203 0.595592 0.702692 0.586642 0.704880 0.274330 0.939145 0.529371 0.825748 0.165977 0.809754 0.496706 0.622282 0.634172 0.296604 0.054273 0.834847 0.553751 0.020376 0.775872 0.939145 0.283969 0.317655 0.183717 0.373678 0.353963 0.126222 0.705042 0.690582 0.771325 0.566993 0.073307 0.760697 0.585574 0.529371 0.283969 x x x x x x x - - x x - x - x - x - x x x x x x - x x x - x x x x x x x - x x x x x x x x x x x x x x - x x x - x x - x x x x x x x - x x x x x - x x x x - x - x | x x x x x - x x x - x - x x - x x x x x x x x x x x x x x x x - x x x - x x x x x | x x . - - x x - x x - x - x x x | x x x | x | x - x x x x x x x x x - x | | x x x x | | x x x x x x - x x - x - x x x x x x x x x x - x x x x x x x - x x x x x x x x x x | x x x x x - - - x - | x | x | x | x x x x . - x - - x x x x x x x | x x x x x x x | x x - x - x - - | x x x | | x x x x x x x x x x - - - x x x x x x x | x | x x | | x x x - - x x | x | x x x x x x x | | x x x x x x x x x | x x | x | x x x | x | | | x x x x - | x x | x | x x | x | x x | | x x x x x x x | x x x x | x | x x | | x x x x x x x x x | x x x x | x | x | x x x | x x . The error in solving: 4.654752e-16 The error in solving: 5.612360e-16 The error in solving: 3.805653e-16 The error in solving: 1.099415e-15 The error in solving: 7.687155e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.960277 0.401019 0.000000 0.000000 0.417905 0.000000 0.000000 0.000000 0.217377 0.000000 0.690538 0.000000 0.000000 0.000000 0.000000 0.208470 0.000000 0.000000 0.000000 0.000000 0.401019 0.218364 0.746728 0.000000 0.000000 0.000000 0.307249 0.180198 0.761059 0.000000 0.000000 0.426372 0.000000 0.038196 0.000000 0.000000 0.000000 0.052780 0.000000 0.000000 0.000000 0.746728 0.633904 0.000000 0.822219 0.435710 0.000000 0.000000 0.000000 0.000000 0.218576 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.264947 0.000000 0.000000 0.000000 0.000000 0.000000 0.184419 0.881204 0.000000 0.000000 0.455566 0.000000 0.000000 0.000000 0.000000 0.814982 0.000000 0.000000 0.664624 0.000000 0.004263 0.000000 0.000000 0.417905 0.000000 0.822219 0.881204 0.315816 0.613382 0.000000 0.126606 0.000000 0.000000 0.000000 0.000000 0.639042 0.215173 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.435710 0.000000 0.613382 0.173320 0.000000 0.000000 0.000000 0.000000 0.110550 0.000000 0.259866 0.000000 0.000000 0.000000 0.055738 0.044990 0.000000 0.000000 0.000000 0.307249 0.000000 0.000000 0.000000 0.000000 0.346846 0.000000 0.000000 0.000000 0.000000 0.812893 0.002487 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.128286 0.000000 0.180198 0.000000 0.455566 0.126606 0.000000 0.000000 0.590950 0.000000 0.825550 0.647752 0.000000 0.000000 0.000000 0.563862 0.317951 0.000000 0.000000 0.000000 0.826645 0.217377 0.761059 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.243840 0.000000 0.997137 0.000000 0.504129 0.000000 0.000000 0.000000 0.000000 0.000000 0.502210 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.825550 0.000000 0.898679 0.000000 0.000000 0.166084 0.000000 0.000000 0.000000 0.000000 0.516765 0.000000 0.000000 0.690538 0.000000 0.218576 0.000000 0.000000 0.110550 0.000000 0.647752 0.997137 0.000000 0.298637 0.000000 0.253140 0.066543 0.000000 0.602871 0.000000 0.000000 0.000000 0.000000 0.000000 0.426372 0.000000 0.000000 0.000000 0.000000 0.812893 0.000000 0.000000 0.000000 0.000000 0.469732 0.000000 0.000000 0.003162 0.141819 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.814982 0.639042 0.259866 0.002487 0.000000 0.504129 0.166084 0.253140 0.000000 0.981525 0.000000 0.516901 0.963001 0.000000 0.000000 0.000000 0.925097 0.000000 0.038196 0.000000 0.000000 0.215173 0.000000 0.000000 0.000000 0.000000 0.000000 0.066543 0.000000 0.000000 0.697615 0.000000 0.000000 0.000000 0.511738 0.174742 0.718403 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.563862 0.000000 0.000000 0.000000 0.003162 0.516901 0.000000 0.799339 0.000000 0.000000 0.000000 0.000000 0.062455 0.208470 0.000000 0.000000 0.664624 0.000000 0.000000 0.000000 0.317951 0.000000 0.000000 0.602871 0.141819 0.963001 0.000000 0.000000 0.496247 0.000000 0.743961 0.000000 0.037777 0.000000 0.000000 0.000000 0.000000 0.000000 0.055738 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.729668 0.507469 0.000000 0.000000 0.000000 0.052780 0.264947 0.004263 0.000000 0.044990 0.000000 0.000000 0.000000 0.516765 0.000000 0.000000 0.000000 0.511738 0.000000 0.743961 0.507469 0.511903 0.335521 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.502210 0.000000 0.000000 0.000000 0.000000 0.174742 0.000000 0.000000 0.000000 0.335521 0.525727 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.128286 0.826645 0.000000 0.000000 0.000000 0.000000 0.925097 0.718403 0.062455 0.037777 0.000000 0.000000 0.000000 0.111598]; Dimension: 20 x 20 Off-diagonal entries: 116 (max 380) Diagonal entries: 0.960277 0.218364 0.633904 0.184419 0.315816 0.173320 0.346846 0.590950 0.243840 0.898679 0.298637 0.469732 0.981525 0.697615 0.799339 0.496247 0.729668 0.511903 0.525727 0.111598 Row indices: 0 5 13 18 23 30 36 40 48 53 56 64 68 78 84 88 96 98 107 110 116 Column indices: 1 4 8 10 15 0 2 6 7 8 11 13 17 1 4 5 10 17 4 7 12 15 17 0 2 3 5 7 12 13 2 4 10 12 16 17 1 11 12 19 1 3 4 9 10 14 15 19 0 1 10 12 18 7 12 17 0 2 5 7 8 12 13 15 1 6 14 15 3 4 5 6 8 9 10 14 15 19 1 4 10 17 18 19 7 11 12 19 0 3 7 10 11 12 17 19 5 17 1 2 3 5 9 13 15 16 18 8 13 17 6 7 12 13 14 15 Off-diagonal values: 0.401019 0.417905 0.217377 0.690538 0.208470 0.401019 0.746728 0.307249 0.180198 0.761059 0.426372 0.038196 0.052780 0.746728 0.822219 0.435710 0.218576 0.264947 0.881204 0.455566 0.814982 0.664624 0.004263 0.417905 0.822219 0.881204 0.613382 0.126606 0.639042 0.215173 0.435710 0.613382 0.110550 0.259866 0.055738 0.044990 0.307249 0.812893 0.002487 0.128286 0.180198 0.455566 0.126606 0.825550 0.647752 0.563862 0.317951 0.826645 0.217377 0.761059 0.997137 0.504129 0.502210 0.825550 0.166084 0.516765 0.690538 0.218576 0.110550 0.647752 0.997137 0.253140 0.066543 0.602871 0.426372 0.812893 0.003162 0.141819 0.814982 0.639042 0.259866 0.002487 0.504129 0.166084 0.253140 0.516901 0.963001 0.925097 0.038196 0.215173 0.066543 0.511738 0.174742 0.718403 0.563862 0.003162 0.516901 0.062455 0.208470 0.664624 0.317951 0.602871 0.141819 0.963001 0.743961 0.037777 0.055738 0.507469 0.052780 0.264947 0.004263 0.044990 0.516765 0.511738 0.743961 0.507469 0.335521 0.502210 0.174742 0.335521 0.128286 0.826645 0.925097 0.718403 0.062455 0.037777 x x - - x - - - x - x - - - - x - - - - x x x - - - x x x - - x - x - - - x - - | x x - x x - - - - x - - - - - - x - - | | | x x - - x - - - - x - - x - x - - x | x x x x - x - - - - x x - - - - - - | | x | x x - - - - x - x - - - x x - - | x | | | | x - - - - x x - - - - - - x | x | x x | | x - x x - - - x x - - - x x x | | | | | | x - x - x - - - - - x - | | | | | | | x | x - - x - - - - x - - x | x | | x | x x | x - x x - x - - - - | x | | | | x | | | | x - - x x - - - - | | | x x x x | x x x | x - x x - - - x | x | | x | | | | | x | | x - - - x x x | | | | | | | x | | | x x | x - - - - x x | | x | | | x | | x x x | | x - x - x | | | | | x | | | | | | | | | | x x - - | x x x | x | | | x | | | x | x x x x - | | | | | | | | x | | | | x | | | x x - | | | | | | x x | | | | x x x x | | | x The error in solving: 5.492804e-16 The error in solving: 5.720275e-16 The error in solving: 4.910953e-16 The error in solving: 6.591584e-16 The error in solving: 7.393260e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.820132 0.000000 0.020827 0.596068 0.269553 0.643508 0.000000 0.663294 0.480017 0.000000 0.000000 0.435021 0.000000 0.000000 0.281325 0.483519 0.000000 0.932643 0.000000 0.306374 0.000000 0.655858 0.719431 0.000000 0.000000 0.232275 0.000000 0.000000 0.561714 0.000000 0.000000 0.000000 0.721782 0.000000 0.000000 0.386052 0.000000 0.000000 0.000000 0.000000 0.020827 0.719431 0.252813 0.000000 0.000000 0.000000 0.347511 0.000000 0.000000 0.844383 0.000000 0.012567 0.000000 0.000000 0.789437 0.169691 0.000000 0.315247 0.035792 0.073883 0.596068 0.000000 0.000000 0.617896 0.000000 0.008343 0.553946 0.000000 0.000000 0.000000 0.000000 0.406198 0.000000 0.231715 0.000000 0.883708 0.000000 0.000000 0.077975 0.952134 0.269553 0.000000 0.000000 0.000000 0.047460 0.000000 0.000000 0.000000 0.000000 0.621138 0.644603 0.511490 0.052718 0.000000 0.000000 0.804485 0.807892 0.000000 0.677101 0.399454 0.643508 0.232275 0.000000 0.008343 0.000000 0.852741 0.116857 0.000000 0.000000 0.000000 0.693435 0.433769 0.204012 0.106083 0.312767 0.000000 0.000000 0.000000 0.693550 0.514936 0.000000 0.000000 0.347511 0.553946 0.000000 0.116857 0.108980 0.614232 0.518983 0.301008 0.000000 0.000000 0.659638 0.000000 0.000000 0.385706 0.000000 0.130595 0.375712 0.979538 0.663294 0.000000 0.000000 0.000000 0.000000 0.000000 0.614232 0.705425 0.807543 0.137926 0.131536 0.724270 0.138967 0.805824 0.277948 0.000000 0.000247 0.115776 0.904398 0.000000 0.480017 0.561714 0.000000 0.000000 0.000000 0.000000 0.518983 0.807543 0.679658 0.436214 0.059493 0.869091 0.000000 0.440542 0.000000 0.908554 0.000000 0.000000 0.235352 0.000000 0.000000 0.000000 0.844383 0.000000 0.621138 0.000000 0.301008 0.137926 0.436214 0.192721 0.723963 0.000000 0.000000 0.000000 0.251617 0.123708 0.000000 0.000000 0.549616 0.000000 0.000000 0.000000 0.000000 0.000000 0.644603 0.693435 0.000000 0.131536 0.059493 0.723963 0.273146 0.564955 0.585733 0.206362 0.730296 0.000000 0.000000 0.632757 0.935550 0.000000 0.435021 0.000000 0.012567 0.406198 0.511490 0.433769 0.000000 0.724270 0.869091 0.000000 0.564955 0.637578 0.133644 0.000000 0.450832 0.000000 0.375381 0.000000 0.888268 0.000000 0.000000 0.721782 0.000000 0.000000 0.052718 0.204012 0.659638 0.138967 0.000000 0.000000 0.585733 0.133644 0.925997 0.569655 0.516086 0.000000 0.000000 0.029058 0.000000 0.000000 0.000000 0.000000 0.000000 0.231715 0.000000 0.106083 0.000000 0.805824 0.440542 0.000000 0.206362 0.000000 0.569655 0.889667 0.000000 0.739830 0.779571 0.063216 0.226435 0.088823 0.281325 0.000000 0.789437 0.000000 0.000000 0.312767 0.000000 0.277948 0.000000 0.251617 0.730296 0.450832 0.516086 0.000000 0.923237 0.469611 0.924780 0.000000 0.000000 0.000000 0.483519 0.386052 0.169691 0.883708 0.804485 0.000000 0.385706 0.000000 0.908554 0.123708 0.000000 0.000000 0.000000 0.739830 0.469611 0.602044 0.000000 0.282409 0.000000 0.098727 0.000000 0.000000 0.000000 0.000000 0.807892 0.000000 0.000000 0.000247 0.000000 0.000000 0.000000 0.375381 0.000000 0.779571 0.924780 0.000000 0.625583 0.200098 0.983647 0.000000 0.932643 0.000000 0.315247 0.000000 0.000000 0.000000 0.130595 0.115776 0.000000 0.000000 0.632757 0.000000 0.029058 0.063216 0.000000 0.282409 0.200098 0.095419 0.597296 0.000000 0.000000 0.000000 0.035792 0.077975 0.677101 0.693550 0.375712 0.904398 0.235352 0.549616 0.935550 0.888268 0.000000 0.226435 0.000000 0.000000 0.983647 0.597296 0.555406 0.000000 0.306374 0.000000 0.073883 0.952134 0.399454 0.514936 0.979538 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.088823 0.000000 0.098727 0.000000 0.000000 0.000000 0.851448]; Dimension: 20 x 20 Off-diagonal entries: 200 (max 380) Diagonal entries: 0.820132 0.655858 0.252813 0.617896 0.047460 0.852741 0.108980 0.705425 0.679658 0.192721 0.273146 0.637578 0.925997 0.889667 0.923237 0.602044 0.625583 0.095419 0.555406 0.851448 Row indices: 0 11 16 26 34 43 54 65 77 87 96 107 119 129 140 150 162 169 179 192 200 Column indices: 2 3 4 5 7 8 11 14 15 17 19 2 5 8 12 15 0 1 6 9 11 14 15 17 18 19 0 5 6 11 13 15 18 19 0 9 10 11 12 15 16 18 19 0 1 3 6 10 11 12 13 14 18 19 2 3 5 7 8 9 12 15 17 18 19 0 6 8 9 10 11 12 13 14 16 17 18 0 1 6 7 9 10 11 13 15 18 2 4 6 7 8 10 14 15 18 4 5 7 8 9 11 12 13 14 17 18 0 2 3 4 5 7 8 10 12 14 16 18 1 4 5 6 7 10 11 13 14 17 3 5 7 8 10 12 15 16 17 18 19 0 2 5 7 9 10 11 12 15 16 0 1 2 3 4 6 8 9 13 14 17 19 4 7 11 13 14 17 18 0 2 6 7 10 12 13 15 16 18 2 3 4 5 6 7 8 9 10 11 13 16 17 0 2 3 4 5 6 13 15 Off-diagonal values: 0.020827 0.596068 0.269553 0.643508 0.663294 0.480017 0.435021 0.281325 0.483519 0.932643 0.306374 0.719431 0.232275 0.561714 0.721782 0.386052 0.020827 0.719431 0.347511 0.844383 0.012567 0.789437 0.169691 0.315247 0.035792 0.073883 0.596068 0.008343 0.553946 0.406198 0.231715 0.883708 0.077975 0.952134 0.269553 0.621138 0.644603 0.511490 0.052718 0.804485 0.807892 0.677101 0.399454 0.643508 0.232275 0.008343 0.116857 0.693435 0.433769 0.204012 0.106083 0.312767 0.693550 0.514936 0.347511 0.553946 0.116857 0.614232 0.518983 0.301008 0.659638 0.385706 0.130595 0.375712 0.979538 0.663294 0.614232 0.807543 0.137926 0.131536 0.724270 0.138967 0.805824 0.277948 0.000247 0.115776 0.904398 0.480017 0.561714 0.518983 0.807543 0.436214 0.059493 0.869091 0.440542 0.908554 0.235352 0.844383 0.621138 0.301008 0.137926 0.436214 0.723963 0.251617 0.123708 0.549616 0.644603 0.693435 0.131536 0.059493 0.723963 0.564955 0.585733 0.206362 0.730296 0.632757 0.935550 0.435021 0.012567 0.406198 0.511490 0.433769 0.724270 0.869091 0.564955 0.133644 0.450832 0.375381 0.888268 0.721782 0.052718 0.204012 0.659638 0.138967 0.585733 0.133644 0.569655 0.516086 0.029058 0.231715 0.106083 0.805824 0.440542 0.206362 0.569655 0.739830 0.779571 0.063216 0.226435 0.088823 0.281325 0.789437 0.312767 0.277948 0.251617 0.730296 0.450832 0.516086 0.469611 0.924780 0.483519 0.386052 0.169691 0.883708 0.804485 0.385706 0.908554 0.123708 0.739830 0.469611 0.282409 0.098727 0.807892 0.000247 0.375381 0.779571 0.924780 0.200098 0.983647 0.932643 0.315247 0.130595 0.115776 0.632757 0.029058 0.063216 0.282409 0.200098 0.597296 0.035792 0.077975 0.677101 0.693550 0.375712 0.904398 0.235352 0.549616 0.935550 0.888268 0.226435 0.983647 0.597296 0.306374 0.073883 0.952134 0.399454 0.514936 0.979538 0.088823 0.098727 x - x x x x - x x - - x - - x x - x - x | x x - - x - - x - - - x - - x - - - - x x x - - - x - - x - x - - x x - x x x x | | x - x x - - - - x - x - x - - x x x | | | x - - - - x x x x - - x x - x x x x | x | x x - - - x x x x x - - - x x | | x x | x x x x x - - x - - x - x x x x | | | | | x x x x x x x x x - x x x - x x | | | | x x x x x x - x - x - - x - | | x | x | x x x x x - - - x x - - x - | | | | x x | x x x x x x x x - - x x - x | x x x x | x x | x x x - x - x - x - | x | | x x x x | | x x x x x - - x - - | | | x | x | x x | x | x x - x x x x x x | x | | x | x | x x x x | x x x - - - x x x x x | x | x x | | | x x x - x - x | | | | x | | x | | | x | x x | x x x - x | x | | | x x | | x | x x | x x x x - | | x x x x x x x x x x | x | | x x x - x | x x x x x | | | | | | x | x | | | x The error in solving: 5.181918e-16 The error in solving: 4.878985e-16 The error in solving: 9.539670e-16 The error in solving: 6.587200e-16 The error in solving: 6.827520e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.134164 0.103829 0.594297 0.055149 0.554234 0.000000 0.499884 0.000000 0.272509 0.733368 0.394721 0.871880 0.884378 0.000000 0.771838 0.163712 0.000000 0.000000 0.543832 0.000000 0.103829 0.435153 0.390163 0.000000 0.746300 0.000000 0.035335 0.819348 0.355398 0.927930 0.646474 0.822751 0.000000 0.000000 0.000000 0.896403 0.000000 0.000000 0.113209 0.479891 0.594297 0.390163 0.111425 0.000000 0.620345 0.690927 0.654917 0.000000 0.000000 0.149997 0.021454 0.000000 0.773203 0.580823 0.000000 0.882689 0.000000 0.265532 0.150324 0.000000 0.055149 0.000000 0.000000 0.721202 0.216034 0.961632 0.664357 0.774927 0.953569 0.000000 0.771164 0.058919 0.000000 0.764375 0.352364 0.395368 0.971732 0.112312 0.031060 0.964932 0.554234 0.746300 0.620345 0.216034 0.607525 0.210582 0.901731 0.818966 0.057970 0.988699 0.631080 0.950798 0.989153 0.740203 0.461987 0.000000 0.956316 0.527207 0.648688 0.766164 0.000000 0.000000 0.690927 0.961632 0.210582 0.595700 0.000000 0.219471 0.154980 0.621149 0.646324 0.000000 0.352378 0.000000 0.606041 0.788727 0.964347 0.332311 0.021543 0.893470 0.499884 0.035335 0.654917 0.664357 0.901731 0.000000 0.548454 0.568301 0.000000 0.000000 0.904437 0.529344 0.141571 0.658786 0.574454 0.822818 0.000000 0.000000 0.281711 0.000000 0.000000 0.819348 0.000000 0.774927 0.818966 0.219471 0.568301 0.039329 0.000000 0.142576 0.257588 0.170024 0.622847 0.689631 0.000000 0.136375 0.542005 0.000000 0.058193 0.625991 0.272509 0.355398 0.000000 0.953569 0.057970 0.154980 0.000000 0.000000 0.236145 0.820670 0.931567 0.000000 0.000000 0.991906 0.468224 0.000000 0.000000 0.000000 0.452141 0.000000 0.733368 0.927930 0.149997 0.000000 0.988699 0.621149 0.000000 0.142576 0.820670 0.701748 0.000000 0.654567 0.741016 0.381640 0.528475 0.000000 0.589839 0.623239 0.860951 0.000000 0.394721 0.646474 0.021454 0.771164 0.631080 0.646324 0.904437 0.257588 0.931567 0.000000 0.404193 0.551665 0.000000 0.000000 0.668965 0.754515 0.711854 0.919278 0.428334 0.000000 0.871880 0.822751 0.000000 0.058919 0.950798 0.000000 0.529344 0.170024 0.000000 0.654567 0.551665 0.686470 0.053636 0.000000 0.500286 0.115404 0.211104 0.242840 0.353133 0.046618 0.884378 0.000000 0.773203 0.000000 0.989153 0.352378 0.141571 0.622847 0.000000 0.741016 0.000000 0.053636 0.321964 0.636394 0.000000 0.297823 0.078523 0.599046 0.021704 0.216807 0.000000 0.000000 0.580823 0.764375 0.740203 0.000000 0.658786 0.689631 0.991906 0.381640 0.000000 0.000000 0.636394 0.121888 0.929683 0.480275 0.000000 0.389857 0.557298 0.075560 0.771838 0.000000 0.000000 0.352364 0.461987 0.606041 0.574454 0.000000 0.468224 0.528475 0.668965 0.500286 0.000000 0.929683 0.938634 0.054141 0.252028 0.221491 0.056179 0.837129 0.163712 0.896403 0.882689 0.395368 0.000000 0.788727 0.822818 0.136375 0.000000 0.000000 0.754515 0.115404 0.297823 0.480275 0.054141 0.625073 0.191479 0.840629 0.468481 0.277359 0.000000 0.000000 0.000000 0.971732 0.956316 0.964347 0.000000 0.542005 0.000000 0.589839 0.711854 0.211104 0.078523 0.000000 0.252028 0.191479 0.282237 0.000000 0.452769 0.532430 0.000000 0.000000 0.265532 0.112312 0.527207 0.332311 0.000000 0.000000 0.000000 0.623239 0.919278 0.242840 0.599046 0.389857 0.221491 0.840629 0.000000 0.052367 0.545841 0.235177 0.543832 0.113209 0.150324 0.031060 0.648688 0.021543 0.281711 0.058193 0.452141 0.860951 0.428334 0.353133 0.021704 0.557298 0.056179 0.468481 0.452769 0.545841 0.706106 0.061933 0.000000 0.479891 0.000000 0.964932 0.766164 0.893470 0.000000 0.625991 0.000000 0.000000 0.000000 0.046618 0.216807 0.075560 0.837129 0.277359 0.532430 0.235177 0.061933 0.152716]; Dimension: 20 x 20 Off-diagonal entries: 280 (max 380) Diagonal entries: 0.134164 0.435153 0.111425 0.721202 0.607525 0.595700 0.548454 0.039329 0.236145 0.701748 0.404193 0.686470 0.321964 0.121888 0.938634 0.625073 0.282237 0.052367 0.706106 0.152716 Row indices: 0 13 25 37 52 70 84 97 111 121 135 150 165 179 192 207 223 235 248 267 280 Column indices: 1 2 3 4 6 8 9 10 11 12 14 15 18 0 2 4 6 7 8 9 10 11 15 18 19 0 1 4 5 6 9 10 12 13 15 17 18 0 4 5 6 7 8 10 11 13 14 15 16 17 18 19 0 1 2 3 5 6 7 8 9 10 11 12 13 14 16 17 18 19 2 3 4 7 8 9 10 12 14 15 16 17 18 19 0 1 2 3 4 7 10 11 12 13 14 15 18 1 3 4 5 6 9 10 11 12 13 15 16 18 19 0 1 3 4 5 9 10 13 14 18 0 1 2 4 5 7 8 11 12 13 14 16 17 18 0 1 2 3 4 5 6 7 8 11 14 15 16 17 18 0 1 3 4 6 7 9 10 12 14 15 16 17 18 19 0 2 4 5 6 7 9 11 13 15 16 17 18 19 2 3 4 6 7 8 9 12 14 15 17 18 19 0 3 4 5 6 8 9 10 11 13 15 16 17 18 19 0 1 2 3 5 6 7 10 11 12 13 14 16 17 18 19 3 4 5 7 9 10 11 12 14 15 18 19 2 3 4 5 9 10 11 12 13 14 15 18 19 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19 1 3 4 5 7 11 12 13 14 15 16 17 18 Off-diagonal values: 0.103829 0.594297 0.055149 0.554234 0.499884 0.272509 0.733368 0.394721 0.871880 0.884378 0.771838 0.163712 0.543832 0.103829 0.390163 0.746300 0.035335 0.819348 0.355398 0.927930 0.646474 0.822751 0.896403 0.113209 0.479891 0.594297 0.390163 0.620345 0.690927 0.654917 0.149997 0.021454 0.773203 0.580823 0.882689 0.265532 0.150324 0.055149 0.216034 0.961632 0.664357 0.774927 0.953569 0.771164 0.058919 0.764375 0.352364 0.395368 0.971732 0.112312 0.031060 0.964932 0.554234 0.746300 0.620345 0.216034 0.210582 0.901731 0.818966 0.057970 0.988699 0.631080 0.950798 0.989153 0.740203 0.461987 0.956316 0.527207 0.648688 0.766164 0.690927 0.961632 0.210582 0.219471 0.154980 0.621149 0.646324 0.352378 0.606041 0.788727 0.964347 0.332311 0.021543 0.893470 0.499884 0.035335 0.654917 0.664357 0.901731 0.568301 0.904437 0.529344 0.141571 0.658786 0.574454 0.822818 0.281711 0.819348 0.774927 0.818966 0.219471 0.568301 0.142576 0.257588 0.170024 0.622847 0.689631 0.136375 0.542005 0.058193 0.625991 0.272509 0.355398 0.953569 0.057970 0.154980 0.820670 0.931567 0.991906 0.468224 0.452141 0.733368 0.927930 0.149997 0.988699 0.621149 0.142576 0.820670 0.654567 0.741016 0.381640 0.528475 0.589839 0.623239 0.860951 0.394721 0.646474 0.021454 0.771164 0.631080 0.646324 0.904437 0.257588 0.931567 0.551665 0.668965 0.754515 0.711854 0.919278 0.428334 0.871880 0.822751 0.058919 0.950798 0.529344 0.170024 0.654567 0.551665 0.053636 0.500286 0.115404 0.211104 0.242840 0.353133 0.046618 0.884378 0.773203 0.989153 0.352378 0.141571 0.622847 0.741016 0.053636 0.636394 0.297823 0.078523 0.599046 0.021704 0.216807 0.580823 0.764375 0.740203 0.658786 0.689631 0.991906 0.381640 0.636394 0.929683 0.480275 0.389857 0.557298 0.075560 0.771838 0.352364 0.461987 0.606041 0.574454 0.468224 0.528475 0.668965 0.500286 0.929683 0.054141 0.252028 0.221491 0.056179 0.837129 0.163712 0.896403 0.882689 0.395368 0.788727 0.822818 0.136375 0.754515 0.115404 0.297823 0.480275 0.054141 0.191479 0.840629 0.468481 0.277359 0.971732 0.956316 0.964347 0.542005 0.589839 0.711854 0.211104 0.078523 0.252028 0.191479 0.452769 0.532430 0.265532 0.112312 0.527207 0.332311 0.623239 0.919278 0.242840 0.599046 0.389857 0.221491 0.840629 0.545841 0.235177 0.543832 0.113209 0.150324 0.031060 0.648688 0.021543 0.281711 0.058193 0.452141 0.860951 0.428334 0.353133 0.021704 0.557298 0.056179 0.468481 0.452769 0.545841 0.061933 0.479891 0.964932 0.766164 0.893470 0.625991 0.046618 0.216807 0.075560 0.837129 0.277359 0.532430 0.235177 0.061933 x x x x x - x - x x x x x - x x - - x - x x x - x - x x x x x x - - - x - - x x x x x - x x x - - x x - x x - x - x x - x | | x x x x x x - x x - x x x x x x x x x x x x x x x x x x x x x x - x x x x | | x x x x - x x x x - x - x x x x x x x x x x x | x x - - x x x x x x - - x - | x | x x x x x - x x x x x - x x - x x x x | x x x | | x x x - - x x - - - x - x x x | x x | x x x - x x x x - x x x - x x x x x x x x x | x x - - x x x x x - x x | x x | x x | x x x x - x x x x x x x | x | x x x x | x | x x x - x x x x x | | x x x | x x x x | | x x x x - x x x x | | x x x x | x x x x | x x x x x x x x x x x | x x x | | x x x x x x x x x x | | | x x x | x | x x x x | x x x - x x | | x x x x | | | x x x x x x x | x x x x x x x x x x x x x x x x x x x x x x x | x | x x x | x | | | x x x x x x x x x The error in solving: 1.062955e-15 The error in solving: 7.054504e-16 The error in solving: 5.490064e-16 The error in solving: 9.714018e-16 The error in solving: 4.552782e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.288885 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.100400 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0.000000 0.917858 0.000000 0.438933 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.237085 0.849593 0.571144 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.166075 0.000000 0.000000 0.000000 0.000000 0.000000 0.407930 0.000000 0.753327 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.790594 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.407930 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 102 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 7 14 23 29 33 41 45 47 53 59 64 70 77 83 85 89 94 99 102 Column indices: 1 16 0 3 11 18 19 3 9 10 15 16 17 18 1 2 5 6 9 10 12 16 18 5 6 10 12 14 16 3 4 6 17 3 4 5 7 9 11 14 17 6 12 13 14 14 19 2 3 6 10 13 14 2 3 4 9 13 15 1 6 12 13 17 3 4 7 11 13 14 7 9 10 11 12 17 18 4 6 7 8 9 12 2 10 0 2 3 4 2 5 6 11 13 1 2 3 13 19 1 8 18 Off-diagonal values: 0.288885 0.100400 0.288885 0.253029 0.375554 0.237085 0.753327 0.879283 0.071270 0.594446 0.253244 0.065862 0.388202 0.849593 0.253029 0.879283 0.547751 0.998641 0.939906 0.033347 0.033852 0.531113 0.571144 0.939219 0.660552 0.732711 0.621378 0.840943 0.969381 0.547751 0.939219 0.014319 0.003884 0.998641 0.660552 0.014319 0.254656 0.521400 0.107094 0.427168 0.118336 0.254656 0.503650 0.377236 0.383957 0.667418 0.790594 0.071270 0.939906 0.521400 0.655371 0.043281 0.641043 0.594446 0.033347 0.732711 0.655371 0.840921 0.864615 0.375554 0.107094 0.980618 0.549337 0.917858 0.033852 0.621378 0.503650 0.980618 0.575652 0.401279 0.377236 0.043281 0.840921 0.549337 0.575652 0.438933 0.166075 0.840943 0.427168 0.383957 0.667418 0.641043 0.401279 0.253244 0.864615 0.100400 0.065862 0.531113 0.969381 0.388202 0.003884 0.118336 0.917858 0.438933 0.237085 0.849593 0.571144 0.166075 0.407930 0.753327 0.790594 0.407930 . x - - - - - - - - - - - - - - x - - - x . - x - - - - - - - x - - - - - - x x | | . x - - - - - x x - - - - x x x x - | x x . - x x - - x x - x - - - x - x - | | | | . x x - - - x - x - x - x - - - | | | x x . x - - - - - - - - - - x - - | | | x x x . x - x - x - - x - - x - - | | | | | | x . - - - - x x x - - - - - | | | | | | | | . - - - - - x - - - - x | | x x | | x | | . x - - x x - - - - - | | x x x | | | | x . - - x - x - - - - | x | | | | x | | | | . x x - - - x - - | | | x x | | x | | | x . x x - - - - - | | | | | | | x | x x x x . - - - x x - | | | | x | x x x x | | x | . - - - - - | | x | | | | | | | x | | | | . - - - - x | x x x | | | | | | | | | | | . - - - | | x | | x x | | | | x | x | | | . - - | x x x | | | | | | | | | x | | | | . x | x | | | | | | x | | | | | | | | | x . The error in solving: 7.350726e-16 The error in solving: 4.702093e-16 The error in solving: 4.484059e-16 The error in solving: 5.059210e-16 The error in solving: 6.123254e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.619504 0.000000 0.500905 0.000000 0.337647 0.170908 0.981152 0.000000 0.000000 0.748657 0.000000 0.000000 0.790639 0.000000 0.172963 0.000000 0.633463 0.050991 0.000000 0.619504 0.000000 0.000000 0.000000 0.961782 0.149077 0.000000 0.175409 0.589190 0.786765 0.943918 0.341717 0.586674 0.233467 0.000000 0.000000 0.000000 0.000000 0.264213 0.000000 0.000000 0.000000 0.000000 0.197166 0.747318 0.881413 0.489668 0.000000 0.017046 0.000000 0.000000 0.000000 0.106053 0.421842 0.000000 0.000000 0.865593 0.037704 0.000000 0.043514 0.500905 0.000000 0.197166 0.000000 0.000000 0.000000 0.000000 0.946824 0.664197 0.922047 0.000000 0.000000 0.491486 0.496970 0.000000 0.000000 0.354908 0.688492 0.000000 0.170176 0.000000 0.961782 0.747318 0.000000 0.000000 0.053849 0.753027 0.397834 0.000000 0.000000 0.000000 0.000000 0.947326 0.597625 0.000000 0.028571 0.000000 0.000000 0.000000 0.000000 0.337647 0.149077 0.881413 0.000000 0.053849 0.000000 0.000000 0.360407 0.223285 0.990377 0.000000 0.611578 0.000000 0.187027 0.508964 0.000000 0.000000 0.000000 0.000000 0.000000 0.170908 0.000000 0.489668 0.000000 0.753027 0.000000 0.000000 0.674354 0.000000 0.000000 0.362683 0.442114 0.000000 0.000000 0.000000 0.109090 0.901109 0.000000 0.736278 0.000000 0.981152 0.175409 0.000000 0.946824 0.397834 0.360407 0.674354 0.000000 0.000000 0.000000 0.534084 0.000000 0.393463 0.605587 0.000000 0.702814 0.000000 0.061581 0.000000 0.000000 0.000000 0.589190 0.017046 0.664197 0.000000 0.223285 0.000000 0.000000 0.000000 0.489042 0.150469 0.000000 0.567146 0.247680 0.000000 0.586552 0.912987 0.459524 0.983667 0.000000 0.000000 0.786765 0.000000 0.922047 0.000000 0.990377 0.000000 0.000000 0.489042 0.000000 0.000000 0.000000 0.850615 0.097172 0.014251 0.000000 0.000000 0.361977 0.914808 0.000000 0.748657 0.943918 0.000000 0.000000 0.000000 0.000000 0.362683 0.534084 0.150469 0.000000 0.000000 0.493617 0.679710 0.000000 0.000000 0.181077 0.960609 0.964438 0.000000 0.000000 0.000000 0.341717 0.000000 0.000000 0.000000 0.611578 0.442114 0.000000 0.000000 0.000000 0.493617 0.000000 0.000000 0.649768 0.873480 0.484496 0.000000 0.222086 0.000000 0.355235 0.000000 0.586674 0.106053 0.491486 0.947326 0.000000 0.000000 0.393463 0.567146 0.850615 0.679710 0.000000 0.000000 0.000000 0.000000 0.000000 0.864926 0.673938 0.000000 0.251913 0.790639 0.233467 0.421842 0.496970 0.597625 0.187027 0.000000 0.605587 0.247680 0.097172 0.000000 0.649768 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.124556 0.181981 0.000000 0.000000 0.000000 0.000000 0.000000 0.508964 0.000000 0.000000 0.000000 0.014251 0.000000 0.873480 0.000000 0.000000 0.000000 0.280633 0.874539 0.386641 0.000000 0.000000 0.172963 0.000000 0.000000 0.000000 0.028571 0.000000 0.109090 0.702814 0.586552 0.000000 0.181077 0.484496 0.000000 0.000000 0.280633 0.000000 0.728928 0.000000 0.077602 0.120427 0.000000 0.000000 0.865593 0.354908 0.000000 0.000000 0.901109 0.000000 0.912987 0.000000 0.960609 0.000000 0.864926 0.000000 0.874539 0.728928 0.000000 0.000000 0.000000 0.000000 0.633463 0.000000 0.037704 0.688492 0.000000 0.000000 0.000000 0.061581 0.459524 0.361977 0.964438 0.222086 0.673938 0.000000 0.386641 0.000000 0.000000 0.000000 0.408651 0.898475 0.050991 0.264213 0.000000 0.000000 0.000000 0.000000 0.736278 0.000000 0.983667 0.914808 0.000000 0.000000 0.000000 0.124556 0.000000 0.077602 0.000000 0.408651 0.000000 0.000000 0.000000 0.000000 0.043514 0.170176 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.355235 0.251913 0.181981 0.000000 0.120427 0.000000 0.898475 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 194 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 10 21 31 41 49 59 68 79 91 100 110 119 130 142 148 159 167 179 187 194 Column indices: 1 3 5 6 7 10 13 15 17 18 0 4 5 7 8 9 10 11 12 13 18 3 4 5 6 8 12 13 16 17 19 0 2 7 8 9 12 13 16 17 19 1 2 5 6 7 12 13 15 0 1 2 4 7 8 9 11 13 14 0 2 4 7 10 11 15 16 18 0 1 3 4 5 6 10 12 13 15 17 1 2 3 5 9 10 12 13 15 16 17 18 1 3 5 8 12 13 14 17 18 0 1 6 7 8 11 12 15 16 17 1 5 6 10 13 14 15 17 19 1 2 3 4 7 8 9 10 16 17 19 0 1 2 3 4 5 7 8 9 11 18 19 5 9 11 15 16 17 0 4 6 7 8 10 11 14 16 18 19 2 3 6 8 10 12 14 15 0 2 3 7 8 9 10 11 12 14 18 19 0 1 6 8 9 13 15 17 2 3 11 12 13 15 17 Off-diagonal values: 0.619504 0.500905 0.337647 0.170908 0.981152 0.748657 0.790639 0.172963 0.633463 0.050991 0.619504 0.961782 0.149077 0.175409 0.589190 0.786765 0.943918 0.341717 0.586674 0.233467 0.264213 0.197166 0.747318 0.881413 0.489668 0.017046 0.106053 0.421842 0.865593 0.037704 0.043514 0.500905 0.197166 0.946824 0.664197 0.922047 0.491486 0.496970 0.354908 0.688492 0.170176 0.961782 0.747318 0.053849 0.753027 0.397834 0.947326 0.597625 0.028571 0.337647 0.149077 0.881413 0.053849 0.360407 0.223285 0.990377 0.611578 0.187027 0.508964 0.170908 0.489668 0.753027 0.674354 0.362683 0.442114 0.109090 0.901109 0.736278 0.981152 0.175409 0.946824 0.397834 0.360407 0.674354 0.534084 0.393463 0.605587 0.702814 0.061581 0.589190 0.017046 0.664197 0.223285 0.489042 0.150469 0.567146 0.247680 0.586552 0.912987 0.459524 0.983667 0.786765 0.922047 0.990377 0.489042 0.850615 0.097172 0.014251 0.361977 0.914808 0.748657 0.943918 0.362683 0.534084 0.150469 0.493617 0.679710 0.181077 0.960609 0.964438 0.341717 0.611578 0.442114 0.493617 0.649768 0.873480 0.484496 0.222086 0.355235 0.586674 0.106053 0.491486 0.947326 0.393463 0.567146 0.850615 0.679710 0.864926 0.673938 0.251913 0.790639 0.233467 0.421842 0.496970 0.597625 0.187027 0.605587 0.247680 0.097172 0.649768 0.124556 0.181981 0.508964 0.014251 0.873480 0.280633 0.874539 0.386641 0.172963 0.028571 0.109090 0.702814 0.586552 0.181077 0.484496 0.280633 0.728928 0.077602 0.120427 0.865593 0.354908 0.901109 0.912987 0.960609 0.864926 0.874539 0.728928 0.633463 0.037704 0.688492 0.061581 0.459524 0.361977 0.964438 0.222086 0.673938 0.386641 0.408651 0.898475 0.050991 0.264213 0.736278 0.983667 0.914808 0.124556 0.077602 0.408651 0.043514 0.170176 0.355235 0.251913 0.181981 0.120427 0.898475 . x - x - x x x - - x - - x - x - x x - x . - - x x - x x x x x x x - - - - x - | | . x x x x - x - - - x x - - x x - x x | x . - - - x x x - - x x - - x x - x | x x | . x x x - - - - x x - x - - - - x x x | x . - x x x - x - x x - - - - - x | x | x | . x - - x x - - - x x - x - x x | x x x x . - - x - x x - x - x - - | x x x | x | | . x x - x x - x x x x - | x | x | x | | x . - - x x x - - x x - x x | | | | x x x | . x x - - x x x - - | x | | | x x | | | x . - x x x - x - x | x x x x | | x x x x | . - - - x x - x x x x x x x | x x x | x | . - - - - x x | | | | | x | | | x | x | | . x x x - - x | | | x | x x x | x x | | x . x - x x | | x x | | x | x | x | x | x x . - - - x | x x | | | x x x x x x | x | | . x x x x | | | | x | x x | | | x | x | x . - | | x x | | | | | | | x x x | x | x | . The error in solving: 5.176486e-16 The error in solving: 6.197019e-16 The error in solving: 6.429251e-16 The error in solving: 7.504278e-16 The error in solving: 7.616681e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.136368 0.000000 0.376325 0.795013 0.000000 0.999194 0.038840 0.637767 0.681457 0.592295 0.709236 0.000000 0.441971 0.247029 0.000000 0.000000 0.856180 0.094128 0.171573 0.136368 0.000000 0.795978 0.069348 0.274778 0.972344 0.632593 0.000000 0.438274 0.993965 0.120077 0.071762 0.779931 0.370582 0.630749 0.365836 0.867667 0.902109 0.663622 0.614043 0.000000 0.795978 0.000000 0.619370 0.630442 0.000000 0.000000 0.269987 0.000000 0.644463 0.891470 0.582590 0.771111 0.799365 0.301330 0.116705 0.000000 0.000000 0.787823 0.848598 0.376325 0.069348 0.619370 0.000000 0.200953 0.000000 0.604673 0.755972 0.076554 0.179181 0.509107 0.996311 0.000000 0.000000 0.391002 0.539096 0.715068 0.505331 0.571376 0.559636 0.795013 0.274778 0.630442 0.200953 0.000000 0.050324 0.118936 0.056397 0.449444 0.809325 0.003361 0.472059 0.010680 0.401940 0.448615 0.750112 0.613249 0.612342 0.402920 0.454900 0.000000 0.972344 0.000000 0.000000 0.050324 0.000000 0.000000 0.711600 0.000000 0.730545 0.516516 0.579160 0.102391 0.782440 0.857777 0.222525 0.000000 0.000000 0.926879 0.688966 0.999194 0.632593 0.000000 0.604673 0.118936 0.000000 0.000000 0.000000 0.368540 0.000000 0.708291 0.887188 0.505263 0.753346 0.742875 0.396093 0.139228 0.631584 0.158863 0.944439 0.038840 0.000000 0.269987 0.755972 0.056397 0.711600 0.000000 0.000000 0.276077 0.787968 0.110442 0.001819 0.509752 0.320133 0.373920 0.182317 0.584565 0.548948 0.000000 0.146924 0.637767 0.438274 0.000000 0.076554 0.449444 0.000000 0.368540 0.276077 0.000000 0.453233 0.959595 0.430414 0.572830 0.643635 0.000000 0.938188 0.000000 0.802261 0.185919 0.021011 0.681457 0.993965 0.644463 0.179181 0.809325 0.730545 0.000000 0.787968 0.453233 0.000000 0.189397 0.071929 0.000000 0.361436 0.592518 0.000000 0.284758 0.572342 0.178811 0.688497 0.592295 0.120077 0.891470 0.509107 0.003361 0.516516 0.708291 0.110442 0.959595 0.189397 0.000000 0.419704 0.784961 0.399982 0.883576 0.000000 0.350581 0.489117 0.113572 0.027278 0.709236 0.071762 0.582590 0.996311 0.472059 0.579160 0.887188 0.001819 0.430414 0.071929 0.419704 0.000000 0.552643 0.025537 0.692992 0.527382 0.804294 0.000000 0.467355 0.074297 0.000000 0.779931 0.771111 0.000000 0.010680 0.102391 0.505263 0.509752 0.572830 0.000000 0.784961 0.552643 0.000000 0.000000 0.000000 0.880231 0.093810 0.863140 0.009694 0.000000 0.441971 0.370582 0.799365 0.000000 0.401940 0.782440 0.753346 0.320133 0.643635 0.361436 0.399982 0.025537 0.000000 0.000000 0.397704 0.147516 0.877621 0.715742 0.169319 0.220566 0.247029 0.630749 0.301330 0.391002 0.448615 0.857777 0.742875 0.373920 0.000000 0.592518 0.883576 0.692992 0.000000 0.397704 0.000000 0.043387 0.000000 0.000000 0.845008 0.491971 0.000000 0.365836 0.116705 0.539096 0.750112 0.222525 0.396093 0.182317 0.938188 0.000000 0.000000 0.527382 0.880231 0.147516 0.043387 0.000000 0.000000 0.703709 0.000033 0.686388 0.000000 0.867667 0.000000 0.715068 0.613249 0.000000 0.139228 0.584565 0.000000 0.284758 0.350581 0.804294 0.093810 0.877621 0.000000 0.000000 0.000000 0.891093 0.705264 0.467705 0.856180 0.902109 0.000000 0.505331 0.612342 0.000000 0.631584 0.548948 0.802261 0.572342 0.489117 0.000000 0.863140 0.715742 0.000000 0.703709 0.891093 0.000000 0.098083 0.000000 0.094128 0.663622 0.787823 0.571376 0.402920 0.926879 0.158863 0.000000 0.185919 0.178811 0.113572 0.467355 0.009694 0.169319 0.845008 0.000033 0.705264 0.098083 0.000000 0.904211 0.171573 0.614043 0.848598 0.559636 0.454900 0.688966 0.944439 0.146924 0.021011 0.688497 0.027278 0.074297 0.000000 0.220566 0.491971 0.686388 0.467705 0.000000 0.904211 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 312 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 14 32 45 61 80 92 107 123 138 154 172 190 203 220 235 250 263 277 295 312 Column indices: 1 3 4 6 7 8 9 10 11 13 14 17 18 19 0 2 3 4 5 6 8 9 10 11 12 13 14 15 16 17 18 19 1 3 4 7 9 10 11 12 13 14 15 18 19 0 1 2 4 6 7 8 9 10 11 14 15 16 17 18 19 0 1 2 3 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 4 7 9 10 11 12 13 14 15 18 19 0 1 3 4 8 10 11 12 13 14 15 16 17 18 19 0 2 3 4 5 8 9 10 11 12 13 14 15 16 17 19 0 1 3 4 6 7 9 10 11 12 13 15 17 18 19 0 1 2 3 4 5 7 8 10 11 13 14 16 17 18 19 0 1 2 3 4 5 6 7 8 9 11 12 13 14 16 17 18 19 0 1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 18 19 1 2 4 5 6 7 8 10 11 15 16 17 18 0 1 2 4 5 6 7 8 9 10 11 14 15 16 17 18 19 0 1 2 3 4 5 6 7 9 10 11 13 15 18 19 1 2 3 4 5 6 7 8 11 12 13 14 17 18 19 1 3 4 6 7 9 10 11 12 13 17 18 19 0 1 3 4 6 7 8 9 10 12 13 15 16 18 0 1 2 3 4 5 6 8 9 10 11 12 13 14 15 16 17 19 0 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 18 Off-diagonal values: 0.136368 0.376325 0.795013 0.999194 0.038840 0.637767 0.681457 0.592295 0.709236 0.441971 0.247029 0.856180 0.094128 0.171573 0.136368 0.795978 0.069348 0.274778 0.972344 0.632593 0.438274 0.993965 0.120077 0.071762 0.779931 0.370582 0.630749 0.365836 0.867667 0.902109 0.663622 0.614043 0.795978 0.619370 0.630442 0.269987 0.644463 0.891470 0.582590 0.771111 0.799365 0.301330 0.116705 0.787823 0.848598 0.376325 0.069348 0.619370 0.200953 0.604673 0.755972 0.076554 0.179181 0.509107 0.996311 0.391002 0.539096 0.715068 0.505331 0.571376 0.559636 0.795013 0.274778 0.630442 0.200953 0.050324 0.118936 0.056397 0.449444 0.809325 0.003361 0.472059 0.010680 0.401940 0.448615 0.750112 0.613249 0.612342 0.402920 0.454900 0.972344 0.050324 0.711600 0.730545 0.516516 0.579160 0.102391 0.782440 0.857777 0.222525 0.926879 0.688966 0.999194 0.632593 0.604673 0.118936 0.368540 0.708291 0.887188 0.505263 0.753346 0.742875 0.396093 0.139228 0.631584 0.158863 0.944439 0.038840 0.269987 0.755972 0.056397 0.711600 0.276077 0.787968 0.110442 0.001819 0.509752 0.320133 0.373920 0.182317 0.584565 0.548948 0.146924 0.637767 0.438274 0.076554 0.449444 0.368540 0.276077 0.453233 0.959595 0.430414 0.572830 0.643635 0.938188 0.802261 0.185919 0.021011 0.681457 0.993965 0.644463 0.179181 0.809325 0.730545 0.787968 0.453233 0.189397 0.071929 0.361436 0.592518 0.284758 0.572342 0.178811 0.688497 0.592295 0.120077 0.891470 0.509107 0.003361 0.516516 0.708291 0.110442 0.959595 0.189397 0.419704 0.784961 0.399982 0.883576 0.350581 0.489117 0.113572 0.027278 0.709236 0.071762 0.582590 0.996311 0.472059 0.579160 0.887188 0.001819 0.430414 0.071929 0.419704 0.552643 0.025537 0.692992 0.527382 0.804294 0.467355 0.074297 0.779931 0.771111 0.010680 0.102391 0.505263 0.509752 0.572830 0.784961 0.552643 0.880231 0.093810 0.863140 0.009694 0.441971 0.370582 0.799365 0.401940 0.782440 0.753346 0.320133 0.643635 0.361436 0.399982 0.025537 0.397704 0.147516 0.877621 0.715742 0.169319 0.220566 0.247029 0.630749 0.301330 0.391002 0.448615 0.857777 0.742875 0.373920 0.592518 0.883576 0.692992 0.397704 0.043387 0.845008 0.491971 0.365836 0.116705 0.539096 0.750112 0.222525 0.396093 0.182317 0.938188 0.527382 0.880231 0.147516 0.043387 0.703709 0.000033 0.686388 0.867667 0.715068 0.613249 0.139228 0.584565 0.284758 0.350581 0.804294 0.093810 0.877621 0.891093 0.705264 0.467705 0.856180 0.902109 0.505331 0.612342 0.631584 0.548948 0.802261 0.572342 0.489117 0.863140 0.715742 0.703709 0.891093 0.098083 0.094128 0.663622 0.787823 0.571376 0.402920 0.926879 0.158863 0.185919 0.178811 0.113572 0.467355 0.009694 0.169319 0.845008 0.000033 0.705264 0.098083 0.904211 0.171573 0.614043 0.848598 0.559636 0.454900 0.688966 0.944439 0.146924 0.021011 0.688497 0.027278 0.074297 0.220566 0.491971 0.686388 0.467705 0.904211 . x - x x - x x x x x x - x x - - x x x x . x x x x x - x x x x x x x x x x x x | x . x x - - x - x x x x x x x - - x x x x x . x - x x x x x x - - x x x x x x x x x x . x x x x x x x x x x x x x x x | x | | x . - x - x x x x x x x - - x x x x | x x | . - x - x x x x x x x x x x x | x x x x | . x x x x x x x x x x - x x x | x x | x x . x x x x x - x - x x x x x x x x x | x x . x x - x x - x x x x x x x x x x x x x x . x x x x - x x x x x x x x x x x x x x x . x x x x x - x x | x x | x x x x x | x x . - - x x x x - x x x | x x x x x x x x | . x x x x x x x x x x x x x x | x x x | x . x - - x x | x x x x x x x x | | x x x x . - x x x | x | x x | x x | x x x x x | | . x x x x x | x x | x x x x x | x x | x x . x - x x x x x x x | x x x x x x x x x x . x x x x x x x x x x x x x | x x x x | x . The error in solving: 7.858776e-16 The error in solving: 8.973468e-16 The error in solving: 5.433646e-16 The error in solving: 4.273480e-16 The error in solving: 4.580196e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.653547 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.059747 0.371808 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.866877 0.000000 0.000000 0.000000 0.000000 -0.994953 0.000000 0.298388 -0.349502 0.000000 0.000000 0.000000 -0.418224 0.000000 0.000000 0.000000 0.000000 0.000000 0.643378 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.241507 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.145811 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.043424 0.097442 0.000000 0.000000 -0.516081 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.985551 0.000000 0.058074 0.000000 0.000000 0.000000 0.000000 0.000000 0.653547 0.000000 0.643378 0.000000 0.000000 0.000000 0.000000 0.000000 0.345114 0.000000 -0.560325 0.000000 0.592844 0.718392 0.000000 0.000000 0.000000 -0.800001 0.864236 0.000000 0.000000 0.000000 0.000000 -0.145811 0.000000 0.000000 0.000000 0.000000 0.000000 0.669279 0.000000 0.000000 0.000000 0.000000 -0.442520 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.866877 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.771582 0.000000 0.000000 0.147468 0.000000 0.000000 0.561751 0.497658 0.690469 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.345114 0.000000 0.771582 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.863433 -0.565580 -0.271966 0.000000 0.072584 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.669279 0.000000 0.000000 0.949376 0.000000 0.000000 0.000000 -0.246201 0.783512 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.560325 0.000000 0.000000 0.000000 0.000000 -0.636376 0.000000 0.000000 0.000000 0.000000 0.000000 -0.799476 0.000000 0.000000 0.159115 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.147468 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.994953 0.000000 0.000000 -0.985551 0.592844 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.615389 0.620364 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.718392 0.000000 0.000000 0.000000 -0.246201 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.931469 -0.806062 -0.762196 0.000000 0.059747 0.298388 0.000000 -0.043424 0.058074 0.000000 -0.442520 0.561751 0.000000 0.783512 0.000000 0.000000 -0.615389 0.000000 0.184811 0.000000 0.000000 -0.615895 0.896090 -0.270064 0.371808 -0.349502 0.000000 0.097442 0.000000 0.000000 0.000000 0.497658 0.863433 0.000000 0.000000 0.000000 0.620364 0.000000 0.000000 0.000000 0.000000 0.073419 0.000000 -0.633613 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.690469 -0.565580 0.000000 -0.799476 0.000000 0.000000 -0.931469 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.800001 0.000000 0.000000 -0.271966 0.000000 0.000000 0.000000 0.000000 -0.806062 -0.615895 0.073419 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.241507 -0.516081 0.000000 0.864236 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.762196 0.896090 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.418224 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.072584 0.000000 0.159115 0.000000 0.000000 0.000000 -0.270064 -0.633613 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 94 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.949376 -0.636376 0.000000 0.000000 0.000000 0.184811 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 3 8 10 14 16 24 27 33 39 42 45 46 51 56 67 75 79 84 89 94 Column indices: 5 14 15 7 12 14 15 19 5 18 6 14 15 18 12 14 0 2 8 10 12 13 17 18 3 9 14 1 8 11 14 15 16 5 7 15 16 17 19 6 13 14 5 16 19 7 1 4 5 14 15 5 9 16 17 18 0 1 3 4 6 7 9 12 17 18 19 0 1 3 7 8 12 17 19 7 8 10 13 5 8 13 14 15 2 3 5 13 14 1 8 10 14 15 Off-diagonal values: 0.653547 0.059747 0.371808 0.866877 -0.994953 0.298388 -0.349502 -0.418224 0.643378 0.241507 -0.145811 -0.043424 0.097442 -0.516081 -0.985551 0.058074 0.653547 0.643378 0.345114 -0.560325 0.592844 0.718392 -0.800001 0.864236 -0.145811 0.669279 -0.442520 0.866877 0.771582 0.147468 0.561751 0.497658 0.690469 0.345114 0.771582 0.863433 -0.565580 -0.271966 0.072584 0.669279 -0.246201 0.783512 -0.560325 -0.799476 0.159115 0.147468 -0.994953 -0.985551 0.592844 -0.615389 0.620364 0.718392 -0.246201 -0.931469 -0.806062 -0.762196 0.059747 0.298388 -0.043424 0.058074 -0.442520 0.561751 0.783512 -0.615389 -0.615895 0.896090 -0.270064 0.371808 -0.349502 0.097442 0.497658 0.863433 0.620364 0.073419 -0.633613 0.690469 -0.565580 -0.799476 -0.931469 -0.800001 -0.271966 -0.806062 -0.615895 0.073419 0.241507 -0.516081 0.864236 -0.762196 0.896090 -0.418224 0.072584 0.159115 -0.270064 -0.633613 . - - - - x - - - - - - - - x x - - - - | . - - - - - x - - - - o - x o - - - o | | . - - x - - - - - - - - - - - - x - | | | . - - o - - - - - - - o x - - o - | | | | . - - - - - - - o - x - - - - - x | x | | . - - x - o - x x - - - o x - | | | o | | . - - x - - - - o - - - - - | x | | | | | . x - - x - - x x x - - - | | | | | x | x . - - - - - - x o o - x | | | | | | x | | x - - - o x - - - - - | | | | | o | | | | o - - - - - o - - x | | | | | | | x | | | . - - - - - - - - | o | | o x | | | | | | . - o x - - - - | | | | | x | | | o | | | . - - o o o - x x | o x | o x | x | | o | x - - o x o x o | x | | | x x | | | x | | . - x - o | | | | | | | x o | o | | o | | . - - - | | | | | o | | o | | | | o o x | . - - | | x o | x | | | | | | | o x | | | . - | o | | | | | | x | x | | | o o | | | . The error in solving: 6.655553e-16 The error in solving: 1.394700e-16 The error in solving: 3.421937e-16 The error in solving: 5.913957e-16 The error in solving: 9.932197e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.500000 [ 0.214833 -0.635478 -0.238421 0.000000 0.000000 -0.225686 -0.238961 0.000000 0.000000 0.000000 0.744751 0.176075 0.000000 0.000000 0.000000 0.000000 0.000000 -0.628216 0.000000 0.542097 -0.635478 0.000000 0.592457 -0.844052 0.965137 0.581872 0.790797 0.708614 0.306766 0.375998 0.000000 0.446661 0.804007 0.000000 0.000000 0.000000 -0.381758 0.000000 0.000000 0.000000 -0.238421 0.592457 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.245387 -0.412873 0.210624 -0.572634 0.000000 0.302402 -0.495288 -0.959790 0.370887 0.000000 0.000000 0.484040 0.000000 -0.844052 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.799045 0.000000 0.000000 -0.805524 -0.197559 -0.047370 0.000000 -0.792189 0.000000 -0.930659 0.000000 0.000000 0.000000 0.965137 0.000000 0.000000 -0.282103 -0.326850 0.000000 -0.788798 0.000000 0.000000 0.224843 -0.505238 -0.830276 0.000000 0.000000 0.938724 0.000000 0.000000 0.008159 -0.134233 -0.225686 0.581872 0.000000 0.000000 -0.326850 -0.502460 0.631399 -0.541411 0.000000 -0.107806 0.410817 0.000000 0.000000 -0.519155 -0.572175 0.000000 0.000000 -0.999172 0.779407 -0.407408 -0.238961 0.790797 0.000000 0.000000 0.000000 0.631399 -0.721745 0.000000 0.000000 0.937920 0.000000 0.000000 -0.579871 0.000000 0.000000 0.360813 -0.623142 0.906343 0.639597 -0.978216 0.000000 0.708614 0.000000 0.000000 -0.788798 -0.541411 0.000000 -0.534767 0.000000 -0.208224 -0.128259 -0.832913 0.000000 0.000000 0.000000 -0.357138 -0.546093 0.000000 -0.601811 0.448478 0.000000 0.306766 -0.245387 0.799045 0.000000 0.000000 0.000000 0.000000 0.000000 0.105429 0.000000 0.000000 0.363878 0.000000 0.222233 0.000000 0.000000 0.000000 0.000000 0.582765 0.000000 0.375998 -0.412873 0.000000 0.000000 -0.107806 0.937920 -0.208224 0.105429 0.000000 -0.320824 0.539032 0.000000 0.612931 0.000000 0.718307 0.000000 0.000000 0.000000 -0.747545 0.744751 0.000000 0.210624 0.000000 0.224843 0.410817 0.000000 -0.128259 0.000000 -0.320824 -0.724507 -0.574622 0.000000 -0.300111 0.000000 -0.887689 0.466877 0.000000 0.000000 0.139626 0.176075 0.446661 -0.572634 -0.805524 -0.505238 0.000000 0.000000 -0.832913 0.000000 0.539032 -0.574622 0.000000 0.000000 -0.524326 0.000000 0.000000 0.000000 0.000000 -0.654317 0.000000 0.000000 0.804007 0.000000 -0.197559 -0.830276 0.000000 -0.579871 0.000000 0.363878 0.000000 0.000000 0.000000 0.000000 0.529956 0.000000 0.074526 0.000000 -0.344256 0.000000 -0.846391 0.000000 0.000000 0.302402 -0.047370 0.000000 -0.519155 0.000000 0.000000 0.000000 0.612931 -0.300111 -0.524326 0.529956 -0.246471 0.000000 -0.350319 0.374257 0.000000 0.735641 -0.488367 0.000000 0.000000 -0.495288 0.000000 0.000000 -0.572175 0.000000 0.000000 0.222233 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.519489 0.000000 -0.078661 0.000000 0.000000 0.000000 0.000000 -0.959790 -0.792189 0.938724 0.000000 0.360813 -0.357138 0.000000 0.718307 -0.887689 0.000000 0.074526 -0.350319 0.519489 0.000000 0.675522 0.000000 0.105050 0.690187 0.000000 -0.381758 0.370887 0.000000 0.000000 0.000000 -0.623142 -0.546093 0.000000 0.000000 0.466877 0.000000 0.000000 0.374257 0.000000 0.675522 0.965736 0.000000 0.942475 0.000000 -0.628216 0.000000 0.000000 -0.930659 0.000000 -0.999172 0.906343 0.000000 0.000000 0.000000 0.000000 0.000000 -0.344256 0.000000 -0.078661 0.000000 0.000000 -0.814196 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.008159 0.779407 0.639597 -0.601811 0.000000 0.000000 0.000000 -0.654317 0.000000 0.735641 0.000000 0.105050 0.942475 0.000000 0.426116 0.316336 0.542097 0.000000 0.484040 0.000000 -0.134233 -0.407408 -0.978216 0.448478 0.582765 -0.747545 0.139626 0.000000 -0.846391 -0.488367 0.000000 0.690187 0.000000 0.000000 0.316336 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 192 (max 380) Diagonal entries: 0.214833 0.000000 0.000000 0.000000 -0.282103 -0.502460 -0.721745 -0.534767 0.000000 0.000000 -0.724507 0.000000 0.000000 -0.246471 0.000000 0.000000 0.965736 -0.814196 0.426116 0.000000 Row indices: 0 8 20 31 38 47 59 69 79 86 97 108 118 127 138 143 156 164 170 179 192 Column indices: 1 2 5 6 10 11 17 19 0 2 3 4 5 6 7 8 9 11 12 16 0 1 8 9 10 11 13 14 15 16 19 1 8 11 12 13 15 17 1 5 7 10 11 12 15 18 19 0 1 4 6 7 9 10 13 14 17 18 19 0 1 5 9 12 15 16 17 18 19 1 4 5 9 10 11 15 16 18 19 1 2 3 9 12 14 19 1 2 5 6 7 8 10 11 13 15 19 0 2 4 5 7 9 11 13 15 16 19 0 1 2 3 4 7 9 10 13 18 1 3 4 6 8 13 15 17 19 2 3 5 9 10 11 12 15 16 18 19 2 5 8 15 17 2 3 4 6 7 9 10 12 13 14 16 18 19 1 2 6 7 10 13 15 18 0 3 5 6 12 14 4 5 6 7 11 13 15 16 19 0 2 4 5 6 7 8 9 10 12 13 15 18 Off-diagonal values: -0.635478 -0.238421 -0.225686 -0.238961 0.744751 0.176075 -0.628216 0.542097 -0.635478 0.592457 -0.844052 0.965137 0.581872 0.790797 0.708614 0.306766 0.375998 0.446661 0.804007 -0.381758 -0.238421 0.592457 -0.245387 -0.412873 0.210624 -0.572634 0.302402 -0.495288 -0.959790 0.370887 0.484040 -0.844052 0.799045 -0.805524 -0.197559 -0.047370 -0.792189 -0.930659 0.965137 -0.326850 -0.788798 0.224843 -0.505238 -0.830276 0.938724 0.008159 -0.134233 -0.225686 0.581872 -0.326850 0.631399 -0.541411 -0.107806 0.410817 -0.519155 -0.572175 -0.999172 0.779407 -0.407408 -0.238961 0.790797 0.631399 0.937920 -0.579871 0.360813 -0.623142 0.906343 0.639597 -0.978216 0.708614 -0.788798 -0.541411 -0.208224 -0.128259 -0.832913 -0.357138 -0.546093 -0.601811 0.448478 0.306766 -0.245387 0.799045 0.105429 0.363878 0.222233 0.582765 0.375998 -0.412873 -0.107806 0.937920 -0.208224 0.105429 -0.320824 0.539032 0.612931 0.718307 -0.747545 0.744751 0.210624 0.224843 0.410817 -0.128259 -0.320824 -0.574622 -0.300111 -0.887689 0.466877 0.139626 0.176075 0.446661 -0.572634 -0.805524 -0.505238 -0.832913 0.539032 -0.574622 -0.524326 -0.654317 0.804007 -0.197559 -0.830276 -0.579871 0.363878 0.529956 0.074526 -0.344256 -0.846391 0.302402 -0.047370 -0.519155 0.612931 -0.300111 -0.524326 0.529956 -0.350319 0.374257 0.735641 -0.488367 -0.495288 -0.572175 0.222233 0.519489 -0.078661 -0.959790 -0.792189 0.938724 0.360813 -0.357138 0.718307 -0.887689 0.074526 -0.350319 0.519489 0.675522 0.105050 0.690187 -0.381758 0.370887 -0.623142 -0.546093 0.466877 0.374257 0.675522 0.942475 -0.628216 -0.930659 -0.999172 0.906343 -0.344256 -0.078661 0.008159 0.779407 0.639597 -0.601811 -0.654317 0.735641 0.105050 0.942475 0.316336 0.542097 0.484040 -0.134233 -0.407408 -0.978216 0.448478 0.582765 -0.747545 0.139626 -0.846391 -0.488367 0.690187 0.316336 x o o - - o o - - - x x - - - - - o - x o . x o x x x x x x - x x - - - o - - - o x . - - - - - o o x o - x o o x - - x | o | . - - - - x - - o o o - o - o - - | x | | o o - o - - x o o - - x - - x o o x | | o o x o - o x - - o o - - o x o o x | | | x o - - x - - o - - x o x x o | x | | o o | o - o o o - - - o o - o x | x o x | | | | . x - - x - x - - - - x | x o | | o x o x . o x - x - x - - - o x | x | x x | o | o o o - o - o x - - x x x o o o | | o | x o . - o - - - - o - | x | o o | o | x | | | . x - x - o - o | | x o | o | | | x o o x o - o x - x o | | o | | o | | x | | | | | . x - o - - | | o o x | x o | x o | x o x . x - x x | o x | | | o o | | x | | x | x x - x - o | | o | o x | | | | | o | o | | o - - | | | | x x x o | | | o | x | x x | x x x | x | o o o x x o x | o o | x | | x . The error in solving: 4.379861e-16 The error in solving: 5.273559e-16 The error in solving: 3.610893e-16 The error in solving: 7.044942e-16 The error in solving: 7.587229e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.750000 [ -0.101580 0.000000 0.623870 -0.469162 0.777000 0.972542 -0.977524 -0.878669 0.000000 -0.923108 0.988473 -0.366770 0.066928 -0.501323 -0.732815 -0.716129 -0.058250 0.187294 -0.598972 -0.027325 0.000000 -0.046715 -0.898926 0.444022 0.706975 0.000000 -0.066719 0.531509 0.000000 0.001574 -0.797092 0.091677 0.660106 0.000000 0.660317 0.000000 0.000000 0.711432 0.997918 -0.486032 0.623870 -0.898926 0.566794 -0.168625 -0.009537 0.374591 -0.326699 0.000000 0.126604 0.721457 0.053623 0.535343 -0.800484 -0.856205 0.138492 -0.494228 -0.088763 -0.777623 0.374636 -0.882870 -0.469162 0.444022 -0.168625 0.583637 -0.706548 0.839399 0.000000 -0.739880 0.556693 0.000000 0.000000 -0.035507 0.534082 0.767781 -0.657042 0.700770 0.758777 0.972419 0.909420 -0.017784 0.777000 0.706975 -0.009537 -0.706548 -0.371692 0.455699 0.709909 0.000000 0.000000 0.000000 0.135139 -0.605879 0.000000 -0.970219 -0.368768 0.419804 0.000000 -0.275503 -0.508108 0.966649 0.972542 0.000000 0.374591 0.839399 0.455699 -0.110570 0.000000 -0.157354 0.916400 0.000000 0.209812 0.152438 0.231574 0.363708 0.152633 0.732492 0.214266 0.046728 0.000000 0.000000 -0.977524 -0.066719 -0.326699 0.000000 0.709909 0.000000 0.575588 -0.976259 -0.364629 -0.183229 0.694462 -0.979051 -0.068751 -0.165211 0.130892 -0.278528 -0.622345 -0.306434 0.393253 0.000000 -0.878669 0.531509 0.000000 -0.739880 0.000000 -0.157354 -0.976259 0.605744 0.000000 -0.407146 -0.652692 0.013291 0.155940 -0.835063 0.000000 0.000000 0.000000 -0.582356 0.000000 -0.546475 0.000000 0.000000 0.126604 0.556693 0.000000 0.916400 -0.364629 0.000000 0.327814 -0.068276 0.121318 0.096735 0.550817 0.580517 0.924110 0.000000 0.160221 -0.923307 -0.386158 -0.837654 -0.923108 0.001574 0.721457 0.000000 0.000000 0.000000 -0.183229 -0.407146 -0.068276 0.000000 0.156987 -0.544604 0.142385 0.000000 -0.066809 0.416777 -0.474525 -0.362277 0.268841 -0.953174 0.988473 -0.797092 0.053623 0.000000 0.135139 0.209812 0.694462 -0.652692 0.121318 0.156987 0.988278 0.000000 0.045968 0.434389 -0.043666 -0.770408 0.599870 0.000000 0.000000 -0.904924 -0.366770 0.091677 0.535343 -0.035507 -0.605879 0.152438 -0.979051 0.013291 0.096735 -0.544604 0.000000 0.000000 -0.405045 -0.933422 -0.213058 0.426647 0.493536 0.000000 -0.211494 0.636802 0.066928 0.660106 -0.800484 0.534082 0.000000 0.231574 -0.068751 0.155940 0.550817 0.142385 0.045968 -0.405045 0.895205 -0.764815 0.490040 -0.521935 -0.952740 -0.951359 -0.518733 -0.600723 -0.501323 0.000000 -0.856205 0.767781 -0.970219 0.363708 -0.165211 -0.835063 0.580517 0.000000 0.434389 -0.933422 -0.764815 0.209318 0.131151 0.000000 -0.256655 0.000000 0.146518 0.079995 -0.732815 0.660317 0.138492 -0.657042 -0.368768 0.152633 0.130892 0.000000 0.924110 -0.066809 -0.043666 -0.213058 0.490040 0.131151 -0.397918 -0.647288 0.706003 0.845697 0.183010 0.000000 -0.716129 0.000000 -0.494228 0.700770 0.419804 0.732492 -0.278528 0.000000 0.000000 0.416777 -0.770408 0.426647 -0.521935 0.000000 -0.647288 0.387522 -0.815579 0.000000 0.246426 0.000000 -0.058250 0.000000 -0.088763 0.758777 0.000000 0.214266 -0.622345 0.000000 0.160221 -0.474525 0.599870 0.493536 -0.952740 -0.256655 0.706003 -0.815579 0.143067 0.759936 -0.160713 0.000000 0.187294 0.711432 -0.777623 0.972419 -0.275503 0.046728 -0.306434 -0.582356 -0.923307 -0.362277 0.000000 0.000000 -0.951359 0.000000 0.845697 0.000000 0.759936 0.000000 -0.256337 0.924998 -0.598972 0.997918 0.374636 0.909420 -0.508108 0.000000 0.393253 0.000000 -0.386158 0.268841 0.000000 -0.211494 -0.518733 0.146518 0.183010 0.246426 -0.160713 -0.256337 0.953107 -0.930103 -0.027325 -0.486032 -0.882870 -0.017784 0.966649 0.000000 0.000000 -0.546475 -0.837654 -0.953174 -0.904924 0.636802 -0.600723 0.079995 0.000000 0.000000 0.000000 0.924998 -0.930103 -0.807299]; Dimension: 20 x 20 Off-diagonal entries: 304 (max 380) Diagonal entries: -0.101580 -0.046715 0.566794 0.583637 -0.371692 -0.110570 0.575588 0.605744 0.327814 0.000000 0.988278 0.000000 0.895205 0.209318 -0.397918 0.387522 0.143067 0.000000 0.953107 -0.807299 Row indices: 0 17 30 48 64 78 92 108 120 134 149 164 181 199 214 231 244 259 274 290 304 Column indices: 2 3 4 5 6 7 9 10 11 12 13 14 15 16 17 18 19 2 3 4 6 7 9 10 11 12 14 17 18 19 0 1 3 4 5 6 8 9 10 11 12 13 14 15 16 17 18 19 0 1 2 4 5 7 8 11 12 13 14 15 16 17 18 19 0 1 2 3 5 6 10 11 13 14 15 17 18 19 0 2 3 4 7 8 10 11 12 13 14 15 16 17 0 1 2 4 7 8 9 10 11 12 13 14 15 16 17 18 0 1 3 5 6 9 10 11 12 13 17 19 2 3 5 6 9 10 11 12 13 14 16 17 18 19 0 1 2 6 7 8 10 11 12 14 15 16 17 18 19 0 1 2 4 5 6 7 8 9 12 13 14 15 16 19 0 1 2 3 4 5 6 7 8 9 12 13 14 15 16 18 19 0 1 2 3 5 6 7 8 9 10 11 13 14 15 16 17 18 19 0 2 3 4 5 6 7 8 10 11 12 14 16 18 19 0 1 2 3 4 5 6 8 9 10 11 12 13 15 16 17 18 0 2 3 4 5 6 9 10 11 12 14 16 18 0 2 3 5 6 8 9 10 11 12 13 14 15 17 18 0 1 2 3 4 5 6 7 8 9 12 14 16 18 19 0 1 2 3 4 6 8 9 11 12 13 14 15 16 17 19 0 1 2 3 4 7 8 9 10 11 12 13 17 18 Off-diagonal values: 0.623870 -0.469162 0.777000 0.972542 -0.977524 -0.878669 -0.923108 0.988473 -0.366770 0.066928 -0.501323 -0.732815 -0.716129 -0.058250 0.187294 -0.598972 -0.027325 -0.898926 0.444022 0.706975 -0.066719 0.531509 0.001574 -0.797092 0.091677 0.660106 0.660317 0.711432 0.997918 -0.486032 0.623870 -0.898926 -0.168625 -0.009537 0.374591 -0.326699 0.126604 0.721457 0.053623 0.535343 -0.800484 -0.856205 0.138492 -0.494228 -0.088763 -0.777623 0.374636 -0.882870 -0.469162 0.444022 -0.168625 -0.706548 0.839399 -0.739880 0.556693 -0.035507 0.534082 0.767781 -0.657042 0.700770 0.758777 0.972419 0.909420 -0.017784 0.777000 0.706975 -0.009537 -0.706548 0.455699 0.709909 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x | | o o o o x o x | | | x o o The error in solving: 4.976692e-16 The error in solving: 5.237400e-16 The error in solving: 7.683082e-16 The error in solving: 6.112531e-16 The error in solving: 4.100741e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.330255 0.000000 -0.893497 -0.412516 0.000000 0.000000 -0.584252 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.433969 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.387052 0.000000 0.000000 0.000000 0.000000 0.489615 0.000000 0.000000 0.000000 -0.476594 -0.923248 0.000000 0.602661 0.409239 0.000000 0.000000 0.000000 0.000000 -0.613176 -0.893497 0.000000 0.190478 0.000000 0.624712 0.000000 0.000000 0.000000 0.000000 -0.811486 0.000000 0.000000 -0.640708 0.000000 0.000000 -0.848251 0.000000 0.455951 0.000000 0.575485 -0.412516 0.000000 0.000000 -0.415327 0.000000 0.000000 0.000000 -0.455049 0.000000 0.000000 0.000000 0.000000 0.000000 0.762116 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.624712 0.000000 0.068927 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.625181 0.000000 0.000000 0.657986 0.000000 0.000000 0.000000 0.000000 0.000000 -0.404449 0.264154 0.000000 0.000000 -0.286644 0.000000 0.000000 0.000000 0.000000 0.000000 -0.652061 0.000000 0.000000 0.000000 0.000000 -0.584252 0.489615 0.000000 0.000000 0.000000 0.264154 0.451940 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.620630 0.000000 0.000000 0.000000 0.000000 -0.455049 0.000000 0.000000 0.000000 0.000334 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.252953 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.425823 0.000000 0.000000 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0.000000 0.409239 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.236286 0.085697 -0.537960 0.000000 0.000000 0.000000 0.000000 -0.067778 0.000000 0.000000 -0.848251 0.000000 0.000000 -0.652061 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.240774 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.625181 0.000000 0.000000 0.252953 0.000000 0.000000 0.000000 0.000000 0.000000 0.802327 0.000000 0.000000 0.897571 0.000000 -0.143428 0.000000 0.000000 0.000000 0.455951 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.106425 0.000000 0.000000 0.000000 0.000000 -0.702816 0.000000 0.422139 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.620630 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.143428 0.000000 -0.751624 0.000000 0.000000 -0.613176 0.575485 0.000000 0.657986 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.976672 -0.620811 -0.280567 -0.067778 0.000000 0.000000 0.422139 0.000000 0.296270]; Dimension: 20 x 20 Off-diagonal entries: 74 (max 380) Diagonal entries: 0.330255 0.387052 0.190478 -0.415327 0.068927 -0.404449 0.451940 0.000334 0.425823 0.144765 -0.972006 -0.342916 0.543583 -0.502407 -0.537960 -0.240774 0.897571 -0.702816 -0.751624 0.296270 Row indices: 0 4 10 17 20 23 26 30 32 33 36 37 39 45 51 55 57 61 64 66 74 Column indices: 2 3 6 13 6 10 11 13 14 19 0 4 9 12 15 17 19 0 7 13 2 16 19 6 9 15 0 1 5 18 3 16 12 2 5 12 1 1 19 2 8 9 14 17 19 0 1 3 14 16 19 1 12 13 19 2 5 4 7 13 18 2 12 19 6 16 1 2 4 11 12 13 14 17 Off-diagonal values: -0.893497 -0.412516 -0.584252 0.433969 0.489615 -0.476594 -0.923248 0.602661 0.409239 -0.613176 -0.893497 0.624712 -0.811486 -0.640708 -0.848251 0.455951 0.575485 -0.412516 -0.455049 0.762116 0.624712 0.625181 0.657986 0.264154 -0.286644 -0.652061 -0.584252 0.489615 0.264154 -0.620630 -0.455049 0.252953 -0.388364 -0.811486 -0.286644 -0.919328 -0.476594 -0.923248 -0.976672 -0.640708 -0.388364 -0.919328 0.236286 -0.106425 -0.620811 0.433969 0.602661 0.762116 0.085697 0.802327 -0.280567 0.409239 0.236286 0.085697 -0.067778 -0.848251 -0.652061 0.625181 0.252953 0.802327 -0.143428 0.455951 -0.106425 0.422139 -0.620630 -0.143428 -0.613176 0.575485 0.657986 -0.976672 -0.620811 -0.280567 -0.067778 0.422139 x - o o - - o - - - - - - x - - - - - - | x - - - - x - - - o o - x x - - - - o o | x - x - - - - o - - o - - o - x - x o | | o - - - o - - - - - x - - - - - - | | x | x - - - - - - - - - - - x - - x | | | | | o x - - o - - - - - o - - - - o x | | | x x - - - - - - - - - - - o - | | | o | | | x - - - - - - - - x - - - | | | | | | | | x - - - o - - - - - - - | | o | | o | | | x - - o - - - - - - - | o | | | | | | | | o - - - - - - - - - | o | | | | | | | | | o - - - - - - - o | | o | | | | | o o | | x - x - - o - o x x | x | | | | | | | | | o x - x - - o | x | | | | | | | | | | x x o - - - - o | | o | | o | | | | | | | | | o - - - - | | | | x | | x | | | | | x | | x - o - | | x | | | | | | | | | o | | | | o - x | | | | | | o | | | | | | | | | o | o - | o x | x | | | | | | o o o o | | x | x The error in solving: 2.026585e-16 The error in solving: 2.577685e-16 The error in solving: 6.955527e-16 The error in solving: 4.458206e-16 The error in solving: 6.667479e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.500000 [ -0.378316 0.048031 0.359800 0.000000 0.000000 0.000000 0.000000 -0.018526 0.000000 0.000000 0.000000 0.776341 0.393591 0.336885 0.000000 0.487498 0.000000 -0.496822 0.037874 0.000000 0.048031 -0.129259 0.000000 0.000000 -0.325629 0.000000 -0.363431 0.000000 0.930352 -0.952201 0.204652 0.000000 0.749570 0.683986 0.000000 0.010045 0.378494 0.000000 0.787062 0.000000 0.359800 0.000000 -0.175349 0.000000 0.000000 -0.283915 -0.260190 0.000000 -0.926699 0.000000 0.000000 0.641551 0.000000 0.151959 0.400338 0.566344 0.205372 0.514339 0.000000 0.396933 0.000000 0.000000 0.000000 -0.810545 0.000000 -0.149194 0.000000 0.000000 -0.921022 0.000000 0.000000 0.000000 -0.856545 0.000000 0.036279 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.325629 0.000000 0.000000 0.076675 -0.156311 0.000000 0.000000 0.888961 -0.724010 0.000000 -0.404450 0.000000 0.000000 0.000000 0.000000 0.000000 -0.515502 0.000000 -0.592829 0.000000 0.000000 -0.283915 -0.149194 -0.156311 0.542399 0.878793 0.781011 0.000000 0.000000 0.000000 0.000000 0.000000 -0.447868 0.000000 -0.303144 0.240288 0.000000 0.000000 0.000000 0.000000 -0.363431 -0.260190 0.000000 0.000000 0.878793 -0.572684 0.000000 0.000000 0.000000 -0.904400 0.949492 0.000000 0.000000 0.227289 0.000000 0.000000 0.001030 0.000000 0.000000 -0.018526 0.000000 0.000000 0.000000 0.000000 0.781011 0.000000 0.382117 0.000000 0.000000 0.000000 -0.359424 0.000000 0.053118 0.840710 0.000000 -0.710888 0.000000 -0.411883 0.000000 0.000000 0.930352 -0.926699 -0.921022 0.888961 0.000000 0.000000 0.000000 -0.045909 0.000000 0.841856 0.000000 0.000000 0.000000 0.000000 -0.689325 -0.071247 0.283534 0.343780 0.000000 0.000000 -0.952201 0.000000 0.000000 -0.724010 0.000000 0.000000 0.000000 0.000000 0.849935 0.000000 0.000000 0.000000 -0.856242 0.000000 0.000000 -0.816178 -0.145558 0.428361 -0.169809 0.000000 0.204652 0.000000 0.000000 0.000000 0.000000 -0.904400 0.000000 0.841856 0.000000 -0.594677 0.094599 0.000000 0.000000 0.000000 -0.429575 0.000000 0.000000 -0.015879 0.000000 0.776341 0.000000 0.641551 0.000000 -0.404450 0.000000 0.949492 -0.359424 0.000000 0.000000 0.094599 -0.676389 0.548630 0.000000 -0.462227 -0.458013 0.000000 0.048309 0.998915 0.000000 0.393591 0.749570 0.000000 -0.856545 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.548630 -0.971043 0.000000 0.276478 0.000000 -0.023019 -0.089758 0.000000 -0.459485 0.336885 0.683986 0.151959 0.000000 0.000000 -0.447868 0.000000 0.053118 0.000000 -0.856242 0.000000 0.000000 0.000000 0.254848 0.000000 0.000000 0.388929 -0.392476 -0.531296 -0.187710 0.000000 0.000000 0.400338 0.036279 0.000000 0.000000 0.227289 0.840710 0.000000 0.000000 0.000000 -0.462227 0.276478 0.000000 -0.413040 0.893054 0.000000 0.000000 0.000000 0.320258 0.487498 0.010045 0.566344 0.000000 0.000000 -0.303144 0.000000 0.000000 -0.689325 0.000000 -0.429575 -0.458013 0.000000 0.000000 0.893054 0.769720 -0.361574 0.000000 0.014700 -0.159314 0.000000 0.378494 0.205372 0.000000 0.000000 0.240288 0.000000 -0.710888 -0.071247 -0.816178 0.000000 0.000000 -0.023019 0.388929 0.000000 -0.361574 -0.143569 -0.911533 -0.437143 -0.908717 -0.496822 0.000000 0.514339 0.000000 -0.515502 0.000000 0.001030 0.000000 0.283534 -0.145558 0.000000 0.048309 -0.089758 -0.392476 0.000000 0.000000 -0.911533 0.321155 -0.663702 0.000000 0.037874 0.787062 0.000000 0.000000 0.000000 0.000000 0.000000 -0.411883 0.343780 0.428361 -0.015879 0.998915 0.000000 -0.531296 0.000000 0.014700 -0.437143 -0.663702 -0.563833 0.028801 0.000000 0.000000 0.396933 0.000000 -0.592829 0.000000 0.000000 0.000000 0.000000 -0.169809 0.000000 0.000000 -0.459485 -0.187710 0.320258 -0.159314 -0.908717 0.000000 0.028801 -0.273848]; Dimension: 20 x 20 Off-diagonal entries: 178 (max 380) Diagonal entries: -0.378316 -0.129259 -0.175349 -0.810545 0.076675 0.542399 -0.572684 0.382117 -0.045909 0.849935 -0.594677 -0.676389 -0.971043 0.254848 -0.413040 0.769720 -0.143569 0.321155 -0.563833 -0.273848 Row indices: 0 9 20 31 35 42 50 57 64 73 80 86 97 105 115 123 134 146 157 169 178 Column indices: 1 2 7 11 12 13 15 17 18 0 4 6 8 9 10 12 13 15 16 18 0 5 6 8 11 13 14 15 16 17 19 5 8 12 14 1 5 8 9 11 17 19 2 3 4 6 7 13 15 16 1 2 5 10 11 14 17 0 5 11 13 14 16 18 1 2 3 4 10 15 16 17 18 1 4 13 16 17 18 19 1 6 8 11 15 18 0 2 4 6 7 10 12 14 15 17 18 0 1 3 11 14 16 17 19 0 1 2 5 7 9 16 17 18 19 2 3 6 7 11 12 15 19 0 1 2 5 8 10 11 14 16 18 19 1 2 5 7 8 9 12 13 15 17 18 19 0 2 4 6 8 9 11 12 13 16 18 0 1 7 8 9 10 11 13 15 16 17 19 2 4 9 12 13 14 15 16 18 Off-diagonal values: 0.048031 0.359800 -0.018526 0.776341 0.393591 0.336885 0.487498 -0.496822 0.037874 0.048031 -0.325629 -0.363431 0.930352 -0.952201 0.204652 0.749570 0.683986 0.010045 0.378494 0.787062 0.359800 -0.283915 -0.260190 -0.926699 0.641551 0.151959 0.400338 0.566344 0.205372 0.514339 0.396933 -0.149194 -0.921022 -0.856545 0.036279 -0.325629 -0.156311 0.888961 -0.724010 -0.404450 -0.515502 -0.592829 -0.283915 -0.149194 -0.156311 0.878793 0.781011 -0.447868 -0.303144 0.240288 -0.363431 -0.260190 0.878793 -0.904400 0.949492 0.227289 0.001030 -0.018526 0.781011 -0.359424 0.053118 0.840710 -0.710888 -0.411883 0.930352 -0.926699 -0.921022 0.888961 0.841856 -0.689325 -0.071247 0.283534 0.343780 -0.952201 -0.724010 -0.856242 -0.816178 -0.145558 0.428361 -0.169809 0.204652 -0.904400 0.841856 0.094599 -0.429575 -0.015879 0.776341 0.641551 -0.404450 0.949492 -0.359424 0.094599 0.548630 -0.462227 -0.458013 0.048309 0.998915 0.393591 0.749570 -0.856545 0.548630 0.276478 -0.023019 -0.089758 -0.459485 0.336885 0.683986 0.151959 -0.447868 0.053118 -0.856242 0.388929 -0.392476 -0.531296 -0.187710 0.400338 0.036279 0.227289 0.840710 -0.462227 0.276478 0.893054 0.320258 0.487498 0.010045 0.566344 -0.303144 -0.689325 -0.429575 -0.458013 0.893054 -0.361574 0.014700 -0.159314 0.378494 0.205372 0.240288 -0.710888 -0.071247 -0.816178 -0.023019 0.388929 -0.361574 -0.911533 -0.437143 -0.908717 -0.496822 0.514339 -0.515502 0.001030 0.283534 -0.145558 0.048309 -0.089758 -0.392476 -0.911533 -0.663702 0.037874 0.787062 -0.411883 0.343780 0.428361 -0.015879 0.998915 -0.531296 0.014700 -0.437143 -0.663702 0.028801 0.396933 -0.592829 -0.169809 -0.459485 -0.187710 0.320258 -0.159314 -0.908717 0.028801 o x x - - - - o - - - x x x - x - o x - x o - - o - o - x o x - x x - x x - x - x | o - - o o - o - - x - x x x x x - x | | | o - o - - o - - - o - x - - - - - | o | | x o - - x o - o - - - - - o - o | | o o o x x x - - - - - o - o x - - - | o o | | x o - - - o x - - x - - x - - o | | | | x | x - - - o - x x - o - o - | x o o x | | | o - x - - - - o o x x - | o | | o | | | | x - - - o - - o o x o | x | | | | o | x | o x - - - o - - o - x | x | o | x o | | x o x - o o - x x - x x | o | | | | | | | x o - x - o o - o x x x | | o | x | o | | | x - - x o o o | | x x | | x x | | | o x | o x - - - x x x x | | o | | o | o o | | x x o - x o | x x | | x | o o o | | o x | o o o o o o | x | o | x | x o | x o o | | o x o - x x | | | | | o x x o x | o | x o o o x | | x | o | | | | o | | o o x o o | x o The error in solving: 4.067991e-16 The error in solving: 5.754368e-16 The error in solving: 4.824826e-16 The error in solving: 5.324471e-16 The error in solving: 6.425880e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.750000 [ -0.507307 -0.590229 0.000000 0.000000 -0.696470 0.133738 0.529598 -0.719811 0.564849 0.000000 0.495463 -0.262424 -0.471230 0.151210 -0.185324 -0.062243 0.156297 0.630841 0.425680 -0.242786 -0.590229 -0.998191 0.139757 0.000000 -0.076152 0.138732 -0.853864 -0.667267 0.398763 -0.899463 -0.768690 0.202577 0.350937 -0.933573 0.353486 0.000000 0.022037 -0.124700 0.000000 -0.835173 0.000000 0.139757 0.583666 0.659376 0.070949 -0.907039 -0.652118 0.000000 -0.361216 0.463856 0.531664 0.213538 0.000000 -0.760381 -0.393333 -0.441592 -0.882463 0.562692 0.000000 0.000000 0.000000 0.000000 0.659376 0.177577 0.296045 0.351014 0.129604 0.468815 0.319994 -0.878984 -0.915985 -0.152931 0.000000 0.741020 -0.876286 0.000000 -0.667277 0.000000 -0.502504 0.000000 -0.696470 -0.076152 0.070949 0.296045 0.051010 0.527882 0.000000 0.885646 -0.465716 -0.199519 0.000000 -0.986934 0.305356 -0.922408 0.000000 -0.506637 -0.586089 0.000000 0.754654 -0.422643 0.133738 0.138732 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0.545539 -0.450018 -0.510074 -0.849316 -0.324434 0.888407 0.000000 0.745139 -0.500693 0.793546 0.994399 -0.262424 0.202577 0.213538 -0.152931 -0.986934 0.688667 0.754307 0.000000 0.861472 -0.463737 -0.510074 0.174396 -0.049891 -0.273602 0.688981 -0.447487 -0.418084 0.378959 0.479568 0.178276 -0.471230 0.350937 0.000000 0.000000 0.305356 0.383802 0.820937 0.146918 0.828079 -0.758382 -0.849316 -0.049891 0.724591 0.290056 -0.329437 0.000000 0.923492 0.420037 -0.952846 0.002390 0.151210 -0.933573 -0.760381 0.741020 -0.922408 0.000000 0.513924 -0.296509 0.000000 0.000000 -0.324434 -0.273602 0.290056 0.288831 0.058762 0.000000 0.000000 0.729577 0.000000 -0.094228 -0.185324 0.353486 -0.393333 -0.876286 0.000000 0.596261 -0.415246 0.000000 0.919451 -0.165991 0.888407 0.688981 -0.329437 0.058762 0.219612 0.709811 0.683446 0.152657 -0.486235 -0.294080 -0.062243 0.000000 -0.441592 0.000000 -0.506637 0.967845 -0.627318 0.182484 0.979241 0.000000 0.000000 -0.447487 0.000000 0.000000 0.709811 0.347234 0.070022 0.000000 -0.753558 0.674222 0.156297 0.022037 -0.882463 -0.667277 -0.586089 0.265679 0.000000 0.000000 0.090852 -0.227861 0.745139 -0.418084 0.923492 0.000000 0.683446 0.070022 0.510198 0.000000 0.852108 0.336777 0.630841 -0.124700 0.562692 0.000000 0.000000 0.482855 -0.724602 0.099643 0.555370 -0.374510 -0.500693 0.378959 0.420037 0.729577 0.152657 0.000000 0.000000 0.589169 0.000000 0.366935 0.425680 0.000000 0.000000 -0.502504 0.754654 -0.015837 0.000000 0.395929 -0.302948 0.000000 0.793546 0.479568 -0.952846 0.000000 -0.486235 -0.753558 0.852108 0.000000 -0.214361 -0.662096 -0.242786 -0.835173 0.000000 0.000000 -0.422643 -0.054234 0.000000 0.000000 -0.328030 0.000000 0.994399 0.178276 0.002390 -0.094228 -0.294080 0.674222 0.336777 0.366935 -0.662096 0.973157]; Dimension: 20 x 20 Off-diagonal entries: 288 (max 380) Diagonal entries: -0.507307 -0.998191 0.583666 0.177577 0.051010 -0.795876 -0.831422 0.066243 -0.289032 -0.027746 -0.450018 0.174396 0.724591 0.288831 0.219612 0.347234 0.510198 0.589169 -0.214361 0.973157 Row indices: 0 16 32 46 59 74 89 101 113 128 139 156 174 190 203 220 232 247 261 274 288 Column indices: 1 4 5 6 7 8 10 11 12 13 14 15 16 17 18 19 0 2 4 5 6 7 8 9 10 11 12 13 14 16 17 19 1 3 4 5 6 8 9 10 11 13 14 15 16 17 2 4 5 6 7 8 9 10 11 13 14 16 18 0 1 2 3 5 7 8 9 11 12 13 15 16 18 19 0 1 2 3 4 7 10 11 12 14 15 16 17 18 19 0 1 2 3 7 10 11 12 13 14 15 17 0 1 3 4 5 6 10 12 13 15 17 18 0 1 2 3 4 9 10 11 12 14 15 16 17 18 19 1 2 3 4 8 10 11 12 14 16 17 0 1 2 3 5 6 7 8 9 11 12 13 14 16 17 18 19 0 1 2 3 4 5 6 8 9 10 12 13 14 15 16 17 18 19 0 1 4 5 6 7 8 9 10 11 13 14 16 17 18 19 0 1 2 3 4 6 7 10 11 12 14 17 19 0 1 2 3 5 6 8 9 10 11 12 13 15 16 17 18 19 0 2 4 5 6 7 8 11 14 16 18 19 0 1 2 3 4 5 8 9 10 11 12 14 15 18 19 0 1 2 5 6 7 8 9 10 11 12 13 14 19 0 3 4 5 7 8 10 11 12 14 15 16 19 0 1 4 5 8 10 11 12 13 14 15 16 17 18 Off-diagonal values: -0.590229 -0.696470 0.133738 0.529598 -0.719811 0.564849 0.495463 -0.262424 -0.471230 0.151210 -0.185324 -0.062243 0.156297 0.630841 0.425680 -0.242786 -0.590229 0.139757 -0.076152 0.138732 -0.853864 -0.667267 0.398763 -0.899463 -0.768690 0.202577 0.350937 -0.933573 0.353486 0.022037 -0.124700 -0.835173 0.139757 0.659376 0.070949 -0.907039 -0.652118 -0.361216 0.463856 0.531664 0.213538 -0.760381 -0.393333 -0.441592 -0.882463 0.562692 0.659376 0.296045 0.351014 0.129604 0.468815 0.319994 -0.878984 -0.915985 -0.152931 0.741020 -0.876286 -0.667277 -0.502504 -0.696470 -0.076152 0.070949 0.296045 0.527882 0.885646 -0.465716 -0.199519 -0.986934 0.305356 -0.922408 -0.506637 -0.586089 0.754654 -0.422643 0.133738 0.138732 -0.907039 0.351014 0.527882 -0.537737 0.599910 0.688667 0.383802 0.596261 0.967845 0.265679 0.482855 -0.015837 -0.054234 0.529598 -0.853864 -0.652118 0.129604 0.437471 0.823341 0.754307 0.820937 0.513924 -0.415246 -0.627318 -0.724602 -0.719811 -0.667267 0.468815 0.885646 -0.537737 0.437471 -0.822327 0.146918 -0.296509 0.182484 0.099643 0.395929 0.564849 0.398763 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-0.062243 -0.441592 -0.506637 0.967845 -0.627318 0.182484 0.979241 -0.447487 0.709811 0.070022 -0.753558 0.674222 0.156297 0.022037 -0.882463 -0.667277 -0.586089 0.265679 0.090852 -0.227861 0.745139 -0.418084 0.923492 0.683446 0.070022 0.852108 0.336777 0.630841 -0.124700 0.562692 0.482855 -0.724602 0.099643 0.555370 -0.374510 -0.500693 0.378959 0.420037 0.729577 0.152657 0.366935 0.425680 -0.502504 0.754654 -0.015837 0.395929 -0.302948 0.793546 0.479568 -0.952846 -0.486235 -0.753558 0.852108 -0.662096 -0.242786 -0.835173 -0.422643 -0.054234 -0.328030 0.994399 0.178276 0.002390 -0.094228 -0.294080 0.674222 0.336777 0.366935 -0.662096 o o - - o x x o x - x o o x o o x x x o o o x - o x o o x o o x x o x - x o - o | x x x x o o - o x x x - o o o o x - - | | x x x x x x x o o o - x o - o - o - o o x x x x - x o o - o x o - o o - x o x x o x x o - o - - x x x - x x x x o o x o o x | | o x - - x x x x o o - o - - o o | x x o x x - - o - x o - x - x x - x x o x o | | | o o x x x - x x x x o o | o x o o | | | o o x o o - o - o o - - x o x o | x x o x x o o o o x - x o x x o x x o o x x | x o o x o o x o o x x x o x | | x x x x x o o o x x o - x x o x x o o x o | x o | | o o x x x - - x - o o x o o | x o | x o x x o x x x x x o o o | o | o x o x x | | o | | x x x - o x x x o o o x | | x o x o x | x x x - x x x o x | | x o x x o o x x x x | | x - x x | | o x o | x o | x x o | o o x | o o o o | | o o | | o | x x x o o x x x o x The error in solving: 5.629064e-16 The error in solving: 9.996825e-16 The error in solving: 4.611103e-16 The error in solving: 3.015027e-16 The error in solving: 6.456994e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.702820 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.164164 0.000000 0.000000 0.220472 0.000000 -0.806292 0.000000 0.902511 0.000000 0.000000 0.702820 0.000000 0.000000 0.000000 0.000000 0.000000 0.765812 0.000000 0.868118 0.000000 0.000000 0.000000 0.000000 0.549890 0.000000 0.813122 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.613379 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.355967 0.000000 0.018874 0.000000 0.298703 0.000000 0.293724 0.000000 0.000000 0.000000 -0.613379 0.000000 0.000000 -0.519488 -0.333200 0.000000 -0.488523 0.000000 -0.230095 0.788636 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.566245 0.000000 0.000000 0.924090 0.000000 0.000000 0.000000 -0.912972 -0.246381 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.519488 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.377221 0.000000 0.000000 -0.845196 0.000000 0.000000 0.000000 0.000000 0.765812 0.000000 -0.333200 0.566245 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.880500 0.000000 0.000000 0.000000 0.000000 -0.763096 -0.291015 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.978352 0.000000 -0.998736 0.000000 0.868118 0.000000 -0.488523 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.924090 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.094598 -0.164164 0.000000 0.000000 -0.230095 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.631672 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.788636 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.003510 0.000000 0.000000 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0.000000 -0.763096 -0.978352 0.000000 0.000000 0.000000 0.000000 0.000000 0.661647 0.000000 0.000000 0.000000 0.000000 0.000000 0.377662 0.000000 0.000000 0.293724 0.000000 0.000000 0.000000 -0.291015 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.449293 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.998736 0.000000 0.094598 0.000000 0.000000 0.000000 0.235849 0.000000 0.000000 0.000000 0.377662 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 80 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 5 10 15 21 25 28 34 36 38 40 43 45 48 57 60 65 68 73 76 80 Column indices: 1 10 13 15 17 0 6 8 13 15 3 12 14 16 18 2 5 6 8 10 11 6 9 13 14 3 13 16 1 3 4 12 17 18 17 19 1 3 4 19 0 3 15 3 13 2 6 16 0 1 4 5 11 15 17 18 19 2 4 15 0 1 10 13 14 2 5 12 0 6 7 13 19 2 6 13 7 9 13 17 Off-diagonal values: 0.702820 -0.164164 0.220472 -0.806292 0.902511 0.702820 0.765812 0.868118 0.549890 0.813122 -0.613379 -0.355967 0.018874 0.298703 0.293724 -0.613379 -0.519488 -0.333200 -0.488523 -0.230095 0.788636 0.566245 0.924090 -0.912972 -0.246381 -0.519488 -0.377221 -0.845196 0.765812 -0.333200 0.566245 -0.880500 -0.763096 -0.291015 -0.978352 -0.998736 0.868118 -0.488523 0.924090 0.094598 -0.164164 -0.230095 -0.631672 0.788636 -0.003510 -0.355967 -0.880500 -0.309185 0.220472 0.549890 -0.912972 -0.377221 -0.003510 0.305922 0.661647 -0.449293 0.235849 0.018874 -0.246381 -0.164838 -0.806292 0.813122 -0.631672 0.305922 -0.164838 0.298703 -0.845196 -0.309185 0.902511 -0.763096 -0.978352 0.661647 0.377662 0.293724 -0.291015 -0.449293 -0.998736 0.094598 0.235849 0.377662 . x - - - - - - - - o - - x - o - x - - x . - - - - x - x - - - - x - x - - - - | | . o - - - - - - - - o - x - x - x - | | o . - o o - o - o x - - - - - - - - | | | | . - x - - x - - - o o - - - - - | | | o | . - - - - - - - o - - o - - - | x | o x | . - - - - - o - - - - o o - | | | | | | | . - - - - - - - - - o - o | x | o | | | | . - - - - - - - - - - - | | | | x | | | | . - - - - - - - - - x o | | o | | | | | | . - - - - o - - - - | | | x | | | | | | | . - o - - - - - - | | o | | | o | | | | | . - - - o - - - x x | | o o | | | | | o | . - x - x o x | | x | o | | | | | | | | | . o - - - - o x | | | | | | | | o | | x o . - - - - | | x | | o | | | | | | o | | | . - - - x | | | | | o o | | | | | x | | | . - x | | x | | | o | | | | | | o | | | | . - | | | | | | | o | x | | | x | | | x | . The error in solving: 6.023663e-16 The error in solving: 5.179595e-16 The error in solving: 4.361579e-16 The error in solving: 3.788239e-16 The error in solving: 7.229329e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.495689 0.000000 -0.920397 0.000000 0.000000 0.519502 0.000000 0.000000 0.000000 -0.287429 0.000000 0.000000 0.000000 -0.920086 0.198850 0.538676 0.000000 0.220717 0.975253 0.495689 0.000000 0.661099 0.000000 -0.710475 0.000000 -0.234406 0.000000 0.000000 0.000000 0.000000 0.204951 0.554285 0.000000 0.000000 -0.960631 -0.517437 0.000000 0.000000 0.329680 0.000000 0.661099 0.000000 0.000000 0.000000 0.000000 0.865252 0.266861 0.000000 0.000000 0.381760 0.983133 0.262806 0.000000 0.000000 0.002713 0.543649 0.000000 0.633119 -0.059834 -0.920397 0.000000 0.000000 0.000000 -0.589539 0.028571 0.307023 0.000000 -0.434225 -0.581119 0.000000 -0.573308 0.000000 0.000000 0.717052 0.000000 0.813983 -0.320266 0.000000 0.860404 0.000000 -0.710475 0.000000 -0.589539 0.000000 0.576505 0.000000 0.000000 0.000000 0.961464 -0.107507 0.000000 0.399420 0.374055 0.000000 0.657805 0.000000 0.626139 0.696491 -0.994034 0.000000 0.000000 0.000000 0.028571 0.576505 0.000000 0.000000 -0.147288 0.000000 0.000000 0.000000 0.000000 -0.785470 0.506454 -0.744401 0.000000 0.000000 0.925042 0.000000 0.497001 0.519502 -0.234406 0.865252 0.307023 0.000000 0.000000 0.000000 0.388054 0.000000 0.000000 -0.864404 0.887398 0.000000 -0.923099 0.072834 0.000000 0.598742 0.000000 0.427276 0.000000 0.000000 0.000000 0.266861 0.000000 0.000000 -0.147288 0.388054 0.000000 0.000000 0.000000 0.000000 0.000000 0.857879 0.000000 0.601260 -0.728055 -0.706174 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.434225 0.000000 0.000000 0.000000 0.000000 0.000000 -0.684814 0.021824 0.000000 -0.772186 0.000000 0.000000 0.000000 0.000000 0.000000 -0.640951 0.025619 0.000000 0.000000 0.000000 -0.581119 0.961464 0.000000 0.000000 0.000000 -0.684814 0.000000 0.948430 0.000000 -0.328737 -0.157250 0.000000 0.000000 0.000000 0.000000 -0.169233 0.797752 -0.287429 0.000000 0.381760 0.000000 -0.107507 0.000000 -0.864404 0.000000 0.021824 0.948430 0.000000 0.000000 0.158163 0.000000 0.000000 0.000000 0.000000 0.000000 -0.562476 -0.289743 0.000000 0.204951 0.983133 -0.573308 0.000000 0.000000 0.887398 0.000000 0.000000 0.000000 0.000000 0.000000 0.988196 0.000000 0.000000 0.000000 -0.859992 0.000000 0.000000 0.000000 0.000000 0.554285 0.262806 0.000000 0.399420 -0.785470 0.000000 0.857879 -0.772186 -0.328737 0.158163 0.988196 0.000000 -0.700394 0.000000 -0.666598 0.000000 0.793386 0.806699 0.000000 0.000000 0.000000 0.000000 0.000000 0.374055 0.506454 -0.923099 0.000000 0.000000 -0.157250 0.000000 0.000000 -0.700394 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.920086 0.000000 0.000000 0.717052 0.000000 -0.744401 0.072834 0.601260 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.497121 0.000000 -0.638362 -0.151872 -0.293854 0.198850 -0.960631 0.002713 0.000000 0.657805 0.000000 0.000000 -0.728055 0.000000 0.000000 0.000000 0.000000 -0.666598 0.000000 -0.497121 0.000000 0.000000 -0.787467 -0.621444 0.000000 0.538676 -0.517437 0.543649 0.813983 0.000000 0.000000 0.598742 -0.706174 0.000000 0.000000 0.000000 -0.859992 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.574443 0.814894 0.000000 0.000000 0.000000 -0.320266 0.626139 0.925042 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.793386 0.000000 -0.638362 -0.787467 0.000000 0.000000 0.000000 0.000000 0.220717 0.000000 0.633119 0.000000 0.696491 0.000000 0.427276 0.000000 -0.640951 -0.169233 -0.562476 0.000000 0.806699 0.000000 -0.151872 -0.621444 0.574443 0.000000 0.000000 0.191118 0.975253 0.329680 -0.059834 0.860404 -0.994034 0.497001 0.000000 0.000000 0.025619 0.797752 -0.289743 0.000000 0.000000 0.000000 -0.293854 0.000000 0.814894 0.000000 0.191118 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 180 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 9 18 28 39 50 58 69 76 82 90 99 105 118 123 132 141 150 156 168 180 Column indices: 1 3 6 10 14 15 16 18 19 0 2 4 6 11 12 15 16 19 1 6 7 10 11 12 15 16 18 19 0 4 5 6 8 9 11 14 16 17 19 1 3 5 9 10 12 13 15 17 18 19 3 4 7 12 13 14 17 19 0 1 2 3 7 10 11 13 14 16 18 2 5 6 12 14 15 16 3 9 10 12 18 19 3 4 8 10 12 13 18 19 0 2 4 6 8 9 12 18 19 1 2 3 6 12 16 1 2 4 5 7 8 9 10 11 13 15 17 18 4 5 6 9 12 0 3 5 6 7 15 17 18 19 0 1 2 4 7 12 14 17 18 0 1 2 3 6 7 11 18 19 3 4 5 12 14 15 0 2 4 6 8 9 10 12 14 15 16 19 0 1 2 3 4 5 8 9 10 14 16 18 Off-diagonal values: 0.495689 -0.920397 0.519502 -0.287429 -0.920086 0.198850 0.538676 0.220717 0.975253 0.495689 0.661099 -0.710475 -0.234406 0.204951 0.554285 -0.960631 -0.517437 0.329680 0.661099 0.865252 0.266861 0.381760 0.983133 0.262806 0.002713 0.543649 0.633119 -0.059834 -0.920397 -0.589539 0.028571 0.307023 -0.434225 -0.581119 -0.573308 0.717052 0.813983 -0.320266 0.860404 -0.710475 -0.589539 0.576505 0.961464 -0.107507 0.399420 0.374055 0.657805 0.626139 0.696491 -0.994034 0.028571 0.576505 -0.147288 -0.785470 0.506454 -0.744401 0.925042 0.497001 0.519502 -0.234406 0.865252 0.307023 0.388054 -0.864404 0.887398 -0.923099 0.072834 0.598742 0.427276 0.266861 -0.147288 0.388054 0.857879 0.601260 -0.728055 -0.706174 -0.434225 -0.684814 0.021824 -0.772186 -0.640951 0.025619 -0.581119 0.961464 -0.684814 0.948430 -0.328737 -0.157250 -0.169233 0.797752 -0.287429 0.381760 -0.107507 -0.864404 0.021824 0.948430 0.158163 -0.562476 -0.289743 0.204951 0.983133 -0.573308 0.887398 0.988196 -0.859992 0.554285 0.262806 0.399420 -0.785470 0.857879 -0.772186 -0.328737 0.158163 0.988196 -0.700394 -0.666598 0.793386 0.806699 0.374055 0.506454 -0.923099 -0.157250 -0.700394 -0.920086 0.717052 -0.744401 0.072834 0.601260 -0.497121 -0.638362 -0.151872 -0.293854 0.198850 -0.960631 0.002713 0.657805 -0.728055 -0.666598 -0.497121 -0.787467 -0.621444 0.538676 -0.517437 0.543649 0.813983 0.598742 -0.706174 -0.859992 0.574443 0.814894 -0.320266 0.626139 0.925042 0.793386 -0.638362 -0.787467 0.220717 0.633119 0.696491 0.427276 -0.640951 -0.169233 -0.562476 0.806699 -0.151872 -0.621444 0.574443 0.191118 0.975253 0.329680 -0.059834 0.860404 -0.994034 0.497001 0.025619 0.797752 -0.289743 -0.293854 0.814894 0.191118 . x - o - - x - - - o - - - o x x - x x x . x - o - o - - - - x x - - o o - - x | x . - - - x x - - x x x - - x x - x o o | | . o x x - o o - o - - x - x o - x | o | o . x - - - x o - x x - x - x x o | | | x x . - o - - - - o x o - - x - x x o x x | | . x - - o x - o x - x - x - | | x | | o x . - - - - x - x o o - - - | | | o | | | | . o x - o - - - - - o x | | | o x | | | o . x - o o - - - - o x o | x | o | o | x x . - x - - - - - o o | x x o | | x | | | | . x - - - o - - - | x x | x o | x o o x x . o - o - x x - | | | | x x o | | o | | o . - - - - - - o | | x | o x x | | | | | | . o - o o o x o x | x | | o | | | | o | o . - o o - x o x x | | x o | | | o | | | | . - x x | | | o x x | | | | | | x | o o | . - - x | x | x | x | o o o | x | o o x | . x x x o x o x | | x x o | | | o | x | x . The error in solving: 5.848874e-16 The error in solving: 7.353918e-16 The error in solving: 6.062703e-16 The error in solving: 6.813556e-16 The error in solving: 3.740653e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.700766 0.351037 -0.182366 -0.518411 -0.514693 0.000000 -0.850739 0.238784 0.969377 -0.704435 0.724893 0.000000 -0.089021 -0.834505 -0.510798 0.005662 0.716041 0.787556 -0.736559 0.700766 0.000000 -0.205729 -0.536616 -0.454873 -0.717429 -0.790184 -0.343707 0.000000 -0.539446 -0.359855 0.000000 -0.079821 0.000000 -0.530887 0.053814 0.750236 0.422347 0.050539 0.039077 0.351037 -0.205729 0.000000 0.000000 0.579096 -0.721478 0.000000 0.992333 -0.108147 0.000000 0.000000 -0.146529 0.000000 0.880841 -0.985759 0.000000 0.000000 0.000000 0.000000 0.785091 -0.182366 -0.536616 0.000000 0.000000 -0.039182 -0.615949 0.557198 0.778824 0.302401 -0.522599 0.564895 0.000000 -0.204804 -0.665902 -0.175307 -0.735951 0.339948 0.000000 -0.027167 -0.378390 -0.518411 -0.454873 0.579096 -0.039182 0.000000 -0.216872 0.000000 0.000000 -0.203864 -0.858804 0.000000 -0.124502 0.000000 0.644592 -0.762123 0.987742 0.348545 -0.614091 0.000000 0.000000 -0.514693 -0.717429 -0.721478 -0.615949 -0.216872 0.000000 0.165493 -0.077693 -0.751068 0.000000 -0.800434 0.574810 0.846176 0.202642 0.000000 -0.998216 0.000000 0.000000 0.869349 -0.692533 0.000000 -0.790184 0.000000 0.557198 0.000000 0.165493 0.000000 0.000000 0.810598 0.612779 -0.694096 -0.693100 -0.687896 -0.562645 0.516584 -0.846304 0.000000 0.000000 0.000000 0.098351 -0.850739 -0.343707 0.992333 0.778824 0.000000 -0.077693 0.000000 0.000000 0.798837 0.000000 0.000000 -0.927661 0.000000 0.926964 0.000000 0.904114 0.000000 0.568163 -0.639824 0.425251 0.238784 0.000000 -0.108147 0.302401 -0.203864 -0.751068 0.810598 0.798837 0.000000 0.968325 0.000000 -0.033360 -0.660600 0.000000 -0.348750 -0.471878 -0.702293 -0.660122 0.709158 0.249350 0.969377 -0.539446 0.000000 -0.522599 -0.858804 0.000000 0.612779 0.000000 0.968325 0.000000 0.556694 0.000000 0.206175 -0.615690 -0.982796 -0.244316 -0.585580 0.605550 -0.477465 0.478241 -0.704435 -0.359855 0.000000 0.564895 0.000000 -0.800434 -0.694096 0.000000 0.000000 0.556694 0.000000 -0.013619 0.486863 0.000000 -0.697595 0.000000 -0.305554 0.929362 -0.098976 -0.784282 0.724893 0.000000 -0.146529 0.000000 -0.124502 0.574810 -0.693100 -0.927661 -0.033360 0.000000 -0.013619 0.000000 -0.275573 0.798983 0.105856 -0.748347 0.870521 0.000000 -0.887956 0.087513 0.000000 -0.079821 0.000000 -0.204804 0.000000 0.846176 -0.687896 0.000000 -0.660600 0.206175 0.486863 -0.275573 0.000000 -0.036199 0.000000 0.000000 0.000000 0.000000 0.000000 0.511871 -0.089021 0.000000 0.880841 -0.665902 0.644592 0.202642 -0.562645 0.926964 0.000000 -0.615690 0.000000 0.798983 -0.036199 0.000000 0.000000 0.000000 -0.994006 -0.895905 0.000941 0.619513 -0.834505 -0.530887 -0.985759 -0.175307 -0.762123 0.000000 0.516584 0.000000 -0.348750 -0.982796 -0.697595 0.105856 0.000000 0.000000 0.000000 0.138778 0.468838 -0.236727 0.428163 -0.754897 -0.510798 0.053814 0.000000 -0.735951 0.987742 -0.998216 -0.846304 0.904114 -0.471878 -0.244316 0.000000 -0.748347 0.000000 0.000000 0.138778 0.000000 -0.003302 -0.714258 0.266154 0.290678 0.005662 0.750236 0.000000 0.339948 0.348545 0.000000 0.000000 0.000000 -0.702293 -0.585580 -0.305554 0.870521 0.000000 -0.994006 0.468838 -0.003302 0.000000 0.000000 0.416282 -0.075072 0.716041 0.422347 0.000000 0.000000 -0.614091 0.000000 0.000000 0.568163 -0.660122 0.605550 0.929362 0.000000 0.000000 -0.895905 -0.236727 -0.714258 0.000000 0.000000 -0.457347 0.000000 0.787556 0.050539 0.000000 -0.027167 0.000000 0.869349 0.000000 -0.639824 0.709158 -0.477465 -0.098976 -0.887956 0.000000 0.000941 0.428163 0.266154 0.416282 -0.457347 0.000000 -0.051532 -0.736559 0.039077 0.785091 -0.378390 0.000000 -0.692533 0.098351 0.425251 0.249350 0.478241 -0.784282 0.087513 0.511871 0.619513 -0.754897 0.290678 -0.075072 0.000000 -0.051532 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 280 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 17 33 43 59 72 87 99 111 127 142 155 170 180 194 209 224 237 248 263 280 Column indices: 1 2 3 4 5 7 8 9 10 11 13 14 15 16 17 18 19 0 2 3 4 5 6 7 9 10 12 14 15 16 17 18 19 0 1 4 5 7 8 11 13 14 19 0 1 4 5 6 7 8 9 10 12 13 14 15 16 18 19 0 1 2 3 5 8 9 11 13 14 15 16 17 0 1 2 3 4 6 7 8 10 11 12 13 15 18 19 1 3 5 8 9 10 11 12 13 14 15 19 0 1 2 3 5 8 11 13 15 17 18 19 0 2 3 4 5 6 7 9 11 12 14 15 16 17 18 19 0 1 3 4 6 8 10 12 13 14 15 16 17 18 19 0 1 3 5 6 9 11 12 14 16 17 18 19 0 2 4 5 6 7 8 10 12 13 14 15 16 18 19 1 3 5 6 8 9 10 11 13 19 0 2 3 4 5 6 7 9 11 12 16 17 18 19 0 1 2 3 4 6 8 9 10 11 15 16 17 18 19 0 1 3 4 5 6 7 8 9 11 14 16 17 18 19 0 1 3 4 8 9 10 11 13 14 15 18 19 0 1 4 7 8 9 10 13 14 15 18 0 1 3 5 7 8 9 10 11 13 14 15 16 17 19 0 1 2 3 5 6 7 8 9 10 11 12 13 14 15 16 18 Off-diagonal values: 0.700766 0.351037 -0.182366 -0.518411 -0.514693 -0.850739 0.238784 0.969377 -0.704435 0.724893 -0.089021 -0.834505 -0.510798 0.005662 0.716041 0.787556 -0.736559 0.700766 -0.205729 -0.536616 -0.454873 -0.717429 -0.790184 -0.343707 -0.539446 -0.359855 -0.079821 -0.530887 0.053814 0.750236 0.422347 0.050539 0.039077 0.351037 -0.205729 0.579096 -0.721478 0.992333 -0.108147 -0.146529 0.880841 -0.985759 0.785091 -0.182366 -0.536616 -0.039182 -0.615949 0.557198 0.778824 0.302401 -0.522599 0.564895 -0.204804 -0.665902 -0.175307 -0.735951 0.339948 -0.027167 -0.378390 -0.518411 -0.454873 0.579096 -0.039182 -0.216872 -0.203864 -0.858804 -0.124502 0.644592 -0.762123 0.987742 0.348545 -0.614091 -0.514693 -0.717429 -0.721478 -0.615949 -0.216872 0.165493 -0.077693 -0.751068 -0.800434 0.574810 0.846176 0.202642 -0.998216 0.869349 -0.692533 -0.790184 0.557198 0.165493 0.810598 0.612779 -0.694096 -0.693100 -0.687896 -0.562645 0.516584 -0.846304 0.098351 -0.850739 -0.343707 0.992333 0.778824 -0.077693 0.798837 -0.927661 0.926964 0.904114 0.568163 -0.639824 0.425251 0.238784 -0.108147 0.302401 -0.203864 -0.751068 0.810598 0.798837 0.968325 -0.033360 -0.660600 -0.348750 -0.471878 -0.702293 -0.660122 0.709158 0.249350 0.969377 -0.539446 -0.522599 -0.858804 0.612779 0.968325 0.556694 0.206175 -0.615690 -0.982796 -0.244316 -0.585580 0.605550 -0.477465 0.478241 -0.704435 -0.359855 0.564895 -0.800434 -0.694096 0.556694 -0.013619 0.486863 -0.697595 -0.305554 0.929362 -0.098976 -0.784282 0.724893 -0.146529 -0.124502 0.574810 -0.693100 -0.927661 -0.033360 -0.013619 -0.275573 0.798983 0.105856 -0.748347 0.870521 -0.887956 0.087513 -0.079821 -0.204804 0.846176 -0.687896 -0.660600 0.206175 0.486863 -0.275573 -0.036199 0.511871 -0.089021 0.880841 -0.665902 0.644592 0.202642 -0.562645 0.926964 -0.615690 0.798983 -0.036199 -0.994006 -0.895905 0.000941 0.619513 -0.834505 -0.530887 -0.985759 -0.175307 -0.762123 0.516584 -0.348750 -0.982796 -0.697595 0.105856 0.138778 0.468838 -0.236727 0.428163 -0.754897 -0.510798 0.053814 -0.735951 0.987742 -0.998216 -0.846304 0.904114 -0.471878 -0.244316 -0.748347 0.138778 -0.003302 -0.714258 0.266154 0.290678 0.005662 0.750236 0.339948 0.348545 -0.702293 -0.585580 -0.305554 0.870521 -0.994006 0.468838 -0.003302 0.416282 -0.075072 0.716041 0.422347 -0.614091 0.568163 -0.660122 0.605550 0.929362 -0.895905 -0.236727 -0.714258 -0.457347 0.787556 0.050539 -0.027167 0.869349 -0.639824 0.709158 -0.477465 -0.098976 -0.887956 0.000941 0.428163 0.266154 0.416282 -0.457347 -0.051532 -0.736559 0.039077 0.785091 -0.378390 -0.692533 0.098351 0.425251 0.249350 0.478241 -0.784282 0.087513 0.511871 0.619513 -0.754897 0.290678 -0.075072 -0.051532 . x x o o o - o x x o x - o o o x x x o x . o o o o o o - o o - o - o x x x x x x o . - x o - x o - - o - x o - - - - x o o | . o o x x x o x - o o o o x - o o o o x o . o - - o o - o - x o x x o - - o o o o o . x o o - o x x x - o - - x o | o | x | x . - x x o o o o x o - - - x o o x x | o | . x - - o - x - x - x o x x | o x o o x x . x - o o - o o o o x x x o | o o | x | x . x - x o o o o x o x o o | x | o o | | x . o x - o - o x o o x | o | o x o o o | o . o x x o x - o x | o | o | x o | o x x o . o - - - - - x o | x o x x o x | o | x o . - - o o x x o o o o o | x | o o o x | | . x x o x o o x | o x o o x o o | o | | x . o o x x x x | x x | | | o o o x | o x o . - x o x x | | o | | x o x x | | o o o | . o - x x | o | x | o x o o o | x x x x o . o o x x o | o x x x x o x x x o x o | o . The error in solving: 5.385869e-16 The error in solving: 5.338892e-16 The error in solving: 4.774241e-16 The error in solving: 7.141332e-16 The error in solving: 8.593029e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a standard normal distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.229806 0.000000 0.000000 0.000000 0.604769 -0.064164 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.010926 0.000000 0.000000 0.052414 0.000000 0.000000 0.000000 0.000000 0.169887 0.000000 0.000000 0.000000 0.000000 0.000000 -0.826592 1.182057 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.314316 0.000000 -0.019864 0.229806 0.169887 0.000000 0.000000 0.000000 0.097024 0.000000 0.000000 0.000000 0.446499 -0.872368 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.051784 1.303525 0.000000 -0.323037 0.000000 0.000000 0.000000 0.000000 0.000000 1.554898 0.000000 0.000000 0.000000 0.956106 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.894223 0.000000 -2.476648 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.097024 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.546946 -0.567716 0.000000 -1.431256 0.604769 0.000000 0.000000 0.051784 0.000000 0.000000 0.000000 0.000000 1.984080 0.000000 0.000000 0.000000 -0.052138 0.000000 -0.996524 0.000000 0.766696 0.000000 -0.803341 0.000000 -0.064164 0.000000 0.000000 1.303525 0.000000 0.000000 0.000000 0.000000 0.000000 -0.274692 0.000000 0.000000 0.000000 0.240883 0.000000 0.000000 -1.961749 0.000000 0.540262 0.000000 0.000000 -0.826592 0.000000 0.000000 0.000000 0.000000 1.984080 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.266236 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.182057 0.446499 -0.323037 0.000000 0.000000 0.000000 -0.274692 0.000000 -0.735322 0.566296 0.000000 0.000000 0.000000 0.000000 1.106735 0.590072 0.000000 0.000000 0.000000 0.000000 0.000000 -0.872368 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.566296 1.228910 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.292907 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.255036 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.894223 0.000000 -0.052138 0.000000 0.000000 0.000000 0.000000 -0.255036 0.000000 0.000000 0.000000 0.000000 -0.503790 0.205722 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.240883 -0.266236 0.000000 0.000000 0.000000 0.000000 2.572451 0.000000 0.000000 0.000000 0.978177 0.000000 0.000000 1.010926 0.000000 0.000000 0.000000 -2.476648 0.000000 -0.996524 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.491734 0.000000 2.396604 0.000000 0.000000 0.000000 1.554898 0.000000 0.000000 0.000000 0.000000 0.000000 1.106735 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.049741 0.000000 -0.885566 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.546946 0.766696 -1.961749 0.000000 0.590072 0.000000 0.000000 -0.503790 0.000000 0.000000 -1.049741 0.000000 0.000000 0.167261 0.000000 0.052414 -0.314316 0.000000 0.000000 0.000000 -0.567716 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.205722 0.978177 -1.491734 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.803341 0.540262 0.000000 0.000000 1.292907 0.000000 0.000000 0.000000 0.000000 -0.885566 0.167261 0.000000 0.000000 0.000000 0.000000 -0.019864 0.000000 0.956106 0.000000 -1.431256 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.396604 0.000000 0.000000 0.000000 0.000000 -0.335330]; Dimension: 20 x 20 Off-diagonal entries: 92 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.735322 1.228910 0.000000 0.000000 2.572451 0.000000 0.000000 0.000000 0.000000 0.000000 -0.335330 Row indices: 0 5 10 15 20 22 26 33 39 42 49 52 53 58 61 66 70 77 83 88 92 Column indices: 2 6 7 14 17 2 8 9 17 19 0 1 5 9 10 6 7 9 15 19 12 14 2 16 17 19 0 3 8 12 14 16 18 0 3 9 13 16 18 1 6 13 1 2 3 7 10 15 16 2 9 18 12 4 6 11 16 17 7 8 17 0 4 6 17 19 3 9 16 18 5 6 7 9 12 15 18 0 1 5 12 13 14 6 7 10 15 16 1 3 5 14 Off-diagonal values: 0.229806 0.604769 -0.064164 1.010926 0.052414 0.169887 -0.826592 1.182057 -0.314316 -0.019864 0.229806 0.169887 0.097024 0.446499 -0.872368 0.051784 1.303525 -0.323037 1.554898 0.956106 -2.894223 -2.476648 0.097024 -1.546946 -0.567716 -1.431256 0.604769 0.051784 1.984080 -0.052138 -0.996524 0.766696 -0.803341 -0.064164 1.303525 -0.274692 0.240883 -1.961749 0.540262 -0.826592 1.984080 -0.266236 1.182057 0.446499 -0.323037 -0.274692 0.566296 1.106735 0.590072 -0.872368 0.566296 1.292907 -0.255036 -2.894223 -0.052138 -0.255036 -0.503790 0.205722 0.240883 -0.266236 0.978177 1.010926 -2.476648 -0.996524 -1.491734 2.396604 1.554898 1.106735 -1.049741 -0.885566 -1.546946 0.766696 -1.961749 0.590072 -0.503790 -1.049741 0.167261 0.052414 -0.314316 -0.567716 0.205722 0.978177 -1.491734 -0.803341 0.540262 1.292907 -0.885566 0.167261 -0.019864 0.956106 -1.431256 2.396604 . - x - - - x o - - - - - - x - - x - - | . x - - - - - o x - - - - - - - o - o x x . - - x - - - x o - - - - - - - - - | | | . - - x x - o - - - - - x - - - x | | | | . - - - - - - - o - o - - - - - | | x | | . - - - - - - - - - - o o - o x | | x | | . - x - - - o - o - x - o - o | | x | | | . - o - - - x - - o - x - | o | | | | x | . - - - - o - - - - - - | x x o | | | o | o x - - - - x x - - - | | o | | | | | | x x - - - - - - - x - | | | | | | | | | | | . o - - - - - - - | | | | o | o | | | | o . - - - o x - - | | | | | | | x o | | | | x - - - x - - x | | | o | o | | | | | | | . - - o - x | | | x | | | | | x | | | | | . o - o - | | | | | o x o | x | | o | | o . - x - x o | | | o | | | | | | x x o | | . - - | | | | | | o x | | x | | | | o x | . - | o | x | o | | | | | | | | x | | | | o The error in solving: 5.929000e-16 The error in solving: 4.857226e-16 The error in solving: 3.152427e-16 The error in solving: 9.045636e-16 The error in solving: 3.445774e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a standard normal distribution with a random diagonal and a density of 0.500000 [ 0.000000 -1.423328 -0.863664 -0.963295 0.000000 0.000000 0.000000 -0.564624 0.000000 0.122468 0.426696 1.746824 0.066821 0.000000 0.369090 -1.183471 0.000000 0.936995 0.000000 -0.495329 -1.423328 -1.776457 -0.765425 0.000000 0.000000 -0.846139 0.000000 0.000000 0.771442 0.339941 0.197117 0.203179 0.828134 0.000000 0.000000 0.000000 -0.667469 2.284536 0.000000 0.710064 -0.863664 -0.765425 0.000000 -0.719519 0.000000 0.977684 0.000000 0.000000 -0.225047 0.000000 -0.042480 1.031688 0.000000 0.159653 0.000000 0.000000 -0.245210 0.838599 -0.078879 0.000000 -0.963295 0.000000 -0.719519 0.000000 -0.207380 0.000000 1.326772 1.729341 0.000000 0.000000 0.000000 -1.708755 0.000000 0.000000 0.000000 -0.592763 0.000000 0.000000 -1.195562 0.208005 0.000000 0.000000 0.000000 -0.207380 -0.468498 -1.103295 0.000000 -0.308513 0.000000 0.896325 1.956083 0.000000 0.000000 1.028155 -1.890682 0.000000 1.419934 0.000000 -0.460114 0.000000 0.000000 -0.846139 0.977684 0.000000 -1.103295 0.000000 0.000000 0.000000 0.312821 -1.543475 0.000000 0.000000 -1.250026 0.000000 0.000000 -1.782139 0.000000 1.064857 0.184077 0.000000 0.000000 0.000000 0.000000 1.326772 0.000000 0.000000 0.000000 -1.364795 -0.241842 0.047717 0.368484 -0.379653 0.157524 -0.071717 0.000000 0.000000 -0.464093 0.108034 -0.406805 0.000000 -0.564624 0.000000 0.000000 1.729341 -0.308513 0.000000 -1.364795 0.000000 0.000000 0.165514 1.853447 0.000000 -1.285062 0.000000 0.000000 0.560398 -0.379812 0.291504 -1.969015 0.000000 0.000000 0.771442 -0.225047 0.000000 0.000000 0.312821 -0.241842 0.000000 -0.459824 -0.302333 0.938557 0.000000 -3.835994 -0.986186 0.696594 0.000000 0.947263 -0.160162 -1.616908 0.212862 0.122468 0.339941 0.000000 0.000000 0.896325 -1.543475 0.047717 0.165514 -0.302333 0.000000 0.000000 0.000000 0.081702 0.000000 0.302167 0.000000 0.822820 2.322790 0.000000 0.000000 0.426696 0.197117 -0.042480 0.000000 1.956083 0.000000 0.368484 1.853447 0.938557 0.000000 0.607334 0.865378 -0.204632 0.695521 -0.242913 -1.723841 0.000000 0.000000 0.655000 0.000000 1.746824 0.203179 1.031688 -1.708755 0.000000 0.000000 -0.379653 0.000000 0.000000 0.000000 0.865378 0.000000 0.000000 -0.045418 0.000000 1.026116 0.000000 0.457290 0.000000 -0.824889 0.066821 0.828134 0.000000 0.000000 0.000000 -1.250026 0.157524 -1.285062 -3.835994 0.081702 -0.204632 0.000000 0.000000 0.076234 0.000000 -0.147231 -1.679710 0.000000 0.000000 0.000000 0.000000 0.000000 0.159653 0.000000 1.028155 0.000000 -0.071717 0.000000 -0.986186 0.000000 0.695521 -0.045418 0.076234 0.000000 0.000000 0.812479 0.000000 0.000000 1.322004 0.000000 0.369090 0.000000 0.000000 0.000000 -1.890682 0.000000 0.000000 0.000000 0.696594 0.302167 -0.242913 0.000000 0.000000 0.000000 0.000000 -1.623000 0.000000 0.000000 0.039053 0.000000 -1.183471 0.000000 0.000000 -0.592763 0.000000 -1.782139 0.000000 0.560398 0.000000 0.000000 -1.723841 1.026116 -0.147231 0.812479 -1.623000 0.000000 0.000000 0.000000 1.567037 -1.187507 0.000000 -0.667469 -0.245210 0.000000 1.419934 0.000000 -0.464093 -0.379812 0.947263 0.822820 0.000000 0.000000 -1.679710 0.000000 0.000000 0.000000 0.592574 0.000000 0.000000 -0.840077 0.936995 2.284536 0.838599 0.000000 0.000000 1.064857 0.108034 0.291504 -0.160162 2.322790 0.000000 0.457290 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.051335 0.000000 0.000000 0.000000 -0.078879 -1.195562 -0.460114 0.184077 -0.406805 -1.969015 -1.616908 0.000000 0.655000 0.000000 0.000000 1.322004 0.039053 1.567037 0.000000 -0.051335 -0.586069 0.000000 -0.495329 0.710064 0.000000 0.208005 0.000000 0.000000 0.000000 0.000000 0.212862 0.000000 0.000000 -0.824889 0.000000 0.000000 0.000000 -1.187507 -0.840077 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 206 (max 380) Diagonal entries: 0.000000 -1.776457 0.000000 0.000000 -0.468498 0.000000 0.000000 0.000000 -0.459824 0.000000 0.607334 0.000000 0.000000 0.000000 0.000000 0.000000 0.592574 0.000000 -0.586069 0.000000 Row indices: 0 12 23 34 43 52 61 72 83 96 107 120 130 141 150 157 168 177 187 199 206 Column indices: 1 2 3 7 9 10 11 12 14 15 17 19 0 2 5 8 9 10 11 12 16 17 19 0 1 3 5 8 10 11 13 16 17 18 0 2 4 6 7 11 15 18 19 3 5 7 9 10 13 14 16 18 1 2 4 8 9 12 15 17 18 3 7 8 9 10 11 12 13 16 17 18 0 3 4 6 9 10 12 15 16 17 18 1 2 5 6 9 10 12 13 14 16 17 18 19 0 1 4 5 6 7 8 12 14 16 17 0 1 2 4 6 7 8 11 12 13 14 15 18 0 1 2 3 6 10 13 15 17 19 0 1 5 6 7 8 9 10 13 15 16 2 4 6 8 10 11 12 15 18 0 4 8 9 10 15 18 0 3 5 7 10 11 12 13 14 18 19 1 2 4 6 7 8 9 12 19 0 1 2 5 6 7 8 9 11 18 2 3 4 5 6 7 8 10 13 14 15 17 0 1 3 8 11 15 16 Off-diagonal values: -1.423328 -0.863664 -0.963295 -0.564624 0.122468 0.426696 1.746824 0.066821 0.369090 -1.183471 0.936995 -0.495329 -1.423328 -0.765425 -0.846139 0.771442 0.339941 0.197117 0.203179 0.828134 -0.667469 2.284536 0.710064 -0.863664 -0.765425 -0.719519 0.977684 -0.225047 -0.042480 1.031688 0.159653 -0.245210 0.838599 -0.078879 -0.963295 -0.719519 -0.207380 1.326772 1.729341 -1.708755 -0.592763 -1.195562 0.208005 -0.207380 -1.103295 -0.308513 0.896325 1.956083 1.028155 -1.890682 1.419934 -0.460114 -0.846139 0.977684 -1.103295 0.312821 -1.543475 -1.250026 -1.782139 1.064857 0.184077 1.326772 -1.364795 -0.241842 0.047717 0.368484 -0.379653 0.157524 -0.071717 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0.822820 -1.679710 -0.840077 0.936995 2.284536 0.838599 1.064857 0.108034 0.291504 -0.160162 2.322790 0.457290 -0.051335 -0.078879 -1.195562 -0.460114 0.184077 -0.406805 -1.969015 -1.616908 0.655000 1.322004 0.039053 1.567037 -0.051335 -0.495329 0.710064 0.208005 0.212862 -0.824889 -1.187507 -0.840077 . o o o - - - o - x x x x - x o - x - o o o o - - o - - x x x x x - - - o x - x o o . o - x - - o - o x - x - - o x o - o | o . o - x x - - - o - - - o - - o x | | | o o o - o - x x - - x o - x - o - | o x | o . - - x o - - o - - o - x x - | | | x | | . o o x x o x o - - o x o - o | | x o | o . - x x - o - - x o x o - | x o | | x o | o o x - o o x - x o o x x x | | x o x x o . - - x - x - x x - - x x o | x | x x x | x x o x o o - - x - x x x o | | o | | | x . - o - x - x - o x x | | | o x o o x o | . x - o o - - - | | x | x | o | o | x o x . - x - - x - x | | | o | | | x x o | | | . o - - x - o | | o | o | x | | o x o x o . - - x o | o o | x | o o x x | | o | | | x - - o x x x | | x x x o x | x | | | | | . o - | | o o o x o o o | x | | x x x | o o - o x | x | | | | x | | o | | | o o | | . The error in solving: 8.936436e-16 The error in solving: 3.905710e-16 The error in solving: 8.151355e-16 The error in solving: 6.211376e-16 The error in solving: 4.486197e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a standard normal distribution with a random diagonal and a density of 0.750000 [ 0.000000 0.703384 -0.334421 -0.200104 0.993997 -1.962630 -0.069128 0.628338 0.292539 -1.938855 0.596045 1.155586 0.000000 0.000000 0.429099 1.156303 -0.704929 0.735263 0.000000 0.000000 0.703384 0.551736 -2.306506 0.866807 0.000000 0.000000 1.356242 0.000000 1.084833 0.026341 -0.778231 0.000000 0.463096 2.022217 -0.577246 -1.476633 0.412942 0.009746 -0.426684 0.000000 -0.334421 -2.306506 0.000000 1.343127 0.000000 -0.003388 0.000000 0.000000 0.000000 0.000000 1.020452 0.000000 -0.024912 0.016427 1.630307 -1.060122 0.784376 0.000000 0.000000 0.824978 -0.200104 0.866807 1.343127 0.000000 -0.993396 -1.306196 0.000000 1.362419 0.508983 1.266562 -0.124317 -0.542495 1.021446 0.368070 -0.350617 0.469318 1.527356 -0.116590 0.000000 -0.752328 0.993997 0.000000 0.000000 -0.993396 -0.198139 1.433665 -0.112485 -0.479948 0.847102 -0.288423 0.284031 -0.038608 -0.560508 -0.765113 -1.838709 -1.246589 -1.549177 -1.743866 -0.915181 -1.012697 -1.962630 0.000000 -0.003388 -1.306196 1.433665 -0.209233 0.000000 0.000000 0.000000 0.000000 0.553079 -0.090126 -1.601830 -0.873258 0.000000 -2.148468 0.000000 0.000000 0.000000 -1.553192 -0.069128 1.356242 0.000000 0.000000 -0.112485 0.000000 -0.745102 0.003514 -0.228215 -0.009776 1.050119 1.082818 0.000000 0.958632 0.871171 0.472538 -0.924370 -0.055159 0.000000 0.243026 0.628338 0.000000 0.000000 1.362419 -0.479948 0.000000 0.003514 0.464247 -0.118839 -0.721088 0.000000 -0.518373 0.000000 0.602413 -0.773709 -1.701041 -0.495682 0.456607 0.294302 -0.072496 0.292539 1.084833 0.000000 0.508983 0.847102 0.000000 -0.228215 -0.118839 0.000000 1.271172 -0.708518 1.663067 0.754938 0.000000 0.587340 -0.578607 -0.482859 -1.941912 -0.609003 -0.150089 -1.938855 0.026341 0.000000 1.266562 -0.288423 0.000000 -0.009776 -0.721088 1.271172 -0.521079 -0.679033 0.000000 -1.744905 -0.201204 -2.257910 -0.179723 -0.024884 -0.143613 -1.001974 0.000000 0.596045 -0.778231 1.020452 -0.124317 0.284031 0.553079 1.050119 0.000000 -0.708518 -0.679033 -1.306566 -0.498428 1.465529 0.355836 -1.363608 1.052552 -1.485114 -2.015490 0.199713 -1.199201 1.155586 0.000000 0.000000 -0.542495 -0.038608 -0.090126 1.082818 -0.518373 1.663067 0.000000 -0.498428 -0.734405 0.969950 -0.568046 0.945663 0.000000 0.000000 0.000000 0.779745 0.000000 0.000000 0.463096 -0.024912 1.021446 -0.560508 -1.601830 0.000000 0.000000 0.754938 -1.744905 1.465529 0.969950 -1.332072 -0.429561 -0.550539 -0.947913 1.221974 -1.258715 -0.045880 0.000000 0.000000 2.022217 0.016427 0.368070 -0.765113 -0.873258 0.958632 0.602413 0.000000 -0.201204 0.355836 -0.568046 -0.429561 1.493292 2.268876 -0.479138 1.768319 -0.642262 -0.443383 0.953019 0.429099 -0.577246 1.630307 -0.350617 -1.838709 0.000000 0.871171 -0.773709 0.587340 -2.257910 -1.363608 0.945663 -0.550539 2.268876 -0.100868 0.000000 0.000000 0.156182 -0.960689 1.018885 1.156303 -1.476633 -1.060122 0.469318 -1.246589 -2.148468 0.472538 -1.701041 -0.578607 -0.179723 1.052552 0.000000 -0.947913 -0.479138 0.000000 -0.067934 -0.078135 -0.305017 -0.726526 1.046472 -0.704929 0.412942 0.784376 1.527356 -1.549177 0.000000 -0.924370 -0.495682 -0.482859 -0.024884 -1.485114 0.000000 1.221974 1.768319 0.000000 -0.078135 -1.084463 0.000000 0.000000 0.000000 0.735263 0.009746 0.000000 -0.116590 -1.743866 0.000000 -0.055159 0.456607 -1.941912 -0.143613 -2.015490 0.000000 -1.258715 -0.642262 0.156182 -0.305017 0.000000 0.697515 -0.999915 -0.641816 0.000000 -0.426684 0.000000 0.000000 -0.915181 0.000000 0.000000 0.294302 -0.609003 -1.001974 0.199713 0.779745 -0.045880 -0.443383 -0.960689 -0.726526 0.000000 -0.999915 0.000000 0.000000 0.000000 0.000000 0.824978 -0.752328 -1.012697 -1.553192 0.243026 -0.072496 -0.150089 0.000000 -1.199201 0.000000 0.000000 0.953019 1.018885 1.046472 0.000000 -0.641816 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 290 (max 380) Diagonal entries: 0.000000 0.551736 0.000000 0.000000 -0.198139 -0.209233 -0.745102 0.464247 0.000000 -0.521079 -1.306566 -0.734405 -1.332072 1.493292 -0.100868 -0.067934 -1.084463 0.697515 0.000000 0.000000 Row indices: 0 15 29 40 57 74 84 98 112 128 143 161 173 188 205 221 238 251 266 278 290 Column indices: 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 0 2 3 6 8 9 10 12 13 14 15 16 17 18 0 1 3 5 10 12 13 14 15 16 19 0 1 2 4 5 7 8 9 10 11 12 13 14 15 16 17 19 0 3 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0 2 3 4 10 11 12 13 15 19 0 1 4 7 8 9 10 11 13 14 15 16 17 19 0 3 4 6 8 9 11 13 14 15 16 17 18 19 0 1 3 4 6 7 9 10 11 12 14 15 16 17 18 19 0 1 3 4 6 7 8 10 12 13 14 15 16 17 18 0 1 2 3 4 5 6 8 9 11 12 13 14 15 16 17 18 19 0 3 4 5 6 7 8 10 12 13 14 18 1 2 3 4 5 8 9 10 11 13 14 15 16 17 18 1 2 3 4 5 6 7 9 10 11 12 14 15 16 17 18 19 0 1 2 3 4 6 7 8 9 10 11 12 13 17 18 19 0 1 2 3 4 5 6 7 8 9 10 12 13 16 17 18 19 0 1 2 3 4 6 7 8 9 10 12 13 15 0 1 3 4 6 7 8 9 10 12 13 14 15 18 19 1 4 7 8 9 10 11 12 13 14 15 17 2 3 4 5 6 7 8 10 13 14 15 17 Off-diagonal values: 0.703384 -0.334421 -0.200104 0.993997 -1.962630 -0.069128 0.628338 0.292539 -1.938855 0.596045 1.155586 0.429099 1.156303 -0.704929 0.735263 0.703384 -2.306506 0.866807 1.356242 1.084833 0.026341 -0.778231 0.463096 2.022217 -0.577246 -1.476633 0.412942 0.009746 -0.426684 -0.334421 -2.306506 1.343127 -0.003388 1.020452 -0.024912 0.016427 1.630307 -1.060122 0.784376 0.824978 -0.200104 0.866807 1.343127 -0.993396 -1.306196 1.362419 0.508983 1.266562 -0.124317 -0.542495 1.021446 0.368070 -0.350617 0.469318 1.527356 -0.116590 -0.752328 0.993997 -0.993396 1.433665 -0.112485 -0.479948 0.847102 -0.288423 0.284031 -0.038608 -0.560508 -0.765113 -1.838709 -1.246589 -1.549177 -1.743866 -0.915181 -1.012697 -1.962630 -0.003388 -1.306196 1.433665 0.553079 -0.090126 -1.601830 -0.873258 -2.148468 -1.553192 -0.069128 1.356242 -0.112485 0.003514 -0.228215 -0.009776 1.050119 1.082818 0.958632 0.871171 0.472538 -0.924370 -0.055159 0.243026 0.628338 1.362419 -0.479948 0.003514 -0.118839 -0.721088 -0.518373 0.602413 -0.773709 -1.701041 -0.495682 0.456607 0.294302 -0.072496 0.292539 1.084833 0.508983 0.847102 -0.228215 -0.118839 1.271172 -0.708518 1.663067 0.754938 0.587340 -0.578607 -0.482859 -1.941912 -0.609003 -0.150089 -1.938855 0.026341 1.266562 -0.288423 -0.009776 -0.721088 1.271172 -0.679033 -1.744905 -0.201204 -2.257910 -0.179723 -0.024884 -0.143613 -1.001974 0.596045 -0.778231 1.020452 -0.124317 0.284031 0.553079 1.050119 -0.708518 -0.679033 -0.498428 1.465529 0.355836 -1.363608 1.052552 -1.485114 -2.015490 0.199713 -1.199201 1.155586 -0.542495 -0.038608 -0.090126 1.082818 -0.518373 1.663067 -0.498428 0.969950 -0.568046 0.945663 0.779745 0.463096 -0.024912 1.021446 -0.560508 -1.601830 0.754938 -1.744905 1.465529 0.969950 -0.429561 -0.550539 -0.947913 1.221974 -1.258715 -0.045880 2.022217 0.016427 0.368070 -0.765113 -0.873258 0.958632 0.602413 -0.201204 0.355836 -0.568046 -0.429561 2.268876 -0.479138 1.768319 -0.642262 -0.443383 0.953019 0.429099 -0.577246 1.630307 -0.350617 -1.838709 0.871171 -0.773709 0.587340 -2.257910 -1.363608 0.945663 -0.550539 2.268876 0.156182 -0.960689 1.018885 1.156303 -1.476633 -1.060122 0.469318 -1.246589 -2.148468 0.472538 -1.701041 -0.578607 -0.179723 1.052552 -0.947913 -0.479138 -0.078135 -0.305017 -0.726526 1.046472 -0.704929 0.412942 0.784376 1.527356 -1.549177 -0.924370 -0.495682 -0.482859 -0.024884 -1.485114 1.221974 1.768319 -0.078135 0.735263 0.009746 -0.116590 -1.743866 -0.055159 0.456607 -1.941912 -0.143613 -2.015490 -1.258715 -0.642262 0.156182 -0.305017 -0.999915 -0.641816 -0.426684 -0.915181 0.294302 -0.609003 -1.001974 0.199713 0.779745 -0.045880 -0.443383 -0.960689 -0.726526 -0.999915 0.824978 -0.752328 -1.012697 -1.553192 0.243026 -0.072496 -0.150089 -1.199201 0.953019 1.018885 1.046472 -0.641816 . x o o x o o x x o x x - - x x o x - - x x o x - - x - x x o - x x o o x x o - o o . x - o - - - - x - o x x o x - - x o x x . o o - x x x o o x x o x x o - o x | | o o x o o x o x o o o o o o o o o o | o o x o - - - - x o o o - o - - - o o x | | o | o x o o x x - x x x o o - x x | | x o | x x o o - o - x o o o x x o x x | x x | o o . x o x x - x o o o o o o x | x o | o o x o o - o o o o o o o - x o x o x x x | o o o o x x o x o o x o x | | o o o x o x | o o x o x - - - x - | x o x o o | | x o x x o o o o x o o - | x x x o o x x | o x o o x x o x o o x x o x o o | x o x o o x o x o - - x o x x o o x o o x o o o x | o o | o o o o x o x x x o | o o o o o | x x | o o - - - x x | o o | o x o o o | o o x o | x o o | o | | o | | x o o x x o o o o | o . - | | x o o o x o o | o | | x x x | o | . The error in solving: 4.489550e-16 The error in solving: 6.598884e-16 The error in solving: 5.813886e-16 The error in solving: 5.545909e-16 The error in solving: 7.157831e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a standard normal distribution with a dense diagonal and a density of 0.250000 [ 1.325334 0.000000 0.745963 0.000000 0.000000 0.000000 0.000000 0.000000 -0.573990 0.000000 -1.968396 -1.240716 0.000000 0.000000 0.000000 0.114727 0.000000 0.000000 0.000000 0.000000 0.000000 0.638530 1.580984 -0.932563 0.000000 0.000000 0.000000 0.000000 -1.449675 0.000000 0.615248 0.888011 0.000000 0.000000 0.000000 -1.615289 -0.508214 0.000000 0.000000 -0.177479 0.745963 1.580984 1.103659 0.000000 0.000000 0.585679 0.000000 0.000000 0.000000 -0.201830 1.449587 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.932563 0.000000 -0.887219 0.000000 0.000000 -1.844809 0.000000 0.000000 1.004578 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.243562 0.000000 0.000000 0.000000 0.000000 -0.574587 0.000000 -1.038318 0.000000 0.000000 0.000000 0.000000 0.701920 0.000000 0.000000 0.000000 0.000000 0.000000 0.585679 0.000000 0.000000 0.478538 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.844809 0.000000 0.000000 -0.456215 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.109890 0.000000 0.000000 0.000000 0.000000 0.317443 0.000000 0.000000 0.000000 0.000000 -1.012885 0.000000 0.000000 -0.573990 -1.449675 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.433628 -1.702717 0.000000 0.000000 0.000000 0.000000 0.000000 0.740517 1.407375 0.000000 0.000000 0.000000 0.000000 0.000000 -0.201830 1.004578 -0.574587 0.000000 0.000000 0.000000 -1.702717 2.123207 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.573379 0.000000 0.000000 -1.968396 0.615248 1.449587 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.285623 0.000000 1.484907 0.000000 0.000000 0.850270 -0.375286 0.000000 0.000000 0.806700 -1.240716 0.888011 0.000000 0.000000 -1.038318 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.125987 0.000000 0.000000 1.331651 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.317443 0.000000 0.000000 1.484907 0.000000 0.059474 0.991806 1.201299 -0.816765 -0.697438 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.991806 1.752875 0.718769 0.000000 0.000000 -0.943564 0.849548 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.331651 1.201299 0.718769 -0.099228 0.000000 0.000000 0.000000 -1.522730 0.000000 0.114727 -1.615289 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.740517 0.000000 0.850270 0.000000 -0.816765 0.000000 0.000000 0.174216 0.000000 0.000000 -0.503326 0.000000 0.000000 -0.508214 0.000000 0.000000 0.701920 0.000000 0.000000 0.000000 1.407375 0.000000 -0.375286 0.000000 -0.697438 0.000000 0.000000 0.000000 -0.375131 -0.038676 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.012885 0.000000 2.573379 0.000000 0.000000 0.000000 -0.943564 0.000000 0.000000 -0.038676 -0.029770 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.849548 -1.522730 -0.503326 0.000000 0.000000 0.045182 1.799275 0.000000 -0.177479 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.806700 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.799275 -0.130092]; Dimension: 20 x 20 Off-diagonal entries: 86 (max 380) Diagonal entries: 1.325334 0.638530 1.103659 -0.887219 -2.243562 0.478538 -0.456215 0.109890 0.433628 2.123207 -0.285623 1.125987 0.059474 1.752875 -0.099228 0.174216 -0.375131 -0.029770 0.045182 -0.130092 Row indices: 0 5 13 18 21 24 25 26 28 33 38 45 49 55 59 63 69 75 79 83 86 Column indices: 2 8 10 11 15 2 3 8 10 11 15 16 19 0 1 5 9 10 1 6 9 9 11 16 2 3 12 17 0 1 9 15 16 2 3 4 8 17 0 1 2 12 15 16 19 0 1 4 14 7 10 13 14 15 16 12 14 17 18 11 12 13 18 0 1 8 10 12 18 1 4 8 10 12 17 7 9 13 16 13 14 15 19 1 10 18 Off-diagonal values: 0.745963 -0.573990 -1.968396 -1.240716 0.114727 1.580984 -0.932563 -1.449675 0.615248 0.888011 -1.615289 -0.508214 -0.177479 0.745963 1.580984 0.585679 -0.201830 1.449587 -0.932563 -1.844809 1.004578 -0.574587 -1.038318 0.701920 0.585679 -1.844809 0.317443 -1.012885 -0.573990 -1.449675 -1.702717 0.740517 1.407375 -0.201830 1.004578 -0.574587 -1.702717 2.573379 -1.968396 0.615248 1.449587 1.484907 0.850270 -0.375286 0.806700 -1.240716 0.888011 -1.038318 1.331651 0.317443 1.484907 0.991806 1.201299 -0.816765 -0.697438 0.991806 0.718769 -0.943564 0.849548 1.331651 1.201299 0.718769 -1.522730 0.114727 -1.615289 0.740517 0.850270 -0.816765 -0.503326 -0.508214 0.701920 1.407375 -0.375286 -0.697438 -0.038676 -1.012885 2.573379 -0.943564 -0.038676 0.849548 -1.522730 -0.503326 1.799275 -0.177479 0.806700 1.799275 x - x - - - - - o - o o - - - x - - - - | x x o - - - - o - x x - - - o o - - o x x x - - x - - - o x - - - - - - - - - | o | o - - o - - x - - - - - - - - - - | | | | o - - - - o - o - - - - x - - - | | x | | x - - - - - - - - - - - - - - | | | o | | o - - - - - - - - - - - - - | | | | | | | x - - - - x - - - - o - - o o | | | | | | x o - - - - - x x - - - | | o x o | | | o x - - - - - - - x - - o x x | | | | | | | o - x - - x o - - x o x | | o | | | | | | x - - x - - - - - | | | | | | | x | | x | x x x o o - - - | | | | | | | | | | | | x x x - - o x - | | | | | | | | | | | x x x o - - - o - x o | | | | | | x | x | o | | x - - o - | o | | x | | | x | o | o | | | o o - - | | | | | | | o | x | | | o | | o o - - | | | | | | | | | | | | | x o o | | x x | o | | | | | | | | x | | | | | | | x o The error in solving: 9.484290e-16 The error in solving: 4.126892e-16 The error in solving: 3.764949e-16 The error in solving: 3.319084e-16 The error in solving: 3.162033e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a standard normal distribution with a dense diagonal and a density of 0.500000 [ -1.332822 0.000000 0.000000 -0.567249 0.000000 0.282029 0.000000 0.000000 -0.222271 0.000000 1.014911 1.657648 -0.419257 0.000000 0.000000 0.000000 0.000000 0.114601 0.744881 0.446703 0.000000 -0.405721 1.815004 0.000000 0.000000 -0.268296 -1.928266 0.140008 0.000000 0.000000 0.000000 -1.906110 0.000000 0.682543 0.000000 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-0.105066 0.717459 -0.722096 0.183617 0.000000 -0.045179 -0.207322 -0.522327 0.000000 -0.266945 0.000000 0.000000 0.682543 0.559586 -0.508767 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.241395 0.000000 0.000000 -0.175304 0.000000 -1.418311 0.000000 -0.359187 0.000000 0.572881 0.000000 0.000000 0.000000 -0.380917 0.014092 0.000000 -0.510931 0.000000 -2.338733 -0.499256 -1.192957 0.000000 -0.045179 0.000000 -0.185053 0.000000 -0.877839 -0.624497 0.000000 -0.149502 0.000000 -0.217923 0.000000 0.000000 -0.313794 1.458623 -0.406282 0.000000 0.936827 -0.215884 0.071781 0.151941 -0.207322 -1.418311 0.000000 -0.734742 0.000000 -0.559002 1.118361 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.241096 0.000000 1.222528 -1.870619 0.000000 0.139957 0.000000 -0.522327 0.000000 -0.877839 0.000000 -0.438920 -2.875618 -0.833178 1.064014 0.114601 0.060524 -0.018425 0.000000 -0.378200 -0.009978 0.000000 0.000000 -0.308349 0.000000 0.000000 0.000000 0.000000 -0.359187 -0.624497 -0.559002 -2.875618 -0.211424 0.000000 -1.711581 0.744881 1.467894 -1.854693 -2.190803 1.226037 -1.189489 -0.451191 0.000000 0.000000 0.780730 0.000000 -0.766719 -0.266945 0.000000 0.000000 1.118361 -0.833178 0.000000 -0.249852 -1.285764 0.446703 0.000000 -0.804442 -0.136151 0.000000 0.000000 0.000000 0.000000 1.686833 0.818752 0.000000 0.378066 0.000000 0.572881 -0.149502 0.000000 1.064014 -1.711581 -1.285764 0.402866]; Dimension: 20 x 20 Off-diagonal entries: 200 (max 380) Diagonal entries: -1.332822 -0.405721 0.451812 1.729451 -0.690728 0.903684 -0.289800 2.794118 -0.296270 -1.097616 -0.191924 0.674023 0.183617 -0.175304 -0.185053 -0.734742 -0.438920 -0.211424 -0.249852 0.402866 Row indices: 0 9 18 30 40 51 60 68 75 86 96 108 117 127 134 144 156 165 176 189 200 Column indices: 3 5 8 10 11 12 17 18 19 2 5 6 7 11 13 15 17 18 1 3 4 5 6 7 9 10 13 17 18 19 0 2 4 7 11 12 13 14 18 19 2 3 6 8 9 10 12 14 15 17 18 0 1 2 7 9 15 16 17 18 1 2 4 8 9 14 15 18 1 2 3 5 8 10 16 0 4 6 7 10 11 14 15 16 17 19 2 4 5 6 10 12 14 15 18 19 0 2 4 7 8 9 11 12 13 14 15 16 0 1 3 8 10 12 15 18 19 0 3 4 9 10 11 14 15 16 18 1 2 3 10 15 17 19 3 4 6 8 9 10 12 16 17 19 1 4 5 6 8 9 10 11 12 13 17 18 5 7 8 10 12 14 17 18 19 0 1 2 4 5 8 13 14 15 16 19 0 1 2 3 4 5 6 9 11 12 15 16 19 0 2 3 8 9 11 13 14 16 17 18 Off-diagonal values: -0.567249 0.282029 -0.222271 1.014911 1.657648 -0.419257 0.114601 0.744881 0.446703 1.815004 -0.268296 -1.928266 0.140008 -1.906110 0.682543 -0.217923 0.060524 1.467894 1.815004 -0.139307 -0.443939 -0.061661 -0.621930 0.620842 -1.454698 -0.361875 0.559586 -0.018425 -1.854693 -0.804442 -0.567249 -0.139307 -0.201162 -1.184528 -0.490133 0.408570 -0.508767 -0.380917 -2.190803 -0.136151 -0.443939 -0.201162 0.903276 0.161004 -1.521725 -0.190314 -1.945844 0.014092 -0.313794 -0.378200 1.226037 0.282029 -0.268296 -0.061661 -0.793484 0.004618 1.458623 0.241096 -0.009978 -1.189489 -1.928266 -0.621930 0.903276 0.607111 0.132775 -0.510931 -0.406282 -0.451191 0.140008 0.620842 -1.184528 -0.793484 -0.732894 -0.515732 1.222528 -0.222271 0.161004 0.607111 -0.732894 -1.511885 -2.136774 -2.338733 0.936827 -1.870619 -0.308349 1.686833 -1.454698 -1.521725 0.004618 0.132775 0.347754 -0.105066 -0.499256 -0.215884 0.780730 0.818752 1.014911 -0.361875 -0.190314 -0.515732 -1.511885 0.347754 -0.605964 0.717459 -1.241395 -1.192957 0.071781 0.139957 1.657648 -1.906110 -0.490133 -2.136774 -0.605964 -0.722096 0.151941 -0.766719 0.378066 -0.419257 0.408570 -1.945844 -0.105066 0.717459 -0.722096 -0.045179 -0.207322 -0.522327 -0.266945 0.682543 0.559586 -0.508767 -1.241395 -1.418311 -0.359187 0.572881 -0.380917 0.014092 -0.510931 -2.338733 -0.499256 -1.192957 -0.045179 -0.877839 -0.624497 -0.149502 -0.217923 -0.313794 1.458623 -0.406282 0.936827 -0.215884 0.071781 0.151941 -0.207322 -1.418311 -0.559002 1.118361 0.241096 1.222528 -1.870619 0.139957 -0.522327 -0.877839 -2.875618 -0.833178 1.064014 0.114601 0.060524 -0.018425 -0.378200 -0.009978 -0.308349 -0.359187 -0.624497 -0.559002 -2.875618 -1.711581 0.744881 1.467894 -1.854693 -2.190803 1.226037 -1.189489 -0.451191 0.780730 -0.766719 -0.266945 1.118361 -0.833178 -1.285764 0.446703 -0.804442 -0.136151 1.686833 0.818752 0.378066 0.572881 -0.149502 1.064014 -1.711581 -1.285764 o - - o - x - - o - x x o - - - - x x x | o x - - o o x - - - o - x - o - x x - | x x o o o o x - o o - - x - - - o o o o | o x o - - o - - - o x o o - - - o o | | o o o - x - x o o - o - x o - o x - x o o | | x - o - x - - - - - x x o o - | o o | x | o - x x - - - - o o - - o - | x x o | o | x o - o - - - - - x - - - o | | | x | x o o - o o - - o x o o - x | | o | o x x | | o x - o - o o - - x x x | o | o | | o o x o o x o o x x - - - x o | o | | | | o | o x o - - x - - o x o | | x o | | | | o x o x - o o o - o - | x x o | | | | | | o | | o - o - o - x | | | o x | o | o o o | o | o - o o - o | o | | o x o | x o x x o o | o - o x - | | | | | x | x o | x | o | o | o o o x x x o | o o | | o | | | | o o o o o - o x x o o x o o | | x | o o | | x o | o o x | o o | | | | x x | x | x o | x o o x The error in solving: 4.628318e-16 The error in solving: 1.867065e-16 The error in solving: 5.527647e-16 The error in solving: 5.910700e-16 The error in solving: 8.205815e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a standard normal distribution with a dense diagonal and a density of 0.750000 [ -0.654994 0.000000 -0.782224 1.282592 -0.363078 0.000000 -0.752997 0.000000 -0.603828 -0.625731 0.233208 0.096027 -1.365093 0.557751 0.000000 1.016577 0.204839 0.000000 1.653615 -0.099030 0.000000 1.170792 -0.138606 -0.876561 0.000000 0.000000 0.546495 -0.579676 0.000000 0.000000 1.332093 -1.271183 0.183680 0.178337 0.407524 0.557987 -0.446291 -0.441561 0.096800 0.210668 -0.782224 -0.138606 -0.488310 -0.199551 1.020134 0.000000 0.116700 -0.328200 -0.150534 0.000000 0.000000 0.000000 1.008832 1.262709 -0.560483 0.000000 -1.544209 0.173865 1.209441 0.000000 1.282592 -0.876561 -0.199551 -0.372726 -0.844473 -0.142856 0.000000 1.118188 0.992463 0.293683 -0.730074 0.694719 -1.830446 -0.457391 0.000000 0.749515 0.876149 -1.102120 -0.052670 0.024490 -0.363078 0.000000 1.020134 -0.844473 0.718918 -0.257020 -0.184734 -0.020756 -1.684537 0.820476 -2.226431 -0.977077 0.000000 0.476926 1.229453 -1.628986 0.000000 1.428138 0.000000 1.197472 0.000000 0.000000 0.000000 -0.142856 -0.257020 -0.935683 -0.380722 -2.027028 0.063155 -0.105415 0.000000 -1.003823 0.114997 0.000000 -0.945490 -0.597354 0.000000 0.000000 -1.611618 1.271844 -0.752997 0.546495 0.116700 0.000000 -0.184734 -0.380722 0.892289 -0.332451 -1.052678 0.545420 0.000000 -0.273203 0.000000 0.338533 -0.446201 1.295685 0.047147 0.000000 0.562572 0.000000 0.000000 -0.579676 -0.328200 1.118188 -0.020756 -2.027028 -0.332451 2.822888 1.386350 1.052853 1.916822 0.268326 -0.733326 0.000000 1.344953 1.059998 2.183378 1.587691 0.000000 -0.589209 -0.603828 0.000000 -0.150534 0.992463 -1.684537 0.063155 -1.052678 1.386350 -0.101837 -2.131097 0.042321 -0.047378 -0.760576 0.000000 0.000000 0.000000 -1.874519 -1.628850 0.017440 0.000000 -0.625731 0.000000 0.000000 0.293683 0.820476 -0.105415 0.545420 1.052853 -2.131097 0.273469 0.000000 0.023477 0.065316 0.756581 -0.394491 0.000000 0.419115 0.000000 -0.625867 0.000000 0.233208 1.332093 0.000000 -0.730074 -2.226431 0.000000 0.000000 1.916822 0.042321 0.000000 2.608175 -0.647950 -0.754352 0.603751 0.000000 -0.483824 -1.108768 -0.764161 1.496724 0.000000 0.096027 -1.271183 0.000000 0.694719 -0.977077 -1.003823 -0.273203 0.268326 -0.047378 0.023477 -0.647950 0.045614 0.062137 0.000000 -0.302442 1.097443 -0.366763 -0.468397 -0.160488 -0.114843 -1.365093 0.183680 1.008832 -1.830446 0.000000 0.114997 0.000000 -0.733326 -0.760576 0.065316 -0.754352 0.062137 1.620017 0.000000 1.923312 0.000000 -0.413488 3.275479 -0.257902 0.724177 0.557751 0.178337 1.262709 -0.457391 0.476926 0.000000 0.338533 0.000000 0.000000 0.756581 0.603751 0.000000 0.000000 -0.850432 0.000000 0.459310 0.516390 1.316819 1.890343 0.000000 0.000000 0.407524 -0.560483 0.000000 1.229453 -0.945490 -0.446201 1.344953 0.000000 -0.394491 0.000000 -0.302442 1.923312 0.000000 0.565640 -0.475202 0.000000 0.297697 0.000000 0.381695 1.016577 0.557987 0.000000 0.749515 -1.628986 -0.597354 1.295685 1.059998 0.000000 0.000000 -0.483824 1.097443 0.000000 0.459310 -0.475202 0.400990 0.000000 0.179576 0.652179 0.000000 0.204839 -0.446291 -1.544209 0.876149 0.000000 0.000000 0.047147 2.183378 -1.874519 0.419115 -1.108768 -0.366763 -0.413488 0.516390 0.000000 0.000000 0.366695 0.860876 1.051594 -0.760906 0.000000 -0.441561 0.173865 -1.102120 1.428138 0.000000 0.000000 1.587691 -1.628850 0.000000 -0.764161 -0.468397 3.275479 1.316819 0.297697 0.179576 0.860876 -0.419493 -0.762122 -0.878021 1.653615 0.096800 1.209441 -0.052670 0.000000 -1.611618 0.562572 0.000000 0.017440 -0.625867 1.496724 -0.160488 -0.257902 1.890343 0.000000 0.652179 1.051594 -0.762122 -0.289374 1.430450 -0.099030 0.210668 0.000000 0.024490 1.197472 1.271844 0.000000 -0.589209 0.000000 0.000000 0.000000 -0.114843 0.724177 0.000000 0.381695 0.000000 -0.760906 -0.878021 1.430450 0.916234]; Dimension: 20 x 20 Off-diagonal entries: 282 (max 380) Diagonal entries: -0.654994 1.170792 -0.488310 -0.372726 0.718918 -0.935683 0.892289 2.822888 -0.101837 0.273469 2.608175 0.045614 1.620017 -0.850432 0.565640 0.400990 0.366695 -0.419493 -0.289374 0.916234 Row indices: 0 14 28 41 58 73 85 99 115 129 142 155 172 187 199 211 224 239 254 270 282 Column indices: 2 3 4 6 8 9 10 11 12 13 15 16 18 19 2 3 6 7 10 11 12 13 14 15 16 17 18 19 0 1 3 4 6 7 8 12 13 14 16 17 18 0 1 2 4 5 7 8 9 10 11 12 13 15 16 17 18 19 0 2 3 5 6 7 8 9 10 11 13 14 15 17 19 3 4 6 7 8 9 11 12 14 15 18 19 0 1 2 4 5 7 8 9 11 13 14 15 16 18 1 2 3 4 5 6 8 9 10 11 12 14 15 16 17 19 0 2 3 4 5 6 7 9 10 11 12 16 17 18 0 3 4 5 6 7 8 11 12 13 14 16 18 0 1 3 4 7 8 11 12 13 15 16 17 18 0 1 3 4 5 6 7 8 9 10 12 14 15 16 17 18 19 0 1 2 3 5 7 8 9 10 11 14 16 17 18 19 0 1 2 3 4 6 9 10 15 16 17 18 1 2 4 5 6 7 9 11 12 15 17 19 0 1 3 4 5 6 7 10 11 13 14 17 18 0 1 2 3 6 7 8 9 10 11 12 13 17 18 19 1 2 3 4 7 8 10 11 12 13 14 15 16 18 19 0 1 2 3 5 6 8 9 10 11 12 13 15 16 17 19 0 1 3 4 5 7 11 12 14 16 17 18 Off-diagonal values: -0.782224 1.282592 -0.363078 -0.752997 -0.603828 -0.625731 0.233208 0.096027 -1.365093 0.557751 1.016577 0.204839 1.653615 -0.099030 -0.138606 -0.876561 0.546495 -0.579676 1.332093 -1.271183 0.183680 0.178337 0.407524 0.557987 -0.446291 -0.441561 0.096800 0.210668 -0.782224 -0.138606 -0.199551 1.020134 0.116700 -0.328200 -0.150534 1.008832 1.262709 -0.560483 -1.544209 0.173865 1.209441 1.282592 -0.876561 -0.199551 -0.844473 -0.142856 1.118188 0.992463 0.293683 -0.730074 0.694719 -1.830446 -0.457391 0.749515 0.876149 -1.102120 -0.052670 0.024490 -0.363078 1.020134 -0.844473 -0.257020 -0.184734 -0.020756 -1.684537 0.820476 -2.226431 -0.977077 0.476926 1.229453 -1.628986 1.428138 1.197472 -0.142856 -0.257020 -0.380722 -2.027028 0.063155 -0.105415 -1.003823 0.114997 -0.945490 -0.597354 -1.611618 1.271844 -0.752997 0.546495 0.116700 -0.184734 -0.380722 -0.332451 -1.052678 0.545420 -0.273203 0.338533 -0.446201 1.295685 0.047147 0.562572 -0.579676 -0.328200 1.118188 -0.020756 -2.027028 -0.332451 1.386350 1.052853 1.916822 0.268326 -0.733326 1.344953 1.059998 2.183378 1.587691 -0.589209 -0.603828 -0.150534 0.992463 -1.684537 0.063155 -1.052678 1.386350 -2.131097 0.042321 -0.047378 -0.760576 -1.874519 -1.628850 0.017440 -0.625731 0.293683 0.820476 -0.105415 0.545420 1.052853 -2.131097 0.023477 0.065316 0.756581 -0.394491 0.419115 -0.625867 0.233208 1.332093 -0.730074 -2.226431 1.916822 0.042321 -0.647950 -0.754352 0.603751 -0.483824 -1.108768 -0.764161 1.496724 0.096027 -1.271183 0.694719 -0.977077 -1.003823 -0.273203 0.268326 -0.047378 0.023477 -0.647950 0.062137 -0.302442 1.097443 -0.366763 -0.468397 -0.160488 -0.114843 -1.365093 0.183680 1.008832 -1.830446 0.114997 -0.733326 -0.760576 0.065316 -0.754352 0.062137 1.923312 -0.413488 3.275479 -0.257902 0.724177 0.557751 0.178337 1.262709 -0.457391 0.476926 0.338533 0.756581 0.603751 0.459310 0.516390 1.316819 1.890343 0.407524 -0.560483 1.229453 -0.945490 -0.446201 1.344953 -0.394491 -0.302442 1.923312 -0.475202 0.297697 0.381695 1.016577 0.557987 0.749515 -1.628986 -0.597354 1.295685 1.059998 -0.483824 1.097443 0.459310 -0.475202 0.179576 0.652179 0.204839 -0.446291 -1.544209 0.876149 0.047147 2.183378 -1.874519 0.419115 -1.108768 -0.366763 -0.413488 0.516390 0.860876 1.051594 -0.760906 -0.441561 0.173865 -1.102120 1.428138 1.587691 -1.628850 -0.764161 -0.468397 3.275479 1.316819 0.297697 0.179576 0.860876 -0.762122 -0.878021 1.653615 0.096800 1.209441 -0.052670 -1.611618 0.562572 0.017440 -0.625867 1.496724 -0.160488 -0.257902 1.890343 0.652179 1.051594 -0.762122 1.430450 -0.099030 0.210668 0.024490 1.197472 1.271844 -0.589209 -0.114843 0.724177 0.381695 -0.760906 -0.878021 1.430450 o - o x o - o - o o x x o x - x x - x o | x o o - - x o - - x o x x x x o o x x o o o o x - x o o - - - x x o - o x x - x o o o o o - x x x o x o o - x x o o x o | x o x o o o o x o o - x x o - x - x | | | o o o o o x o - o x - o o - - o x o x x | o o x o o x - o - x o x x - x - | o o x o o o x x x x x o - x x x x - o o | o x o x o x o o x o o - - - o o x - o | | x x o x x o x - x x x o - x - o - x x | o o | | x x | x o o x - o o o x - x o | x o o o x o x o x x - o x o o o o o x x o | x | o o x o x x - x - o x o x x x x o x | x | | x x | | o - x x x x - | x o | x o o x | o | o x | x o - x - x x x | x o o x x | | o x | x o x - x x - x o o x | | x x o x o o o x | | x x x o | o x o x | | x o | o o x x x x x o o o x x x o | o x | x o x o o x | x x o o x o x | x x x | o | | | o x | x | o o x x The error in solving: 5.734672e-16 The error in solving: 5.933464e-16 The error in solving: 7.055869e-16 The error in solving: 4.601172e-16 The error in solving: 3.805653e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a standard normal distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.075009 0.000000 0.000000 0.550953 0.000000 1.264419 1.943398 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.158912 2.193559 0.000000 0.000000 0.000000 0.000000 1.905111 0.000000 0.000000 1.520658 0.968599 0.000000 1.374897 0.000000 0.000000 0.204676 0.000000 0.000000 0.000000 0.000000 0.000000 0.132381 0.000000 0.000000 0.162879 0.000000 0.000000 0.000000 0.000000 0.718380 -0.350725 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.552077 0.000000 0.000000 0.000000 0.000000 0.588824 0.000000 0.370450 -0.731861 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.158912 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 -0.798391 -1.180185 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.001042 0.000000 0.000000 0.000000 1.374897 0.000000 0.000000 0.000000 -0.037608 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.545395 0.000000 0.000000 0.000000 0.000000 -0.613586 0.000000 -1.581365 0.000000 0.000000 0.000000 0.000000 0.000000 0.532139 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.076832 0.001042 -0.613586 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.255912 0.000000 -0.176760 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.178420 0.000000 0.204676 0.000000 0.000000 0.000000 0.000000 0.000000 -1.822114 0.000000 0.000000 0.000000 0.000000 0.000000 0.474030 0.000000 0.000000 -1.581365 0.000000 0.178420 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 94 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 4 11 15 19 20 25 30 36 41 45 50 54 60 68 73 77 82 86 89 94 Column indices: 9 12 14 15 4 5 10 13 14 16 19 5 8 13 14 5 10 12 13 1 1 2 3 16 17 7 10 11 12 13 6 11 13 15 18 19 2 11 12 13 15 0 10 13 18 1 3 6 9 14 6 7 8 12 0 3 6 8 11 16 1 2 3 6 7 8 9 19 0 1 2 10 17 0 7 8 17 1 5 12 17 19 5 14 15 16 7 9 19 1 7 13 16 18 Off-diagonal values: 1.075009 0.550953 1.264419 1.943398 1.158912 2.193559 1.905111 1.520658 0.968599 1.374897 0.204676 0.132381 0.162879 0.718380 -0.350725 -0.552077 0.588824 0.370450 -0.731861 1.158912 2.193559 0.132381 -0.552077 -0.037608 0.532139 0.567465 -0.655052 1.063667 -1.297271 0.123701 0.567465 0.006456 -0.901219 -0.798391 -0.255912 -1.822114 0.162879 -1.491719 -0.931432 -0.427543 -1.180185 1.075009 -0.233533 0.535933 -0.176760 1.905111 0.588824 -0.655052 -0.233533 -1.823523 1.063667 0.006456 -1.491719 0.529483 0.550953 0.370450 -1.297271 -0.931432 0.529483 -0.545395 1.520658 0.718380 -0.731861 0.123701 -0.901219 -0.427543 0.535933 0.474030 1.264419 0.968599 -0.350725 -1.823523 -1.076832 1.943398 -0.798391 -1.180185 0.001042 1.374897 -0.037608 -0.545395 -0.613586 -1.581365 0.532139 -1.076832 0.001042 -0.613586 -0.255912 -0.176760 0.178420 0.204676 -1.822114 0.474030 -1.581365 0.178420 . - - - - - - - - x - - x - x x - - - - | . - - x x - - - - x - - x x - x - - x | | . - - x - - x - - - - x o - - - - - | | | . - o - - - - x - x o - - - - - - | x | | . - - - - - - - - - - - - - - - | x x o | . - - - - - - - - - - o x - - | | | | | | . x - - o x o x - - - - - - | | | | | | x . - - - x - o - o - - o o | | x | | | | | . - - o o o - o - - - - x | | | | | | | | . o - - x - - - - o - | x | x | | o | | o . - - - o - - - - - | | | | | | x x o | | . x - - - - - - - x | | x | | o | o | | x . - - - o - - - | x x o | | x o o x | | | . - - - - - x x x o | | | | | | | o | | | . - - o - - x | | | | | | o o | | | | | | . - x - - | x | | | o | | | | | | o | | | . o - o | | | | | x | | | | | | | | o x o . - - | | | | | | | o | o | | | | | | | | . x | x | | | | | o | | | | | x | | o | x . The error in solving: 5.701728e-16 The error in solving: 8.349770e-16 The error in solving: 4.336670e-16 The error in solving: 6.331147e-16 The error in solving: 3.219677e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a standard normal distribution with a zero diagonal and a density of 0.500000 [ 0.000000 -0.085000 0.000000 0.000000 0.000000 0.000000 -0.873855 0.712213 0.000000 0.000000 -1.102216 1.503552 0.590324 0.631080 0.000000 0.000000 0.688776 0.000000 0.000000 1.274380 -0.085000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.492440 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.568614 0.163289 -0.120704 0.000000 -0.234059 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.088228 0.000000 0.712116 0.000000 -0.684893 -0.795187 0.000000 0.000000 0.565594 0.000000 0.000000 1.184113 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.252385 1.061525 0.000000 0.000000 0.000000 0.000000 1.087782 0.000000 1.894650 -1.454870 -0.019287 1.798397 -0.698161 0.401017 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.487867 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.923799 0.392635 0.000000 -0.596753 -0.754709 0.000000 0.000000 2.088228 0.252385 0.000000 0.000000 -1.116818 -1.155657 0.588415 0.000000 -0.985716 0.000000 0.511327 -0.707400 -0.431845 0.992166 0.000000 0.043850 0.571091 -1.412437 -0.873855 0.000000 0.000000 1.061525 0.000000 -1.116818 0.000000 0.000000 0.000000 -0.426365 -1.284361 0.000000 0.979792 0.000000 0.000000 0.000000 -0.679170 0.000000 -1.109651 0.000000 0.712213 0.492440 0.712116 0.000000 -2.487867 -1.155657 0.000000 0.000000 0.000000 0.256413 0.000000 -0.223528 0.000000 -0.987905 -1.447520 0.879400 0.000000 0.206074 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.588415 0.000000 0.000000 0.000000 -0.838182 -0.254932 0.000000 0.000000 -0.303659 0.016452 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.684893 0.000000 0.000000 0.000000 -0.426365 0.256413 -0.838182 0.000000 0.369997 0.000000 0.000000 0.000000 -1.328100 0.175442 -1.980191 0.000000 0.000000 -0.088702 -1.102216 0.000000 -0.795187 0.000000 0.000000 -0.985716 -1.284361 0.000000 -0.254932 0.369997 0.000000 0.000000 0.000000 -0.147609 0.000000 0.000000 0.449622 -1.032731 0.000000 0.084739 1.503552 0.000000 0.000000 1.087782 0.000000 0.000000 0.000000 -0.223528 0.000000 0.000000 0.000000 0.000000 0.371424 -0.884875 -0.868361 0.000000 0.810830 -0.870547 -1.083425 0.998942 0.590324 0.000000 0.000000 0.000000 0.000000 0.511327 0.979792 0.000000 0.000000 0.000000 0.000000 0.371424 0.000000 0.594208 0.000000 1.822464 -0.213853 -1.489860 0.000000 -0.357094 0.631080 0.000000 0.565594 1.894650 0.000000 -0.707400 0.000000 -0.987905 -0.303659 0.000000 -0.147609 -0.884875 0.594208 0.000000 0.000000 0.000000 -1.070783 0.000000 -0.254810 0.000000 0.000000 -0.568614 0.000000 -1.454870 0.000000 -0.431845 0.000000 -1.447520 0.016452 -1.328100 0.000000 -0.868361 0.000000 0.000000 0.000000 0.350005 0.331113 -0.332914 0.101760 0.818061 0.000000 0.163289 0.000000 -0.019287 -0.923799 0.992166 0.000000 0.879400 0.000000 0.175442 0.000000 0.000000 1.822464 0.000000 0.350005 0.000000 0.000000 -0.017347 -1.533871 0.000000 0.688776 -0.120704 1.184113 1.798397 0.392635 0.000000 -0.679170 0.000000 0.000000 -1.980191 0.449622 0.810830 -0.213853 -1.070783 0.331113 0.000000 0.000000 -0.577373 -1.182172 0.012538 0.000000 0.000000 0.000000 -0.698161 0.000000 0.043850 0.000000 0.206074 0.000000 0.000000 -1.032731 -0.870547 -1.489860 0.000000 -0.332914 -0.017347 -0.577373 0.000000 0.000000 1.387198 0.000000 -0.234059 0.000000 0.401017 -0.596753 0.571091 -1.109651 0.000000 0.000000 0.000000 0.000000 -1.083425 0.000000 -0.254810 0.101760 -1.533871 -1.182172 0.000000 0.000000 0.000000 1.274380 0.000000 0.000000 0.000000 -0.754709 -1.412437 0.000000 0.000000 0.000000 -0.088702 0.084739 0.998942 -0.357094 0.000000 0.818061 0.000000 0.012538 1.387198 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 188 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 9 15 21 30 35 48 56 67 72 81 91 101 110 121 133 143 158 168 178 188 Column indices: 1 6 7 10 11 12 13 16 19 0 7 14 15 16 18 5 7 9 10 13 16 5 6 11 13 14 15 16 17 18 7 15 16 18 19 2 3 6 7 8 10 12 13 14 15 17 18 19 0 3 5 9 10 12 16 18 0 1 2 4 5 9 11 13 14 15 17 5 9 10 13 14 2 6 7 8 10 14 15 16 19 0 2 5 6 8 9 13 16 17 19 0 3 7 12 13 14 16 17 18 19 0 5 6 11 13 15 16 17 19 0 2 3 5 7 8 10 11 12 16 18 1 3 5 7 8 9 11 15 16 17 18 19 1 3 4 5 7 9 12 14 17 18 0 1 2 3 4 6 9 10 11 12 13 14 17 18 19 3 5 7 10 11 12 14 15 16 19 1 3 4 5 6 11 13 14 15 16 0 4 5 9 10 11 12 14 16 17 Off-diagonal values: -0.085000 -0.873855 0.712213 -1.102216 1.503552 0.590324 0.631080 0.688776 1.274380 -0.085000 0.492440 -0.568614 0.163289 -0.120704 -0.234059 2.088228 0.712116 -0.684893 -0.795187 0.565594 1.184113 0.252385 1.061525 1.087782 1.894650 -1.454870 -0.019287 1.798397 -0.698161 0.401017 -2.487867 -0.923799 0.392635 -0.596753 -0.754709 2.088228 0.252385 -1.116818 -1.155657 0.588415 -0.985716 0.511327 -0.707400 -0.431845 0.992166 0.043850 0.571091 -1.412437 -0.873855 1.061525 -1.116818 -0.426365 -1.284361 0.979792 -0.679170 -1.109651 0.712213 0.492440 0.712116 -2.487867 -1.155657 0.256413 -0.223528 -0.987905 -1.447520 0.879400 0.206074 0.588415 -0.838182 -0.254932 -0.303659 0.016452 -0.684893 -0.426365 0.256413 -0.838182 0.369997 -1.328100 0.175442 -1.980191 -0.088702 -1.102216 -0.795187 -0.985716 -1.284361 -0.254932 0.369997 -0.147609 0.449622 -1.032731 0.084739 1.503552 1.087782 -0.223528 0.371424 -0.884875 -0.868361 0.810830 -0.870547 -1.083425 0.998942 0.590324 0.511327 0.979792 0.371424 0.594208 1.822464 -0.213853 -1.489860 -0.357094 0.631080 0.565594 1.894650 -0.707400 -0.987905 -0.303659 -0.147609 -0.884875 0.594208 -1.070783 -0.254810 -0.568614 -1.454870 -0.431845 -1.447520 0.016452 -1.328100 -0.868361 0.350005 0.331113 -0.332914 0.101760 0.818061 0.163289 -0.019287 -0.923799 0.992166 0.879400 0.175442 1.822464 0.350005 -0.017347 -1.533871 0.688776 -0.120704 1.184113 1.798397 0.392635 -0.679170 -1.980191 0.449622 0.810830 -0.213853 -1.070783 0.331113 -0.577373 -1.182172 0.012538 -0.698161 0.043850 0.206074 -1.032731 -0.870547 -1.489860 -0.332914 -0.017347 -0.577373 1.387198 -0.234059 0.401017 -0.596753 0.571091 -1.109651 -1.083425 -0.254810 0.101760 -1.533871 -1.182172 1.274380 -0.754709 -1.412437 -0.088702 0.084739 0.998942 -0.357094 0.818061 0.012538 1.387198 . o - - - - o x - - o x x x - - x - - x o . - - - - - x - - - - - - o x o - o - | | . - - x - x - o o - - x - - x - - - | | | . - x x - - - - x - x o o x o x - | | | | . - - o - - - - - - - o x - o o | | x x | . o o x - o - x o o x - x x o o | | x | o . - - o o - x - - - o - o - x x x | o o | . - x - o - o o x - x - - | | | | | x | | . o o - - o x - - - - - | | o | | | o x o . x - - - o x o - - o o | o | | o o | o x . - - o - - x o - x x | | x | | | o | | | . x o o - x o o x x | | | | x x | | | | x . x - x o o - o x | x x | o | o o | o o x . - - o - o - | o | o | o | o x o | o | | . x x o x x | x | o o x | x | x | | x | x . - o o - x o x x x | o | | o x x o o x | . o o x | | | o | x | x | | o o o | o o o . - x | o | x o x o | | | | o | o x o o | . - x | | | o o | | | o x x o | x | x x | . The error in solving: 4.514016e-16 The error in solving: 3.110335e-16 The error in solving: 3.440016e-16 The error in solving: 5.887847e-16 The error in solving: 5.768888e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A symmetric matrix using a standard normal distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 -0.929853 -0.314687 0.000000 0.000000 0.964999 1.019185 0.069451 2.022344 -0.098891 -0.444208 0.546738 -0.502467 0.375845 0.000000 0.000000 -0.937260 1.321647 0.358003 0.000000 0.000000 0.056786 -0.097486 1.929262 0.000000 0.000000 0.000000 0.000000 1.026695 0.000000 0.147384 -0.807367 -0.160406 0.213768 0.176246 -0.833229 -1.243266 1.659056 -1.394241 -0.929853 0.056786 0.000000 0.000000 1.718410 -0.096637 -0.715684 -1.121352 -1.242005 0.842129 -1.326064 0.266465 0.000000 0.000000 0.000000 1.042030 -0.523169 2.035004 1.775299 0.610065 -0.314687 -0.097486 0.000000 0.000000 -1.080636 -1.359176 0.000000 -0.738533 0.694528 0.095560 0.000000 -1.644540 0.421799 0.000000 0.000000 0.000000 0.036944 0.000000 1.103524 -0.367986 0.000000 1.929262 1.718410 -1.080636 0.000000 2.278828 0.000000 1.259322 3.198865 0.000000 -1.111537 -0.220237 -1.177921 -1.575938 0.824520 0.000000 0.000000 0.000000 -1.920641 0.570719 0.000000 0.000000 -0.096637 -1.359176 2.278828 0.000000 0.809190 0.014149 0.895663 0.467098 0.950816 -0.111958 -0.781984 0.000000 -0.156281 0.592133 -1.237903 -0.675575 0.581754 -1.196328 0.964999 0.000000 -0.715684 0.000000 0.000000 0.809190 0.000000 0.922310 0.000000 0.000000 -3.379454 -0.565582 -0.350573 0.213981 0.000000 1.102046 -0.321608 0.000000 0.000000 0.382924 1.019185 0.000000 -1.121352 -0.738533 1.259322 0.014149 0.922310 0.000000 -1.085118 -0.611562 -0.526144 0.062857 0.060443 0.455943 0.000000 0.395311 0.000000 0.000000 0.000000 -1.174729 0.069451 0.000000 -1.242005 0.694528 3.198865 0.895663 0.000000 -1.085118 0.000000 0.000000 0.000000 0.966234 -0.418826 0.456431 1.724251 -1.052310 0.956079 -1.218057 0.000000 -0.252817 2.022344 1.026695 0.842129 0.095560 0.000000 0.467098 0.000000 -0.611562 0.000000 0.000000 -0.663748 0.050320 0.359809 0.845076 1.185020 -1.399975 0.000000 0.040950 -0.814544 0.000000 -0.098891 0.000000 -1.326064 0.000000 -1.111537 0.950816 -3.379454 -0.526144 0.000000 -0.663748 0.000000 0.000000 -0.178432 0.000000 0.000000 0.000000 0.000000 0.629038 1.175043 0.000000 -0.444208 0.147384 0.266465 -1.644540 -0.220237 -0.111958 -0.565582 0.062857 0.966234 0.050320 0.000000 0.000000 0.000000 0.000000 -0.159064 1.573095 -1.116997 -1.251075 -0.627323 0.000000 0.546738 -0.807367 0.000000 0.421799 -1.177921 -0.781984 -0.350573 0.060443 -0.418826 0.359809 -0.178432 0.000000 0.000000 0.789857 0.000000 0.637981 0.000000 1.030215 2.283880 -2.759499 -0.502467 -0.160406 0.000000 0.000000 -1.575938 0.000000 0.213981 0.455943 0.456431 0.845076 0.000000 0.000000 0.789857 0.000000 -0.509405 1.307376 0.171472 -2.275991 0.354595 0.307878 0.375845 0.213768 0.000000 0.000000 0.824520 -0.156281 0.000000 0.000000 1.724251 1.185020 0.000000 -0.159064 0.000000 -0.509405 0.000000 0.000000 0.000000 -0.331179 1.734371 -0.466682 0.000000 0.176246 1.042030 0.000000 0.000000 0.592133 1.102046 0.395311 -1.052310 -1.399975 0.000000 1.573095 0.637981 1.307376 0.000000 0.000000 0.544871 -1.196776 0.388931 0.630775 0.000000 -0.833229 -0.523169 0.036944 0.000000 -1.237903 -0.321608 0.000000 0.956079 0.000000 0.000000 -1.116997 0.000000 0.171472 0.000000 0.544871 0.000000 0.348524 -0.119601 0.680109 -0.937260 -1.243266 2.035004 0.000000 0.000000 -0.675575 0.000000 0.000000 -1.218057 0.040950 0.629038 -1.251075 1.030215 -2.275991 -0.331179 -1.196776 0.348524 0.000000 0.566502 -0.386028 1.321647 1.659056 1.775299 1.103524 -1.920641 0.581754 0.000000 0.000000 0.000000 -0.814544 1.175043 -0.627323 2.283880 0.354595 1.734371 0.388931 -0.119601 0.566502 0.000000 -0.734938 0.358003 -1.394241 0.610065 -0.367986 0.570719 -1.196328 0.382924 -1.174729 -0.252817 0.000000 0.000000 0.000000 -2.759499 0.307878 -0.466682 0.630775 0.680109 -0.386028 -0.734938 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 274 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 14 27 42 54 67 83 94 108 122 136 146 161 176 190 201 215 227 242 258 274 Column indices: 2 3 6 7 8 9 10 11 12 13 14 17 18 19 2 3 4 9 11 12 13 14 15 16 17 18 19 0 1 4 5 6 7 8 9 10 11 15 16 17 18 19 0 1 4 5 7 8 9 11 12 16 18 19 1 2 3 5 7 8 10 11 12 13 14 18 19 2 3 4 6 7 8 9 10 11 12 14 15 16 17 18 19 0 2 5 7 10 11 12 13 15 16 19 0 2 3 4 5 6 8 9 10 11 12 13 15 19 0 2 3 4 5 7 11 12 13 14 15 16 17 19 0 1 2 3 5 7 10 11 12 13 14 15 17 18 0 2 4 5 6 7 9 12 17 18 0 1 2 3 4 5 6 7 8 9 14 15 16 17 18 0 1 3 4 5 6 7 8 9 10 13 15 17 18 19 0 1 4 6 7 8 9 12 14 15 16 17 18 19 0 1 4 5 8 9 11 13 17 18 19 1 2 5 6 7 8 9 11 12 13 16 17 18 19 1 2 3 5 6 8 11 13 15 17 18 19 0 1 2 5 8 9 10 11 12 13 14 15 16 18 19 0 1 2 3 4 5 9 10 11 12 13 14 15 16 17 19 0 1 2 3 4 5 6 7 8 12 13 14 15 16 17 18 Off-diagonal values: -0.929853 -0.314687 0.964999 1.019185 0.069451 2.022344 -0.098891 -0.444208 0.546738 -0.502467 0.375845 -0.937260 1.321647 0.358003 0.056786 -0.097486 1.929262 1.026695 0.147384 -0.807367 -0.160406 0.213768 0.176246 -0.833229 -1.243266 1.659056 -1.394241 -0.929853 0.056786 1.718410 -0.096637 -0.715684 -1.121352 -1.242005 0.842129 -1.326064 0.266465 1.042030 -0.523169 2.035004 1.775299 0.610065 -0.314687 -0.097486 -1.080636 -1.359176 -0.738533 0.694528 0.095560 -1.644540 0.421799 0.036944 1.103524 -0.367986 1.929262 1.718410 -1.080636 2.278828 1.259322 3.198865 -1.111537 -0.220237 -1.177921 -1.575938 0.824520 -1.920641 0.570719 -0.096637 -1.359176 2.278828 0.809190 0.014149 0.895663 0.467098 0.950816 -0.111958 -0.781984 -0.156281 0.592133 -1.237903 -0.675575 0.581754 -1.196328 0.964999 -0.715684 0.809190 0.922310 -3.379454 -0.565582 -0.350573 0.213981 1.102046 -0.321608 0.382924 1.019185 -1.121352 -0.738533 1.259322 0.014149 0.922310 -1.085118 -0.611562 -0.526144 0.062857 0.060443 0.455943 0.395311 -1.174729 0.069451 -1.242005 0.694528 3.198865 0.895663 -1.085118 0.966234 -0.418826 0.456431 1.724251 -1.052310 0.956079 -1.218057 -0.252817 2.022344 1.026695 0.842129 0.095560 0.467098 -0.611562 -0.663748 0.050320 0.359809 0.845076 1.185020 -1.399975 0.040950 -0.814544 -0.098891 -1.326064 -1.111537 0.950816 -3.379454 -0.526144 -0.663748 -0.178432 0.629038 1.175043 -0.444208 0.147384 0.266465 -1.644540 -0.220237 -0.111958 -0.565582 0.062857 0.966234 0.050320 -0.159064 1.573095 -1.116997 -1.251075 -0.627323 0.546738 -0.807367 0.421799 -1.177921 -0.781984 -0.350573 0.060443 -0.418826 0.359809 -0.178432 0.789857 0.637981 1.030215 2.283880 -2.759499 -0.502467 -0.160406 -1.575938 0.213981 0.455943 0.456431 0.845076 0.789857 -0.509405 1.307376 0.171472 -2.275991 0.354595 0.307878 0.375845 0.213768 0.824520 -0.156281 1.724251 1.185020 -0.159064 -0.509405 -0.331179 1.734371 -0.466682 0.176246 1.042030 0.592133 1.102046 0.395311 -1.052310 -1.399975 1.573095 0.637981 1.307376 0.544871 -1.196776 0.388931 0.630775 -0.833229 -0.523169 0.036944 -1.237903 -0.321608 0.956079 -1.116997 0.171472 0.544871 0.348524 -0.119601 0.680109 -0.937260 -1.243266 2.035004 -0.675575 -1.218057 0.040950 0.629038 -1.251075 1.030215 -2.275991 -0.331179 -1.196776 0.348524 0.566502 -0.386028 1.321647 1.659056 1.775299 1.103524 -1.920641 0.581754 -0.814544 1.175043 -0.627323 2.283880 0.354595 1.734371 0.388931 -0.119601 0.566502 -0.734938 0.358003 -1.394241 0.610065 -0.367986 0.570719 -1.196328 0.382924 -1.174729 -0.252817 -2.759499 0.307878 -0.466682 0.630775 0.680109 -0.386028 -0.734938 . - o o - - x x x x o o x o x - - o x x | . x o x - - - - x - x o o x x o o x o o x . - x o o o o x o x - - - x o x x x o o | . o o - o x x - o x - - - x - x o | x x o . x - x x - o o o o x - - - o x | | o o x . x x x x x o o - o x o o x o x | o | | x . x - - o o o x - x o - - x x | o o x x x . o o o x x x - x - - - o x | o x x x | o . - - x o x x o x o - o x x x x | x | o | . o x x x x o - x o - o | o | o x o o | o . - o - - - - x x - o x x o o o o x x x | . - - o x o o o - x o | x o o o x o x o | . x - x - x x o o o | | o | x x x x | | x . o x x o x x x x | | x o | | x x | o | o . - - o x o | x x | | x x x o o | x x x | . x o x x | o o x | o o | x | | o | x | x . x o x o o x | | o | | o x x o x o o o x . x o x x x x o x | | | o x o x x x x o x . o x o x o x o x o o | | | o x o x x o o . The error in solving: 7.938289e-16 The error in solving: 4.460365e-16 The error in solving: 4.380306e-16 The error in solving: 5.775561e-16 The error in solving: 6.295684e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 -0.365769 0.984307 0.000000 0.000000 0.000000 0.000000 0.000000 0.379305 0.000000 0.000000 0.000000 0.000000 -0.147398 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.923442 0.000000 0.119672 0.851635 0.575917 0.000000 0.327380 0.000000 0.000000 0.000000 0.000000 0.000000 -0.417783 0.000000 -0.879952 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.245042 0.000000 0.000000 0.541811 0.000000 -0.945832 0.000000 0.000000 -0.300766 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.092436 0.000000 0.000000 0.000000 0.000000 -0.408170 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.983551 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.365769 -0.923442 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.416095 0.000000 0.000000 0.000000 0.356737 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.984307 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.091213 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.119672 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.769453 0.000000 0.093964 0.000000 -0.851635 0.245042 0.000000 0.000000 -0.416095 0.000000 0.000000 0.000000 0.000000 0.000000 0.446870 0.000000 0.000000 0.000000 0.000000 0.000000 0.694956 0.000000 0.000000 0.000000 -0.575917 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.745263 -0.377291 0.000000 0.000000 0.000000 0.000000 0.767248 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.745263 0.000000 0.000000 0.737715 0.000000 0.000000 0.000000 0.000000 0.142494 0.000000 0.000000 0.000000 -0.327380 -0.541811 0.000000 0.000000 0.000000 0.000000 0.000000 -0.446870 0.377291 0.000000 0.000000 0.000000 0.000000 -0.840085 0.000000 0.000000 0.000000 0.000000 0.000000 -0.379305 0.000000 0.000000 -0.092436 0.000000 -0.356737 0.000000 0.000000 0.000000 0.000000 -0.737715 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.945832 0.000000 -0.983551 0.000000 -0.091213 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.840085 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.300766 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.767248 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.545075 0.147398 0.417783 0.000000 0.408170 0.000000 0.000000 0.000000 -0.769453 -0.694956 0.000000 -0.142494 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.813952 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.863809 0.000000 0.879952 0.000000 0.000000 0.000000 0.000000 0.000000 -0.093964 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.545075 -0.813952 -0.863809 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 68 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 4 11 15 17 18 22 24 27 32 36 39 44 48 51 52 52 55 62 63 68 Column indices: 5 6 12 17 5 7 8 9 11 17 19 8 11 13 16 12 17 13 0 1 8 12 0 13 1 17 19 1 2 5 11 17 1 10 11 16 9 12 17 1 2 8 9 14 0 3 5 10 2 4 6 11 2 9 19 0 1 3 7 8 10 19 19 1 7 16 17 18 Off-diagonal values: -0.365769 0.984307 0.379305 -0.147398 0.923442 0.119672 0.851635 0.575917 0.327380 -0.417783 -0.879952 -0.245042 0.541811 -0.945832 -0.300766 0.092436 -0.408170 0.983551 0.365769 -0.923442 0.416095 0.356737 -0.984307 0.091213 -0.119672 0.769453 0.093964 -0.851635 0.245042 -0.416095 0.446870 0.694956 -0.575917 -0.745263 -0.377291 0.767248 0.745263 0.737715 0.142494 -0.327380 -0.541811 -0.446870 0.377291 -0.840085 -0.379305 -0.092436 -0.356737 -0.737715 0.945832 -0.983551 -0.091213 0.840085 0.300766 -0.767248 0.545075 0.147398 0.417783 0.408170 -0.769453 -0.694956 -0.142494 0.813952 0.863809 0.879952 -0.093964 -0.545075 -0.813952 -0.863809 . - - - - o x - - - - - x - - - - o - - | . - - - x - x x x - x - - - - - o - o | | . - - - - - o - - x - o - - o - - - | | | . - - - - - - - - x - - - - o - - | | | | . - - - - - - - - x - - - - - - x o | | | . - - x - - - x - - - - - - - o | | | | | . - - - - - - x - - - - - - | o | | | | | . - - - - - - - - - x - x | o x | | o | | . - - x - - - - - x - - | o | | | | | | | . o o - - - - x - - - | | | | | | | | | x . - x - - - - x - - | o o | | | | | o x | . - - o - - - - - o | | o | o | | | | o | . - - - - - - - | | x | o | o | | | | | | . - - - - - - | | | | | | | | | | | x | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | x | | | | | | o | | | | | | . - - x x x | x | | | o o | o | | | | | | . - x | | | | | | | | | | | | | | | | | | . x | x | | | | | o | | | | | | | | o o o . The error in solving: 2.779025e-16 The error in solving: 6.776000e-16 The error in solving: 4.311058e-16 The error in solving: 5.246097e-16 The error in solving: 4.081580e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 -0.408421 0.615348 -0.623909 0.259738 0.000000 0.000000 0.000000 0.000000 0.000000 0.507914 -0.641973 0.175501 0.866499 0.792912 0.000000 -0.360699 0.389053 -0.654886 0.000000 0.408421 0.000000 0.275097 0.000000 -0.502581 -0.255800 0.000000 0.000000 0.896864 0.606060 0.000000 0.459232 0.271295 -0.326690 0.000000 0.691324 0.000000 0.037922 -0.846543 -0.198373 -0.615348 -0.275097 0.000000 0.000000 0.000000 -0.404306 0.301538 0.000000 0.000000 -0.291435 0.000000 0.000000 0.000000 -0.547203 0.000000 0.000000 0.000000 0.878516 0.347955 -0.505107 0.623909 0.000000 0.000000 0.000000 0.384279 0.398545 0.563257 0.000000 0.693347 0.000000 0.000000 0.000000 0.294803 0.000000 0.447093 -0.420103 0.000000 0.658966 0.000000 -0.521203 -0.259738 0.502581 0.000000 -0.384279 0.000000 0.000000 0.176969 -0.581679 -0.323707 0.000000 0.000000 0.000000 -0.496798 0.000000 0.520634 0.553077 0.000000 0.000000 -0.514186 0.000000 0.000000 0.255800 0.404306 -0.398545 0.000000 0.000000 0.000000 0.986873 -0.877525 0.000000 0.000000 -0.284409 0.359773 -0.205616 0.000000 0.000000 0.514659 -0.789466 0.993150 0.000000 0.000000 0.000000 -0.301538 -0.563257 -0.176969 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.427877 0.000000 0.000000 -0.119092 0.589166 0.329117 0.556196 0.000000 0.000000 0.000000 0.000000 0.000000 0.581679 -0.986873 0.000000 0.000000 -0.521345 0.000000 0.000000 0.000000 0.000000 0.000000 -0.989878 -0.315311 -0.159741 0.034276 0.000000 -0.363351 0.000000 -0.896864 0.000000 -0.693347 0.323707 0.877525 0.000000 0.521345 0.000000 0.502614 0.000000 0.497063 -0.854393 0.055035 0.000000 -0.654287 0.000000 0.000000 0.000000 0.000000 0.000000 -0.606060 0.291435 0.000000 0.000000 0.000000 0.000000 0.000000 -0.502614 0.000000 0.009753 0.000000 0.964664 0.000000 0.000000 0.671732 -0.939915 0.012659 0.000000 0.000000 -0.507914 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.009753 0.000000 0.000000 0.000000 0.000000 0.000000 0.153823 0.000000 0.000000 0.604520 -0.690956 0.641973 -0.459232 0.000000 0.000000 0.000000 0.284409 0.000000 0.000000 -0.497063 0.000000 0.000000 0.000000 -0.473129 0.000000 0.000000 0.000000 0.751648 0.000000 0.000000 -0.405673 -0.175501 -0.271295 0.000000 -0.294803 0.496798 -0.359773 -0.427877 0.000000 0.854393 -0.964664 0.000000 0.473129 0.000000 0.533563 0.000000 -0.896284 -0.038613 0.000000 0.000000 0.000000 -0.866499 0.326690 0.547203 0.000000 0.000000 0.205616 0.000000 0.000000 -0.055035 0.000000 0.000000 0.000000 -0.533563 0.000000 -0.007241 0.000000 0.000000 -0.355723 0.000000 0.000000 -0.792912 0.000000 0.000000 -0.447093 -0.520634 0.000000 0.000000 0.989878 0.000000 0.000000 0.000000 0.000000 0.000000 0.007241 0.000000 0.000000 0.081327 0.000000 0.373571 0.000000 0.000000 -0.691324 0.000000 0.420103 -0.553077 0.000000 0.119092 0.315311 0.654287 -0.671732 -0.153823 0.000000 0.896284 0.000000 0.000000 0.000000 0.573113 -0.297997 0.000000 0.899849 0.360699 0.000000 0.000000 0.000000 0.000000 -0.514659 -0.589166 0.159741 0.000000 0.939915 0.000000 -0.751648 0.038613 0.000000 -0.081327 -0.573113 0.000000 0.000000 0.000000 0.000000 -0.389053 -0.037922 -0.878516 -0.658966 0.000000 0.789466 -0.329117 -0.034276 0.000000 -0.012659 0.000000 0.000000 0.000000 0.355723 0.000000 0.297997 0.000000 0.000000 0.627283 0.000000 0.654886 0.846543 -0.347955 0.000000 0.514186 -0.993150 -0.556196 0.000000 0.000000 0.000000 -0.604520 0.000000 0.000000 0.000000 -0.373571 0.000000 0.000000 -0.627283 0.000000 0.000000 0.000000 0.198373 0.505107 0.521203 0.000000 0.000000 0.000000 0.363351 0.000000 0.000000 0.690956 0.405673 0.000000 0.000000 0.000000 -0.899849 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 186 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 12 25 34 44 54 65 73 81 91 99 104 111 123 131 138 150 159 170 179 186 Column indices: 1 2 3 4 10 11 12 13 14 16 17 18 0 2 4 5 8 9 11 12 13 15 17 18 19 0 1 5 6 9 13 17 18 19 0 4 5 6 8 12 14 15 17 19 0 1 3 6 7 8 12 14 15 18 1 2 3 7 8 11 12 13 16 17 18 2 3 4 12 15 16 17 18 4 5 8 14 15 16 17 19 1 3 4 5 7 9 11 12 13 15 1 2 8 10 12 15 16 17 0 9 15 18 19 0 1 5 8 12 16 19 0 1 3 4 5 6 8 9 11 13 15 16 0 1 2 5 8 12 14 17 0 3 4 7 13 16 18 1 3 4 6 7 8 9 10 12 16 17 19 0 5 6 7 9 11 12 14 15 0 1 2 3 5 6 7 9 13 15 18 0 1 2 4 5 6 10 14 17 1 2 3 7 10 11 15 Off-diagonal values: -0.408421 0.615348 -0.623909 0.259738 0.507914 -0.641973 0.175501 0.866499 0.792912 -0.360699 0.389053 -0.654886 0.408421 0.275097 -0.502581 -0.255800 0.896864 0.606060 0.459232 0.271295 -0.326690 0.691324 0.037922 -0.846543 -0.198373 -0.615348 -0.275097 -0.404306 0.301538 -0.291435 -0.547203 0.878516 0.347955 -0.505107 0.623909 0.384279 0.398545 0.563257 0.693347 0.294803 0.447093 -0.420103 0.658966 -0.521203 -0.259738 0.502581 -0.384279 0.176969 -0.581679 -0.323707 -0.496798 0.520634 0.553077 -0.514186 0.255800 0.404306 -0.398545 0.986873 -0.877525 -0.284409 0.359773 -0.205616 0.514659 -0.789466 0.993150 -0.301538 -0.563257 -0.176969 0.427877 -0.119092 0.589166 0.329117 0.556196 0.581679 -0.986873 -0.521345 -0.989878 -0.315311 -0.159741 0.034276 -0.363351 -0.896864 -0.693347 0.323707 0.877525 0.521345 0.502614 0.497063 -0.854393 0.055035 -0.654287 -0.606060 0.291435 -0.502614 0.009753 0.964664 0.671732 -0.939915 0.012659 -0.507914 -0.009753 0.153823 0.604520 -0.690956 0.641973 -0.459232 0.284409 -0.497063 -0.473129 0.751648 -0.405673 -0.175501 -0.271295 -0.294803 0.496798 -0.359773 -0.427877 0.854393 -0.964664 0.473129 0.533563 -0.896284 -0.038613 -0.866499 0.326690 0.547203 0.205616 -0.055035 -0.533563 -0.007241 -0.355723 -0.792912 -0.447093 -0.520634 0.989878 0.007241 0.081327 0.373571 -0.691324 0.420103 -0.553077 0.119092 0.315311 0.654287 -0.671732 -0.153823 0.896284 0.573113 -0.297997 0.899849 0.360699 -0.514659 -0.589166 0.159741 0.939915 -0.751648 0.038613 -0.081327 -0.573113 -0.389053 -0.037922 -0.878516 -0.658966 0.789466 -0.329117 -0.034276 -0.012659 0.355723 0.297997 0.627283 0.654886 0.846543 -0.347955 0.514186 -0.993150 -0.556196 -0.604520 -0.373571 -0.627283 0.198373 0.505107 0.521203 0.363351 0.690956 0.405673 -0.899849 . o x o x - - - - - x o x x x - o x o - x . x - o o - - x x - x x o - x - x o o o o . - - o x - - o - - - o - - - x x o x | | . x x x - x - - - x - x o - x - o o x | o . - x o o - - - o - x x - - o - | x x o | . - x o - - o x o - - x o x - | | o o o | . - - - - - x - - o x x x - | | | | x o | . o - - - - - o o o x - o | o | o x x | x . x - x o x - o - - - - | o x | | | | | o . x - x - - x o x - - o | | | | | | | | o . - - - - x - - x o x o | | | x | | o | | . o - - - x - - o o o | o x o o | x o | x . x - o o - - - o x x | | x | | o | | | o . o - - o - - o | | o o | | x | | | | | x . - x - x - | o | x o | x x x o o | x | | . x o - x x | | | | o o x | x | o x | o o . - - - o o o o | x o o | o | | | x | x | . x - x x o | x o o | | | o | | | o | | o . - | x x x | | | x | | x x | | | o | | | . The error in solving: 7.256371e-16 The error in solving: 6.017265e-16 The error in solving: 7.515818e-16 The error in solving: 4.022165e-16 The error in solving: 6.216025e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.750000 [ 0.000000 -0.559315 0.000000 0.335132 -0.516105 0.565872 -0.253007 0.577181 0.560877 -0.693698 -0.947270 0.191310 0.000000 0.736895 -0.311624 -0.560389 -0.056677 -0.858175 0.000000 -0.620378 0.559315 0.000000 -0.363393 0.936310 0.000000 0.308233 -0.248126 0.000000 0.764748 0.000000 0.000000 0.000000 0.000000 0.000000 0.061839 -0.920009 -0.598619 -0.797892 -0.140805 0.514683 0.000000 0.363393 0.000000 0.000000 -0.328398 0.186415 0.824942 0.000000 0.162225 0.000000 -0.854816 -0.548278 0.000000 0.000000 0.188845 0.459621 -0.492218 0.000000 0.861609 0.673356 -0.335132 -0.936310 0.000000 0.000000 -0.828726 0.316881 0.332431 0.000000 0.070322 0.000000 0.000000 0.902618 0.000000 0.326238 0.000000 0.577417 0.000000 0.000000 0.428281 0.770521 0.516105 0.000000 0.328398 0.828726 0.000000 0.929143 0.334544 -0.827338 0.313273 -0.532121 -0.667930 0.648214 0.791725 0.773351 0.124924 0.000000 0.962274 -0.166487 0.000000 0.000000 -0.565872 -0.308233 -0.186415 -0.316881 -0.929143 0.000000 -0.147784 0.020017 0.000000 -0.734129 0.700008 0.989251 0.000000 0.000000 -0.535687 0.000000 0.000000 0.798992 0.353374 0.409133 0.253007 0.248126 -0.824942 -0.332431 -0.334544 0.147784 0.000000 0.000000 0.094521 -0.605061 0.533042 0.000000 0.000000 -0.467800 -0.828161 -0.752283 0.000000 0.446300 -0.795810 -0.028680 -0.577181 0.000000 0.000000 0.000000 0.827338 -0.020017 0.000000 0.000000 0.000000 -0.206485 0.694934 0.194174 0.819829 -0.926869 -0.326489 0.000000 0.000000 -0.585016 0.000000 0.990484 -0.560877 -0.764748 -0.162225 -0.070322 -0.313273 0.000000 -0.094521 0.000000 0.000000 -0.410385 0.932679 -0.624725 0.998311 -0.629093 0.298472 -0.671562 -0.471089 0.000000 0.000000 0.495059 0.693698 0.000000 0.000000 0.000000 0.532121 0.734129 0.605061 0.206485 0.410385 0.000000 -0.798164 0.000000 -0.071410 0.960991 0.419807 0.485046 -0.799983 0.712758 0.401707 0.477347 0.947270 0.000000 0.854816 0.000000 0.667930 -0.700008 -0.533042 -0.694934 -0.932679 0.798164 0.000000 0.000000 0.454625 0.000000 0.000000 0.909174 0.601013 0.000000 -0.495467 0.227529 -0.191310 0.000000 0.548278 -0.902618 -0.648214 -0.989251 0.000000 -0.194174 0.624725 0.000000 0.000000 0.000000 -0.547730 -0.230394 0.594139 0.783238 0.000000 0.000000 -0.258965 0.000000 0.000000 0.000000 0.000000 0.000000 -0.791725 0.000000 0.000000 -0.819829 -0.998311 0.071410 -0.454625 0.547730 0.000000 0.000000 0.613474 0.000000 -0.256251 0.000000 -0.561164 0.000000 -0.736895 0.000000 0.000000 -0.326238 -0.773351 0.000000 0.467800 0.926869 0.629093 -0.960991 0.000000 0.230394 0.000000 0.000000 -0.464912 -0.639467 -0.305422 0.361417 0.000000 0.860469 0.311624 -0.061839 -0.188845 0.000000 -0.124924 0.535687 0.828161 0.326489 -0.298472 -0.419807 0.000000 -0.594139 -0.613474 0.464912 0.000000 -0.723871 0.558032 0.293840 0.000000 0.000000 0.560389 0.920009 -0.459621 -0.577417 0.000000 0.000000 0.752283 0.000000 0.671562 -0.485046 -0.909174 -0.783238 0.000000 0.639467 0.723871 0.000000 0.847047 -0.370682 -0.310333 0.070165 0.056677 0.598619 0.492218 0.000000 -0.962274 0.000000 0.000000 0.000000 0.471089 0.799983 -0.601013 0.000000 0.256251 0.305422 -0.558032 -0.847047 0.000000 0.000000 0.279096 -0.910989 0.858175 0.797892 0.000000 0.000000 0.166487 -0.798992 -0.446300 0.585016 0.000000 -0.712758 0.000000 0.000000 0.000000 -0.361417 -0.293840 0.370682 0.000000 0.000000 -0.081373 0.000000 0.000000 0.140805 -0.861609 -0.428281 0.000000 -0.353374 0.795810 0.000000 0.000000 -0.401707 0.495467 0.258965 0.561164 0.000000 0.000000 0.310333 -0.279096 0.081373 0.000000 0.000000 0.620378 -0.514683 -0.673356 -0.770521 0.000000 -0.409133 0.028680 -0.990484 -0.495059 -0.477347 -0.227529 0.000000 0.000000 -0.860469 0.000000 -0.070165 0.910989 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 262 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 16 28 40 51 66 80 95 106 121 136 149 161 170 183 198 213 226 237 249 262 Column indices: 1 3 4 5 6 7 8 9 10 11 13 14 15 16 17 19 0 2 3 5 6 8 14 15 16 17 18 19 1 4 5 6 8 10 11 14 15 16 18 19 0 1 4 5 6 8 11 13 15 18 19 0 2 3 5 6 7 8 9 10 11 12 13 14 16 17 0 1 2 3 4 6 7 9 10 11 14 17 18 19 0 1 2 3 4 5 8 9 10 13 14 15 17 18 19 0 4 5 9 10 11 12 13 14 17 19 0 1 2 3 4 6 9 10 11 12 13 14 15 16 19 0 4 5 6 7 8 10 12 13 14 15 16 17 18 19 0 2 4 5 6 7 8 9 12 15 16 18 19 0 2 3 4 5 7 8 12 13 14 15 18 4 7 8 9 10 11 14 16 18 0 3 4 6 7 8 9 11 14 15 16 17 19 0 1 2 4 5 6 7 8 9 11 12 13 15 16 17 0 1 2 3 6 8 9 10 11 13 14 16 17 18 19 0 1 2 4 8 9 10 12 13 14 15 18 19 0 1 4 5 6 7 9 13 14 15 18 1 2 3 5 6 9 10 11 12 15 16 17 0 1 2 3 5 6 7 8 9 10 13 15 16 Off-diagonal values: -0.559315 0.335132 -0.516105 0.565872 -0.253007 0.577181 0.560877 -0.693698 -0.947270 0.191310 0.736895 -0.311624 -0.560389 -0.056677 -0.858175 -0.620378 0.559315 -0.363393 0.936310 0.308233 -0.248126 0.764748 0.061839 -0.920009 -0.598619 -0.797892 -0.140805 0.514683 0.363393 -0.328398 0.186415 0.824942 0.162225 -0.854816 -0.548278 0.188845 0.459621 -0.492218 0.861609 0.673356 -0.335132 -0.936310 -0.828726 0.316881 0.332431 0.070322 0.902618 0.326238 0.577417 0.428281 0.770521 0.516105 0.328398 0.828726 0.929143 0.334544 -0.827338 0.313273 -0.532121 -0.667930 0.648214 0.791725 0.773351 0.124924 0.962274 -0.166487 -0.565872 -0.308233 -0.186415 -0.316881 -0.929143 -0.147784 0.020017 -0.734129 0.700008 0.989251 -0.535687 0.798992 0.353374 0.409133 0.253007 0.248126 -0.824942 -0.332431 -0.334544 0.147784 0.094521 -0.605061 0.533042 -0.467800 -0.828161 -0.752283 0.446300 -0.795810 -0.028680 -0.577181 0.827338 -0.020017 -0.206485 0.694934 0.194174 0.819829 -0.926869 -0.326489 -0.585016 0.990484 -0.560877 -0.764748 -0.162225 -0.070322 -0.313273 -0.094521 -0.410385 0.932679 -0.624725 0.998311 -0.629093 0.298472 -0.671562 -0.471089 0.495059 0.693698 0.532121 0.734129 0.605061 0.206485 0.410385 -0.798164 -0.071410 0.960991 0.419807 0.485046 -0.799983 0.712758 0.401707 0.477347 0.947270 0.854816 0.667930 -0.700008 -0.533042 -0.694934 -0.932679 0.798164 0.454625 0.909174 0.601013 -0.495467 0.227529 -0.191310 0.548278 -0.902618 -0.648214 -0.989251 -0.194174 0.624725 -0.547730 -0.230394 0.594139 0.783238 -0.258965 -0.791725 -0.819829 -0.998311 0.071410 -0.454625 0.547730 0.613474 -0.256251 -0.561164 -0.736895 -0.326238 -0.773351 0.467800 0.926869 0.629093 -0.960991 0.230394 -0.464912 -0.639467 -0.305422 0.361417 0.860469 0.311624 -0.061839 -0.188845 -0.124924 0.535687 0.828161 0.326489 -0.298472 -0.419807 -0.594139 -0.613474 0.464912 -0.723871 0.558032 0.293840 0.560389 0.920009 -0.459621 -0.577417 0.752283 0.671562 -0.485046 -0.909174 -0.783238 0.639467 0.723871 0.847047 -0.370682 -0.310333 0.070165 0.056677 0.598619 0.492218 -0.962274 0.471089 0.799983 -0.601013 0.256251 0.305422 -0.558032 -0.847047 0.279096 -0.910989 0.858175 0.797892 0.166487 -0.798992 -0.446300 0.585016 -0.712758 -0.361417 -0.293840 0.370682 -0.081373 0.140805 -0.861609 -0.428281 -0.353374 0.795810 -0.401707 0.495467 0.258965 0.561164 0.310333 -0.279096 0.081373 0.620378 -0.514683 -0.673356 -0.770521 -0.409133 0.028680 -0.990484 -0.495059 -0.477347 -0.227529 -0.860469 -0.070165 0.910989 . o - x o x o x x o o x - x o o o o - o x . o x - x o - x - - - - - x o o o o x | x . - o x x - x - o o - - x x o - x x o o | . o x x - x - - x - x - x - - x x x | x x . x x o x o o x x x x - x o - - o o o o o . o x - o x x - - o - - x x x x x o o o x . - x o x - - o o o - x o o o | | | x o | . - o x x x o o - - o - x o o o o o | o | . o x o x o x o o - - x x | | | x x x x x . o - o x x x o x x x x | x | x o o o o x . - x - - x x - o x o | x o o o | o x | | . o o x x - - o - | | | | o | | o o x o x . - x - o - o - o | | o o | x x x o | x | . o o o x - x x o o | o x x x o o | o o x . o x x - - x x o o | | x | x o o o | x x . x o o x x x x | o | | | x x o | x x o o . - x o x x | | x o o x | o | | | o o x | . o - | x o o | o x | | o x x x | | x o x . - x o o o | o x o o o o | | o | o x | | . The error in solving: 5.587533e-16 The error in solving: 4.165730e-16 The error in solving: 5.874748e-16 The error in solving: 7.393606e-16 The error in solving: 6.330766e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.000000 -0.625687 0.714695 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.843284 0.772923 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.400572 0.000000 0.000000 0.625687 0.000000 0.000000 0.000000 0.000000 0.416896 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.519647 0.000000 0.000000 0.000000 -0.714695 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.325649 -0.342973 -0.676103 0.000000 0.664296 0.154431 0.130131 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.461609 0.000000 0.000000 0.000000 0.000000 0.000000 -0.631616 0.000000 0.000000 0.000000 0.000000 0.000000 -0.353538 0.295168 0.000000 0.295854 0.000000 0.000000 0.000000 0.461609 0.000000 0.000000 0.000000 0.000000 -0.942003 0.000000 0.000000 0.000000 -0.868141 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.416896 0.000000 0.000000 0.000000 0.000000 0.160912 -0.736139 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.160912 0.000000 0.000000 0.000000 0.358267 0.000000 0.000000 0.000000 0.000000 -0.739630 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.736139 0.000000 0.000000 0.000000 0.000000 0.551169 0.045035 -0.057352 0.000000 0.224324 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.942003 0.000000 0.000000 0.000000 0.000000 -0.116284 0.000000 0.903671 0.000000 -0.605416 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.843284 0.000000 -0.325649 0.000000 0.000000 0.000000 -0.358267 0.000000 0.116284 0.000000 -0.670098 0.919227 -0.478055 0.000000 0.028767 0.000000 0.494289 0.000000 0.000000 0.000000 -0.772923 0.000000 0.342973 0.631616 0.000000 0.000000 0.000000 -0.551169 0.000000 0.670098 0.000000 0.681784 0.000000 0.000000 0.000000 -0.542853 0.000000 -0.426525 0.000000 0.384423 0.000000 0.000000 0.676103 0.000000 0.000000 0.000000 0.000000 -0.045035 -0.903671 -0.919227 -0.681784 0.000000 -0.091045 0.000000 0.000000 -0.444787 0.000000 0.000000 -0.956664 0.000000 0.000000 0.000000 0.000000 0.000000 0.868141 0.000000 0.000000 0.057352 0.000000 0.478055 0.000000 0.091045 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.664296 0.000000 0.000000 0.000000 0.000000 0.000000 0.605416 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.057512 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.154431 0.000000 0.000000 0.000000 0.739630 -0.224324 0.000000 -0.028767 0.000000 0.000000 0.000000 0.000000 0.000000 -0.164220 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.130131 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.542853 0.444787 0.000000 0.057512 0.164220 0.000000 0.000000 0.815011 0.000000 0.000000 0.000000 0.519647 0.000000 0.353538 0.000000 0.000000 0.000000 0.000000 0.000000 -0.494289 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.390445 -0.712680 -0.551903 0.400572 0.000000 0.000000 -0.295168 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.426525 0.000000 0.000000 0.000000 0.000000 -0.815011 -0.390445 0.000000 -0.418669 -0.610685 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.956664 0.000000 0.000000 0.000000 0.000000 0.712680 0.418669 0.000000 0.000000 0.000000 0.000000 0.000000 -0.295854 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.384423 0.000000 0.000000 0.000000 0.000000 0.000000 0.551903 0.610685 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 102 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 5 8 15 20 23 26 29 34 38 47 56 64 68 71 76 82 88 95 98 102 Column indices: 1 2 9 10 17 0 5 16 0 9 10 11 13 14 15 4 10 16 17 19 3 8 12 1 6 7 5 9 14 5 10 11 12 14 4 9 11 13 0 2 6 8 10 11 12 14 16 0 2 3 7 9 11 15 17 19 2 7 8 9 10 12 15 18 4 7 9 11 2 8 15 2 6 7 9 15 2 10 11 13 14 17 1 3 9 17 18 19 0 3 10 15 16 18 19 11 16 17 3 10 16 17 Off-diagonal values: -0.625687 0.714695 0.843284 0.772923 -0.400572 0.625687 0.416896 -0.519647 -0.714695 0.325649 -0.342973 -0.676103 0.664296 0.154431 0.130131 -0.461609 -0.631616 -0.353538 0.295168 0.295854 0.461609 -0.942003 -0.868141 -0.416896 0.160912 -0.736139 -0.160912 0.358267 -0.739630 0.736139 0.551169 0.045035 -0.057352 0.224324 0.942003 -0.116284 0.903671 -0.605416 -0.843284 -0.325649 -0.358267 0.116284 -0.670098 0.919227 -0.478055 0.028767 0.494289 -0.772923 0.342973 0.631616 -0.551169 0.670098 0.681784 -0.542853 -0.426525 0.384423 0.676103 -0.045035 -0.903671 -0.919227 -0.681784 -0.091045 -0.444787 -0.956664 0.868141 0.057352 0.478055 0.091045 -0.664296 0.605416 -0.057512 -0.154431 0.739630 -0.224324 -0.028767 -0.164220 -0.130131 0.542853 0.444787 0.057512 0.164220 0.815011 0.519647 0.353538 -0.494289 0.390445 -0.712680 -0.551903 0.400572 -0.295168 0.426525 -0.815011 -0.390445 -0.418669 -0.610685 0.956664 0.712680 0.418669 -0.295854 -0.384423 0.551903 0.610685 . o x - - - - - - x x - - - - - - o - - x . - - - x - - - - - - - - - - o - - - o | . - - - - - - x o o - x x x - - - - | | | . o - - - - - o - - - - - o x - x | | | x . - - - o - - - o - - - - - - - | o | | | . x o - - - - - - - - - - - - | | | | | o . - - x - - - - o - - - - - | | | | | x | . - - x x o - x - - - - - | | | | x | | | . o - x - o - - - - - - o | o | | | o | x . o x o - x - x - - - o | x x | | | o | x . x - - - o - o - x | | x | | | | o o o o . o - - o - - o - | | | | x | | x | x | x . - - - - - - - | | o | | | | | x | | | | . - o - - - - | | o | | | x o | o | | | | . o - - - - | | o | | | | | | | x x | x x . - x - - | x | x | | | | | o | | | | | | . x o o x | | o | | | | | | x | | | | o o . o o | | | | | | | | | | | x | | | | x x . - | | | o | | | | | | o | | | | | x x | . The error in solving: 3.775166e-16 The error in solving: 5.559809e-16 The error in solving: 5.886032e-16 The error in solving: 5.250140e-16 The error in solving: 5.311767e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.000000 -0.121949 0.000000 0.000000 -0.548166 -0.979794 -0.237987 0.465879 -0.328059 -0.205359 -0.443475 0.803348 0.000000 -0.579942 0.273441 0.989400 0.783793 0.000000 0.000000 0.731667 0.121949 0.000000 0.165161 0.924089 0.000000 0.011099 0.815297 0.000000 0.000000 -0.083557 0.150596 0.000000 0.000000 -0.121575 0.000000 -0.194295 0.724528 0.000000 0.813841 0.000000 0.000000 -0.165161 0.000000 -0.901700 0.552578 0.000000 0.000000 0.000000 0.000000 0.586661 0.000000 0.511324 -0.776596 0.000000 0.988529 0.000000 0.510240 0.000000 0.000000 -0.245433 0.000000 -0.924089 0.901700 0.000000 0.177337 -0.492202 0.969027 0.000000 0.000000 0.000000 -0.864291 0.000000 0.004844 0.000000 -0.729709 0.000000 0.000000 0.000000 0.000000 0.000000 0.548166 0.000000 -0.552578 -0.177337 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.143573 -0.386465 0.000000 0.000000 0.638627 0.178144 0.483098 0.000000 0.830651 0.979794 -0.011099 0.000000 0.492202 0.000000 0.000000 0.651310 0.027796 0.000000 0.000000 0.000000 0.000000 -0.521284 -0.148562 0.000000 -0.582744 -0.330461 0.000000 0.000000 0.000000 0.237987 -0.815297 0.000000 -0.969027 0.000000 -0.651310 0.000000 0.000000 0.968060 0.164069 0.000000 0.870682 0.000000 0.000000 -0.868494 0.000000 -0.265545 -0.146878 -0.732613 0.949381 -0.465879 0.000000 0.000000 0.000000 0.000000 -0.027796 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.093372 0.000000 0.609585 -0.753183 0.079862 -0.408941 0.328059 0.000000 0.000000 0.000000 0.000000 0.000000 -0.968060 0.000000 0.000000 0.000000 -0.683200 0.000000 0.647256 0.000000 0.000000 -0.416021 -0.485291 0.968065 0.000000 -0.393400 0.205359 0.083557 -0.586661 0.000000 0.000000 0.000000 -0.164069 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.595309 0.000000 0.000000 0.457542 -0.639150 0.443475 -0.150596 0.000000 0.864291 0.000000 0.000000 0.000000 0.000000 0.683200 0.000000 0.000000 0.000000 0.000000 -0.061097 -0.860005 0.000000 -0.767446 -0.636579 -0.548883 0.000000 -0.803348 0.000000 -0.511324 0.000000 0.143573 0.000000 -0.870682 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.074565 -0.637154 -0.243459 0.000000 0.000000 0.866093 -0.996675 0.000000 0.000000 0.776596 -0.004844 0.386465 0.521284 0.000000 0.000000 -0.647256 0.000000 0.000000 0.000000 0.000000 0.902973 -0.031687 0.000000 0.000000 -0.610814 -0.870085 -0.311275 0.579942 0.121575 0.000000 0.000000 0.000000 0.148562 0.000000 0.000000 0.000000 0.000000 0.061097 0.074565 -0.902973 0.000000 0.000000 0.000000 0.000000 0.333732 -0.731546 0.000000 -0.273441 0.000000 -0.988529 0.729709 0.000000 0.000000 0.868494 0.093372 0.000000 0.000000 0.860005 0.637154 0.031687 0.000000 0.000000 0.000000 0.281957 0.244034 0.553243 0.093918 -0.989400 0.194295 0.000000 0.000000 -0.638627 0.582744 0.000000 0.000000 0.416021 0.595309 0.000000 0.243459 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.783793 -0.724528 -0.510240 0.000000 -0.178144 0.330461 0.265545 -0.609585 0.485291 0.000000 0.767446 0.000000 0.000000 0.000000 -0.281957 0.000000 0.000000 -0.597298 0.000000 0.197175 0.000000 0.000000 0.000000 0.000000 -0.483098 0.000000 0.146878 0.753183 -0.968065 0.000000 0.636579 0.000000 0.610814 -0.333732 -0.244034 0.000000 0.597298 0.000000 0.219683 0.000000 0.000000 -0.813841 0.000000 0.000000 0.000000 0.000000 0.732613 -0.079862 0.000000 -0.457542 0.548883 -0.866093 0.870085 0.731546 -0.553243 0.000000 0.000000 -0.219683 0.000000 -0.333086 -0.731667 0.000000 0.245433 0.000000 -0.830651 0.000000 -0.949381 0.408941 0.393400 0.639150 0.000000 0.996675 0.311275 0.000000 -0.093918 0.000000 -0.197175 0.000000 0.333086 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 194 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 14 25 34 42 51 60 72 79 87 94 103 112 122 130 142 149 161 171 182 194 Column indices: 1 4 5 6 7 8 9 10 11 13 14 15 16 19 0 2 3 5 6 9 10 13 15 16 18 1 3 4 9 11 12 14 16 19 1 2 4 5 6 10 12 14 0 2 3 11 12 15 16 17 19 0 1 3 6 7 12 13 15 16 0 1 3 5 8 9 11 14 16 17 18 19 0 5 14 16 17 18 19 0 6 10 12 15 16 17 19 0 1 2 6 15 18 19 0 1 3 8 13 14 16 17 18 0 2 4 6 13 14 15 18 19 2 3 4 5 8 13 14 17 18 19 0 1 5 10 11 12 17 18 0 2 3 6 7 10 11 12 16 17 18 19 0 1 4 5 8 9 11 0 1 2 4 5 6 7 8 10 14 17 19 4 6 7 8 10 12 13 14 16 18 1 6 7 9 10 11 12 13 14 17 19 0 2 4 6 7 8 9 11 12 14 16 18 Off-diagonal values: -0.121949 -0.548166 -0.979794 -0.237987 0.465879 -0.328059 -0.205359 -0.443475 0.803348 -0.579942 0.273441 0.989400 0.783793 0.731667 0.121949 0.165161 0.924089 0.011099 0.815297 -0.083557 0.150596 -0.121575 -0.194295 0.724528 0.813841 -0.165161 -0.901700 0.552578 0.586661 0.511324 -0.776596 0.988529 0.510240 -0.245433 -0.924089 0.901700 0.177337 -0.492202 0.969027 -0.864291 0.004844 -0.729709 0.548166 -0.552578 -0.177337 -0.143573 -0.386465 0.638627 0.178144 0.483098 0.830651 0.979794 -0.011099 0.492202 0.651310 0.027796 -0.521284 -0.148562 -0.582744 -0.330461 0.237987 -0.815297 -0.969027 -0.651310 0.968060 0.164069 0.870682 -0.868494 -0.265545 -0.146878 -0.732613 0.949381 -0.465879 -0.027796 -0.093372 0.609585 -0.753183 0.079862 -0.408941 0.328059 -0.968060 -0.683200 0.647256 -0.416021 -0.485291 0.968065 -0.393400 0.205359 0.083557 -0.586661 -0.164069 -0.595309 0.457542 -0.639150 0.443475 -0.150596 0.864291 0.683200 -0.061097 -0.860005 -0.767446 -0.636579 -0.548883 -0.803348 -0.511324 0.143573 -0.870682 -0.074565 -0.637154 -0.243459 0.866093 -0.996675 0.776596 -0.004844 0.386465 0.521284 -0.647256 0.902973 -0.031687 -0.610814 -0.870085 -0.311275 0.579942 0.121575 0.148562 0.061097 0.074565 -0.902973 0.333732 -0.731546 -0.273441 -0.988529 0.729709 0.868494 0.093372 0.860005 0.637154 0.031687 0.281957 0.244034 0.553243 0.093918 -0.989400 0.194295 -0.638627 0.582744 0.416021 0.595309 0.243459 -0.783793 -0.724528 -0.510240 -0.178144 0.330461 0.265545 -0.609585 0.485291 0.767446 -0.281957 -0.597298 0.197175 -0.483098 0.146878 0.753183 -0.968065 0.636579 0.610814 -0.333732 -0.244034 0.597298 0.219683 -0.813841 0.732613 -0.079862 -0.457542 0.548883 -0.866093 0.870085 0.731546 -0.553243 -0.219683 -0.333086 -0.731667 0.245433 -0.830651 -0.949381 0.408941 0.393400 0.639150 0.996675 0.311275 -0.093918 -0.197175 0.333086 . o - - o o o x o o o x - o x x x - - x x . x x - x x - - o x - - o - o x - x - | o . o x - - - - x - x o - x - x - - o | o x . x o x - - - o - x - o - - - - - x | o o . - - - - - - o o - - x x x - x x o | x | . x x - - - - o o - o o - - - x o | o | o . - x x - x - - o - o o o x o | | | | o | . - - - - - - o - x o x o x | | | | | o | . - o - x - - o o x - o x x o | | | o | | . - - - - - o - - x o x o | x | | | | x | . - - o o - o o o - o | o | x | o | | | | . - o o o - - x o | | x o x x | | o | | | . x o - - o o o x x | | | x | | | | x x o . - - - x o - o | o x | | x x | | x x x | . - x x x x o x | | o x | | x x | x | | | . - - - - o o o | o x x o x | x | | | o | . o - x | | | | o | x x o | x | x o o | x . x - | o | | | | x o | o x o x x o | | o . o o | x | o | o x x x | x x | o | o | x . The error in solving: 6.408248e-16 The error in solving: 3.395098e-16 The error in solving: 6.310961e-16 The error in solving: 6.799851e-16 The error in solving: 4.988288e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.000000 -0.583986 0.424229 0.287849 -0.213405 -0.768308 -0.355649 0.471118 -0.256453 0.000000 0.955327 0.432260 0.399717 -0.846578 0.000000 0.000000 -0.274674 0.362413 -0.408305 -0.025410 0.583986 0.000000 0.000000 0.222297 -0.281927 0.869107 -0.340787 0.177230 -0.492360 -0.827025 0.707660 0.554340 0.296485 0.587770 -0.243169 0.569431 0.000000 -0.292700 -0.506442 0.000000 -0.424229 0.000000 0.000000 0.000000 -0.945411 -0.431353 0.053634 0.000000 0.021009 0.638858 -0.052206 -0.607223 0.238580 -0.944548 0.476006 0.273672 0.042296 -0.893863 0.000000 0.858246 -0.287849 -0.222297 0.000000 0.000000 -0.383903 0.957270 0.873925 0.040493 0.907498 -0.424780 -0.900960 0.482476 -0.814922 -0.313731 0.071546 0.102383 0.794939 0.317888 0.000000 -0.148480 0.213405 0.281927 0.945411 0.383903 0.000000 0.000000 0.896623 -0.572780 -0.746947 0.000000 0.000000 0.740331 0.000000 0.000000 0.620617 -0.923780 0.452406 0.169427 0.272950 -0.780105 0.768308 -0.869107 0.431353 -0.957270 0.000000 0.000000 0.268055 0.000000 0.000000 0.591800 -0.293118 0.000000 -0.980103 -0.129533 0.000000 0.000000 -0.500469 0.000000 0.000000 0.000000 0.355649 0.340787 -0.053634 -0.873925 -0.896623 -0.268055 0.000000 0.767381 0.000000 0.016441 0.429079 -0.122140 0.000000 -0.652053 -0.632764 0.000000 -0.893525 0.420174 0.000000 -0.036562 -0.471118 -0.177230 0.000000 -0.040493 0.572780 0.000000 -0.767381 0.000000 0.162181 -0.076984 -0.086176 0.496257 -0.598950 0.888603 -0.330128 -0.768941 0.000000 0.000000 0.522993 -0.812006 0.256453 0.492360 -0.021009 -0.907498 0.746947 0.000000 0.000000 -0.162181 0.000000 0.343235 0.787258 -0.674242 -0.657540 0.104069 0.369612 -0.173179 0.000000 0.435280 0.000000 0.610968 0.000000 0.827025 -0.638858 0.424780 0.000000 -0.591800 -0.016441 0.076984 -0.343235 0.000000 0.000000 0.615530 -0.168181 0.982673 -0.857456 -0.320690 -0.614709 -0.977407 0.000000 0.000000 -0.955327 -0.707660 0.052206 0.900960 0.000000 0.293118 -0.429079 0.086176 -0.787258 0.000000 0.000000 0.967277 0.000000 0.727872 0.442842 0.081081 -0.446373 0.605476 -0.448472 0.689684 -0.432260 -0.554340 0.607223 -0.482476 -0.740331 0.000000 0.122140 -0.496257 0.674242 -0.615530 -0.967277 0.000000 0.000000 -0.835122 0.300223 -0.117783 -0.971549 -0.441051 -0.902866 0.391288 -0.399717 -0.296485 -0.238580 0.814922 0.000000 0.980103 0.000000 0.598950 0.657540 0.168181 0.000000 0.000000 0.000000 0.528538 0.788325 0.315724 0.457640 -0.724241 0.000000 0.325823 0.846578 -0.587770 0.944548 0.313731 0.000000 0.129533 0.652053 -0.888603 -0.104069 -0.982673 -0.727872 0.835122 -0.528538 0.000000 0.539390 0.000000 -0.378821 0.000000 0.988678 -0.865491 0.000000 0.243169 -0.476006 -0.071546 -0.620617 0.000000 0.632764 0.330128 -0.369612 0.857456 -0.442842 -0.300223 -0.788325 -0.539390 0.000000 -0.394290 -0.123842 -0.704477 -0.687580 0.156292 0.000000 -0.569431 -0.273672 -0.102383 0.923780 0.000000 0.000000 0.768941 0.173179 0.320690 -0.081081 0.117783 -0.315724 0.000000 0.394290 0.000000 0.109309 0.000000 -0.178583 -0.271181 0.274674 0.000000 -0.042296 -0.794939 -0.452406 0.500469 0.893525 0.000000 0.000000 0.614709 0.446373 0.971549 -0.457640 0.378821 0.123842 -0.109309 0.000000 -0.917825 -0.923824 0.308329 -0.362413 0.292700 0.893863 -0.317888 -0.169427 0.000000 -0.420174 0.000000 -0.435280 0.977407 -0.605476 0.441051 0.724241 0.000000 0.704477 0.000000 0.917825 0.000000 0.000000 0.000000 0.408305 0.506442 0.000000 0.000000 -0.272950 0.000000 0.000000 -0.522993 0.000000 0.000000 0.448472 0.902866 0.000000 -0.988678 0.687580 0.178583 0.923824 0.000000 0.000000 0.000000 0.025410 0.000000 -0.858246 0.148480 0.780105 0.000000 0.036562 0.812006 -0.610968 0.000000 -0.689684 -0.391288 -0.325823 0.865491 -0.156292 0.271181 -0.308329 0.000000 0.000000 0.000000]; 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The error in solving: 7.972182e-16 The error in solving: 6.061909e-16 The error in solving: 7.596108e-16 The error in solving: 6.458765e-16 The error in solving: 4.819910e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.866607 0.000000 0.000000 -0.950078 0.000000 0.000000 0.000000 0.000000 0.000000 -0.581723 0.957874 0.000000 0.000000 0.000000 0.000000 0.751705 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.860851 0.000000 0.000000 0.000000 0.000000 0.000000 -0.459054 0.000000 0.000000 -0.866607 0.000000 0.000000 0.000000 0.000000 0.911783 0.000000 -0.998572 0.000000 0.000000 0.000000 0.000000 0.429182 0.000000 0.000000 0.700657 0.000000 -0.067061 0.000000 0.046654 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.975310 0.000000 0.000000 0.000000 0.137053 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.161199 -0.872691 -0.609534 0.000000 0.000000 0.497527 0.950078 0.000000 -0.911783 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.796179 0.100635 0.000000 -0.199705 -0.603878 -0.423616 -0.440683 0.858680 0.000000 0.000000 0.000000 -0.975310 0.000000 0.000000 0.000000 0.000000 -0.637121 0.000000 0.000000 -0.394963 0.000000 0.000000 0.000000 0.000000 0.000000 0.398704 0.000000 0.000000 0.000000 0.000000 0.998572 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.439700 0.000000 0.000000 -0.145132 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.637121 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.723043 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.361009 0.000000 0.000000 0.000000 0.000000 -0.137053 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.524442 0.000000 0.581723 -0.860851 0.000000 0.000000 0.000000 0.000000 0.394963 0.000000 0.000000 0.000000 0.000000 0.000000 0.165562 0.000000 0.000000 0.000000 0.000000 0.422478 0.000000 0.000000 -0.957874 0.000000 -0.429182 0.000000 0.000000 0.796179 0.000000 0.000000 0.000000 0.000000 0.000000 -0.165562 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.100635 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.161199 0.000000 0.000000 -0.439700 0.723043 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.396421 0.000000 0.353910 0.000000 0.000000 0.000000 -0.700657 0.000000 0.872691 0.199705 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.609534 0.603878 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.396421 0.000000 0.000000 -0.010262 0.000000 0.000000 -0.751705 0.459054 0.067061 0.000000 0.000000 0.423616 -0.398704 0.145132 0.000000 0.000000 0.000000 -0.422478 0.000000 0.000000 0.000000 0.000000 0.010262 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.440683 0.000000 0.000000 0.000000 0.361009 0.524442 0.000000 0.000000 0.000000 -0.353910 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.046654 0.000000 -0.497527 -0.858680 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 78 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 5 7 14 16 20 29 33 36 38 39 41 46 50 51 56 59 63 71 75 78 Column indices: 2 5 11 12 17 11 17 0 5 7 12 15 17 19 6 10 14 15 16 19 0 2 12 13 15 16 17 18 19 3 8 11 17 2 14 17 6 14 18 3 18 0 1 6 12 17 0 2 5 11 5 4 7 8 16 18 2 4 5 4 5 14 17 0 1 2 5 6 7 11 16 5 9 10 14 2 4 5 Off-diagonal values: 0.866607 -0.950078 -0.581723 0.957874 0.751705 0.860851 -0.459054 -0.866607 0.911783 -0.998572 0.429182 0.700657 -0.067061 0.046654 0.975310 0.137053 -0.161199 -0.872691 -0.609534 0.497527 0.950078 -0.911783 -0.796179 0.100635 -0.199705 -0.603878 -0.423616 -0.440683 0.858680 -0.975310 -0.637121 -0.394963 0.398704 0.998572 0.439700 -0.145132 0.637121 -0.723043 -0.361009 -0.137053 -0.524442 0.581723 -0.860851 0.394963 0.165562 0.422478 -0.957874 -0.429182 0.796179 -0.165562 -0.100635 0.161199 -0.439700 0.723043 -0.396421 0.353910 -0.700657 0.872691 0.199705 0.609534 0.603878 0.396421 -0.010262 -0.751705 0.459054 0.067061 0.423616 -0.398704 0.145132 -0.422478 0.010262 0.440683 0.361009 0.524442 -0.353910 -0.046654 -0.497527 -0.858680 . - x - - o - - - - - o x - - - - x - - | . - - - - - - - - - x - - - - - o - - o | . - - x - o - - - - x - - x - o - x | | | . - - x - - - x - - - - - - - - - | | | | . - - - - - - - - - o o o - - x x | o | | . - - - - - - o x - o o o o x | | | o | | . - o - - o - - - - - x - - | | x | | | | . - - - - - - x - - o - - | | | | | | x | . - - - - - o - - - - - | | | | | | | | | . - - - - - - - - o - | | | o | | | | | | . - - - - - - - o - x o | | | | x | | | | . x - - - - x - - o | o | | x | | | | | o . - - - - - - - | | | | | o | | | | | | | . - - - - - - | | | | x | | o x | | | | | . - o - x - | | o | x x | | | | | | | | | . - - - - | | | | x x | | | | | | | | x | . o - - o x x | | x o x | | | o | | | | x . - - | | | | | x | | | x x | | | o | | | . - | | o | o o | | | | | | | | | | | | | . The error in solving: 3.296522e-16 The error in solving: 5.933870e-16 The error in solving: 6.061909e-16 The error in solving: 5.102830e-16 The error in solving: 6.081338e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 -0.670964 0.894653 0.000000 0.000000 0.000000 0.033055 -0.561163 0.000000 0.152729 0.000000 -0.762323 0.800007 0.000000 0.928439 -0.140376 -0.315290 0.000000 0.000000 0.000000 0.000000 0.282218 0.000000 0.181345 -0.608166 0.000000 0.000000 0.000000 0.000000 -0.487061 0.000000 -0.548219 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.234908 0.670964 -0.282218 0.000000 0.000000 0.123967 -0.364439 -0.736060 0.000000 -0.490695 -0.566953 0.319438 0.000000 0.292299 0.000000 -0.683084 0.152243 0.993538 0.715385 0.215258 0.000000 -0.894653 0.000000 0.000000 0.000000 0.000000 -0.682350 -0.473084 -0.437787 0.000000 0.000000 0.932286 0.000000 -0.993498 0.531561 0.000000 0.000000 0.000000 0.216261 0.000000 0.000000 0.000000 -0.181345 -0.123967 0.000000 0.000000 0.000000 -0.912275 -0.641969 -0.923210 0.000000 0.000000 0.000000 -0.844710 -0.748439 -0.885900 0.000000 0.709411 0.678473 0.000000 0.930419 0.000000 0.608166 0.364439 0.682350 0.000000 0.000000 0.000000 0.138264 0.000000 0.000000 -0.076371 -0.340989 -0.663287 0.242351 0.000000 0.000000 0.000000 -0.599181 -0.778988 -0.460201 0.000000 0.000000 0.736060 0.473084 0.912275 0.000000 0.000000 0.000000 0.000000 -0.653475 -0.765215 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.736031 0.000000 0.000000 -0.033055 0.000000 0.000000 0.437787 0.641969 -0.138264 0.000000 0.000000 0.000000 -0.317790 0.000000 0.648763 -0.756368 0.123772 0.000000 -0.846105 0.000000 0.369581 -0.966364 0.000000 0.561163 0.000000 0.490695 0.000000 0.923210 0.000000 0.000000 0.000000 0.000000 0.000000 0.871763 0.000000 0.034578 0.000000 0.000000 0.016834 0.000000 0.000000 0.749814 -0.455714 0.000000 0.000000 0.566953 0.000000 0.000000 0.000000 0.653475 0.317790 0.000000 0.000000 0.000000 0.117351 0.756911 0.000000 0.000000 -0.990199 0.842899 0.000000 0.000000 -0.342225 -0.152729 0.487061 -0.319438 -0.932286 0.000000 0.076371 0.765215 0.000000 -0.871763 0.000000 0.000000 -0.594130 0.560352 0.675938 0.000000 0.878682 0.000000 0.000000 0.000000 -0.544114 0.000000 0.000000 0.000000 0.000000 0.000000 0.340989 0.000000 -0.648763 0.000000 -0.117351 0.594130 0.000000 -0.606713 0.000000 0.000000 0.000000 0.000000 0.000000 -0.175524 0.516430 0.762323 0.548219 -0.292299 0.993498 0.844710 0.663287 0.000000 0.756368 -0.034578 -0.756911 -0.560352 0.606713 0.000000 0.000000 0.856256 0.000000 0.000000 -0.159562 0.000000 0.000000 -0.800007 0.000000 0.000000 -0.531561 0.748439 -0.242351 0.000000 -0.123772 0.000000 0.000000 -0.675938 0.000000 0.000000 0.000000 -0.787298 0.340347 0.356094 0.547773 -0.506723 0.000000 0.000000 0.000000 0.683084 0.000000 0.885900 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.856256 0.787298 0.000000 -0.230628 -0.417554 0.886226 0.000000 0.975529 -0.928439 0.000000 -0.152243 0.000000 0.000000 0.000000 0.000000 0.846105 -0.016834 0.990199 -0.878682 0.000000 0.000000 -0.340347 0.230628 0.000000 0.000000 -0.818000 0.509276 -0.931661 0.140376 0.000000 -0.993538 0.000000 -0.709411 0.000000 0.000000 0.000000 0.000000 -0.842899 0.000000 0.000000 0.000000 -0.356094 0.417554 0.000000 0.000000 0.000000 0.125021 0.901642 0.315290 0.000000 -0.715385 -0.216261 -0.678473 0.599181 -0.736031 -0.369581 0.000000 0.000000 0.000000 0.000000 0.159562 -0.547773 -0.886226 0.818000 0.000000 0.000000 0.000000 0.642332 0.000000 0.000000 -0.215258 0.000000 0.000000 0.778988 0.000000 0.966364 -0.749814 0.000000 0.000000 0.175524 0.000000 0.506723 0.000000 -0.509276 -0.125021 0.000000 0.000000 -0.791693 0.000000 -0.234908 0.000000 0.000000 -0.930419 0.460201 0.000000 0.000000 0.455714 0.342225 0.544114 -0.516430 0.000000 0.000000 -0.975529 0.931661 -0.901642 -0.642332 0.791693 0.000000]; 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The error in solving: 3.750214e-16 The error in solving: 3.400058e-16 The error in solving: 5.484800e-16 The error in solving: 5.615790e-16 The error in solving: 7.283096e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 -0.477877 0.387617 -0.888091 -0.602645 0.052187 0.000000 0.263386 0.000000 0.290818 0.000000 0.000000 -0.086043 0.000000 -0.444416 0.871480 0.000000 0.000000 0.000000 0.318295 0.477877 0.000000 0.234506 0.000000 0.000000 0.098350 -0.654095 -0.709754 -0.605646 -0.208277 -0.916515 -0.833289 -0.040314 0.083430 0.253167 0.732601 0.236967 0.659318 0.017048 0.000000 -0.387617 -0.234506 0.000000 -0.900424 0.052245 0.646133 0.000000 0.382438 0.155235 0.799851 -0.445201 0.000000 -0.671279 -0.222260 0.694926 0.000000 -0.778288 -0.195965 -0.014827 0.809410 0.888091 0.000000 0.900424 0.000000 0.629119 0.884950 0.000000 0.000000 0.737186 -0.264921 0.000000 0.588041 0.000000 0.000000 -0.715032 -0.288165 0.000000 0.661134 0.642870 0.114908 0.602645 0.000000 -0.052245 -0.629119 0.000000 0.000000 0.089346 -0.658640 0.398814 -0.302922 -0.864062 -0.744540 -0.595905 0.479551 0.155450 -0.867096 0.278362 0.246286 0.846283 0.887716 -0.052187 -0.098350 -0.646133 -0.884950 0.000000 0.000000 0.228088 0.101365 0.590091 0.225235 0.716059 -0.764094 0.000000 -0.182865 -0.496834 -0.247500 0.016467 -0.427598 0.000000 0.000000 0.000000 0.654095 0.000000 0.000000 -0.089346 -0.228088 0.000000 0.555749 0.671401 -0.644442 0.656214 0.430012 0.226859 0.000000 -0.535340 0.783734 -0.408856 0.000000 0.000000 0.810315 -0.263386 0.709754 -0.382438 0.000000 0.658640 -0.101365 -0.555749 0.000000 0.603866 0.921670 0.000000 -0.933886 0.000000 0.000000 0.000000 0.666037 0.230039 -0.341990 -0.108987 0.000000 0.000000 0.605646 -0.155235 -0.737186 -0.398814 -0.590091 -0.671401 -0.603866 0.000000 0.220622 0.000000 0.401708 -0.049237 0.643174 0.000000 -0.280713 0.752606 0.000000 0.000000 0.398272 -0.290818 0.208277 -0.799851 0.264921 0.302922 -0.225235 0.644442 -0.921670 -0.220622 0.000000 0.000000 -0.723849 -0.090663 -0.079289 0.000000 0.575608 0.446132 0.210010 0.844831 -0.463676 0.000000 0.916515 0.445201 0.000000 0.864062 -0.716059 -0.656214 0.000000 0.000000 0.000000 0.000000 0.000000 -0.439902 -0.116469 -0.934990 0.000000 -0.562647 0.913344 0.784202 0.000000 0.000000 0.833289 0.000000 -0.588041 0.744540 0.764094 -0.430012 0.933886 -0.401708 0.723849 0.000000 0.000000 -0.326127 -0.300402 0.653922 -0.908072 0.000000 0.000000 -0.028640 -0.351891 0.086043 0.040314 0.671279 0.000000 0.595905 0.000000 -0.226859 0.000000 0.049237 0.090663 0.439902 0.326127 0.000000 -0.585429 -0.171018 -0.999574 0.000000 0.031694 -0.047407 0.484695 0.000000 -0.083430 0.222260 0.000000 -0.479551 0.182865 0.000000 0.000000 -0.643174 0.079289 0.116469 0.300402 0.585429 0.000000 0.000000 0.400613 0.663940 0.000000 -0.232371 -0.923527 0.444416 -0.253167 -0.694926 0.715032 -0.155450 0.496834 0.535340 0.000000 0.000000 0.000000 0.934990 -0.653922 0.171018 0.000000 0.000000 0.563020 -0.769572 0.852480 0.000000 0.060067 -0.871480 -0.732601 0.000000 0.288165 0.867096 0.247500 -0.783734 -0.666037 0.280713 -0.575608 0.000000 0.908072 0.999574 -0.400613 -0.563020 0.000000 0.000000 -0.750401 -0.775096 -0.571174 0.000000 -0.236967 0.778288 0.000000 -0.278362 -0.016467 0.408856 -0.230039 -0.752606 -0.446132 0.562647 0.000000 0.000000 -0.663940 0.769572 0.000000 0.000000 -0.036909 0.000000 0.357293 0.000000 -0.659318 0.195965 -0.661134 -0.246286 0.427598 0.000000 0.341990 0.000000 -0.210010 -0.913344 0.000000 -0.031694 0.000000 -0.852480 0.750401 0.036909 0.000000 0.000000 0.000000 0.000000 -0.017048 0.014827 -0.642870 -0.846283 0.000000 0.000000 0.108987 0.000000 -0.844831 -0.784202 0.028640 0.047407 0.232371 0.000000 0.775096 0.000000 0.000000 0.000000 -0.965267 -0.318295 0.000000 -0.809410 -0.114908 -0.887716 0.000000 -0.810315 0.000000 -0.398272 0.463676 0.000000 0.351891 -0.484695 0.923527 -0.060067 0.571174 -0.357293 0.000000 0.965267 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 278 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 11 27 43 55 72 87 100 113 127 144 155 169 184 197 211 227 240 252 264 278 Column indices: 1 2 3 4 5 7 9 12 14 15 19 0 2 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 3 4 5 7 8 9 10 12 13 14 16 17 18 19 0 2 4 5 8 9 11 14 15 17 18 19 0 2 3 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0 1 2 3 6 7 8 9 10 11 13 14 15 16 17 1 4 5 7 8 9 10 11 12 14 15 16 19 0 1 2 4 5 6 8 9 11 15 16 17 18 1 2 3 4 5 6 7 9 11 12 13 15 16 19 0 1 2 3 4 5 6 7 8 11 12 13 15 16 17 18 19 1 2 4 5 6 12 13 14 16 17 18 1 3 4 5 6 7 8 9 12 13 14 15 18 19 0 1 2 4 6 8 9 10 11 13 14 15 17 18 19 1 2 4 5 8 9 10 11 12 15 16 18 19 0 1 2 3 4 5 6 10 11 12 15 16 17 19 0 1 3 4 5 6 7 8 9 11 12 13 14 17 18 19 1 2 4 5 6 7 8 9 10 13 14 17 19 1 2 3 4 5 7 9 10 12 14 15 16 1 2 3 4 7 9 10 11 12 13 15 19 0 2 3 4 6 8 9 11 12 13 14 15 16 18 Off-diagonal values: -0.477877 0.387617 -0.888091 -0.602645 0.052187 0.263386 0.290818 -0.086043 -0.444416 0.871480 0.318295 0.477877 0.234506 0.098350 -0.654095 -0.709754 -0.605646 -0.208277 -0.916515 -0.833289 -0.040314 0.083430 0.253167 0.732601 0.236967 0.659318 0.017048 -0.387617 -0.234506 -0.900424 0.052245 0.646133 0.382438 0.155235 0.799851 -0.445201 -0.671279 -0.222260 0.694926 -0.778288 -0.195965 -0.014827 0.809410 0.888091 0.900424 0.629119 0.884950 0.737186 -0.264921 0.588041 -0.715032 -0.288165 0.661134 0.642870 0.114908 0.602645 -0.052245 -0.629119 0.089346 -0.658640 0.398814 -0.302922 -0.864062 -0.744540 -0.595905 0.479551 0.155450 -0.867096 0.278362 0.246286 0.846283 0.887716 -0.052187 -0.098350 -0.646133 -0.884950 0.228088 0.101365 0.590091 0.225235 0.716059 -0.764094 -0.182865 -0.496834 -0.247500 0.016467 -0.427598 0.654095 -0.089346 -0.228088 0.555749 0.671401 -0.644442 0.656214 0.430012 0.226859 -0.535340 0.783734 -0.408856 0.810315 -0.263386 0.709754 -0.382438 0.658640 -0.101365 -0.555749 0.603866 0.921670 -0.933886 0.666037 0.230039 -0.341990 -0.108987 0.605646 -0.155235 -0.737186 -0.398814 -0.590091 -0.671401 -0.603866 0.220622 0.401708 -0.049237 0.643174 -0.280713 0.752606 0.398272 -0.290818 0.208277 -0.799851 0.264921 0.302922 -0.225235 0.644442 -0.921670 -0.220622 -0.723849 -0.090663 -0.079289 0.575608 0.446132 0.210010 0.844831 -0.463676 0.916515 0.445201 0.864062 -0.716059 -0.656214 -0.439902 -0.116469 -0.934990 -0.562647 0.913344 0.784202 0.833289 -0.588041 0.744540 0.764094 -0.430012 0.933886 -0.401708 0.723849 -0.326127 -0.300402 0.653922 -0.908072 -0.028640 -0.351891 0.086043 0.040314 0.671279 0.595905 -0.226859 0.049237 0.090663 0.439902 0.326127 -0.585429 -0.171018 -0.999574 0.031694 -0.047407 0.484695 -0.083430 0.222260 -0.479551 0.182865 -0.643174 0.079289 0.116469 0.300402 0.585429 0.400613 0.663940 -0.232371 -0.923527 0.444416 -0.253167 -0.694926 0.715032 -0.155450 0.496834 0.535340 0.934990 -0.653922 0.171018 0.563020 -0.769572 0.852480 0.060067 -0.871480 -0.732601 0.288165 0.867096 0.247500 -0.783734 -0.666037 0.280713 -0.575608 0.908072 0.999574 -0.400613 -0.563020 -0.750401 -0.775096 -0.571174 -0.236967 0.778288 -0.278362 -0.016467 0.408856 -0.230039 -0.752606 -0.446132 0.562647 -0.663940 0.769572 -0.036909 0.357293 -0.659318 0.195965 -0.661134 -0.246286 0.427598 0.341990 -0.210010 -0.913344 -0.031694 -0.852480 0.750401 0.036909 -0.017048 0.014827 -0.642870 -0.846283 0.108987 -0.844831 -0.784202 0.028640 0.047407 0.232371 0.775096 -0.965267 -0.318295 -0.809410 -0.114908 -0.887716 -0.810315 -0.398272 0.463676 0.351891 -0.484695 0.923527 -0.060067 0.571174 -0.357293 0.965267 . o x o o x - x - x - - o - o x - - - x x . x - - x o o o o o o o x x x x x x - o o . o x x - x x x o - o o x - o o o x x | x . x x - - x o - x - - o o - x x x x | o o . - x o x o o o o x x o x x x x o o o o | . x x x x x o - o o o x o - - | x | | o o . x x o x x x - o x o - - x o x o | x o o . x x - o - - - x x o o - | x o o o o o o . x - x o x - o x - - x o x o x x o x o o . - o o o - x x x x o | x x | x o o | | | . - o o o - o x x - | x | o x x o x o x | . o o x o - - o o x x x | x | o | x x x x . o o o - x o x | o x | o x | | o x x x x . - x x - o o x o o x o x x | | | x o x | . x o x - x o o | x x x o o x o | x x o o . - o o o | o x | o o x o o o x | | o x | . o - x | o x o o x | x | o o | o | o x x . - - | o x o o | | x | o o x x x | x | | . o o | o o o | o | o x | x o x o x o | x . The error in solving: 7.621420e-16 The error in solving: 6.504820e-16 The error in solving: 5.216645e-16 The error in solving: 8.474546e-16 The error in solving: 5.941574e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.466731 0.000000 0.000000 0.291376 0.000000 0.000000 0.000000 -0.459433 0.592862 0.000000 -0.381889 0.000000 0.000000 0.000000 -0.653096 0.000000 0.000000 0.000000 -0.592851 0.883315 0.000000 0.000000 0.649685 0.000000 0.000000 0.000000 0.000000 0.000000 0.769617 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.592164 0.000000 0.000000 -0.978902 0.000000 0.000000 -0.738816 0.858269 0.000000 0.000000 0.459433 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.658965 0.000000 0.000000 0.000000 -0.592862 -0.769617 0.000000 0.000000 0.000000 0.746542 0.000000 0.000000 0.000000 0.000000 0.000000 0.178571 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.556958 -0.329970 -0.325836 0.000000 0.855231 0.000000 0.000000 0.161090 0.767263 0.000000 0.000000 0.000000 0.000000 0.000000 0.381889 0.000000 0.000000 -0.746542 0.000000 0.000000 -0.212619 0.000000 0.000000 0.000000 0.601007 -0.215815 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.994983 0.000000 0.000000 0.000000 0.000000 0.000000 -0.556958 0.212619 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.391144 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.329970 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.915538 0.000000 0.000000 0.000000 0.760285 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.325836 0.000000 0.000000 0.000000 0.000000 0.000000 0.908955 0.000000 0.889064 0.000000 0.000000 0.000000 -0.694763 0.000000 0.000000 0.000000 0.653096 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.758827 0.000000 -0.232855 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.592164 0.000000 0.000000 -0.855231 -0.601007 0.000000 0.000000 -0.908955 0.758827 0.000000 0.000000 0.740398 0.000000 0.615641 0.000000 0.000000 0.000000 0.935021 0.000000 0.000000 0.000000 0.000000 -0.178571 0.000000 0.215815 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.701534 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.915538 -0.889064 0.232855 -0.740398 0.000000 0.000000 0.000000 0.000000 0.000000 -0.163806 0.000000 0.000000 0.000000 0.592851 0.978902 0.000000 0.000000 -0.161090 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.118014 0.000000 0.000000 0.000000 -0.162472 0.000000 -0.883315 0.000000 0.000000 0.000000 -0.767263 0.000000 0.000000 0.000000 0.000000 0.000000 -0.615641 0.000000 0.000000 0.118014 0.000000 0.706609 0.000000 0.000000 -0.269404 0.466731 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.706609 0.000000 -0.289672 0.000000 -0.995630 0.000000 0.000000 0.738816 0.658965 0.000000 0.000000 0.000000 -0.391144 -0.760285 0.694763 0.000000 0.000000 0.000000 0.163806 0.000000 0.000000 0.289672 0.000000 -0.426003 -0.745330 0.000000 -0.649685 -0.858269 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.701534 0.000000 0.000000 0.000000 0.000000 0.426003 0.000000 0.638316 -0.291376 0.000000 0.000000 0.000000 0.000000 0.000000 -0.994983 0.000000 0.000000 0.000000 0.000000 -0.935021 0.000000 0.000000 0.162472 0.269404 0.995630 0.745330 -0.638316 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 98 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 9 14 16 20 26 32 35 38 42 45 53 56 61 66 72 76 85 90 98 Column indices: 16 19 3 4 6 10 14 15 18 4 11 14 17 18 1 17 1 2 6 12 7 8 9 11 14 15 1 4 7 11 12 19 5 6 17 5 13 17 5 11 13 17 1 11 13 2 5 6 9 10 13 15 19 4 6 18 8 9 10 11 17 1 2 5 15 19 1 5 11 14 16 19 0 15 17 19 2 3 7 8 9 13 16 18 19 1 2 12 17 19 0 6 11 14 15 16 17 18 Off-diagonal values: -0.466731 0.291376 -0.459433 0.592862 -0.381889 -0.653096 -0.592851 0.883315 0.649685 0.769617 -0.592164 -0.978902 -0.738816 0.858269 0.459433 -0.658965 -0.592862 -0.769617 0.746542 0.178571 0.556958 -0.329970 -0.325836 0.855231 0.161090 0.767263 0.381889 -0.746542 -0.212619 0.601007 -0.215815 0.994983 -0.556958 0.212619 0.391144 0.329970 0.915538 0.760285 0.325836 0.908955 0.889064 -0.694763 0.653096 -0.758827 -0.232855 0.592164 -0.855231 -0.601007 -0.908955 0.758827 0.740398 0.615641 0.935021 -0.178571 0.215815 0.701534 -0.915538 -0.889064 0.232855 -0.740398 -0.163806 0.592851 0.978902 -0.161090 -0.118014 -0.162472 -0.883315 -0.767263 -0.615641 0.118014 0.706609 -0.269404 0.466731 -0.706609 -0.289672 -0.995630 0.738816 0.658965 -0.391144 -0.760285 0.694763 0.163806 0.289672 -0.426003 -0.745330 -0.649685 -0.858269 -0.701534 0.426003 0.638316 -0.291376 -0.994983 -0.935021 0.162472 0.269404 0.995630 0.745330 -0.638316 . - - - - - - - - - - - - - - - o - - x | . - o x - o - - - o - - - o x - - x - | | . - x - - - - - - o - - o - - o x - | x | . - - - - - - - - - - - - - o - - | o o | . - x - - - - - x - - - - - - - | | | | | . - x o o - x - - x x - - - - | x | | o | . o - - - x o - - - - - - x | | | | | o x . - - - - - - - - - x - - | | | | | x | | . - - - - x - - - x - - | | | | | x | | | . - x - x - - - o - - | x | | | | | | | | . o - o - - - - - - | | x | | o o | | o x . - x - x - - - x | | | | o | x | | | | | . - - - - - x - | | | | | | | | o o x o | . - - - o - - | x x | | o | | | | | | | | . o - - - o | o | | | o | | | | | o | | x . x - - o x | | | | | | | | | | | | | | o . o - o | | x x | | | o o x | | | x | | x . o o | o o | | | | | | | | | o | | | | x . x o | | | | | o | | | | o | | x x x x o . The error in solving: 9.659092e-16 The error in solving: 6.342923e-16 The error in solving: 9.570896e-16 The error in solving: 4.951473e-16 The error in solving: 4.973304e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.879986 -0.360122 0.000000 0.000000 0.000000 -0.059623 0.000000 0.000000 0.794176 0.000000 -0.839177 -0.034669 0.950441 0.000000 -0.053778 0.000000 0.000000 -0.098035 0.338237 0.742203 0.590245 0.000000 0.416349 0.357874 0.000000 0.000000 0.000000 0.966315 0.000000 0.000000 0.000000 0.738713 -0.632898 -0.957476 -0.241508 0.000000 0.098035 0.000000 -0.814347 -0.417075 0.379003 -0.237283 0.000000 0.000000 0.000000 0.405967 0.000000 0.468446 0.430112 0.120364 0.748279 0.000000 0.000000 0.136261 -0.765358 0.000000 -0.338237 0.814347 0.000000 -0.641017 0.000000 0.418760 -0.075043 -0.756816 0.000000 -0.789998 0.866726 -0.179803 0.000000 -0.014327 -0.361120 -0.775980 -0.526693 0.000000 0.000000 0.000000 -0.742203 0.417075 0.641017 0.000000 0.000000 -0.326614 0.000000 0.000000 0.000000 0.000000 0.000000 0.904178 -0.709477 0.824692 -0.778615 0.892546 0.000000 0.000000 -0.503237 -0.879986 -0.590245 -0.379003 0.000000 0.000000 0.000000 -0.750414 0.000000 0.945318 0.117266 0.000000 0.347793 0.000000 -0.164103 0.103743 0.000000 -0.026545 0.000000 0.326205 0.000000 0.360122 0.000000 0.237283 -0.418760 0.326614 0.750414 0.000000 -0.312791 0.000000 0.000000 0.784869 0.000000 0.000000 0.000000 0.777093 0.000000 0.556702 0.000000 -0.830370 0.000000 0.000000 -0.416349 0.000000 0.075043 0.000000 0.000000 0.312791 0.000000 0.000000 0.000000 0.000000 0.114186 0.000000 0.000000 0.180575 0.000000 0.000000 0.000000 0.000000 -0.695890 0.000000 -0.357874 0.000000 0.756816 0.000000 -0.945318 0.000000 0.000000 0.000000 0.003599 0.589574 -0.205895 0.000000 0.131909 0.000000 -0.610799 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.117266 0.000000 0.000000 -0.003599 0.000000 0.000000 0.000000 -0.631041 0.000000 -0.080769 0.000000 -0.781790 -0.561485 0.627191 0.953206 0.059623 0.000000 -0.405967 0.789998 0.000000 0.000000 -0.784869 0.000000 -0.589574 0.000000 0.000000 -0.427746 0.629434 -0.225508 0.000000 -0.940123 0.000000 -0.296062 0.883069 -0.875339 0.000000 0.000000 0.000000 -0.866726 0.000000 -0.347793 0.000000 -0.114186 0.205895 0.000000 0.427746 0.000000 0.000000 0.181053 0.000000 0.000000 0.532193 0.000000 0.616294 -0.157072 0.000000 -0.966315 -0.468446 0.179803 -0.904178 0.000000 0.000000 0.000000 0.000000 0.631041 -0.629434 0.000000 0.000000 0.000000 0.000000 -0.047202 0.297994 0.000000 0.000000 0.000000 -0.794176 0.000000 -0.430112 0.000000 0.709477 0.164103 0.000000 0.000000 -0.131909 0.000000 0.225508 -0.181053 0.000000 0.000000 0.000000 -0.239560 0.446843 0.000000 -0.379501 -0.836344 0.000000 0.000000 -0.120364 0.014327 -0.824692 -0.103743 -0.777093 -0.180575 0.000000 0.080769 0.000000 0.000000 0.000000 0.000000 0.000000 -0.881418 0.000000 0.638735 0.000000 0.000000 0.839177 0.000000 -0.748279 0.361120 0.778615 0.000000 0.000000 0.000000 0.610799 0.000000 0.940123 0.000000 0.047202 0.239560 0.881418 0.000000 0.776479 0.104935 0.000000 0.590936 0.034669 -0.738713 0.000000 0.775980 -0.892546 0.026545 -0.556702 0.000000 0.000000 0.781790 0.000000 -0.532193 -0.297994 -0.446843 0.000000 -0.776479 0.000000 0.000000 0.179273 -0.276104 -0.950441 0.632898 0.000000 0.526693 0.000000 0.000000 0.000000 0.000000 0.000000 0.561485 0.296062 0.000000 0.000000 0.000000 -0.638735 -0.104935 0.000000 0.000000 0.000000 0.000000 0.000000 0.957476 -0.136261 0.000000 0.000000 -0.326205 0.830370 0.000000 0.000000 -0.627191 -0.883069 -0.616294 0.000000 0.379501 0.000000 0.000000 -0.179273 0.000000 0.000000 0.055583 0.053778 0.241508 0.765358 0.000000 0.503237 0.000000 0.000000 0.695890 0.000000 -0.953206 0.875339 0.157072 0.000000 0.836344 0.000000 -0.590936 0.276104 0.000000 -0.055583 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 200 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 8 19 31 44 54 65 75 81 89 97 109 118 126 137 146 158 171 178 188 200 Column indices: 5 6 10 13 15 16 17 19 2 3 4 5 7 8 12 16 17 18 19 1 3 4 5 6 10 12 13 14 15 18 19 1 2 4 6 7 8 10 11 12 14 15 16 17 1 2 3 6 12 13 14 15 16 19 0 1 2 6 8 9 11 13 14 16 18 0 2 3 4 5 7 10 14 16 18 1 3 6 11 14 19 1 3 5 9 10 11 13 15 5 8 12 14 16 17 18 19 0 2 3 6 8 11 12 13 15 17 18 19 3 5 7 8 10 13 16 18 19 1 2 3 4 9 10 15 16 0 2 4 5 8 10 11 15 16 18 19 2 3 4 5 6 7 9 15 17 0 2 3 4 8 10 12 13 14 16 17 19 0 1 3 4 5 6 9 11 12 13 15 18 19 0 1 3 9 10 14 15 1 2 5 6 9 10 11 13 16 19 0 1 2 4 7 9 10 11 13 15 16 18 Off-diagonal values: 0.879986 -0.360122 -0.059623 0.794176 -0.839177 -0.034669 0.950441 -0.053778 -0.098035 0.338237 0.742203 0.590245 0.416349 0.357874 0.966315 0.738713 -0.632898 -0.957476 -0.241508 0.098035 -0.814347 -0.417075 0.379003 -0.237283 0.405967 0.468446 0.430112 0.120364 0.748279 0.136261 -0.765358 -0.338237 0.814347 -0.641017 0.418760 -0.075043 -0.756816 -0.789998 0.866726 -0.179803 -0.014327 -0.361120 -0.775980 -0.526693 -0.742203 0.417075 0.641017 -0.326614 0.904178 -0.709477 0.824692 -0.778615 0.892546 -0.503237 -0.879986 -0.590245 -0.379003 -0.750414 0.945318 0.117266 0.347793 -0.164103 0.103743 -0.026545 0.326205 0.360122 0.237283 -0.418760 0.326614 0.750414 -0.312791 0.784869 0.777093 0.556702 -0.830370 -0.416349 0.075043 0.312791 0.114186 0.180575 -0.695890 -0.357874 0.756816 -0.945318 0.003599 0.589574 -0.205895 0.131909 -0.610799 -0.117266 -0.003599 -0.631041 -0.080769 -0.781790 -0.561485 0.627191 0.953206 0.059623 -0.405967 0.789998 -0.784869 -0.589574 -0.427746 0.629434 -0.225508 -0.940123 -0.296062 0.883069 -0.875339 -0.866726 -0.347793 -0.114186 0.205895 0.427746 0.181053 0.532193 0.616294 -0.157072 -0.966315 -0.468446 0.179803 -0.904178 0.631041 -0.629434 -0.047202 0.297994 -0.794176 -0.430112 0.709477 0.164103 -0.131909 0.225508 -0.181053 -0.239560 0.446843 -0.379501 -0.836344 -0.120364 0.014327 -0.824692 -0.103743 -0.777093 -0.180575 0.080769 -0.881418 0.638735 0.839177 -0.748279 0.361120 0.778615 0.610799 0.940123 0.047202 0.239560 0.881418 0.776479 0.104935 0.590936 0.034669 -0.738713 0.775980 -0.892546 0.026545 -0.556702 0.781790 -0.532193 -0.297994 -0.446843 -0.776479 0.179273 -0.276104 -0.950441 0.632898 0.526693 0.561485 0.296062 -0.638735 -0.104935 0.957476 -0.136261 -0.326205 0.830370 -0.627191 -0.883069 -0.616294 0.379501 -0.179273 0.055583 0.053778 0.241508 0.765358 0.503237 0.695890 -0.953206 0.875339 0.157072 0.836344 -0.590936 0.276104 -0.055583 . - - - - x o - - - o - - x - o o x - o | . o x x x - x x - - - x - - - x o o o | x . o o x o - - - x - x x x x - - x o | o x . o - x o o - o x o - o o o o - - | o x x . - o - - - - - x o x o x - - o o o o | | . o - x x - x - o x - o - x - x | x o x x . o - - x - - - x - x - o - | o | x | | x . - - - x - - x - - - - o | o | x | o | | . x x o - x - o - - - - | | | | | o | | o . - - o - o - o o x x x | o x | | o | o | . o x o - o - o x o | | | o | o | o x | x . - x - - x - x o | o o x o | | | | x o | . - - o x - - - o | o | x x | | o | x o | . - o x - o o | | o x o o o o | x | | | | . o - x - - x | o x x | | | x | x | x x x . x x - x x o | x o x o | | x | o o o | o . - x o o x | x | | | | | x x | | | o o | . - - | x o | | o x | | o o o | x | | o | . x x x x | x | | x | o x x | x | o x | o . The error in solving: 4.191000e-16 The error in solving: 7.877708e-16 The error in solving: 3.213689e-16 The error in solving: 3.106269e-16 The error in solving: 7.355228e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.750000 [ 0.000000 0.000000 0.524873 0.000000 0.757417 0.000000 -0.159996 0.823665 0.878375 0.000000 0.000000 -0.347030 0.842970 0.794881 -0.819521 0.548518 0.283578 0.588347 -0.565360 -0.829178 0.000000 0.000000 0.928514 0.000000 0.656131 -0.222307 0.905554 0.860061 0.385150 -0.946008 -0.035342 0.930827 0.000000 0.000000 0.386432 0.674157 0.751060 -0.910502 0.000000 -0.303537 -0.524873 -0.928514 0.000000 0.114489 0.000000 0.045691 -0.332918 0.648151 0.228243 -0.253501 0.000000 0.394960 0.861092 -0.975291 -0.939982 0.882193 0.000000 0.000000 0.777621 -0.956946 0.000000 0.000000 -0.114489 0.000000 0.909514 0.745372 -0.371880 -0.035111 0.999707 0.000000 0.437774 0.000000 -0.705745 0.358369 0.359824 0.496045 0.027906 -0.884183 -0.850008 -0.826153 -0.757417 -0.656131 0.000000 -0.909514 0.000000 -0.994115 0.740234 0.000000 -0.278215 -0.047894 0.477106 0.000000 0.000000 -0.512121 0.000000 0.024140 0.231113 0.230827 -0.053063 0.171594 0.000000 0.222307 -0.045691 -0.745372 0.994115 0.000000 0.393965 0.999391 0.714265 -0.274452 0.182154 0.908590 0.201085 0.000000 -0.936060 0.667099 -0.936973 -0.675215 -0.334676 -0.914429 0.159996 -0.905554 0.332918 0.371880 -0.740234 -0.393965 0.000000 0.696602 0.493665 0.000000 0.000000 -0.978105 -0.289133 0.000000 0.000000 -0.369222 0.628726 0.000000 -0.477912 -0.045920 -0.823665 -0.860061 -0.648151 0.035111 0.000000 -0.999391 -0.696602 0.000000 -0.022864 0.915534 0.000000 0.000000 0.000000 -0.322475 0.000000 0.546697 0.000000 -0.535420 -0.254759 -0.884494 -0.878375 -0.385150 -0.228243 -0.999707 0.278215 -0.714265 -0.493665 0.022864 0.000000 -0.046838 0.143051 -0.902143 0.821819 0.000000 -0.519815 0.877641 0.000000 0.301794 0.000000 0.000000 0.000000 0.946008 0.253501 0.000000 0.047894 0.274452 0.000000 -0.915534 0.046838 0.000000 0.125192 0.150079 -0.567524 0.286708 0.925154 0.670408 -0.399709 -0.369552 -0.317745 -0.207981 0.000000 0.035342 0.000000 -0.437774 -0.477106 -0.182154 0.000000 0.000000 -0.143051 -0.125192 0.000000 -0.933142 -0.669216 0.000000 -0.911041 0.000000 0.000000 0.000000 0.808842 0.000000 0.347030 -0.930827 -0.394960 0.000000 0.000000 -0.908590 0.978105 0.000000 0.902143 -0.150079 0.933142 0.000000 -0.332418 0.813711 0.596411 0.515319 0.000000 0.214342 0.281189 0.000000 -0.842970 0.000000 -0.861092 0.705745 0.000000 -0.201085 0.289133 0.000000 -0.821819 0.567524 0.669216 0.332418 0.000000 0.000000 0.675724 -0.771726 0.385385 -0.298569 0.235090 -0.719599 -0.794881 0.000000 0.975291 -0.358369 0.512121 0.000000 0.000000 0.322475 0.000000 -0.286708 0.000000 -0.813711 0.000000 0.000000 0.290587 0.000000 0.903981 0.050303 0.369747 -0.567247 0.819521 -0.386432 0.939982 -0.359824 0.000000 0.936060 0.000000 0.000000 0.519815 -0.925154 0.911041 -0.596411 -0.675724 -0.290587 0.000000 0.336373 0.000000 0.421924 -0.595767 0.475381 -0.548518 -0.674157 -0.882193 -0.496045 -0.024140 -0.667099 0.369222 -0.546697 -0.877641 -0.670408 0.000000 -0.515319 0.771726 0.000000 -0.336373 0.000000 -0.255906 -0.485777 -0.031915 -0.890614 -0.283578 -0.751060 0.000000 -0.027906 -0.231113 0.936973 -0.628726 0.000000 0.000000 0.399709 0.000000 0.000000 -0.385385 -0.903981 0.000000 0.255906 0.000000 0.277770 -0.448334 -0.273215 -0.588347 0.910502 0.000000 0.884183 -0.230827 0.675215 0.000000 0.535420 -0.301794 0.369552 0.000000 -0.214342 0.298569 -0.050303 -0.421924 0.485777 -0.277770 0.000000 -0.827470 0.000000 0.565360 0.000000 -0.777621 0.850008 0.053063 0.334676 0.477912 0.254759 0.000000 0.317745 -0.808842 -0.281189 -0.235090 -0.369747 0.595767 0.031915 0.448334 0.827470 0.000000 0.709695 0.829178 0.303537 0.956946 0.826153 -0.171594 0.914429 0.045920 0.884494 0.000000 0.207981 0.000000 0.000000 0.719599 0.567247 -0.475381 0.890614 0.273215 0.000000 -0.709695 0.000000]; 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The error in solving: 3.721338e-16 The error in solving: 5.541675e-16 The error in solving: 5.606888e-16 The error in solving: 4.496516e-16 The error in solving: 6.535834e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.985696 0.000000 0.000000 0.000000 0.000000 0.017181 0.800865 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.602901 0.000000 0.000000 0.056411 -0.939980 0.000000 0.000000 0.594841 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.185321 0.000000 0.000000 0.000000 0.000000 0.000000 0.377437 -0.081963 0.000000 0.000000 0.000000 0.000000 0.000000 0.689937 0.000000 0.000000 0.000000 0.000000 0.000000 -0.185321 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.129676 0.000000 0.000000 0.000000 -0.024044 0.000000 -0.538627 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.853619 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.360025 0.000000 0.832511 0.000000 0.514414 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.834279 0.000000 0.000000 0.470221 -0.393612 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.590138 0.000000 0.000000 0.000000 -0.984706 -0.881414 0.554086 0.000000 -0.732460 0.765347 0.000000 0.000000 -0.708646 0.000000 0.000000 0.000000 0.000000 0.853619 -0.834279 0.590138 0.000000 0.000000 -0.585632 0.000000 0.000000 0.000000 0.000000 0.691382 0.000000 0.662359 0.000000 0.000000 0.533303 0.000000 0.602901 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.758143 0.000000 0.505479 -0.644340 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.377437 0.129676 0.000000 0.000000 0.000000 0.585632 0.000000 0.000000 0.000000 0.000000 -0.910132 0.000000 0.834309 0.695208 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.081963 0.000000 0.000000 -0.470221 0.000000 0.000000 0.758143 0.000000 0.000000 0.000000 0.000000 -0.333266 0.000000 0.000000 0.175726 -0.745937 0.000000 0.000000 0.000000 -0.056411 0.000000 0.000000 0.000000 0.393612 0.984706 0.000000 0.000000 0.000000 0.000000 0.000000 -0.161495 0.000000 0.801736 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.939980 0.000000 0.000000 0.000000 0.000000 0.881414 0.000000 -0.505479 0.910132 0.000000 0.161495 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.940728 0.000000 0.985696 0.000000 0.000000 0.024044 0.000000 0.000000 -0.554086 0.000000 0.644340 0.000000 0.333266 0.000000 0.000000 0.000000 0.000000 -0.049598 0.000000 -0.343242 0.000000 0.735946 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.691382 0.000000 -0.834309 0.000000 -0.801736 0.000000 0.000000 0.000000 0.000000 -0.816677 0.000000 0.000000 0.749360 0.000000 -0.594841 0.000000 0.538627 -0.360025 0.000000 0.732460 0.000000 0.000000 -0.695208 0.000000 0.000000 0.000000 0.049598 0.000000 0.000000 0.000000 0.000000 0.000000 -0.984228 0.000000 0.000000 -0.689937 0.000000 0.000000 0.000000 -0.765347 -0.662359 0.000000 0.000000 -0.175726 0.000000 0.000000 0.000000 0.816677 0.000000 0.000000 0.000000 0.000000 0.550293 0.000000 0.000000 0.000000 0.000000 -0.832511 0.000000 0.000000 0.000000 0.000000 0.000000 0.745937 0.000000 0.000000 0.343242 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.017181 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.940728 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.800865 0.000000 0.000000 0.000000 -0.514414 0.000000 0.708646 -0.533303 0.000000 0.000000 0.000000 0.000000 0.000000 -0.735946 -0.749360 0.984228 -0.550293 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 102 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 3 7 11 15 19 22 29 36 40 46 52 57 63 71 76 83 89 92 94 102 Column indices: 13 18 19 8 11 12 15 3 9 10 16 2 9 13 15 7 15 17 19 7 10 11 7 11 12 13 15 16 19 4 5 6 9 14 16 19 1 10 12 13 2 3 7 12 14 15 2 5 8 13 16 17 1 5 6 12 14 1 6 8 9 11 18 0 3 6 8 10 15 17 19 7 9 11 16 19 1 3 4 6 9 13 19 2 6 7 10 14 19 4 10 13 0 12 0 4 6 7 13 14 15 16 Off-diagonal values: -0.985696 0.017181 0.800865 -0.602901 0.056411 -0.939980 0.594841 0.185321 0.377437 -0.081963 0.689937 -0.185321 -0.129676 -0.024044 -0.538627 -0.853619 0.360025 0.832511 0.514414 0.834279 0.470221 -0.393612 -0.590138 -0.984706 -0.881414 0.554086 -0.732460 0.765347 -0.708646 0.853619 -0.834279 0.590138 -0.585632 0.691382 0.662359 0.533303 0.602901 -0.758143 0.505479 -0.644340 -0.377437 0.129676 0.585632 -0.910132 0.834309 0.695208 0.081963 -0.470221 0.758143 -0.333266 0.175726 -0.745937 -0.056411 0.393612 0.984706 -0.161495 0.801736 0.939980 0.881414 -0.505479 0.910132 0.161495 -0.940728 0.985696 0.024044 -0.554086 0.644340 0.333266 -0.049598 -0.343242 0.735946 -0.691382 -0.834309 -0.801736 -0.816677 0.749360 -0.594841 0.538627 -0.360025 0.732460 -0.695208 0.049598 -0.984228 -0.689937 -0.765347 -0.662359 -0.175726 0.816677 0.550293 -0.832511 0.745937 0.343242 -0.017181 0.940728 -0.800865 -0.514414 0.708646 -0.533303 -0.735946 -0.749360 0.984228 -0.550293 . - - - - - - - - - - - - o - - - - x x | . - - - - - - o - - x o - - x - - - - | | . x - - - - - x o - - - - - x - - - | | o . - - - - - o - - - o - o - - - - | | | | . - - o - - - - - - - x - x - x | | | | | . - x - - x o - - - - - - - - | | | | | | . o - - - o o x - o x - - o | | | | x o x . - o - - - - x - x - - x | x | | | | | | . - o - x o - - - - - - | | o x | | | x | . - - o - x x - - - - | | x | | o | | x | . - - o - - x o - - | o | | | x x | | | | . o - x - - - - - | x | | | | x | o x | x . - - - - - o - x | | x | | o | x | x | | . - o - o - x | | | | | | | o | o | o | | . - o - - x | o | x o | x | | o | | | x | . - - - o | | o | | | o o | | o | | | x | . - - x | | | | o | | | | | x | | x | | | . - - o | | | | | | | | | | | x | | | | | . - o | | | o | x o | | | | | o o x o | | . The error in solving: 7.654201e-16 The error in solving: 5.831974e-16 The error in solving: 6.866898e-16 The error in solving: 9.836601e-16 The error in solving: 4.043208e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.759603 -0.613882 0.000000 -0.634223 0.000000 -0.256084 0.000000 0.000000 -0.648036 0.000000 0.000000 0.000000 -0.297551 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.249704 -0.910074 0.000000 0.000000 0.379108 0.000000 0.000000 -0.310164 0.663521 0.756253 0.000000 -0.155998 0.000000 0.000000 -0.340717 0.149317 0.000000 0.000000 0.000000 -0.206794 0.946704 0.000000 0.000000 -0.880208 -0.128463 0.000000 0.265839 0.000000 0.000000 0.000000 -0.607060 0.771183 0.063375 0.000000 -0.128494 -0.242189 -0.759603 0.000000 0.206794 0.000000 -0.482926 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.790142 0.000000 0.335253 -0.971029 0.000000 0.000000 0.108744 0.000000 0.613882 0.249704 -0.946704 0.482926 0.000000 0.000000 -0.246101 0.578114 0.203645 0.000000 0.000000 0.950799 0.000000 0.000000 0.000000 -0.600587 0.450136 0.567699 0.549973 0.000000 0.000000 0.910074 0.000000 0.000000 0.000000 0.000000 0.000000 0.642443 -0.493835 -0.253827 0.000000 0.000000 0.837816 0.325006 0.000000 0.069268 0.000000 0.012251 0.095368 0.000000 0.634223 0.000000 0.000000 0.000000 0.246101 0.000000 0.000000 -0.544644 0.947659 -0.109001 0.667852 0.000000 -0.312717 0.720711 0.000000 0.509328 0.000000 -0.069581 0.000000 0.000000 0.000000 0.000000 0.880208 0.000000 -0.578114 -0.642443 0.544644 0.000000 0.794234 0.633935 0.980129 -0.665973 0.000000 0.000000 0.000000 -0.997462 0.963361 -0.534013 0.000000 -0.473851 0.256084 -0.379108 0.128463 0.000000 -0.203645 0.493835 -0.947659 -0.794234 0.000000 0.804601 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.030414 0.281815 -0.831037 0.000000 0.000000 0.000000 0.000000 0.000000 0.253827 0.109001 -0.633935 -0.804601 0.000000 0.000000 0.000000 -0.091858 0.000000 -0.106854 -0.954158 -0.463033 0.000000 0.708603 0.000000 0.000000 0.000000 -0.265839 0.000000 0.000000 0.000000 -0.667852 -0.980129 0.000000 0.000000 0.000000 0.076624 -0.762170 0.000000 -0.822206 -0.919346 0.755982 0.000000 -0.767463 -0.640983 0.648036 0.310164 0.000000 0.000000 -0.950799 0.000000 0.000000 0.665973 0.000000 0.000000 -0.076624 0.000000 0.000000 -0.551487 0.000000 0.000000 0.339764 0.000000 0.000000 0.358805 0.000000 -0.663521 0.000000 0.790142 0.000000 -0.837816 0.312717 0.000000 0.000000 0.091858 0.762170 0.000000 0.000000 0.000000 0.000000 -0.782712 -0.997412 0.472308 -0.134854 0.447450 0.000000 -0.756253 0.000000 0.000000 0.000000 -0.325006 -0.720711 0.000000 0.000000 0.000000 0.000000 0.551487 0.000000 0.000000 0.191951 0.197153 0.000000 -0.716197 0.000000 0.836508 0.000000 0.000000 0.607060 -0.335253 0.000000 0.000000 0.000000 0.000000 0.000000 0.106854 0.822206 0.000000 0.000000 -0.191951 0.000000 0.000000 -0.516149 0.000000 0.000000 -0.095283 0.297551 0.155998 -0.771183 0.971029 0.600587 -0.069268 -0.509328 0.997462 0.000000 0.954158 0.919346 0.000000 0.782712 -0.197153 0.000000 0.000000 -0.195439 -0.013727 -0.322550 0.000000 0.000000 0.000000 -0.063375 0.000000 -0.450136 0.000000 0.000000 -0.963361 0.000000 0.463033 -0.755982 -0.339764 0.997412 0.000000 0.516149 0.195439 0.000000 -0.787811 -0.086030 -0.782987 0.000000 0.000000 0.000000 0.000000 -0.567699 -0.012251 0.069581 0.534013 -0.030414 0.000000 0.000000 0.000000 -0.472308 0.716197 0.000000 0.013727 0.787811 0.000000 0.000000 0.000000 0.000000 0.340717 0.128494 -0.108744 -0.549973 -0.095368 0.000000 0.000000 -0.281815 -0.708603 0.767463 0.000000 0.134854 0.000000 0.000000 0.322550 0.086030 0.000000 0.000000 0.000000 0.000000 -0.149317 0.242189 0.000000 0.000000 0.000000 0.000000 0.473851 0.831037 0.000000 0.640983 -0.358805 -0.447450 -0.836508 0.095283 0.000000 0.782987 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 196 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 6 15 25 32 44 53 63 75 86 95 105 113 124 132 139 154 166 175 186 196 Column indices: 3 4 6 8 11 15 4 5 8 11 12 13 15 18 19 3 4 7 8 10 14 15 16 18 19 0 2 4 12 14 15 18 0 1 2 3 6 7 8 11 15 16 17 18 1 7 8 9 12 13 15 17 18 0 4 7 8 9 10 12 13 15 17 2 4 5 6 8 9 10 11 15 16 17 19 0 1 2 4 5 6 7 9 17 18 19 5 6 7 8 12 14 15 16 18 2 6 7 11 12 14 15 16 18 19 0 1 4 7 10 13 16 19 1 3 5 6 9 10 15 16 17 18 19 1 5 6 11 14 15 17 19 2 3 9 10 13 16 19 0 1 2 3 4 5 6 7 9 10 12 13 16 17 18 2 4 7 9 10 11 12 14 15 17 18 19 4 5 6 7 8 12 13 15 16 1 2 3 4 5 8 9 10 12 15 16 1 2 7 8 10 11 12 13 14 16 Off-diagonal values: 0.759603 -0.613882 -0.634223 -0.256084 -0.648036 -0.297551 -0.249704 -0.910074 0.379108 -0.310164 0.663521 0.756253 -0.155998 -0.340717 0.149317 -0.206794 0.946704 -0.880208 -0.128463 0.265839 -0.607060 0.771183 0.063375 -0.128494 -0.242189 -0.759603 0.206794 -0.482926 -0.790142 0.335253 -0.971029 0.108744 0.613882 0.249704 -0.946704 0.482926 -0.246101 0.578114 0.203645 0.950799 -0.600587 0.450136 0.567699 0.549973 0.910074 0.642443 -0.493835 -0.253827 0.837816 0.325006 0.069268 0.012251 0.095368 0.634223 0.246101 -0.544644 0.947659 -0.109001 0.667852 -0.312717 0.720711 0.509328 -0.069581 0.880208 -0.578114 -0.642443 0.544644 0.794234 0.633935 0.980129 -0.665973 -0.997462 0.963361 -0.534013 -0.473851 0.256084 -0.379108 0.128463 -0.203645 0.493835 -0.947659 -0.794234 0.804601 0.030414 0.281815 -0.831037 0.253827 0.109001 -0.633935 -0.804601 -0.091858 -0.106854 -0.954158 -0.463033 0.708603 -0.265839 -0.667852 -0.980129 0.076624 -0.762170 -0.822206 -0.919346 0.755982 -0.767463 -0.640983 0.648036 0.310164 -0.950799 0.665973 -0.076624 -0.551487 0.339764 0.358805 -0.663521 0.790142 -0.837816 0.312717 0.091858 0.762170 -0.782712 -0.997412 0.472308 -0.134854 0.447450 -0.756253 -0.325006 -0.720711 0.551487 0.191951 0.197153 -0.716197 0.836508 0.607060 -0.335253 0.106854 0.822206 -0.191951 -0.516149 -0.095283 0.297551 0.155998 -0.771183 0.971029 0.600587 -0.069268 -0.509328 0.997462 0.954158 0.919346 0.782712 -0.197153 -0.195439 -0.013727 -0.322550 -0.063375 -0.450136 -0.963361 0.463033 -0.755982 -0.339764 0.997412 0.516149 0.195439 -0.787811 -0.086030 -0.782987 -0.567699 -0.012251 0.069581 0.534013 -0.030414 -0.472308 0.716197 0.013727 0.787811 0.340717 0.128494 -0.108744 -0.549973 -0.095368 -0.281815 -0.708603 0.767463 0.134854 0.322550 0.086030 -0.149317 0.242189 0.473851 0.831037 0.640983 -0.358805 -0.447450 -0.836508 0.095283 0.782987 . - - x o - o - o - - o - - - o - - - - | . - - o o - - x - - o x x - o - - o x | | . o x - - o o - x - - - o x x - o o o | x . o - - - - - - - o - x o - - x - x x o x . - o x x - - x - - - o x x x - | x | | | . - x o o - - x x - x - x x - x | | | x | . o x o x - o x - x - o - - | | x | o o x . x x x o - - - o x o - o x o x | o x o o . x - - - - - - - x x o | | | | | x x o o . - - o - o o o - x - | | o | | | o o | | . x o - o o x - o o x x | | o | | x | | o . - o - - x - - x | o | x | o x | | x x | . - - o o x o x | o | | | o o | | | | x | . x x - o - x | | x o | | | | | x x | | o . - o - - o x x o x x o o x | x x | x o | . o o o - | | o | o | | o | x o o x | x x . o o o | | | | o o x x o | | | o x | x x . - - | x x o o o | | o o x | x | | x x | . - | o x | | | | x x | x o o o x | x | | . The error in solving: 3.838406e-16 The error in solving: 5.481287e-16 The error in solving: 7.661746e-16 The error in solving: 6.979693e-16 The error in solving: 5.613647e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.000000 0.000000 0.409966 -0.398779 -0.104695 -0.293712 -0.156651 0.000000 0.000000 -0.921909 0.000000 0.000000 0.212063 0.000000 -0.391072 -0.145151 0.774352 -0.542550 0.898956 0.000000 0.000000 0.000000 0.000000 0.407643 0.760749 -0.083459 0.061819 0.796117 0.000000 -0.008954 -0.632744 -0.190790 0.728897 0.614285 -0.961395 -0.939290 -0.853298 -0.085950 0.586778 -0.199534 -0.409966 0.000000 0.000000 -0.746762 0.569291 -0.264912 0.001521 0.000000 0.729629 0.334042 -0.876746 0.000000 -0.404287 0.213176 -0.757122 -0.293205 0.000000 0.722604 -0.712839 0.355017 0.398779 -0.407643 0.746762 0.000000 0.227045 -0.701148 0.452381 -0.256629 -0.853887 0.437601 -0.404382 0.000000 0.628379 -0.330294 -0.430168 -0.756424 -0.548655 0.563864 -0.319579 -0.141217 0.104695 -0.760749 -0.569291 -0.227045 0.000000 0.000000 0.558525 0.000000 0.388591 0.246609 0.000000 0.000000 0.000000 -0.803284 0.000000 -0.393203 -0.955016 0.490684 -0.569170 0.000000 0.293712 0.083459 0.264912 0.701148 0.000000 0.000000 0.348996 -0.138904 -0.444695 -0.804294 -0.011416 0.000000 -0.907652 -0.050600 -0.452885 0.000000 -0.036163 0.000000 0.000000 0.903421 0.156651 -0.061819 -0.001521 -0.452381 -0.558525 -0.348996 0.000000 -0.382657 -0.550193 0.000000 0.887917 -0.784951 0.848321 0.000000 0.404530 0.591739 -0.863289 0.000000 0.000000 0.000000 0.000000 -0.796117 0.000000 0.256629 0.000000 0.138904 0.382657 0.000000 -0.020045 0.000000 0.148167 0.000000 0.000000 0.043727 0.007604 -0.814012 0.000000 0.000000 0.508905 0.000000 0.000000 0.000000 -0.729629 0.853887 -0.388591 0.444695 0.550193 0.020045 0.000000 0.046838 0.916591 0.286520 0.000000 0.000000 0.000000 0.536374 0.944334 0.000000 0.000000 0.955862 0.921909 0.008954 -0.334042 -0.437601 -0.246609 0.804294 0.000000 0.000000 -0.046838 0.000000 -0.281085 -0.438944 -0.161409 0.000000 -0.270660 -0.144512 0.875556 -0.152042 0.234195 0.000000 0.000000 0.632744 0.876746 0.404382 0.000000 0.011416 -0.887917 -0.148167 -0.916591 0.281085 0.000000 0.000000 0.000000 0.373352 0.000000 0.000000 0.405981 0.467279 -0.805015 0.000000 0.000000 0.190790 0.000000 0.000000 0.000000 0.000000 0.784951 0.000000 -0.286520 0.438944 0.000000 0.000000 0.398070 0.888753 0.000000 0.047101 0.000000 -0.394659 -0.055794 0.109479 -0.212063 -0.728897 0.404287 -0.628379 0.000000 0.907652 -0.848321 0.000000 0.000000 0.161409 0.000000 -0.398070 0.000000 -0.683436 -0.497635 0.000000 -0.673064 0.000000 0.886857 -0.995309 0.000000 -0.614285 -0.213176 0.330294 0.803284 0.050600 0.000000 -0.043727 0.000000 0.000000 -0.373352 -0.888753 0.683436 0.000000 -0.290399 -0.742316 -0.402685 0.196280 0.014258 0.000000 0.391072 0.961395 0.757122 0.430168 0.000000 0.452885 -0.404530 -0.007604 0.000000 0.270660 0.000000 0.000000 0.497635 0.290399 0.000000 -0.558564 0.000000 -0.011945 -0.102658 0.000000 0.145151 0.939290 0.293205 0.756424 0.393203 0.000000 -0.591739 0.814012 -0.536374 0.144512 0.000000 -0.047101 0.000000 0.742316 0.558564 0.000000 0.021083 -0.444799 0.000000 -0.562095 -0.774352 0.853298 0.000000 0.548655 0.955016 0.036163 0.863289 0.000000 -0.944334 -0.875556 -0.405981 0.000000 0.673064 0.402685 0.000000 -0.021083 0.000000 -0.882370 0.229883 -0.532006 0.542550 0.085950 -0.722604 -0.563864 -0.490684 0.000000 0.000000 0.000000 0.000000 0.152042 -0.467279 0.394659 0.000000 -0.196280 0.011945 0.444799 0.882370 0.000000 0.000000 0.086281 -0.898956 -0.586778 0.712839 0.319579 0.569170 0.000000 0.000000 -0.508905 0.000000 -0.234195 0.805015 0.055794 -0.886857 -0.014258 0.102658 0.000000 -0.229883 0.000000 0.000000 -0.942690 0.000000 0.199534 -0.355017 0.141217 0.000000 -0.903421 0.000000 0.000000 -0.955862 0.000000 0.000000 -0.109479 0.995309 0.000000 0.000000 0.562095 0.532006 -0.086281 0.942690 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 268 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 12 28 43 61 73 87 101 111 123 138 150 160 173 187 200 215 230 243 257 268 Column indices: 2 3 4 5 6 9 12 14 15 16 17 18 3 4 5 6 7 9 10 11 12 13 14 15 16 17 18 19 0 3 4 5 6 8 9 10 12 13 14 15 17 18 19 0 1 2 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19 0 1 2 3 6 8 9 13 15 16 17 18 0 1 2 3 6 7 8 9 10 12 13 14 16 19 0 1 2 3 4 5 7 8 10 11 12 14 15 16 1 3 5 6 8 10 13 14 15 18 2 3 4 5 6 7 9 10 11 15 16 19 0 1 2 3 4 5 8 10 11 12 14 15 16 17 18 1 2 3 5 6 7 8 9 13 16 17 18 1 6 8 9 12 13 15 17 18 19 0 1 2 3 5 6 9 11 13 14 16 18 19 1 2 3 4 5 7 10 11 12 14 15 16 17 18 0 1 2 3 5 6 7 9 12 13 15 17 18 0 1 2 3 4 6 7 8 9 11 13 14 16 17 19 0 1 3 4 5 6 8 9 10 12 13 15 17 18 19 0 1 2 3 4 9 10 11 13 14 15 16 19 0 1 2 3 4 7 9 10 11 12 13 14 16 19 1 2 3 5 8 11 12 15 16 17 18 Off-diagonal values: 0.409966 -0.398779 -0.104695 -0.293712 -0.156651 -0.921909 0.212063 -0.391072 -0.145151 0.774352 -0.542550 0.898956 0.407643 0.760749 -0.083459 0.061819 0.796117 -0.008954 -0.632744 -0.190790 0.728897 0.614285 -0.961395 -0.939290 -0.853298 -0.085950 0.586778 -0.199534 -0.409966 -0.746762 0.569291 -0.264912 0.001521 0.729629 0.334042 -0.876746 -0.404287 0.213176 -0.757122 -0.293205 0.722604 -0.712839 0.355017 0.398779 -0.407643 0.746762 0.227045 -0.701148 0.452381 -0.256629 -0.853887 0.437601 -0.404382 0.628379 -0.330294 -0.430168 -0.756424 -0.548655 0.563864 -0.319579 -0.141217 0.104695 -0.760749 -0.569291 -0.227045 0.558525 0.388591 0.246609 -0.803284 -0.393203 -0.955016 0.490684 -0.569170 0.293712 0.083459 0.264912 0.701148 0.348996 -0.138904 -0.444695 -0.804294 -0.011416 -0.907652 -0.050600 -0.452885 -0.036163 0.903421 0.156651 -0.061819 -0.001521 -0.452381 -0.558525 -0.348996 -0.382657 -0.550193 0.887917 -0.784951 0.848321 0.404530 0.591739 -0.863289 -0.796117 0.256629 0.138904 0.382657 -0.020045 0.148167 0.043727 0.007604 -0.814012 0.508905 -0.729629 0.853887 -0.388591 0.444695 0.550193 0.020045 0.046838 0.916591 0.286520 0.536374 0.944334 0.955862 0.921909 0.008954 -0.334042 -0.437601 -0.246609 0.804294 -0.046838 -0.281085 -0.438944 -0.161409 -0.270660 -0.144512 0.875556 -0.152042 0.234195 0.632744 0.876746 0.404382 0.011416 -0.887917 -0.148167 -0.916591 0.281085 0.373352 0.405981 0.467279 -0.805015 0.190790 0.784951 -0.286520 0.438944 0.398070 0.888753 0.047101 -0.394659 -0.055794 0.109479 -0.212063 -0.728897 0.404287 -0.628379 0.907652 -0.848321 0.161409 -0.398070 -0.683436 -0.497635 -0.673064 0.886857 -0.995309 -0.614285 -0.213176 0.330294 0.803284 0.050600 -0.043727 -0.373352 -0.888753 0.683436 -0.290399 -0.742316 -0.402685 0.196280 0.014258 0.391072 0.961395 0.757122 0.430168 0.452885 -0.404530 -0.007604 0.270660 0.497635 0.290399 -0.558564 -0.011945 -0.102658 0.145151 0.939290 0.293205 0.756424 0.393203 -0.591739 0.814012 -0.536374 0.144512 -0.047101 0.742316 0.558564 0.021083 -0.444799 -0.562095 -0.774352 0.853298 0.548655 0.955016 0.036163 0.863289 -0.944334 -0.875556 -0.405981 0.673064 0.402685 -0.021083 -0.882370 0.229883 -0.532006 0.542550 0.085950 -0.722604 -0.563864 -0.490684 0.152042 -0.467279 0.394659 -0.196280 0.011945 0.444799 0.882370 0.086281 -0.898956 -0.586778 0.712839 0.319579 0.569170 -0.508905 -0.234195 0.805015 0.055794 -0.886857 -0.014258 0.102658 -0.229883 -0.942690 0.199534 -0.355017 0.141217 -0.903421 -0.955862 -0.109479 0.995309 0.562095 0.532006 -0.086281 0.942690 . - x o o o o - - o - - x - o o x o x - | . - x x o x x - o o o x x o o o o x o o | . o x o x - x x o - o x o o - x o x x o x . x o x o o x o - x o o o o x o o x o o o . - x - x x - - - o - o o x o - x x x x | . x o o o o - o o o - o - - x x o o o o o . o o - x o x - x x o - - - | o | x | x x . o - x - - x x o - - x - | | o x o x x x . x x x - - - x x - - x x x o o o x | | o . o o o - o o x o x - | x x x | x o o o x . - - x - - x x o - | x | | | | x | o x | . x x - x - o o x o o x o | x o | | x | o . o o - o - x o | o o x x x | o | | o o x . o o o x x - x x x x | x o o | x | | x x . o - o o - x x x x x | o x o x | o | x x . x o - o o x | x x x x | o o o | x x | o . o x o x x o o o | | | | x o x | o x x x . - x o o x x x | | o | o x x o o x | o | . o | x o x | o | | o | | o x | | x x o x . The error in solving: 4.855243e-16 The error in solving: 1.175523e-15 The error in solving: 4.390736e-16 The error in solving: 4.406198e-16 The error in solving: 4.107487e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.199213 -0.554687 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.322024 0.987436 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.647359 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.406662 0.000000 0.000000 0.000000 0.000000 0.035914 0.000000 -0.996513 -0.481416 0.000000 0.000000 0.000000 -0.224658 0.000000 0.619546 0.000000 0.000000 0.000000 0.000000 -0.979141 0.000000 0.000000 0.000000 -0.478808 -0.238987 -0.735002 0.000000 -0.642119 0.000000 0.736761 0.000000 0.000000 0.435984 0.000000 0.000000 0.000000 0.000000 0.000000 0.979141 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.074188 0.000000 0.000000 -0.230149 0.093284 0.000000 0.000000 0.574245 0.000000 0.000000 0.000000 0.000000 -0.406662 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.658982 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.027799 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.712952 0.000000 0.000000 0.000000 0.000000 0.660072 0.195565 0.000000 -0.786884 0.000000 0.000000 0.000000 0.000000 -0.199213 0.000000 0.000000 0.000000 0.000000 0.000000 -0.712952 0.000000 0.000000 0.000000 0.000000 0.560949 0.000000 0.000000 0.000000 0.000000 0.000000 -0.451317 -0.083150 0.000000 0.554687 0.000000 0.000000 0.478808 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.636615 0.000000 0.000000 0.000000 0.000000 0.000000 0.238987 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.154246 -0.391756 0.000000 0.000000 -0.380250 0.000000 0.000000 -0.695005 0.284479 -0.680920 0.000000 0.000000 -0.035914 0.735002 -0.074188 -0.658982 0.000000 0.000000 0.000000 0.154246 0.000000 0.000000 0.000000 0.000000 0.624783 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.560949 0.000000 0.391756 0.000000 0.000000 0.379629 0.167082 -0.868577 0.000000 0.000000 -0.865586 0.000000 0.000000 0.000000 0.000000 0.996513 0.642119 0.000000 0.000000 -0.660072 0.000000 0.000000 0.000000 0.000000 -0.379629 0.000000 0.000000 0.646025 0.000000 0.000000 0.000000 0.000000 -0.801700 0.000000 0.000000 0.481416 0.000000 0.230149 0.000000 -0.195565 0.000000 0.000000 0.000000 0.000000 -0.167082 0.000000 0.000000 0.000000 0.000000 0.000000 0.942362 0.000000 0.000000 0.000000 0.000000 0.000000 -0.736761 -0.093284 0.000000 0.000000 0.000000 0.000000 0.380250 -0.624783 0.868577 -0.646025 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.786884 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.647359 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.322024 0.000000 0.224658 -0.435984 -0.574245 -0.027799 0.000000 0.451317 0.636615 0.695005 0.000000 0.865586 0.000000 -0.942362 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.987436 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.083150 0.000000 -0.284479 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.619546 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.680920 0.000000 0.000000 0.801700 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 92 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 4 5 11 18 23 26 30 35 38 45 51 57 63 68 74 75 76 86 89 92 Column indices: 7 8 17 18 16 5 10 12 13 17 19 4 8 9 10 12 14 17 3 10 13 14 17 2 10 17 7 12 13 15 0 6 11 17 18 0 3 17 3 10 11 14 17 18 19 2 3 4 5 9 14 7 9 12 13 14 17 2 3 6 11 14 19 2 4 6 11 17 3 4 9 10 11 12 6 1 0 2 3 4 5 7 8 9 11 13 0 7 9 2 9 12 Off-diagonal values: 0.199213 -0.554687 -0.322024 0.987436 -0.647359 0.406662 0.035914 -0.996513 -0.481416 -0.224658 0.619546 -0.979141 -0.478808 -0.238987 -0.735002 -0.642119 0.736761 0.435984 0.979141 0.074188 -0.230149 0.093284 0.574245 -0.406662 0.658982 0.027799 0.712952 0.660072 0.195565 -0.786884 -0.199213 -0.712952 0.560949 -0.451317 -0.083150 0.554687 0.478808 -0.636615 0.238987 -0.154246 -0.391756 -0.380250 -0.695005 0.284479 -0.680920 -0.035914 0.735002 -0.074188 -0.658982 0.154246 0.624783 -0.560949 0.391756 0.379629 0.167082 -0.868577 -0.865586 0.996513 0.642119 -0.660072 -0.379629 0.646025 -0.801700 0.481416 0.230149 -0.195565 -0.167082 0.942362 -0.736761 -0.093284 0.380250 -0.624783 0.868577 -0.646025 0.786884 0.647359 0.322024 0.224658 -0.435984 -0.574245 -0.027799 0.451317 0.636615 0.695005 0.865586 -0.942362 -0.987436 0.083150 -0.284479 -0.619546 0.680920 0.801700 . - - - - - - x o - - - - - - - - o x - | . - - - - - - - - - - - - - - o - - - | | . - - x - - - - x - o o - - - o - x | | | . o - - - o o o - o - x - - x - - | | | x . - - - - - x - - o x - - x - - | | o | | . - - - - x - - - - - - x - - | | | | | | . x - - - - x x - o - - - - o | | | | | o . - - - x - - - - - o o - x | | x | | | | . - - - - - - - - o - - | | | x | | | | | . o o - - o - - o x o | | o x o o | | | x . - - - x - - - - - | | | | | | | o | x | . x x o - - o - - | | x x | | o | | | | o . - x - - - - o | | x | x | o | | | | o | . - - - x - - | | | o o | | | | x o x o | . - - - - - | | | | | | x | | | | | | | | . - - - - | x | | | | | | | | | | | | | | . - - - x | x o o o | x x x | x | o | | | . - - o | | | | | | x | o | | | | | | | | . - | | o | | | | | | x | | x | | | | | | . The error in solving: 4.080548e-16 The error in solving: 5.155590e-16 The error in solving: 2.938245e-16 The error in solving: 9.899056e-16 The error in solving: 6.017265e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 -0.813475 -0.741384 -0.221626 0.000000 0.000000 0.000000 0.000000 -0.555068 0.000000 0.000000 0.000000 -0.665630 -0.523622 0.000000 0.000000 0.000000 0.000000 -0.306975 -0.223876 0.813475 0.000000 0.066303 0.409188 0.000000 -0.125625 0.000000 0.000000 0.950607 -0.189829 -0.919416 0.000000 0.000000 0.000000 -0.836365 0.195344 0.000000 0.000000 0.710261 0.000000 0.741384 -0.066303 0.000000 0.000000 0.216574 0.981539 0.000000 -0.141256 -0.021696 -0.080843 0.000000 0.000000 0.532251 0.571710 0.164100 0.544065 -0.317446 0.000000 0.000000 -0.851539 0.221626 -0.409188 0.000000 0.000000 0.000000 -0.006675 0.000000 -0.641432 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.180411 0.000000 -0.510038 -0.467411 -0.247121 0.000000 0.000000 0.000000 -0.216574 0.000000 0.000000 0.000000 -0.259500 -0.743980 -0.643032 0.869338 0.000000 0.796679 0.000000 0.000000 0.319731 0.000000 0.510935 0.888408 -0.084003 0.155072 0.000000 0.125625 -0.981539 0.006675 0.000000 0.000000 0.164609 0.000000 -0.885260 0.078946 0.000000 0.000000 0.000000 0.000000 0.000000 -0.032562 -0.922366 0.000000 -0.604566 -0.229946 0.000000 0.000000 0.000000 0.000000 0.259500 -0.164609 0.000000 0.000000 0.518899 0.000000 -0.835752 -0.707461 -0.652964 0.000000 0.653901 0.295479 0.000000 0.439898 0.456794 0.000000 0.000000 0.000000 0.141256 0.641432 0.743980 0.000000 0.000000 0.000000 0.000000 -0.907911 -0.908103 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.090352 0.133474 0.000000 0.555068 -0.950607 0.021696 0.000000 0.643032 0.885260 -0.518899 0.000000 0.000000 0.082642 0.902591 -0.332264 0.030704 0.234407 0.466097 -0.058618 0.984671 -0.550237 0.000000 -0.634165 0.000000 0.189829 0.080843 0.000000 -0.869338 -0.078946 0.000000 0.907911 -0.082642 0.000000 0.000000 0.000000 -0.797802 0.646391 0.000000 -0.795365 0.786065 0.393105 0.000000 -0.678383 0.000000 0.919416 0.000000 0.000000 0.000000 0.000000 0.835752 0.908103 -0.902591 0.000000 0.000000 -0.816845 0.000000 0.497888 0.178351 0.000000 -0.044979 0.465954 0.000000 -0.531164 0.000000 0.000000 0.000000 0.000000 -0.796679 0.000000 0.707461 0.000000 0.332264 0.000000 0.816845 0.000000 0.231385 -0.036456 0.000000 -0.613781 0.000000 0.990370 0.000000 -0.575837 0.665630 0.000000 -0.532251 0.000000 0.000000 0.000000 0.652964 0.000000 -0.030704 0.797802 0.000000 -0.231385 0.000000 0.668796 -0.835474 0.000000 0.273066 0.000000 0.000000 0.000000 0.523622 0.000000 -0.571710 0.000000 0.000000 0.000000 0.000000 0.000000 -0.234407 -0.646391 -0.497888 0.036456 -0.668796 0.000000 -0.029655 0.000000 0.000000 -0.946709 0.140753 0.000000 0.000000 0.836365 -0.164100 -0.180411 -0.319731 0.000000 -0.653901 0.000000 -0.466097 0.000000 -0.178351 0.000000 0.835474 0.029655 0.000000 0.974038 -0.714303 -0.369007 0.000000 0.000000 0.000000 -0.195344 -0.544065 0.000000 0.000000 0.032562 -0.295479 0.000000 0.058618 0.795365 0.000000 0.613781 0.000000 0.000000 -0.974038 0.000000 0.000000 0.000000 0.748107 0.609213 0.000000 0.000000 0.317446 0.510038 -0.510935 0.922366 0.000000 0.000000 -0.984671 -0.786065 0.044979 0.000000 -0.273066 0.000000 0.714303 0.000000 0.000000 0.006029 0.000000 -0.273246 0.000000 0.000000 0.000000 0.467411 -0.888408 0.000000 -0.439898 -0.090352 0.550237 -0.393105 -0.465954 -0.990370 0.000000 0.946709 0.369007 0.000000 -0.006029 0.000000 0.000000 -0.866617 0.306975 -0.710261 0.000000 0.247121 0.084003 0.604566 -0.456794 -0.133474 0.000000 0.000000 0.000000 0.000000 0.000000 -0.140753 0.000000 -0.748107 0.000000 0.000000 0.000000 0.802932 0.223876 0.000000 0.851539 0.000000 -0.155072 0.229946 0.000000 0.000000 0.634165 0.678383 0.531164 0.575837 0.000000 0.000000 0.000000 -0.609213 0.273246 0.866617 -0.802932 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 210 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 8 18 31 39 50 60 70 77 93 105 115 124 133 143 155 165 176 188 198 210 Column indices: 1 2 3 8 12 13 18 19 0 2 3 5 8 9 10 14 15 18 0 1 4 5 7 8 9 12 13 14 15 16 19 0 1 5 7 14 16 17 18 2 6 7 8 9 11 14 16 17 18 19 1 2 3 6 8 9 15 16 18 19 4 5 8 10 11 12 14 15 17 18 2 3 4 9 10 17 18 0 1 2 4 5 6 9 10 11 12 13 14 15 16 17 19 1 2 4 5 7 8 12 13 15 16 17 19 1 6 7 8 11 13 14 16 17 19 4 6 8 10 12 13 15 17 19 0 2 6 8 9 11 13 14 16 0 2 8 9 10 11 12 14 17 18 1 2 3 4 6 8 10 12 13 15 16 17 1 2 5 6 8 9 11 14 18 19 2 3 4 5 8 9 10 12 14 17 19 3 4 6 7 8 9 10 11 13 14 16 19 0 1 3 4 5 6 7 13 15 19 0 2 4 5 8 9 10 11 15 16 17 18 Off-diagonal values: -0.813475 -0.741384 -0.221626 -0.555068 -0.665630 -0.523622 -0.306975 -0.223876 0.813475 0.066303 0.409188 -0.125625 0.950607 -0.189829 -0.919416 -0.836365 0.195344 0.710261 0.741384 -0.066303 0.216574 0.981539 -0.141256 -0.021696 -0.080843 0.532251 0.571710 0.164100 0.544065 -0.317446 -0.851539 0.221626 -0.409188 -0.006675 -0.641432 0.180411 -0.510038 -0.467411 -0.247121 -0.216574 -0.259500 -0.743980 -0.643032 0.869338 0.796679 0.319731 0.510935 0.888408 -0.084003 0.155072 0.125625 -0.981539 0.006675 0.164609 -0.885260 0.078946 -0.032562 -0.922366 -0.604566 -0.229946 0.259500 -0.164609 0.518899 -0.835752 -0.707461 -0.652964 0.653901 0.295479 0.439898 0.456794 0.141256 0.641432 0.743980 -0.907911 -0.908103 0.090352 0.133474 0.555068 -0.950607 0.021696 0.643032 0.885260 -0.518899 0.082642 0.902591 -0.332264 0.030704 0.234407 0.466097 -0.058618 0.984671 -0.550237 -0.634165 0.189829 0.080843 -0.869338 -0.078946 0.907911 -0.082642 -0.797802 0.646391 -0.795365 0.786065 0.393105 -0.678383 0.919416 0.835752 0.908103 -0.902591 -0.816845 0.497888 0.178351 -0.044979 0.465954 -0.531164 -0.796679 0.707461 0.332264 0.816845 0.231385 -0.036456 -0.613781 0.990370 -0.575837 0.665630 -0.532251 0.652964 -0.030704 0.797802 -0.231385 0.668796 -0.835474 0.273066 0.523622 -0.571710 -0.234407 -0.646391 -0.497888 0.036456 -0.668796 -0.029655 -0.946709 0.140753 0.836365 -0.164100 -0.180411 -0.319731 -0.653901 -0.466097 -0.178351 0.835474 0.029655 0.974038 -0.714303 -0.369007 -0.195344 -0.544065 0.032562 -0.295479 0.058618 0.795365 0.613781 -0.974038 0.748107 0.609213 0.317446 0.510038 -0.510935 0.922366 -0.984671 -0.786065 0.044979 -0.273066 0.714303 0.006029 -0.273246 0.467411 -0.888408 -0.439898 -0.090352 0.550237 -0.393105 -0.465954 -0.990370 0.946709 0.369007 -0.006029 -0.866617 0.306975 -0.710261 0.247121 0.084003 0.604566 -0.456794 -0.133474 -0.140753 -0.748107 0.802932 0.223876 0.851539 -0.155072 0.229946 0.634165 0.678383 0.531164 0.575837 -0.609213 0.273246 0.866617 -0.802932 . o o o - - - - o - - - o o - - - - o o x . x x - o - - x o o - - - o x - - x - x o . - x x - o o o - - x x x x o - - o x o | . - o - o - - - - - - x - o o o - | | o | . - o o o x - x - - x - x x o x | x o x | . x - o x - - - - - o o - o o | | | | x o . - x - o o o - x x - x x - | | x x x | | . - o o - - - - - - x x - x o x | x x o | . x x o x x x o x o - o | x x | o o | x o . - - o x - o x x - o | x | | | | x x o | . o - x x - o x - o | | | | o | x | x | x . x o - o - x - o x | o | | | x | o x | o . x o - x - - - x | o | | | | | o o o x o . o - - o x - | x o o o | o | o | o | x x . x o o - - | o o | | x o | x x | x | | o . - - x x | | x x o x | | o o x | o | x | . x - o | | | x o | o o x o o o | x x | o . - o x o | x x x o o | | | | | o | o | | . x x | x | o x | | x x x x | | | o x x o . The error in solving: 7.818602e-16 The error in solving: 1.148424e-15 The error in solving: 7.136021e-16 The error in solving: 7.965007e-16 The error in solving: 3.727396e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 -0.826846 -0.912942 -0.982005 0.000000 0.000000 0.000000 0.000000 -0.228627 -0.256001 0.836841 0.000000 0.000000 0.000000 0.002953 0.000000 0.000000 -0.696079 -0.181330 0.000000 0.000000 -0.390925 0.581537 0.000000 0.000000 0.084163 0.033449 -0.894908 0.976073 0.000000 0.569208 0.000000 -0.063111 0.591913 0.407002 0.849506 -0.984368 -0.335435 -0.849974 0.826846 0.390925 0.000000 0.000000 -0.093599 -0.767337 0.582835 0.607722 0.000000 -0.202261 0.245184 0.470025 -0.623566 -0.827102 0.911270 -0.443725 -0.508262 -0.514523 0.000000 -0.769966 0.912942 -0.581537 0.000000 0.000000 0.000000 0.000000 0.279974 -0.116006 0.000000 0.499102 0.966083 0.478422 0.674594 -0.103636 0.764166 0.295948 0.146824 0.621815 0.236912 0.000000 0.982005 0.000000 0.093599 0.000000 0.000000 0.101659 -0.077367 -0.288725 0.000000 0.906417 -0.809377 0.000000 0.282576 -0.450298 -0.403262 -0.930605 -0.656587 0.598464 0.416329 -0.294681 0.000000 0.000000 0.767337 0.000000 -0.101659 0.000000 -0.724027 0.620254 0.243580 0.000000 0.859220 0.000000 -0.210962 -0.493501 -0.576521 -0.648130 -0.606366 0.867681 -0.074802 0.000000 0.000000 -0.084163 -0.582835 -0.279974 0.077367 0.724027 0.000000 0.857999 0.097111 0.783739 0.513222 -0.845880 -0.219831 0.642895 0.828301 -0.741467 -0.246221 0.000000 -0.834940 -0.176268 0.000000 -0.033449 -0.607722 0.116006 0.288725 -0.620254 -0.857999 0.000000 -0.131336 0.000000 0.786156 -0.777022 0.000000 -0.981483 0.000000 0.639022 0.951716 0.000000 0.000000 -0.828947 0.000000 0.894908 0.000000 0.000000 0.000000 -0.243580 -0.097111 0.131336 0.000000 0.457724 -0.782479 0.068617 0.000000 0.000000 0.316877 -0.965586 0.000000 0.698901 0.000000 0.508995 0.228627 -0.976073 0.202261 -0.499102 -0.906417 0.000000 -0.783739 0.000000 -0.457724 0.000000 0.532946 -0.178289 0.477853 0.022660 0.469342 0.000000 0.000000 0.000000 0.000000 0.000000 0.256001 0.000000 -0.245184 -0.966083 0.809377 -0.859220 -0.513222 -0.786156 0.782479 -0.532946 0.000000 -0.998462 0.000000 0.153440 0.019291 0.821274 0.000000 0.000000 0.498394 0.756209 -0.836841 -0.569208 -0.470025 -0.478422 0.000000 0.000000 0.845880 0.777022 -0.068617 0.178289 0.998462 0.000000 0.000000 0.791939 0.000000 0.603787 0.078044 0.000000 0.469089 0.000000 0.000000 0.000000 0.623566 -0.674594 -0.282576 0.210962 0.219831 0.000000 0.000000 -0.477853 0.000000 0.000000 0.000000 0.467069 0.000000 0.768990 0.000000 0.831474 0.245203 0.000000 0.000000 0.063111 0.827102 0.103636 0.450298 0.493501 -0.642895 0.981483 0.000000 -0.022660 -0.153440 -0.791939 -0.467069 0.000000 -0.944165 -0.868068 -0.033066 -0.395228 -0.068630 -0.983953 0.000000 -0.591913 -0.911270 -0.764166 0.403262 0.576521 -0.828301 0.000000 -0.316877 -0.469342 -0.019291 0.000000 0.000000 0.944165 0.000000 0.000000 0.037935 0.503839 -0.540938 0.000000 -0.002953 -0.407002 0.443725 -0.295948 0.930605 0.648130 0.741467 -0.639022 0.965586 0.000000 -0.821274 -0.603787 -0.768990 0.868068 0.000000 0.000000 0.561696 -0.427079 -0.774906 -0.583175 0.000000 -0.849506 0.508262 -0.146824 0.656587 0.606366 0.246221 -0.951716 0.000000 0.000000 0.000000 -0.078044 0.000000 0.033066 -0.037935 -0.561696 0.000000 -0.559666 0.386555 0.009428 0.000000 0.984368 0.514523 -0.621815 -0.598464 -0.867681 0.000000 0.000000 -0.698901 0.000000 0.000000 0.000000 -0.831474 0.395228 -0.503839 0.427079 0.559666 0.000000 -0.765410 0.000000 0.696079 0.335435 0.000000 -0.236912 -0.416329 0.074802 0.834940 0.000000 0.000000 0.000000 -0.498394 -0.469089 -0.245203 0.068630 0.540938 0.774906 -0.386555 0.765410 0.000000 -0.324115 0.181330 0.849974 0.769966 0.000000 0.294681 0.000000 0.176268 0.828947 -0.508995 0.000000 -0.756209 0.000000 0.000000 0.983953 0.000000 0.583175 -0.009428 0.000000 0.324115 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 272 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 9 23 39 53 68 81 98 111 122 134 149 162 172 189 202 219 233 245 260 272 Column indices: 2 3 4 9 10 11 15 18 19 2 3 6 7 8 9 11 13 14 15 16 17 18 19 0 1 4 5 6 7 9 10 11 12 13 14 15 16 17 19 0 1 6 7 9 10 11 12 13 14 15 16 17 18 0 2 5 6 7 9 10 12 13 14 15 16 17 18 19 2 4 6 7 8 10 12 13 14 15 16 17 18 1 2 3 4 5 7 8 9 10 11 12 13 14 15 16 18 19 1 2 3 4 5 6 8 10 11 13 15 16 19 1 5 6 7 9 10 11 14 15 17 19 0 1 2 3 4 6 8 10 11 12 13 14 0 2 3 4 5 6 7 8 9 11 13 14 15 18 19 0 1 2 3 6 7 8 9 10 13 15 16 18 2 3 4 5 6 9 13 15 17 18 1 2 3 4 5 6 7 9 10 11 12 14 15 16 17 18 19 1 2 3 4 5 6 8 9 10 13 16 17 18 0 1 2 3 4 5 6 7 8 10 11 12 13 16 17 18 19 1 2 3 4 5 6 7 11 13 14 15 17 18 19 1 2 3 4 5 8 12 13 14 15 16 18 0 1 3 4 5 6 10 11 12 13 14 15 16 17 19 0 1 2 4 6 7 8 10 13 15 16 18 Off-diagonal values: -0.826846 -0.912942 -0.982005 -0.228627 -0.256001 0.836841 0.002953 -0.696079 -0.181330 -0.390925 0.581537 0.084163 0.033449 -0.894908 0.976073 0.569208 -0.063111 0.591913 0.407002 0.849506 -0.984368 -0.335435 -0.849974 0.826846 0.390925 -0.093599 -0.767337 0.582835 0.607722 -0.202261 0.245184 0.470025 -0.623566 -0.827102 0.911270 -0.443725 -0.508262 -0.514523 -0.769966 0.912942 -0.581537 0.279974 -0.116006 0.499102 0.966083 0.478422 0.674594 -0.103636 0.764166 0.295948 0.146824 0.621815 0.236912 0.982005 0.093599 0.101659 -0.077367 -0.288725 0.906417 -0.809377 0.282576 -0.450298 -0.403262 -0.930605 -0.656587 0.598464 0.416329 -0.294681 0.767337 -0.101659 -0.724027 0.620254 0.243580 0.859220 -0.210962 -0.493501 -0.576521 -0.648130 -0.606366 0.867681 -0.074802 -0.084163 -0.582835 -0.279974 0.077367 0.724027 0.857999 0.097111 0.783739 0.513222 -0.845880 -0.219831 0.642895 0.828301 -0.741467 -0.246221 -0.834940 -0.176268 -0.033449 -0.607722 0.116006 0.288725 -0.620254 -0.857999 -0.131336 0.786156 -0.777022 -0.981483 0.639022 0.951716 -0.828947 0.894908 -0.243580 -0.097111 0.131336 0.457724 -0.782479 0.068617 0.316877 -0.965586 0.698901 0.508995 0.228627 -0.976073 0.202261 -0.499102 -0.906417 -0.783739 -0.457724 0.532946 -0.178289 0.477853 0.022660 0.469342 0.256001 -0.245184 -0.966083 0.809377 -0.859220 -0.513222 -0.786156 0.782479 -0.532946 -0.998462 0.153440 0.019291 0.821274 0.498394 0.756209 -0.836841 -0.569208 -0.470025 -0.478422 0.845880 0.777022 -0.068617 0.178289 0.998462 0.791939 0.603787 0.078044 0.469089 0.623566 -0.674594 -0.282576 0.210962 0.219831 -0.477853 0.467069 0.768990 0.831474 0.245203 0.063111 0.827102 0.103636 0.450298 0.493501 -0.642895 0.981483 -0.022660 -0.153440 -0.791939 -0.467069 -0.944165 -0.868068 -0.033066 -0.395228 -0.068630 -0.983953 -0.591913 -0.911270 -0.764166 0.403262 0.576521 -0.828301 -0.316877 -0.469342 -0.019291 0.944165 0.037935 0.503839 -0.540938 -0.002953 -0.407002 0.443725 -0.295948 0.930605 0.648130 0.741467 -0.639022 0.965586 -0.821274 -0.603787 -0.768990 0.868068 0.561696 -0.427079 -0.774906 -0.583175 -0.849506 0.508262 -0.146824 0.656587 0.606366 0.246221 -0.951716 -0.078044 0.033066 -0.037935 -0.561696 -0.559666 0.386555 0.009428 0.984368 0.514523 -0.621815 -0.598464 -0.867681 -0.698901 -0.831474 0.395228 -0.503839 0.427079 0.559666 -0.765410 0.696079 0.335435 -0.236912 -0.416329 0.074802 0.834940 -0.498394 -0.469089 -0.245203 0.068630 0.540938 0.774906 -0.386555 0.765410 -0.324115 0.181330 0.849974 0.769966 0.294681 0.176268 0.828947 -0.508995 -0.756209 0.983953 0.583175 -0.009428 0.324115 . - o o o - - - - o o x - - - x - - o o | . o x - - x x o x - x - o x x x o o o x x . - o o x x - o x x o o x o o o - o x o | . - - x o - x x x x o x x x x x - x | x | . x o o - x o - x o o o o x x o | | x | o . o x x - x - o o o o o x o - | o o o x x . x x x x o o x x o o - o o | o o x x o o . o - x o - o - x x - - o | x | | | o o x . x o x - - x o - x - x x o x o o | o | o . x o x x x - - - - - x | o o x o o o x o . o - x x x - - x x o o o o | | x x o x x . - x - x x - x - | | x o o x x | | o | | . x - x - x x - | x x x x x o x | o o o o . o o o o o o | o o o x x o | o o o | | x . - x x o - o o x o x x x o x | o o o x | . x o o o | o x o x x x o | | | o | x o o . o x x | x x o o o | | o | | | o x o x x . o - x x | o o x x | | | o o o x x x o x . o x x x | x | x x o | o | | x | x o | x . The error in solving: 8.563843e-16 The error in solving: 4.757066e-16 The error in solving: 6.473657e-16 The error in solving: 2.486410e-16 The error in solving: 5.897677e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a standard normal distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 -0.546997 0.900269 0.000000 0.000000 0.000000 0.000000 0.000000 -0.002380 0.000000 2.911555 0.728639 -0.678332 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.117467 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -3.089610 0.000000 0.000000 0.000000 0.546997 0.000000 0.000000 0.669407 0.000000 0.000000 -1.245499 0.172408 0.000000 0.000000 0.448596 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.428897 0.000000 0.029592 -0.900269 0.000000 -0.669407 0.000000 0.000000 0.000000 0.000000 0.000000 -1.532716 0.000000 0.000000 0.000000 0.000000 0.000000 -0.001845 -0.945389 -0.066295 -0.051618 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.065517 0.000000 -0.525298 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.236761 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.081071 0.000000 0.000000 0.000000 -0.165359 0.000000 0.000000 0.000000 1.245499 0.000000 0.000000 0.236761 0.000000 0.000000 0.000000 0.382990 0.000000 0.418857 0.000000 -0.969054 0.000000 -0.491280 0.000000 0.000000 0.000000 0.000000 0.000000 1.117467 -0.172408 0.000000 0.000000 0.000000 0.000000 0.000000 0.829294 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.505524 -1.117806 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.532716 0.000000 0.000000 0.000000 -0.829294 0.000000 0.000000 -0.166051 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.655792 -0.334962 0.000000 0.002380 0.000000 0.000000 0.000000 0.000000 0.000000 -0.382990 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.550340 0.000000 0.000000 0.000000 -0.448596 0.000000 0.000000 0.000000 0.000000 0.000000 0.166051 0.000000 0.000000 0.000000 0.000000 0.000000 -0.370964 0.000000 0.000000 0.000000 0.000000 0.000000 -2.911555 0.000000 0.000000 0.000000 0.000000 0.000000 -0.418857 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.558471 0.000000 -0.468921 0.000000 0.000000 0.000000 0.000000 -0.728639 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.460067 0.000000 -0.123619 0.000000 0.000000 0.000000 0.678332 0.000000 0.000000 0.000000 0.000000 0.000000 0.969054 0.000000 0.000000 0.000000 0.000000 0.558471 0.000000 0.000000 0.678438 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.001845 0.065517 -1.081071 0.000000 0.000000 0.000000 0.000000 0.370964 0.000000 0.460067 -0.678438 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.945389 0.000000 0.000000 0.491280 0.505524 0.000000 0.000000 0.000000 0.468921 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 3.089610 0.000000 0.066295 0.525298 0.000000 0.000000 1.117806 0.000000 0.000000 0.000000 0.000000 0.123619 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.428897 0.051618 0.000000 0.000000 0.000000 0.000000 2.655792 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.165359 0.000000 0.000000 0.334962 0.550340 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.029592 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 82 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 6 8 15 22 24 27 33 38 43 46 49 53 56 60 66 70 75 78 81 82 Column indices: 2 3 9 11 12 13 7 16 0 3 6 7 10 17 19 0 2 8 14 15 16 17 14 16 6 14 18 2 5 9 11 13 15 1 2 8 15 16 3 7 10 17 18 0 6 18 2 8 14 0 6 13 15 0 14 16 0 6 11 14 3 4 5 10 12 13 3 6 7 11 1 3 4 7 12 2 3 8 5 8 9 2 Off-diagonal values: -0.546997 0.900269 -0.002380 2.911555 0.728639 -0.678332 -1.117467 -3.089610 0.546997 0.669407 -1.245499 0.172408 0.448596 0.428897 0.029592 -0.900269 -0.669407 -1.532716 -0.001845 -0.945389 -0.066295 -0.051618 -0.065517 -0.525298 -0.236761 1.081071 -0.165359 1.245499 0.236761 0.382990 0.418857 -0.969054 -0.491280 1.117467 -0.172408 0.829294 -0.505524 -1.117806 1.532716 -0.829294 -0.166051 -2.655792 -0.334962 0.002380 -0.382990 -0.550340 -0.448596 0.166051 -0.370964 -2.911555 -0.418857 -0.558471 -0.468921 -0.728639 -0.460067 -0.123619 0.678332 0.969054 0.558471 0.678438 0.001845 0.065517 -1.081071 0.370964 0.460067 -0.678438 0.945389 0.491280 0.505524 0.468921 3.089610 0.066295 0.525298 1.117806 0.123619 -0.428897 0.051618 2.655792 0.165359 0.334962 0.550340 -0.029592 . - o x - - - - - o - x x o - - - - - - | . - - - - - o - - - - - - - - o - - - x | . x - - o x - - x - - - - - - x - x o | o . - - - - o - - - - - o o o o - - | | | | . - - - - - - - - - o - o - - - | | | | | . o - - - - - - - x - - - o - | | x | | x . - - x - x - o - o - - - - | x o | | | | . x - - - - - - o o - - - | | | x | | | o . - o - - - - - - o o - x | | | | | o | | . - - - - - - - - o - | | o | | | | | x | . - - - o - - - - - o | | | | | o | | | | . - o - o - - - - o | | | | | | | | | | | . - o - o - - - x | | | | | x | | | | x | . x - - - - - | | | x x o | | | | x | x o . - - - - - | | | x | | x x | | | x | | | . - - - - | x | x x | | x | | | | x | | | . - - - | | o x | | | | x | | | | | | | | . - - | | | | | x | | x x | | | | | | | | . - | | o | | | | | | | | | | | | | | | | . The error in solving: 6.280370e-16 The error in solving: 1.082112e-15 The error in solving: 8.715428e-16 The error in solving: 5.954626e-16 The error in solving: 5.476124e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a standard normal distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 -1.340359 0.000000 0.369464 0.000000 0.955245 0.843003 -1.414012 0.000000 0.797295 0.000000 -0.307900 -0.244081 0.623547 -1.329318 -0.468011 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.337916 0.000000 0.000000 0.151900 0.688018 0.000000 0.000000 0.000000 0.000000 -0.384962 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.340359 0.000000 0.000000 0.804153 0.000000 -2.126464 0.000000 0.635550 0.000000 0.471274 1.535485 -0.001557 0.000000 0.000000 0.000000 0.000000 0.999265 0.554608 0.000000 -0.339420 0.000000 -1.337916 -0.804153 0.000000 0.041093 0.000000 -0.159959 -2.797592 1.982507 0.000000 2.460045 0.000000 -1.544273 0.000000 -0.799620 1.658841 0.000000 0.000000 0.354490 1.052533 -0.369464 0.000000 0.000000 -0.041093 0.000000 0.685158 0.000000 0.625039 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.786634 1.259368 -0.317396 0.000000 0.000000 0.000000 2.126464 0.000000 -0.685158 0.000000 0.000000 0.000000 0.122397 0.000000 0.173081 1.582936 -0.379764 -0.635366 0.000000 -1.529773 0.000000 0.000000 0.000000 0.000000 -0.955245 -0.151900 0.000000 0.159959 0.000000 0.000000 0.000000 1.503138 0.000000 0.000000 -0.248012 -1.021379 0.000000 0.969485 0.000000 -0.038931 0.000000 0.000000 1.367771 0.174948 -0.843003 -0.688018 -0.635550 2.797592 -0.625039 0.000000 -1.503138 0.000000 1.666619 0.000000 0.000000 1.008436 0.000000 0.000000 0.000000 0.000000 -1.381865 2.294922 1.080561 0.000000 1.414012 0.000000 0.000000 -1.982507 0.000000 -0.122397 0.000000 -1.666619 0.000000 0.861600 0.000000 1.894840 -1.921487 0.000000 2.039571 -0.656156 1.186890 0.912124 0.242913 0.000000 0.000000 0.000000 -0.471274 0.000000 0.000000 0.000000 0.000000 0.000000 -0.861600 0.000000 -2.103910 0.000000 0.000000 -0.161793 1.201393 0.000000 1.220257 -0.752069 1.831879 0.013932 -0.797295 0.000000 -1.535485 -2.460045 0.000000 -0.173081 0.248012 0.000000 0.000000 2.103910 0.000000 0.000000 0.473725 0.000000 0.000000 0.000000 0.000000 0.000000 0.276215 0.000000 0.000000 0.000000 0.001557 0.000000 0.000000 -1.582936 1.021379 -1.008436 -1.894840 0.000000 0.000000 0.000000 0.000000 0.133299 0.045878 -0.875795 0.828040 0.000000 0.000000 0.045018 0.307900 0.384962 0.000000 1.544273 0.000000 0.379764 0.000000 0.000000 1.921487 0.000000 -0.473725 0.000000 0.000000 -0.686735 0.000000 -0.688247 0.000000 0.749118 -0.655199 0.000000 0.244081 0.000000 0.000000 0.000000 0.000000 0.635366 -0.969485 0.000000 0.000000 0.161793 0.000000 -0.133299 0.686735 0.000000 -0.596309 0.000000 -0.543640 0.000000 -0.064715 0.000000 -0.623547 0.000000 0.000000 0.799620 0.000000 0.000000 0.000000 0.000000 -2.039571 -1.201393 0.000000 -0.045878 0.000000 0.596309 0.000000 1.513423 0.000000 0.413472 -1.203595 0.000000 1.329318 0.000000 0.000000 -1.658841 0.000000 1.529773 0.038931 0.000000 0.656156 0.000000 0.000000 0.875795 0.688247 0.000000 -1.513423 0.000000 0.000000 0.634261 1.156196 0.000000 0.468011 0.000000 -0.999265 0.000000 -0.786634 0.000000 0.000000 1.381865 -1.186890 -1.220257 0.000000 -0.828040 0.000000 0.543640 0.000000 0.000000 0.000000 0.000000 -0.360820 0.000000 0.000000 0.000000 -0.554608 0.000000 -1.259368 0.000000 0.000000 -2.294922 -0.912124 0.752069 0.000000 0.000000 -0.749118 0.000000 -0.413472 -0.634261 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.354490 0.317396 0.000000 -1.367771 -1.080561 -0.242913 -1.831879 -0.276215 0.000000 0.655199 0.064715 1.203595 -1.156196 0.360820 0.000000 0.000000 0.000000 0.000000 0.000000 0.339420 -1.052533 0.000000 0.000000 -0.174948 0.000000 0.000000 -0.013932 0.000000 -0.045018 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 184 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 11 15 25 37 44 52 62 73 85 94 102 112 122 131 140 150 159 167 179 184 Column indices: 2 4 6 7 8 10 12 13 14 15 16 3 6 7 12 0 3 5 7 9 10 11 16 17 19 1 2 4 6 7 8 10 12 14 15 18 19 0 3 5 7 16 17 18 2 4 8 10 11 12 13 15 0 1 3 7 10 11 13 15 18 19 0 1 2 3 4 6 8 11 16 17 18 0 3 5 7 9 11 12 14 15 16 17 18 2 8 10 13 14 16 17 18 19 0 2 3 5 6 9 12 18 2 5 6 7 8 13 14 15 16 19 0 1 3 5 8 10 13 15 17 18 0 5 6 9 11 12 14 16 18 0 3 8 9 11 13 15 17 18 0 3 5 6 8 11 12 14 17 18 0 2 4 7 8 9 11 13 18 2 4 7 8 9 12 14 15 3 4 6 7 8 9 10 12 13 14 15 16 2 3 6 9 11 Off-diagonal values: -1.340359 0.369464 0.955245 0.843003 -1.414012 0.797295 -0.307900 -0.244081 0.623547 -1.329318 -0.468011 1.337916 0.151900 0.688018 -0.384962 1.340359 0.804153 -2.126464 0.635550 0.471274 1.535485 -0.001557 0.999265 0.554608 -0.339420 -1.337916 -0.804153 0.041093 -0.159959 -2.797592 1.982507 2.460045 -1.544273 -0.799620 1.658841 0.354490 1.052533 -0.369464 -0.041093 0.685158 0.625039 0.786634 1.259368 -0.317396 2.126464 -0.685158 0.122397 0.173081 1.582936 -0.379764 -0.635366 -1.529773 -0.955245 -0.151900 0.159959 1.503138 -0.248012 -1.021379 0.969485 -0.038931 1.367771 0.174948 -0.843003 -0.688018 -0.635550 2.797592 -0.625039 -1.503138 1.666619 1.008436 -1.381865 2.294922 1.080561 1.414012 -1.982507 -0.122397 -1.666619 0.861600 1.894840 -1.921487 2.039571 -0.656156 1.186890 0.912124 0.242913 -0.471274 -0.861600 -2.103910 -0.161793 1.201393 1.220257 -0.752069 1.831879 0.013932 -0.797295 -1.535485 -2.460045 -0.173081 0.248012 2.103910 0.473725 0.276215 0.001557 -1.582936 1.021379 -1.008436 -1.894840 0.133299 0.045878 -0.875795 0.828040 0.045018 0.307900 0.384962 1.544273 0.379764 1.921487 -0.473725 -0.686735 -0.688247 0.749118 -0.655199 0.244081 0.635366 -0.969485 0.161793 -0.133299 0.686735 -0.596309 -0.543640 -0.064715 -0.623547 0.799620 -2.039571 -1.201393 -0.045878 0.596309 1.513423 0.413472 -1.203595 1.329318 -1.658841 1.529773 0.038931 0.656156 0.875795 0.688247 -1.513423 0.634261 1.156196 0.468011 -0.999265 -0.786634 1.381865 -1.186890 -1.220257 -0.828040 0.543640 -0.360820 -0.554608 -1.259368 -2.294922 -0.912124 0.752069 -0.749118 -0.413472 -0.634261 -0.354490 0.317396 -1.367771 -1.080561 -0.242913 -1.831879 -0.276215 0.655199 0.064715 1.203595 -1.156196 0.360820 0.339420 -1.052533 -0.174948 -0.013932 -0.045018 . - o - x - x x o - x - o o x o o - - - | . - x - - x x - - - - o - - - - - - - x | . x - o - x - x x o - - - - x x - o | o o . x - o o x - x - o - o x - - x x o | | o . x - x - - - - - - - - x x o - | | x | o . - - x - x x o o - o - - - - o o | x | | . x - - o o - x - o - - x x o o o x o | o . x - - x - - - - o x x - x | | o | o | o . x - x o - x o x x x - | | o | | | | | o . o - - o x - x o x x o | o o | o x | | x . - x - - - - - x - | | x | | o x o o | | . - x x o x - - x x x | x | x | | x | o | . o - o - x o - x | | | | x o | | x | o x . o - o - o - o | | x | | | | o o | o | x . x - x o - x | | o | x x | x | | x x | o . - x x - x | o | o | | x o o | o | x | | . - o - | | o | o | | o o x | | o | o o | . - - | | | o x | o o o o o | x x x o x | . - | | x o | | o | | o | o | | | | | | | . The error in solving: 3.251670e-16 The error in solving: 7.706859e-16 The error in solving: 4.013777e-16 The error in solving: 5.608069e-16 The error in solving: 1.026980e-15 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a standard normal distribution with a random diagonal and a density of 0.750000 [ 0.000000 -0.793697 0.000000 0.000000 1.999707 -0.422599 0.000000 -0.532102 -1.328185 -1.500205 0.000000 -0.293800 -0.638544 0.000000 0.000000 0.546682 0.380935 -0.906556 -1.126189 0.000000 0.793697 0.000000 0.706534 -0.708089 0.000000 0.000000 -0.041394 -0.470629 -0.625882 2.111740 -1.151244 -0.007714 0.000000 0.000000 -0.132287 1.211544 0.404320 0.206200 -1.529382 0.000000 0.000000 -0.706534 0.000000 -0.197605 0.000000 1.897793 -0.679005 -0.281157 0.000000 -1.124159 0.677598 -1.822558 0.000000 0.000000 0.000000 -1.003413 0.000000 -1.630152 1.294352 0.000000 0.000000 0.708089 0.197605 0.000000 0.000000 0.000000 0.000000 0.427590 0.750372 0.154713 -0.731154 0.000000 -1.604310 0.664252 1.242950 -0.618628 0.528742 0.000000 -0.238037 0.000000 -1.999707 0.000000 0.000000 0.000000 0.000000 0.513465 0.000000 -2.412386 0.216948 0.315954 -0.885195 0.139791 1.644862 0.000000 0.000000 1.494150 0.000000 0.489524 0.203287 -0.622930 0.422599 0.000000 -1.897793 0.000000 -0.513465 0.000000 0.135015 -0.319966 0.000000 0.403935 1.990489 0.000000 -0.499416 -1.395131 1.604342 0.000000 1.106287 0.000000 -0.790370 0.342365 0.000000 0.041394 0.679005 0.000000 0.000000 -0.135015 0.000000 -0.573109 0.152942 0.599292 0.402254 -0.143828 0.000000 0.042683 1.097380 0.000000 0.002739 1.410158 2.005655 -0.042397 0.532102 0.470629 0.281157 -0.427590 2.412386 0.319966 0.573109 0.000000 0.000000 -0.137014 -0.166043 -0.269606 -0.841074 0.486364 0.218277 -0.900039 -0.604760 1.578452 -2.500434 -0.110399 1.328185 0.625882 0.000000 -0.750372 -0.216948 0.000000 -0.152942 0.000000 0.000000 0.482133 0.000000 -1.092398 -1.353676 0.000000 0.000000 -1.519734 -0.048824 -0.286246 -0.361550 -0.164731 1.500205 -2.111740 1.124159 -0.154713 -0.315954 -0.403935 -0.599292 0.137014 -0.482133 0.000000 -0.487485 0.814718 -0.448533 -1.222778 0.000000 -0.072698 0.000000 -1.712040 1.645618 -1.212591 0.000000 1.151244 -0.677598 0.731154 0.885195 -1.990489 -0.402254 0.166043 0.000000 0.487485 0.000000 -0.348603 1.643950 -1.002177 0.000000 -0.029490 0.000000 0.000000 -0.185454 -0.474561 0.293800 0.007714 1.822558 0.000000 -0.139791 0.000000 0.143828 0.269606 1.092398 -0.814718 0.348603 0.000000 -1.460025 -1.165394 0.210366 0.340473 1.635415 -0.122413 0.000000 -1.082389 0.638544 0.000000 0.000000 1.604310 -1.644862 0.499416 0.000000 0.841074 1.353676 0.448533 -1.643950 1.460025 0.000000 0.766461 1.297001 -0.131796 0.000000 0.913929 0.000000 -0.517887 0.000000 0.000000 0.000000 -0.664252 0.000000 1.395131 -0.042683 -0.486364 0.000000 1.222778 1.002177 1.165394 -0.766461 0.000000 0.000000 0.000000 -0.942302 0.984772 0.474767 -1.055305 0.000000 0.132287 0.000000 -1.242950 0.000000 -1.604342 -1.097380 -0.218277 0.000000 0.000000 0.000000 -0.210366 -1.297001 0.000000 0.000000 0.095157 0.495079 0.000000 0.454653 0.989407 -0.546682 -1.211544 1.003413 0.618628 -1.494150 0.000000 0.000000 0.900039 1.519734 0.072698 0.029490 -0.340473 0.131796 0.000000 -0.095157 0.000000 -0.103728 -0.961479 0.448202 0.254192 -0.380935 -0.404320 0.000000 -0.528742 0.000000 -1.106287 -0.002739 0.604760 0.048824 0.000000 0.000000 -1.635415 0.000000 0.942302 -0.495079 0.103728 0.000000 -0.409254 -1.836790 1.779879 0.906556 -0.206200 1.630152 0.000000 -0.489524 0.000000 -1.410158 -1.578452 0.286246 1.712040 0.000000 0.122413 -0.913929 -0.984772 0.000000 0.961479 0.409254 0.000000 1.456883 -0.721024 1.126189 1.529382 -1.294352 0.238037 -0.203287 0.790370 -2.005655 2.500434 0.361550 -1.645618 0.185454 0.000000 0.000000 -0.474767 -0.454653 -0.448202 1.836790 -1.456883 0.000000 -0.357587 0.000000 0.000000 0.000000 0.000000 0.622930 -0.342365 0.042397 0.110399 0.164731 1.212591 0.474561 1.082389 0.517887 1.055305 -0.989407 -0.254192 -1.779879 0.721024 0.357587 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 280 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 12 26 37 49 61 74 88 106 119 136 150 166 180 192 203 219 233 248 265 280 Column indices: 1 4 5 7 8 9 11 12 15 16 17 18 0 2 3 6 7 8 9 10 11 14 15 16 17 18 1 3 5 6 7 9 10 11 15 17 18 1 2 7 8 9 10 12 13 14 15 16 18 0 5 7 8 9 10 11 12 15 17 18 19 0 2 4 6 7 9 10 12 13 14 16 18 19 1 2 5 7 8 9 10 11 13 14 16 17 18 19 0 1 2 3 4 5 6 9 10 11 12 13 14 15 16 17 18 19 0 1 3 4 6 9 11 12 15 16 17 18 19 0 1 2 3 4 5 6 7 8 10 11 12 13 15 17 18 19 1 2 3 4 5 6 7 9 11 12 13 15 18 19 0 1 2 4 6 7 8 9 10 12 13 14 15 16 17 19 0 3 4 5 7 8 9 10 11 13 14 15 17 19 3 5 6 7 9 10 11 12 16 17 18 19 1 3 5 6 7 11 12 15 16 18 19 0 1 2 3 4 7 8 9 10 11 12 14 16 17 18 19 0 1 3 5 6 7 8 11 13 14 15 17 18 19 0 1 2 4 6 7 8 9 11 12 13 15 16 18 19 0 1 2 3 4 5 6 7 8 9 10 13 14 15 16 17 19 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Off-diagonal values: -0.793697 1.999707 -0.422599 -0.532102 -1.328185 -1.500205 -0.293800 -0.638544 0.546682 0.380935 -0.906556 -1.126189 0.793697 0.706534 -0.708089 -0.041394 -0.470629 -0.625882 2.111740 -1.151244 -0.007714 -0.132287 1.211544 0.404320 0.206200 -1.529382 -0.706534 -0.197605 1.897793 -0.679005 -0.281157 -1.124159 0.677598 -1.822558 -1.003413 -1.630152 1.294352 0.708089 0.197605 0.427590 0.750372 0.154713 -0.731154 -1.604310 0.664252 1.242950 -0.618628 0.528742 -0.238037 -1.999707 0.513465 -2.412386 0.216948 0.315954 -0.885195 0.139791 1.644862 1.494150 0.489524 0.203287 -0.622930 0.422599 -1.897793 -0.513465 0.135015 -0.319966 0.403935 1.990489 -0.499416 -1.395131 1.604342 1.106287 -0.790370 0.342365 0.041394 0.679005 -0.135015 -0.573109 0.152942 0.599292 0.402254 -0.143828 0.042683 1.097380 0.002739 1.410158 2.005655 -0.042397 0.532102 0.470629 0.281157 -0.427590 2.412386 0.319966 0.573109 -0.137014 -0.166043 -0.269606 -0.841074 0.486364 0.218277 -0.900039 -0.604760 1.578452 -2.500434 -0.110399 1.328185 0.625882 -0.750372 -0.216948 -0.152942 0.482133 -1.092398 -1.353676 -1.519734 -0.048824 -0.286246 -0.361550 -0.164731 1.500205 -2.111740 1.124159 -0.154713 -0.315954 -0.403935 -0.599292 0.137014 -0.482133 -0.487485 0.814718 -0.448533 -1.222778 -0.072698 -1.712040 1.645618 -1.212591 1.151244 -0.677598 0.731154 0.885195 -1.990489 -0.402254 0.166043 0.487485 -0.348603 1.643950 -1.002177 -0.029490 -0.185454 -0.474561 0.293800 0.007714 1.822558 -0.139791 0.143828 0.269606 1.092398 -0.814718 0.348603 -1.460025 -1.165394 0.210366 0.340473 1.635415 -0.122413 -1.082389 0.638544 1.604310 -1.644862 0.499416 0.841074 1.353676 0.448533 -1.643950 1.460025 0.766461 1.297001 -0.131796 0.913929 -0.517887 -0.664252 1.395131 -0.042683 -0.486364 1.222778 1.002177 1.165394 -0.766461 -0.942302 0.984772 0.474767 -1.055305 0.132287 -1.242950 -1.604342 -1.097380 -0.218277 -0.210366 -1.297001 0.095157 0.495079 0.454653 0.989407 -0.546682 -1.211544 1.003413 0.618628 -1.494150 0.900039 1.519734 0.072698 0.029490 -0.340473 0.131796 -0.095157 -0.103728 -0.961479 0.448202 0.254192 -0.380935 -0.404320 -0.528742 -1.106287 -0.002739 0.604760 0.048824 -1.635415 0.942302 -0.495079 0.103728 -0.409254 -1.836790 1.779879 0.906556 -0.206200 1.630152 -0.489524 -1.410158 -1.578452 0.286246 1.712040 0.122413 -0.913929 -0.984772 0.961479 0.409254 1.456883 -0.721024 1.126189 1.529382 -1.294352 0.238037 -0.203287 0.790370 -2.005655 2.500434 0.361550 -1.645618 0.185454 -0.474767 -0.454653 -0.448202 1.836790 -1.456883 -0.357587 0.622930 -0.342365 0.042397 0.110399 0.164731 1.212591 0.474561 1.082389 0.517887 1.055305 -0.989407 -0.254192 -1.779879 0.721024 0.357587 . o - - x o - o o o - o o - - x x o o - x . x o - - o o o x o o - - o x x x o - | o . o - x o o - o x o - - - o - o x - | x x . - - - x x x o - o x x o x - o - o | | | . x - o x x o x x - - x - x x o x | o | o . x o - x x - o o x - x - o x | x x | | o . o x x x o - x x - x x x o x x x o x x x . - o o o o x x o o x o o x x | o o | o | . x - o o - - o o o o o x o x o o o o x o . o x o o - o - o x o | x o x x o o x | x . o x o - o - - o o x x x | o | x x x o x . o o x x x o - o x | | x o x | x x x o x . x x o - x - o | | | o | x o o | x x x o . - - o x x o | x | o | o o o | | | o o | . x x - x x o o x x o | | x x x x o x | o . o o x x o o | o | o o x x | | o | x o x . o o x x o x | o | o o x x | x o o | x x . x o x x o x o x o x x o x | | o o o x o . o | | | | x o x x x x x x x x o o o x x . The error in solving: 6.824235e-16 The error in solving: 4.520411e-16 The error in solving: 4.757857e-16 The error in solving: 9.392146e-16 The error in solving: 6.258867e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a standard normal distribution with a dense diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.472088 0.000000 0.000000 0.000000 0.000000 0.000000 -1.362360 0.000000 1.632951 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.116543 -0.741641 0.000000 0.000000 -0.181765 -0.821474 0.000000 0.000000 0.000000 0.000000 -0.856648 0.000000 0.000000 0.000000 0.574553 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.036803 0.000000 0.000000 0.000000 -0.588362 0.000000 0.000000 -0.533698 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.587431 0.000000 0.522931 0.000000 0.000000 0.000000 0.000000 0.483339 0.785438 0.000000 0.000000 0.000000 0.000000 0.000000 0.195460 0.000000 0.000000 0.000000 0.000000 1.587431 0.000000 0.000000 1.104995 0.000000 -0.450223 0.000000 0.000000 -0.003441 0.395676 0.566419 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.116543 0.000000 0.000000 0.000000 0.000000 0.000000 -0.742529 0.000000 0.387049 0.000000 0.000000 0.000000 0.689326 0.000000 0.000000 0.000000 1.356122 0.000000 0.000000 -2.472088 0.741641 0.000000 -0.522931 -1.104995 0.000000 0.000000 0.000000 -1.716832 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.742529 0.000000 0.000000 -1.101356 0.877657 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.467693 0.000000 0.000000 0.000000 0.000000 0.000000 -0.036803 0.000000 0.450223 0.000000 1.716832 1.101356 0.000000 0.000000 0.613674 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.181765 0.000000 0.000000 0.000000 -0.387049 0.000000 -0.877657 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.097314 0.000000 0.821474 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.613674 0.000000 0.000000 -0.666144 0.000000 0.000000 0.804914 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.483339 0.003441 0.000000 0.000000 0.000000 0.000000 0.000000 0.666144 0.000000 0.000000 -0.732452 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.362360 0.000000 0.588362 -0.785438 -0.395676 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.363498 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.566419 -0.689326 0.000000 0.000000 0.000000 0.000000 0.000000 0.732452 0.000000 0.000000 -0.909477 0.000000 0.647679 0.000000 0.727485 0.000000 -1.632951 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.804914 0.000000 0.000000 0.909477 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.856648 0.533698 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.467693 0.000000 0.000000 0.000000 0.000000 0.000000 -0.647679 0.000000 0.000000 0.000000 0.000000 0.000000 0.719955 0.000000 0.000000 0.000000 0.000000 0.000000 -1.356122 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.363498 0.000000 0.000000 0.000000 0.000000 0.000000 -0.154870 0.000000 0.000000 0.000000 0.000000 -0.195460 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.727485 0.000000 0.000000 0.000000 0.154870 0.000000 0.000000 0.000000 -0.574553 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.097314 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.719955 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 82 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 3 9 12 17 23 28 33 37 42 46 50 54 59 65 68 70 73 76 79 82 Column indices: 6 12 14 5 6 9 10 15 19 8 12 15 4 6 11 12 18 3 6 8 11 12 13 1 7 9 13 17 0 1 3 4 8 5 8 9 16 2 4 6 7 10 1 5 7 19 1 8 11 14 3 4 10 13 0 2 3 4 17 4 5 11 14 16 18 0 10 13 1 2 7 13 19 5 12 18 3 13 17 1 9 16 Off-diagonal values: 2.472088 -1.362360 1.632951 0.116543 -0.741641 -0.181765 -0.821474 -0.856648 0.574553 0.036803 -0.588362 -0.533698 -1.587431 0.522931 0.483339 0.785438 0.195460 1.587431 1.104995 -0.450223 -0.003441 0.395676 0.566419 -0.116543 -0.742529 0.387049 0.689326 1.356122 -2.472088 0.741641 -0.522931 -1.104995 -1.716832 0.742529 -1.101356 0.877657 -0.467693 -0.036803 0.450223 1.716832 1.101356 0.613674 0.181765 -0.387049 -0.877657 -0.097314 0.821474 -0.613674 -0.666144 0.804914 -0.483339 0.003441 0.666144 -0.732452 1.362360 0.588362 -0.785438 -0.395676 -0.363498 -0.566419 -0.689326 0.732452 -0.909477 0.647679 0.727485 -1.632951 -0.804914 0.909477 0.856648 0.533698 0.467693 -0.647679 0.719955 -1.356122 0.363498 -0.154870 -0.195460 -0.727485 0.154870 -0.574553 0.097314 -0.719955 . - - - - - x - - - - - o - x - - - - - | . - - - x o - - o o - - - - o - - - x | | . - - - - - x - - - o - - o - - - - | | | . o - x - - - - x x - - - - - x - | | | x . - x - o - - o x x - - - - - - | o | | | . - o - x - - - x - - - x - - o x | o o | . - o - - - - - - - - - - - | | | | | x | . o x - - - - - - o - - - | | o | x | x x . - x - - - - - - - - - | x | | | o | o | . - - - - - - - - - o | x | | | | | | o | . o - - x - - - - - | | | o x | | | | | x . - o - - - - - - x | x o o | | | | | | | . - - - - o - - | | | | o o | | | | | x | . o - x - x - o | | | | | | | | | o | | x . - - - - - | x x | | | | | | | | | | | | . - - - - | | | | | | | x | | | | | o | | . - - x | | | | | o | | | | | | x | | | | . o - | | | o | | | | | | | | | o | | | x . - | o | | | | | | | x | | | | | | o | | . The error in solving: 3.927684e-16 The error in solving: 8.349770e-16 The error in solving: 6.288032e-16 The error in solving: 6.169083e-16 The error in solving: 4.209341e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a standard normal distribution with a dense diagonal and a density of 0.500000 [ 0.000000 0.000000 -0.974192 -0.218138 -1.134371 -0.823535 0.000000 0.511439 -0.815916 -0.429771 0.000000 0.000000 0.000000 0.563849 -0.181827 0.000000 0.233115 -0.008016 -1.132251 0.000000 0.000000 0.000000 0.000000 0.764337 0.620055 0.000000 0.809692 0.000000 -0.595796 -1.217748 -0.461387 0.000000 1.558316 1.017980 0.117870 0.000000 0.498145 0.000000 0.000000 0.000000 0.974192 0.000000 0.000000 0.000000 0.044773 0.846054 1.821494 -0.123103 0.000000 0.554620 0.000000 1.018845 0.000000 -1.167602 0.000000 0.500394 0.783899 0.000000 0.000000 -0.580925 0.218138 -0.764337 0.000000 0.000000 -0.047420 0.000000 0.413708 -1.770209 -1.232439 -0.288113 0.000000 0.000000 0.478543 -1.618900 0.000000 -0.380883 0.144176 0.000000 0.037254 0.000000 1.134371 -0.620055 -0.044773 0.047420 0.000000 0.534071 0.000000 0.249587 -0.858126 0.000000 0.745414 0.837549 -0.057849 0.000000 0.000000 -0.402569 1.144158 -0.006061 0.560297 0.000000 0.823535 0.000000 -0.846054 0.000000 -0.534071 0.000000 0.000000 -0.407707 0.000000 0.000000 0.000000 0.000000 0.000000 -0.057326 -0.201931 0.000000 -0.062113 0.875326 0.868491 1.001291 0.000000 -0.809692 -1.821494 -0.413708 0.000000 0.000000 0.000000 0.000000 0.215898 0.000000 -0.514651 -0.936590 0.385564 0.000000 0.000000 -0.199895 1.070267 0.599954 0.000000 0.000000 -0.511439 0.000000 0.123103 1.770209 -0.249587 0.407707 0.000000 0.000000 -1.565383 0.000000 0.000000 0.000000 -0.859810 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.997999 0.815916 0.595796 0.000000 1.232439 0.858126 0.000000 -0.215898 1.565383 0.000000 -0.564485 0.424548 0.000000 -1.204041 0.000000 0.000000 0.000000 0.000000 -0.157996 0.000000 0.000000 0.429771 1.217748 -0.554620 0.288113 0.000000 0.000000 0.000000 0.000000 0.564485 0.000000 0.000000 0.376512 0.000000 -0.263131 0.000000 0.000000 0.000000 0.057962 1.169896 0.840870 0.000000 0.461387 0.000000 0.000000 -0.745414 0.000000 0.514651 0.000000 -0.424548 0.000000 0.000000 -0.747744 -0.498561 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.018845 0.000000 -0.837549 0.000000 0.936590 0.000000 0.000000 -0.376512 0.747744 0.000000 1.067234 0.000000 0.000000 0.000000 -1.170473 -0.418728 0.000000 -0.184717 0.000000 -1.558316 0.000000 -0.478543 0.057849 0.000000 -0.385564 0.859810 1.204041 0.000000 0.498561 -1.067234 0.000000 0.000000 0.000000 0.000000 0.000000 -0.168840 0.000000 -1.460258 -0.563849 -1.017980 1.167602 1.618900 0.000000 0.057326 0.000000 0.000000 0.000000 0.263131 0.000000 0.000000 0.000000 0.000000 -1.906779 0.000000 -0.535341 -1.486227 0.000000 0.000000 0.181827 -0.117870 0.000000 0.000000 0.000000 0.201931 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.906779 0.000000 0.000000 -0.271655 -0.894457 0.000000 0.000000 0.000000 0.000000 -0.500394 0.380883 0.402569 0.000000 0.199895 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.202617 0.000000 -0.233115 -0.498145 -0.783899 -0.144176 -1.144158 0.062113 -1.070267 0.000000 0.000000 0.000000 0.000000 1.170473 0.000000 0.535341 0.271655 0.000000 0.000000 0.387888 -1.535393 0.117013 0.008016 0.000000 0.000000 0.000000 0.006061 -0.875326 -0.599954 0.000000 0.157996 -0.057962 0.000000 0.418728 0.168840 1.486227 0.894457 0.000000 -0.387888 0.000000 0.000000 0.236511 1.132251 0.000000 0.000000 -0.037254 -0.560297 -0.868491 0.000000 0.000000 0.000000 -1.169896 0.000000 0.000000 0.000000 0.000000 0.000000 0.202617 1.535393 0.000000 0.000000 0.122974 0.000000 0.000000 0.580925 0.000000 0.000000 -1.001291 0.000000 -0.997999 0.000000 -0.840870 0.000000 0.184717 1.460258 0.000000 0.000000 0.000000 -0.117013 -0.236511 -0.122974 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 194 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 12 22 33 45 59 69 79 87 97 107 113 122 132 141 147 152 165 177 185 194 Column indices: 2 3 4 5 7 8 9 13 14 16 17 18 3 4 6 8 9 10 12 13 14 16 0 4 5 6 7 9 11 13 15 16 19 0 1 4 6 7 8 9 12 13 15 16 18 0 1 2 3 5 7 8 10 11 12 15 16 17 18 0 2 4 7 13 14 16 17 18 19 1 2 3 8 10 11 12 15 16 17 0 2 3 4 5 8 12 19 0 1 3 4 6 7 9 10 12 17 0 1 2 3 8 11 13 17 18 19 1 4 6 8 11 12 2 4 6 9 10 12 16 17 19 1 3 4 6 7 8 10 11 17 19 0 1 2 3 5 9 14 16 17 0 1 5 13 16 17 2 3 4 6 18 0 1 2 3 4 5 6 11 13 14 17 18 19 0 4 5 6 8 9 11 12 13 14 16 19 0 3 4 5 9 15 16 19 2 5 7 9 11 12 16 17 18 Off-diagonal values: -0.974192 -0.218138 -1.134371 -0.823535 0.511439 -0.815916 -0.429771 0.563849 -0.181827 0.233115 -0.008016 -1.132251 0.764337 0.620055 0.809692 -0.595796 -1.217748 -0.461387 1.558316 1.017980 0.117870 0.498145 0.974192 0.044773 0.846054 1.821494 -0.123103 0.554620 1.018845 -1.167602 0.500394 0.783899 -0.580925 0.218138 -0.764337 -0.047420 0.413708 -1.770209 -1.232439 -0.288113 0.478543 -1.618900 -0.380883 0.144176 0.037254 1.134371 -0.620055 -0.044773 0.047420 0.534071 0.249587 -0.858126 0.745414 0.837549 -0.057849 -0.402569 1.144158 -0.006061 0.560297 0.823535 -0.846054 -0.534071 -0.407707 -0.057326 -0.201931 -0.062113 0.875326 0.868491 1.001291 -0.809692 -1.821494 -0.413708 0.215898 -0.514651 -0.936590 0.385564 -0.199895 1.070267 0.599954 -0.511439 0.123103 1.770209 -0.249587 0.407707 -1.565383 -0.859810 0.997999 0.815916 0.595796 1.232439 0.858126 -0.215898 1.565383 -0.564485 0.424548 -1.204041 -0.157996 0.429771 1.217748 -0.554620 0.288113 0.564485 0.376512 -0.263131 0.057962 1.169896 0.840870 0.461387 -0.745414 0.514651 -0.424548 -0.747744 -0.498561 -1.018845 -0.837549 0.936590 -0.376512 0.747744 1.067234 -1.170473 -0.418728 -0.184717 -1.558316 -0.478543 0.057849 -0.385564 0.859810 1.204041 0.498561 -1.067234 -0.168840 -1.460258 -0.563849 -1.017980 1.167602 1.618900 0.057326 0.263131 -1.906779 -0.535341 -1.486227 0.181827 -0.117870 0.201931 1.906779 -0.271655 -0.894457 -0.500394 0.380883 0.402569 0.199895 -0.202617 -0.233115 -0.498145 -0.783899 -0.144176 -1.144158 0.062113 -1.070267 1.170473 0.535341 0.271655 0.387888 -1.535393 0.117013 0.008016 0.006061 -0.875326 -0.599954 0.157996 -0.057962 0.418728 0.168840 1.486227 0.894457 -0.387888 0.236511 1.132251 -0.037254 -0.560297 -0.868491 -1.169896 0.202617 1.535393 0.122974 0.580925 -1.001291 -0.997999 -0.840870 0.184717 1.460258 -0.117013 -0.236511 -0.122974 . - o o o o - x o o - - - x o - x o o - | . - x x - x - o o o - x x x - x - - - x | . - x x x o - x - x - o - x x - - o x o | . o - x o o o - - x o - o x - x - x o o x . x - x o - x x o - - o x o x - x | o | o . - o - - - - - o o - o x x x | o o o | | . - x - o o x - - o x x - - o | x x o x | . o - - - o - - - - - - x x x | x x | o x . o x - o - - - - o - - x x o x | | | | x . - x - o - - - x x x | x | | o | x | o | . o o - - - - - - - | | o | o | x | | o x . x - - - o o - o | o | o x | o x x | x o . - - - - o - o o o x x | x | | | x | | | . o - o o - - x o | | | x | | | | | | | x . - o o - - | | o x x | x | | | | | | | | . - - o - o o o o o x o | | | | x | x x | . x o x x | | | x o o | x o | x x x x | o . - x x | | o o o | | | o | | | | | x x | . x | | x | | o | o | o | x x | | | o o o . The error in solving: 6.907250e-16 The error in solving: 3.554448e-16 The error in solving: 2.455476e-16 The error in solving: 4.164493e-16 The error in solving: 4.054506e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a standard normal distribution with a dense diagonal and a density of 0.750000 [ 0.000000 0.340390 -0.959396 -1.146751 -0.117725 0.156597 -0.144723 0.000000 0.865020 -0.611628 0.000000 0.933498 0.858417 0.097338 0.415810 -1.709267 -1.858682 0.173684 -0.408477 -0.285568 -0.340390 0.000000 0.000000 -0.462488 0.000000 0.000000 0.248621 0.305142 0.000000 -0.339708 0.224815 -1.121305 -1.472162 0.000000 0.351230 0.000000 0.321935 0.761206 0.553371 0.479141 0.959396 0.000000 0.000000 -1.116501 0.000000 0.539127 0.959391 0.439988 0.000000 -0.201703 0.000000 1.287656 -0.884887 0.000000 0.219856 0.024419 0.000000 1.890140 0.286705 0.678143 1.146751 0.462488 1.116501 0.000000 -1.199723 -0.308304 -0.245579 -0.063420 0.000000 -1.416099 -1.824977 -1.076352 -0.911318 0.194953 -0.006297 -0.251775 -1.970538 -0.331141 0.903950 -0.155213 0.117725 0.000000 0.000000 1.199723 0.000000 0.000000 0.878668 0.064098 0.000000 -1.436154 -0.811551 -2.059568 -0.738176 -1.121704 1.096080 0.000000 0.000000 0.821110 -2.030341 -0.825368 -0.156597 0.000000 -0.539127 0.308304 0.000000 0.000000 -0.840889 0.000000 0.000000 0.157961 0.000000 0.850838 0.000000 0.000000 0.764377 0.740819 -2.143280 -0.042012 0.000000 0.000000 0.144723 -0.248621 -0.959391 0.245579 -0.878668 0.840889 0.000000 -0.354841 -0.273722 0.108403 0.584933 0.352608 0.000000 0.770089 1.456344 0.000000 -0.334256 -1.979160 0.087167 0.971596 0.000000 -0.305142 -0.439988 0.063420 -0.064098 0.000000 0.354841 0.000000 1.059341 -0.456715 1.182437 0.000000 0.318329 0.197875 -1.381438 0.000000 -0.039471 0.630356 0.000000 0.940799 -0.865020 0.000000 0.000000 0.000000 0.000000 0.000000 0.273722 -1.059341 0.000000 -1.961997 0.000000 0.000000 0.000000 0.000000 -0.061122 1.989098 -0.693321 0.188717 -1.291722 0.144555 0.611628 0.339708 0.201703 1.416099 1.436154 -0.157961 -0.108403 0.456715 1.961997 0.000000 0.000000 0.000000 0.000000 0.000000 -0.665276 -1.096123 -0.589847 -0.684598 2.100542 0.980784 0.000000 -0.224815 0.000000 1.824977 0.811551 0.000000 -0.584933 -1.182437 0.000000 0.000000 0.000000 0.265150 1.074308 0.000000 0.998579 -1.341390 -1.289507 -1.271544 0.000000 -1.765542 -0.933498 1.121305 -1.287656 1.076352 2.059568 -0.850838 -0.352608 0.000000 0.000000 0.000000 -0.265150 0.000000 -0.245238 0.000000 0.000000 -0.365717 0.000000 -1.439657 -0.521093 0.000000 -0.858417 1.472162 0.884887 0.911318 0.738176 0.000000 0.000000 -0.318329 0.000000 0.000000 -1.074308 0.245238 0.000000 0.627733 1.197183 0.000000 0.000000 0.546915 0.000000 1.687834 -0.097338 0.000000 0.000000 -0.194953 1.121704 0.000000 -0.770089 -0.197875 0.000000 0.000000 0.000000 0.000000 -0.627733 0.000000 0.743137 1.118944 0.607173 0.781540 -1.021668 0.000000 -0.415810 -0.351230 -0.219856 0.006297 -1.096080 -0.764377 -1.456344 1.381438 0.061122 0.665276 -0.998579 0.000000 -1.197183 -0.743137 0.000000 1.254310 0.000000 2.285600 -1.146423 0.000000 1.709267 0.000000 -0.024419 0.251775 0.000000 -0.740819 0.000000 0.000000 -1.989098 1.096123 1.341390 0.365717 0.000000 -1.118944 -1.254310 0.000000 -0.740428 -1.967446 0.566148 0.000000 1.858682 -0.321935 0.000000 1.970538 0.000000 2.143280 0.334256 0.039471 0.693321 0.589847 1.289507 0.000000 0.000000 -0.607173 0.000000 0.740428 0.000000 0.055147 -1.333485 -0.055513 -0.173684 -0.761206 -1.890140 0.331141 -0.821110 0.042012 1.979160 -0.630356 -0.188717 0.684598 1.271544 1.439657 -0.546915 -0.781540 -2.285600 1.967446 -0.055147 0.000000 0.081572 0.000000 0.408477 -0.553371 -0.286705 -0.903950 2.030341 0.000000 -0.087167 0.000000 1.291722 -2.100542 0.000000 0.521093 0.000000 1.021668 1.146423 -0.566148 1.333485 -0.081572 0.000000 0.000000 0.285568 -0.479141 -0.678143 0.155213 0.825368 0.000000 -0.971596 -0.940799 -0.144555 -0.980784 1.765542 0.000000 -1.687834 0.000000 0.000000 0.000000 0.055513 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 274 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 17 30 43 61 74 84 101 115 125 140 152 164 176 187 203 216 230 248 262 274 Column indices: 1 2 3 4 5 6 8 9 11 12 13 14 15 16 17 18 19 0 3 6 7 9 10 11 12 14 16 17 18 19 0 3 5 6 7 9 11 12 14 15 17 18 19 0 1 2 4 5 6 7 9 10 11 12 13 14 15 16 17 18 19 0 3 6 7 9 10 11 12 13 14 17 18 19 0 2 3 6 9 11 14 15 16 17 0 1 2 3 4 5 7 8 9 10 11 13 14 16 17 18 19 1 2 3 4 6 8 9 10 12 13 14 16 17 19 0 6 7 9 14 15 16 17 18 19 0 1 2 3 4 5 6 7 8 14 15 16 17 18 19 1 3 4 6 7 11 12 14 15 16 17 19 0 1 2 3 4 5 6 10 12 15 17 18 0 1 2 3 4 7 10 11 13 14 17 19 0 3 4 6 7 12 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 12 13 15 17 18 0 2 3 5 8 9 10 11 13 14 16 17 18 0 1 3 5 6 7 8 9 10 13 15 17 18 19 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 0 1 2 3 4 6 8 9 11 13 14 15 16 17 0 1 2 3 4 6 7 8 9 10 12 16 Off-diagonal values: 0.340390 -0.959396 -1.146751 -0.117725 0.156597 -0.144723 0.865020 -0.611628 0.933498 0.858417 0.097338 0.415810 -1.709267 -1.858682 0.173684 -0.408477 -0.285568 -0.340390 -0.462488 0.248621 0.305142 -0.339708 0.224815 -1.121305 -1.472162 0.351230 0.321935 0.761206 0.553371 0.479141 0.959396 -1.116501 0.539127 0.959391 0.439988 -0.201703 1.287656 -0.884887 0.219856 0.024419 1.890140 0.286705 0.678143 1.146751 0.462488 1.116501 -1.199723 -0.308304 -0.245579 -0.063420 -1.416099 -1.824977 -1.076352 -0.911318 0.194953 -0.006297 -0.251775 -1.970538 -0.331141 0.903950 -0.155213 0.117725 1.199723 0.878668 0.064098 -1.436154 -0.811551 -2.059568 -0.738176 -1.121704 1.096080 0.821110 -2.030341 -0.825368 -0.156597 -0.539127 0.308304 -0.840889 0.157961 0.850838 0.764377 0.740819 -2.143280 -0.042012 0.144723 -0.248621 -0.959391 0.245579 -0.878668 0.840889 -0.354841 -0.273722 0.108403 0.584933 0.352608 0.770089 1.456344 -0.334256 -1.979160 0.087167 0.971596 -0.305142 -0.439988 0.063420 -0.064098 0.354841 1.059341 -0.456715 1.182437 0.318329 0.197875 -1.381438 -0.039471 0.630356 0.940799 -0.865020 0.273722 -1.059341 -1.961997 -0.061122 1.989098 -0.693321 0.188717 -1.291722 0.144555 0.611628 0.339708 0.201703 1.416099 1.436154 -0.157961 -0.108403 0.456715 1.961997 -0.665276 -1.096123 -0.589847 -0.684598 2.100542 0.980784 -0.224815 1.824977 0.811551 -0.584933 -1.182437 0.265150 1.074308 0.998579 -1.341390 -1.289507 -1.271544 -1.765542 -0.933498 1.121305 -1.287656 1.076352 2.059568 -0.850838 -0.352608 -0.265150 -0.245238 -0.365717 -1.439657 -0.521093 -0.858417 1.472162 0.884887 0.911318 0.738176 -0.318329 -1.074308 0.245238 0.627733 1.197183 0.546915 1.687834 -0.097338 -0.194953 1.121704 -0.770089 -0.197875 -0.627733 0.743137 1.118944 0.607173 0.781540 -1.021668 -0.415810 -0.351230 -0.219856 0.006297 -1.096080 -0.764377 -1.456344 1.381438 0.061122 0.665276 -0.998579 -1.197183 -0.743137 1.254310 2.285600 -1.146423 1.709267 -0.024419 0.251775 -0.740819 -1.989098 1.096123 1.341390 0.365717 -1.118944 -1.254310 -0.740428 -1.967446 0.566148 1.858682 -0.321935 1.970538 2.143280 0.334256 0.039471 0.693321 0.589847 1.289507 -0.607173 0.740428 0.055147 -1.333485 -0.055513 -0.173684 -0.761206 -1.890140 0.331141 -0.821110 0.042012 1.979160 -0.630356 -0.188717 0.684598 1.271544 1.439657 -0.546915 -0.781540 -2.285600 1.967446 -0.055147 0.081572 0.408477 -0.553371 -0.286705 -0.903950 2.030341 -0.087167 1.291722 -2.100542 0.521093 1.021668 1.146423 -0.566148 1.333485 -0.081572 0.285568 -0.479141 -0.678143 0.155213 0.825368 -0.971596 -0.940799 -0.144555 -0.980784 1.765542 -1.687834 0.055513 . x o o o x o - x o - x x x x o o x o o o . - o - - x x - o x o o - x - x x x x x | . o - x x x - o - x o - x x - x x x x x x . o o o o - o o o o x o o o o x o x | | x . - x x - o o o o o x - - x o o o | o x | . o - - x - x - - x x o o - - x o o x o x . o o x x x - x x - o o x x | o o x o | x . x o x - x x o - o x - x o | | | | | x o . o - - - - o x o x o x x x x x x o o x x . - - - - o o o o x x | o | x x | o o | | . x x - x o o o - o o x o x x o o | | | o . o - - o - o o - o x x x x | | o | | o x . x x - - x - x o | | o x | o o | | | | o . x x x x o - o o o x o o o x x x o | o o . x - x o - x | o x | o | | o x x x | o o . o o x - x o | x | x x x x x x | | o | x . x o o o o o x o x x o o x x x o o o x o . x - x o o o x | o | x o | x | x x o x o . - x o o x x | o o o o x | o | | | x | | . The error in solving: 3.787899e-16 The error in solving: 8.167877e-16 The error in solving: 3.983675e-16 The error in solving: 6.139255e-16 The error in solving: 7.774039e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a standard normal distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 -1.006877 0.000000 0.144371 0.000000 0.000000 0.000000 0.176200 0.000000 0.000000 0.000000 -1.483694 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.930408 0.000000 0.000000 0.000000 0.000000 0.000000 0.390824 0.000000 0.181934 0.000000 -1.935909 0.000000 0.000000 0.000000 0.000000 0.000000 1.516512 -1.312592 0.000000 0.000000 0.000000 0.000000 -0.368916 0.000000 0.000000 -0.726548 0.000000 0.000000 0.000000 0.000000 0.297154 0.000000 0.000000 0.000000 0.000000 -0.261749 0.000000 -0.814007 0.000000 0.000000 -0.018729 0.583451 0.000000 0.000000 0.000000 0.000000 -1.499330 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.261749 0.000000 0.000000 2.250967 0.000000 0.000000 0.000000 0.000000 0.000000 0.482649 0.000000 0.374978 0.000000 1.065003 0.000000 0.183397 -0.341550 1.006877 0.000000 -1.516512 0.000000 0.000000 0.000000 1.337657 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.340422 1.666218 0.000000 0.000000 0.000000 0.000000 -0.934564 0.000000 0.000000 1.312592 0.814007 -2.250967 -1.337657 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.579548 0.000000 0.000000 0.000000 -0.144371 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.851521 0.000000 0.000000 0.000000 0.000000 0.000000 -1.337149 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.947271 0.449198 0.561641 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.930408 0.000000 0.018729 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.583451 0.000000 0.000000 0.000000 -1.851521 0.000000 0.000000 0.000000 -0.131131 0.000000 0.241849 0.723737 -0.034988 0.000000 0.000000 0.000000 0.929590 -0.176200 0.000000 0.368916 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.131131 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.191619 0.000000 0.000000 0.000000 0.000000 0.000000 -0.482649 0.000000 0.000000 0.000000 0.947271 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.101208 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.340422 0.000000 0.000000 -0.449198 0.000000 -0.241849 0.000000 0.000000 0.000000 -0.208797 1.306382 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.726548 0.000000 -0.374978 -1.666218 0.000000 0.000000 -0.561641 0.000000 -0.723737 0.000000 0.000000 0.208797 0.000000 -0.963900 0.000000 0.000000 0.000000 0.000000 1.483694 -0.390824 0.000000 1.499330 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.034988 0.000000 0.000000 -1.306382 0.963900 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.065003 0.000000 1.579548 1.337149 0.000000 0.000000 0.000000 0.000000 0.101208 0.000000 0.000000 0.000000 0.000000 1.148800 0.000000 0.000000 0.000000 -0.181934 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.148800 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.183397 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.191619 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.398693 0.000000 1.935909 -0.297154 0.000000 0.341550 0.934564 0.000000 0.000000 0.000000 0.000000 -0.929590 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.398693 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 92 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 4 8 13 18 25 31 36 39 42 44 51 55 58 63 70 76 81 83 86 92 Column indices: 5 7 11 15 9 15 17 19 5 6 11 14 19 4 6 9 10 15 3 6 12 14 16 18 19 0 2 6 13 14 19 2 3 4 5 16 0 10 16 12 13 14 1 3 3 7 11 13 14 15 19 0 2 10 18 4 8 16 5 8 10 14 15 2 4 5 8 10 13 15 0 1 3 10 13 14 4 6 7 12 17 1 16 4 11 19 1 2 4 5 10 18 Off-diagonal values: -1.006877 0.144371 0.176200 -1.483694 0.930408 0.390824 0.181934 -1.935909 1.516512 -1.312592 -0.368916 -0.726548 0.297154 -0.261749 -0.814007 -0.018729 0.583451 -1.499330 0.261749 2.250967 0.482649 0.374978 1.065003 0.183397 -0.341550 1.006877 -1.516512 1.337657 0.340422 1.666218 -0.934564 1.312592 0.814007 -2.250967 -1.337657 -1.579548 -0.144371 1.851521 -1.337149 -0.947271 0.449198 0.561641 -0.930408 0.018729 -0.583451 -1.851521 -0.131131 0.241849 0.723737 -0.034988 0.929590 -0.176200 0.368916 0.131131 2.191619 -0.482649 0.947271 -0.101208 -0.340422 -0.449198 -0.241849 -0.208797 1.306382 0.726548 -0.374978 -1.666218 -0.561641 -0.723737 0.208797 -0.963900 1.483694 -0.390824 1.499330 0.034988 -1.306382 0.963900 -1.065003 1.579548 1.337149 0.101208 1.148800 -0.181934 -1.148800 -0.183397 -2.191619 0.398693 1.935909 -0.297154 0.341550 0.934564 -0.929590 -0.398693 . - - - - o - x - - - x - - - o - - - - | . - - - - - - - x - - - - - x - x - o | | . - - x o - - - - o - - o - - - - x | | | . o - o - - o x - - - - o - - - - | | | x . - x - - - - - x - x - x - x o x | o | | . x - - - - - - x x - - - - o | | x x o o . - - - - - - - - - o - - - o | | | | | | . - - x - - - - - o - - - | | | | | | | | . - - - o x x - - - - - | o | x | | | | | . - - - - - - - - - - | | | o | | | o | | . o - x x o - - - x o | x | | | | | | | x . - - - - - - x - | | | | o | | | x | | | . - - - o - - - | | | | | o | | o | o | | . o x - - - - | | x | o o | | o | o | | x . o - - - - x o | x | | | | | | x | | o x . - - - - | | | | o | x x | | | | x | | | . x - - | o | | | | | | | | | | | | | | o . - - | | | | o | | | | | | o | | | | | | . x | x o | x x | | | | o | | | | | | | o . The error in solving: 6.194323e-16 The error in solving: 3.795528e-16 The error in solving: 3.775166e-16 The error in solving: 5.006714e-16 The error in solving: 4.795875e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a standard normal distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 -0.588750 0.000000 0.253744 0.000000 -0.263562 0.000000 0.000000 0.000000 -1.175306 -0.842981 0.000000 0.000000 0.000000 0.000000 -1.775926 0.000000 0.000000 -0.180253 0.000000 0.000000 -0.406916 0.150828 1.182241 0.000000 -1.452100 0.000000 0.000000 0.000000 0.000000 0.988399 0.000000 1.226670 2.147781 -0.616343 0.000000 0.000000 0.705263 -2.399259 0.588750 0.406916 0.000000 -0.167469 1.254122 0.000000 0.000000 0.000000 0.000000 0.000000 -0.239620 0.000000 0.000000 0.000000 0.000000 -2.383722 -2.267133 0.000000 0.000000 0.000000 0.000000 -0.150828 0.167469 0.000000 0.000000 0.000000 0.113582 0.000000 0.000000 -0.778875 -0.919715 -0.273483 0.000000 0.000000 -0.634680 -1.605084 -0.592376 0.000000 -1.076240 0.000000 -0.253744 -1.182241 -1.254122 0.000000 0.000000 0.392370 0.000000 0.000000 0.523395 0.000000 0.000000 0.000000 1.205641 -0.963289 0.000000 0.000000 -0.739935 0.000000 0.327816 -0.475311 0.000000 0.000000 0.000000 0.000000 -0.392370 0.000000 -1.174249 0.371354 0.000000 0.000000 0.861211 0.000000 0.128408 0.000000 0.000000 0.053435 0.000000 0.000000 0.066352 -0.236666 0.263562 1.452100 0.000000 -0.113582 0.000000 1.174249 0.000000 0.000000 -1.317077 0.000000 0.589183 0.749081 -1.985783 0.000000 0.000000 2.406222 0.000000 0.873805 -1.612957 0.863180 0.000000 0.000000 0.000000 0.000000 0.000000 -0.371354 0.000000 0.000000 0.000000 -2.590050 0.088232 -0.323316 0.256162 -0.767287 -0.060989 0.000000 -1.016412 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.523395 0.000000 1.317077 0.000000 0.000000 0.490549 0.000000 0.000000 -0.609732 0.281496 0.000000 0.000000 0.000000 0.000000 -0.262140 0.000000 0.000000 0.000000 0.000000 0.778875 0.000000 0.000000 0.000000 2.590050 -0.490549 0.000000 -0.875510 -0.346546 0.310201 -1.349049 0.014235 1.154500 -0.041151 0.849706 -0.836848 0.519512 1.175306 0.000000 0.239620 0.919715 0.000000 -0.861211 -0.589183 -0.088232 0.000000 0.875510 0.000000 0.000000 -0.118068 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.833507 0.842981 -0.988399 0.000000 0.273483 0.000000 0.000000 -0.749081 0.323316 0.000000 0.346546 0.000000 0.000000 0.000000 -0.193443 0.000000 0.000000 -1.424342 2.046913 2.272187 0.000000 0.000000 0.000000 0.000000 0.000000 -1.205641 -0.128408 1.985783 -0.256162 0.609732 -0.310201 0.118068 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.009240 0.410511 0.000000 0.000000 -1.226670 0.000000 0.000000 0.963289 0.000000 0.000000 0.767287 -0.281496 1.349049 0.000000 0.193443 0.000000 0.000000 0.000000 -1.175945 0.000000 0.706903 0.000000 0.000000 0.000000 -2.147781 0.000000 0.634680 0.000000 0.000000 0.000000 0.060989 0.000000 -0.014235 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.704612 0.000000 1.277394 -0.602575 0.000000 0.616343 2.383722 1.605084 0.000000 -0.053435 -2.406222 0.000000 0.000000 -1.154500 0.000000 0.000000 0.000000 1.175945 0.000000 0.000000 0.000000 -0.460547 0.000000 -0.526984 1.775926 0.000000 2.267133 0.592376 0.739935 0.000000 0.000000 1.016412 0.000000 0.041151 0.000000 1.424342 0.000000 0.000000 0.704612 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.873805 0.000000 0.000000 -0.849706 0.000000 -2.046913 1.009240 -0.706903 0.000000 0.460547 0.000000 0.000000 0.000000 0.000000 0.000000 -0.705263 0.000000 1.076240 -0.327816 -0.066352 1.612957 0.000000 0.262140 0.836848 0.000000 -2.272187 -0.410511 0.000000 -1.277394 0.000000 0.000000 0.000000 0.000000 -1.821237 0.180253 2.399259 0.000000 0.000000 0.475311 0.236666 -0.863180 0.000000 0.000000 -0.519512 0.833507 0.000000 0.000000 0.000000 0.602575 0.526984 0.000000 0.000000 1.821237 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 178 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 7 17 24 34 44 52 64 72 78 91 100 110 119 127 134 143 151 157 168 178 Column indices: 2 4 6 10 11 16 19 2 3 4 6 11 13 14 15 18 19 0 1 3 4 10 15 16 1 2 6 9 10 11 14 15 16 18 0 1 2 5 8 12 13 16 18 19 4 6 7 10 12 15 18 19 0 1 3 5 8 10 11 12 15 17 18 19 5 9 10 11 12 13 14 16 4 6 9 12 13 18 3 7 8 10 11 12 13 14 15 16 17 18 19 0 2 3 5 6 7 9 12 19 0 1 3 6 7 9 13 16 17 18 4 5 6 7 8 9 10 17 18 1 4 7 8 9 11 15 17 1 3 7 9 16 18 19 1 2 3 5 6 9 13 17 19 0 2 3 4 7 9 11 14 6 9 11 12 13 15 1 3 4 5 6 8 9 11 12 14 19 0 1 4 5 6 9 10 14 15 18 Off-diagonal values: -0.588750 0.253744 -0.263562 -1.175306 -0.842981 -1.775926 -0.180253 -0.406916 0.150828 1.182241 -1.452100 0.988399 1.226670 2.147781 -0.616343 0.705263 -2.399259 0.588750 0.406916 -0.167469 1.254122 -0.239620 -2.383722 -2.267133 -0.150828 0.167469 0.113582 -0.778875 -0.919715 -0.273483 -0.634680 -1.605084 -0.592376 -1.076240 -0.253744 -1.182241 -1.254122 0.392370 0.523395 1.205641 -0.963289 -0.739935 0.327816 -0.475311 -0.392370 -1.174249 0.371354 0.861211 0.128408 0.053435 0.066352 -0.236666 0.263562 1.452100 -0.113582 1.174249 -1.317077 0.589183 0.749081 -1.985783 2.406222 0.873805 -1.612957 0.863180 -0.371354 -2.590050 0.088232 -0.323316 0.256162 -0.767287 -0.060989 -1.016412 -0.523395 1.317077 0.490549 -0.609732 0.281496 -0.262140 0.778875 2.590050 -0.490549 -0.875510 -0.346546 0.310201 -1.349049 0.014235 1.154500 -0.041151 0.849706 -0.836848 0.519512 1.175306 0.239620 0.919715 -0.861211 -0.589183 -0.088232 0.875510 -0.118068 -0.833507 0.842981 -0.988399 0.273483 -0.749081 0.323316 0.346546 -0.193443 -1.424342 2.046913 2.272187 -1.205641 -0.128408 1.985783 -0.256162 0.609732 -0.310201 0.118068 -1.009240 0.410511 -1.226670 0.963289 0.767287 -0.281496 1.349049 0.193443 -1.175945 0.706903 -2.147781 0.634680 0.060989 -0.014235 -0.704612 1.277394 -0.602575 0.616343 2.383722 1.605084 -0.053435 -2.406222 -1.154500 1.175945 -0.460547 -0.526984 1.775926 2.267133 0.592376 0.739935 1.016412 0.041151 1.424342 0.704612 -0.873805 -0.849706 -2.046913 1.009240 -0.706903 0.460547 -0.705263 1.076240 -0.327816 -0.066352 1.612957 0.262140 0.836848 -2.272187 -0.410511 -1.277394 -1.821237 0.180253 2.399259 0.475311 0.236666 -0.863180 -0.519512 0.833507 0.602575 0.526984 1.821237 . - o - x - o - - - o o - - - - o - - o | . o x x - o - - - - x - x x o - - x o x x . o x - - - - - o - - - - o o - - - | o x . - - x - - o o o - - o o o - o - o o o | . x - - x - - - x o - - o - x o | | | | o . o x - - x - x - - x - - x o x x | o | x . - o - x x o - - x - x o x | | | | | o | . - o x o x o o - o - - - | | | | o | x | . x - - o x - - - - o - | | | x | | | x o . o o x o x x o x o x x | x x | o o o | x . - o - - - - - - o x o | x | | o x | x | . - o - - o x x - | | | | o o x o x o x | . - - - - o x - | o | | x | | x o x | x | . - o - x - - | o | x | | | x | o | | | | . - o - x o | x x x | o o | | o | | | x | . - o - o x | x x x | | x | x | x | | x | . - - - | | | | | | o | | o | o x o | x | . - - | o | x o o x | x x | o o | o | | | . o x x | | x x o | | o x | | | x x | | x . The error in solving: 4.942227e-16 The error in solving: 6.162054e-16 The error in solving: 9.139771e-16 The error in solving: 3.974599e-16 The error in solving: 7.836977e-16 - MATRIX ------------------------------------------------------------------------------------------------------------------ A skew-symmetric matrix using a standard normal distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 0.000000 -0.531686 0.393272 -0.127824 -0.233919 0.000000 -0.848093 -2.457130 0.000000 -0.353890 -1.589482 0.270303 0.000000 1.033117 -0.184100 0.000000 0.990689 0.000000 0.000000 0.000000 0.298911 -1.117968 0.000000 0.000000 0.000000 -1.289627 -0.235680 0.597143 0.000000 0.983038 -1.957618 -0.675665 -0.042996 0.000000 -0.218332 0.000000 -0.080532 0.000000 0.000000 -0.298911 0.000000 0.000000 -0.020688 0.049247 0.935284 0.000000 0.000000 0.000000 0.000000 -0.071684 0.000000 0.000000 1.651673 0.000000 -0.719438 1.779342 -0.347398 -1.206604 0.531686 1.117968 0.000000 0.000000 0.000000 0.000000 0.010873 -0.307724 -1.231157 0.000000 0.000000 1.075334 -0.367880 -0.087302 0.000000 0.884623 -0.663142 0.472420 -1.008523 0.000000 -0.393272 0.000000 0.020688 0.000000 0.000000 0.000000 -2.473365 -1.019783 0.918199 0.306127 -1.463666 0.747259 -0.646553 -0.339711 2.182921 0.712664 0.226777 0.000000 0.000000 -0.103075 0.127824 0.000000 -0.049247 0.000000 0.000000 0.000000 0.408961 -1.167736 0.000000 2.916896 -0.032863 0.000000 0.000000 -0.647602 0.293362 0.000000 0.000000 0.000000 0.000000 -0.140728 0.233919 0.000000 -0.935284 -0.010873 2.473365 -0.408961 0.000000 -0.011802 0.000000 0.886631 0.000000 -0.530377 -0.128784 0.000000 0.000000 -0.212354 -1.065112 -0.696366 -1.228457 0.000000 0.000000 1.289627 0.000000 0.307724 1.019783 1.167736 0.011802 0.000000 0.342436 -0.585627 0.963898 -0.388043 -0.358539 0.000000 0.000000 -0.373810 1.066115 0.436961 0.000000 0.862762 0.848093 0.235680 0.000000 1.231157 -0.918199 0.000000 0.000000 -0.342436 0.000000 1.045339 0.000000 1.915044 0.678699 0.174019 0.000000 -1.269855 0.449061 0.783937 0.444397 0.000000 2.457130 -0.597143 0.000000 0.000000 -0.306127 -2.916896 -0.886631 0.585627 -1.045339 0.000000 -0.136092 0.000000 -1.503048 2.561783 0.031778 0.000000 0.000000 -0.219749 0.000000 -0.238796 0.000000 0.000000 0.000000 0.000000 1.463666 0.032863 0.000000 -0.963898 0.000000 0.136092 0.000000 0.000000 0.400017 1.005005 -0.004296 0.000000 -1.012388 0.000000 0.000000 -0.889410 0.353890 -0.983038 0.071684 -1.075334 -0.747259 0.000000 0.530377 0.388043 -1.915044 0.000000 0.000000 0.000000 0.000000 -0.160564 -1.313022 -0.680532 1.130103 0.541441 -0.387493 -0.275996 1.589482 1.957618 0.000000 0.367880 0.646553 0.000000 0.128784 0.358539 -0.678699 1.503048 -0.400017 0.000000 0.000000 -0.279194 0.566608 0.926477 0.486142 0.037699 -0.947950 -0.252701 -0.270303 0.675665 0.000000 0.087302 0.339711 0.647602 0.000000 0.000000 -0.174019 -2.561783 -1.005005 0.160564 0.279194 0.000000 1.511189 -0.478554 0.000000 -0.763069 0.000000 1.571058 0.000000 0.042996 -1.651673 0.000000 -2.182921 -0.293362 0.000000 0.000000 0.000000 -0.031778 0.004296 1.313022 -0.566608 -1.511189 0.000000 0.935379 -0.143936 0.000000 0.000000 -0.052766 -1.033117 0.000000 0.000000 -0.884623 -0.712664 0.000000 0.212354 0.373810 1.269855 0.000000 0.000000 0.680532 -0.926477 0.478554 -0.935379 0.000000 0.256515 2.019355 0.666590 1.215043 0.184100 0.218332 0.719438 0.663142 -0.226777 0.000000 1.065112 -1.066115 -0.449061 0.000000 1.012388 -1.130103 -0.486142 0.000000 0.143936 -0.256515 0.000000 0.000000 1.811714 -1.275583 0.000000 0.000000 -1.779342 -0.472420 0.000000 0.000000 0.696366 -0.436961 -0.783937 0.219749 0.000000 -0.541441 -0.037699 0.763069 0.000000 -2.019355 0.000000 0.000000 0.000000 -1.436370 -0.990689 0.080532 0.347398 1.008523 0.000000 0.000000 1.228457 0.000000 -0.444397 0.000000 0.000000 0.387493 0.947950 0.000000 0.000000 -0.666590 -1.811714 0.000000 0.000000 0.290265 0.000000 0.000000 1.206604 0.000000 0.103075 0.140728 0.000000 -0.862762 0.000000 0.238796 0.889410 0.275996 0.252701 -1.571058 0.052766 -1.215043 1.275583 1.436370 -0.290265 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 252 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 12 23 33 45 59 68 81 95 108 121 130 145 161 175 187 201 216 227 238 252 Column indices: 3 4 5 6 8 9 11 12 13 15 16 18 2 3 7 8 9 11 12 13 14 16 18 1 4 5 6 11 14 16 17 18 19 0 1 6 7 8 11 12 13 15 16 17 18 0 2 6 7 8 9 10 11 12 13 14 15 16 19 0 2 6 7 9 10 13 14 19 0 2 3 4 5 7 9 11 12 15 16 17 18 1 3 4 5 6 8 9 10 11 12 15 16 17 19 0 1 3 4 7 9 11 12 13 15 16 17 18 0 1 4 5 6 7 8 10 12 13 14 17 19 4 5 7 9 12 13 14 16 19 0 1 2 3 4 6 7 8 13 14 15 16 17 18 19 0 1 3 4 6 7 8 9 10 13 14 15 16 17 18 19 0 1 3 4 5 8 9 10 11 12 14 15 17 19 1 2 4 5 9 10 11 12 13 15 16 19 0 3 4 6 7 8 11 12 13 14 16 17 18 19 0 1 2 3 4 6 7 8 10 11 12 14 15 18 19 2 3 6 7 8 9 11 12 13 15 19 0 1 2 3 6 8 11 12 15 16 19 2 4 5 7 9 10 11 12 13 14 15 16 17 18 Off-diagonal values: -0.531686 0.393272 -0.127824 -0.233919 -0.848093 -2.457130 -0.353890 -1.589482 0.270303 1.033117 -0.184100 0.990689 0.298911 -1.117968 -1.289627 -0.235680 0.597143 0.983038 -1.957618 -0.675665 -0.042996 -0.218332 -0.080532 -0.298911 -0.020688 0.049247 0.935284 -0.071684 1.651673 -0.719438 1.779342 -0.347398 -1.206604 0.531686 1.117968 0.010873 -0.307724 -1.231157 1.075334 -0.367880 -0.087302 0.884623 -0.663142 0.472420 -1.008523 -0.393272 0.020688 -2.473365 -1.019783 0.918199 0.306127 -1.463666 0.747259 -0.646553 -0.339711 2.182921 0.712664 0.226777 -0.103075 0.127824 -0.049247 0.408961 -1.167736 2.916896 -0.032863 -0.647602 0.293362 -0.140728 0.233919 -0.935284 -0.010873 2.473365 -0.408961 -0.011802 0.886631 -0.530377 -0.128784 -0.212354 -1.065112 -0.696366 -1.228457 1.289627 0.307724 1.019783 1.167736 0.011802 0.342436 -0.585627 0.963898 -0.388043 -0.358539 -0.373810 1.066115 0.436961 0.862762 0.848093 0.235680 1.231157 -0.918199 -0.342436 1.045339 1.915044 0.678699 0.174019 -1.269855 0.449061 0.783937 0.444397 2.457130 -0.597143 -0.306127 -2.916896 -0.886631 0.585627 -1.045339 -0.136092 -1.503048 2.561783 0.031778 -0.219749 -0.238796 1.463666 0.032863 -0.963898 0.136092 0.400017 1.005005 -0.004296 -1.012388 -0.889410 0.353890 -0.983038 0.071684 -1.075334 -0.747259 0.530377 0.388043 -1.915044 -0.160564 -1.313022 -0.680532 1.130103 0.541441 -0.387493 -0.275996 1.589482 1.957618 0.367880 0.646553 0.128784 0.358539 -0.678699 1.503048 -0.400017 -0.279194 0.566608 0.926477 0.486142 0.037699 -0.947950 -0.252701 -0.270303 0.675665 0.087302 0.339711 0.647602 -0.174019 -2.561783 -1.005005 0.160564 0.279194 1.511189 -0.478554 -0.763069 1.571058 0.042996 -1.651673 -2.182921 -0.293362 -0.031778 0.004296 1.313022 -0.566608 -1.511189 0.935379 -0.143936 -0.052766 -1.033117 -0.884623 -0.712664 0.212354 0.373810 1.269855 0.680532 -0.926477 0.478554 -0.935379 0.256515 2.019355 0.666590 1.215043 0.184100 0.218332 0.719438 0.663142 -0.226777 1.065112 -1.066115 -0.449061 1.012388 -1.130103 -0.486142 0.143936 -0.256515 1.811714 -1.275583 -1.779342 -0.472420 0.696366 -0.436961 -0.783937 0.219749 -0.541441 -0.037699 0.763069 -2.019355 -1.436370 -0.990689 0.080532 0.347398 1.008523 1.228457 -0.444397 0.387493 0.947950 -0.666590 -1.811714 0.290265 1.206604 0.103075 0.140728 -0.862762 0.238796 0.889410 0.275996 0.252701 -1.571058 0.052766 -1.215043 1.275583 1.436370 -0.290265 . - - o x o o - o o - o o x - x o - x - | . x o - - - o o x - x o o o - o - o - | o . - o x x - - - - o - - x - o x o o x x | . - - x o o - - x o o - x o x o - o | x | . - o o x x o x o o x x x - - o x | o | | . x o - x o - - o x - - - - o x | o o x o . o - x - o o - - o o o o - | x | x x x x . x o x o o - - o x x - x x x | x o | | o . x - x x x - o x x x - x o | | o o o x o . o - o x x - - o - o | | | | x x | o | x . - x x o - o - - o x o x o o | x x o | | . - o o o x x o o x x | x x | x x o x o | . o x x x x o o o x | x x x | | o o o x x . x o - o - x | x o | o o | | | o x x o o . x o - - o o | | o o | x x x | | x o x o . x x x x x x x x o | x o o | x o o | x o . - x o | | o o | | x o o x | o o x | o | . - o o x x x | | x | o | | x x | | o o | . x | | x | x x | o | x x x x o x o x x o . The error in solving: 5.930218e-16 The error in solving: 6.350510e-16 The error in solving: 5.311767e-16 The error in solving: 6.965557e-16 The error in solving: 6.391344e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.013802 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.154184 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.776293 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.069815 0.979663 0.663470 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.343529 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.158794 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.552571 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.168162 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.984221 0.000000 0.608746 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.346646 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.406940 0.291853 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 10 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.776293 0.979663 0.000000 0.000000 0.000000 0.552571 0.168162 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.406940 0.000000 Row indices: 0 0 1 1 2 2 4 5 5 6 6 6 8 8 9 9 9 9 9 10 10 Column indices: 2 2 4 6 5 9 10 12 12 19 Off-diagonal values: 0.013802 0.154184 0.069815 0.663470 0.343529 0.158794 0.984221 0.608746 0.346646 0.291853 . - - - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | x x x - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | x . x - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | x . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | | . The error in solving: 1.359740e-16 The error in solving: 4.611103e-16 The error in solving: 2.676651e-16 The error in solving: 3.554448e-16 The error in solving: 2.719480e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.500000 [ 0.761511 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.043098 0.785098 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.094132 0.301319 0.259911 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.932161 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.118497 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.417788 0.518036 0.996824 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.098704 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.595335 0.000000 0.489307 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.441263 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.940495 0.430105 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.958889 0.912476 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.033816 0.000000 0.660531 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.829606]; Dimension: 20 x 20 Off-diagonal entries: 19 (max 380) Diagonal entries: 0.761511 0.785098 0.301319 0.000000 0.000000 0.000000 0.000000 0.064326 0.294615 0.118497 0.518036 0.000000 0.000000 0.000000 0.000000 0.940495 0.000000 0.912476 0.000000 0.829606 Row indices: 0 0 1 3 4 5 6 6 7 9 9 11 12 12 14 15 16 16 17 19 19 Column indices: 0 1 3 4 3 4 6 7 9 9 11 10 12 14 15 16 16 17 19 Off-diagonal values: 0.043098 0.094132 0.259911 0.932161 0.000782 0.055705 0.081524 0.612016 0.109207 0.417788 0.996824 0.098704 0.595335 0.489307 0.441263 0.430105 0.958889 0.033816 0.660531 x - - - - - - - - - - - - - - - - - - - x x - - - - - - - - - - - - - - - - - - | x x x - - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | | x . - - - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | x x x - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | x x x - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | x . x - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | x . x | | | | | | | | | | | | | | | | | | | x The error in solving: 1.595946e-16 The error in solving: 1.241267e-16 The error in solving: 1.146625e-16 The error in solving: 1.271920e-16 The error in solving: 2.662221e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.750000 [ 0.469638 0.136284 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.221997 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0.838815 0.814913 0.860650 0.573648 0.694717 0.034778 0.335794 x x - - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - | x x x - - - - - - - - - - - - - - - - | | | x - - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | x x x - - - - - - - - - - - | | | | | | | x . x - - - - - - - - - - | | | | | | | | x x x - - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | x x x - - - - - - - | | | | | | | | | | | x . - - - - - - - | | | | | | | | | | | | x . x - - - - - | | | | | | | | | | | | | x . x - - - - | | | | | | | | | | | | | | x x x - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | x x x | | | | | | | | | | | | | | | | | | x . The error in solving: 3.491581e-16 The error in solving: 4.003567e-16 The error in solving: 3.703056e-16 The error in solving: 3.576729e-16 The error in solving: 3.723801e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.598807 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.919408 0.000000 0.000000 0.361363 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.650405 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.786554 0.000000 0.170341 0.000000 0.324541 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.662645 0.443434 0.649526 0.345524 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.610844 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.220619 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.503227 0.000000 0.616136 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.527878 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.740903 0.000000 0.436246 0.532324 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.269006 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.344319 0.000000 0.915853 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.505165 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.858768 0.000000 0.000000 0.540141 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.388136 0.041956 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.874607 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 24 (max 380) Diagonal entries: 0.000000 0.000000 0.650405 0.170341 0.443434 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.041956 0.000000 0.000000 Row indices: 0 1 3 3 5 8 9 10 12 13 16 16 17 17 17 19 20 22 23 24 24 Column indices: 2 0 3 1 5 3 5 6 4 4 6 8 10 8 10 11 10 13 15 13 14 17 16 19 Off-diagonal values: 0.598807 0.919408 0.361363 0.786554 0.324541 0.662645 0.649526 0.345524 0.610844 0.220619 0.503227 0.616136 0.527878 0.740903 0.436246 0.532324 0.269006 0.344319 0.915853 0.505165 0.858768 0.540141 0.388136 0.874607 . - x - - - - - - - - - - - - - - - - - x . - x - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | x | x - x - - - - - - - - - - - - - - | | | x x x x - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | x | . - - - - - - - - - - - - - | | | | | | x . x - - - - - - - - - - - | | | | | | | | . - x - - - - - - - - - | | | | | | | | x . x x - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | x . x - - - - | | | | | | | | | | | | | x | . - - - - | | | | | | | | | | | | | | x | . x - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | | . The error in solving: 3.858424e-16 The error in solving: 2.618456e-16 The error in solving: 2.543841e-16 The error in solving: 6.475144e-16 The error in solving: 5.147892e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.500000 [ 0.269314 0.000000 0.425149 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.571465 0.733458 0.000000 0.119424 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.156055 0.812900 0.034614 0.000000 0.214808 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.811128 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.173779 0.000000 0.876905 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.682947 0.000000 0.000000 0.000000 0.540296 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.762783 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.611022 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.416951 0.000000 0.777866 0.320504 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.655714 0.929236 0.825825 0.691198 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.415651 0.000000 0.690463 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.572526 0.000000 0.000000 0.972052 0.151892 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.614198 0.017002 0.731250 0.119469 0.913348 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.905823 0.000000 0.000000 0.529654 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.888036 0.000000 0.273752 0.206238 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.678149 0.917306 0.062236 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 33 (max 380) Diagonal entries: 0.269314 0.000000 0.000000 0.034614 0.000000 0.876905 0.000000 0.000000 0.000000 0.000000 0.825825 0.415651 0.000000 0.731250 0.000000 0.000000 0.273752 0.678149 0.000000 0.000000 Row indices: 0 1 1 4 7 8 9 11 12 13 16 19 20 23 27 27 29 31 33 33 33 Column indices: 2 0 1 3 1 2 5 6 3 4 8 8 7 8 10 11 8 9 11 13 10 13 14 11 12 14 15 13 16 14 17 18 19 Off-diagonal values: 0.425149 0.571465 0.733458 0.119424 0.156055 0.812900 0.214808 0.811128 0.173779 0.682947 0.540296 0.762783 0.611022 0.416951 0.777866 0.320504 0.655714 0.929236 0.691198 0.690463 0.572526 0.972052 0.151892 0.614198 0.017002 0.119469 0.913348 0.905823 0.529654 0.888036 0.206238 0.917306 0.062236 x - x - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - x x . x - - - - - - - - - - - - - - - - | x x x - x - - - - - - - - - - - - - - | | | | . - x - - - - - - - - - - - - - | | | x | x - - - - - - - - - - - - - - | | | | x | . - x - - - - - - - - - - - | | | | | | | . x - - - - - - - - - - - | | | | | | | x . - - - - - - - - - - - | | | | | | | | x . x x - - - - - - - - | | | | | | | | x x x x - - - - - - - - | | | | | | | | | | | x - x - - - - - - | | | | | | | | | | x | . x x - - - - - | | | | | | | | | | | x x x x x - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | x | . x - - - | | | | | | | | | | | | | | x | x x - - | | | | | | | | | | | | | | | | | x x x | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 4.017411e-16 The error in solving: 3.555125e-16 The error in solving: 4.065089e-16 The error in solving: 2.237726e-16 The error in solving: 3.167664e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.750000 [ 0.104085 0.953261 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.282658 0.337114 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.021258 0.000000 0.000000 0.760377 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.002432 0.291744 0.091661 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0.054933 0.201647 0.855775 0.643527 x x - - - - - - - - - - - - - - - - - - x x - - - - - - - - - - - - - - - - - - | x . - x - - - - - - - - - - - - - - - | | x x x x - - - - - - - - - - - - - - | | x x x x x - - - - - - - - - - - - - | | | | x x x x - - - - - - - - - - - - | | | | | | x x x - - - - - - - - - - - | | | | | | x x x x - - - - - - - - - - | | | | | | x x x x x - - - - - - - - - | | | | | | | x x x x x - - - - - - - - | | | | | | | | x x x x x - - - - - - - | | | | | | | | | x x x x x - - - - - - | | | | | | | | | | | x . x x - - - - - | | | | | | | | | | | x x x x x - - - - | | | | | | | | | | | | x x x - x - - - | | | | | | | | | | | | | x x . x x - - | | | | | | | | | | | | | | x | . x x - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | x x x | | | | | | | | | | | | | | | | | x x x The error in solving: 2.938193e-16 The error in solving: 4.095711e-16 The error in solving: 3.248707e-16 The error in solving: 5.236912e-16 The error in solving: 4.186402e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.855737 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.998852 0.534296 0.183056 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.373469 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.728809 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.530419 0.199218 0.933890 0.813734 0.863782 0.718935 0.709209 0.396722 0.676883 0.202439 0.389249 0.796872 Row indices: 0 0 2 2 2 3 3 3 4 5 5 5 6 8 8 8 8 9 10 11 11 Column indices: 0 2 5 6 7 12 11 13 17 18 19 Off-diagonal values: 0.998852 0.183056 0.784087 0.035136 0.917288 0.447882 0.537860 0.459663 0.118665 0.443844 0.386789 x - - - - - - - - - - - - - - - - - - - x x x - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | | x - - - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | | x x - - - - - - - | | | | | | | | | | | x x x - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | | x The error in solving: 2.482534e-16 The error in solving: 1.110223e-16 The error in solving: 1.665335e-16 The error in solving: 4.163336e-17 The error in solving: 5.117875e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.279920 0.132317 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.735899 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.885458 0.852815 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.444171]; Dimension: 20 x 20 Off-diagonal entries: 17 (max 380) Diagonal entries: 0.279920 0.735899 0.852815 0.693487 0.103331 0.534945 0.075569 0.999823 0.881984 0.413182 0.824521 0.989038 0.024822 0.687511 0.557621 0.324430 0.488607 0.432906 0.968719 0.444171 Row indices: 0 1 1 2 3 4 5 7 8 10 10 10 10 10 12 13 14 14 16 17 17 Column indices: 1 1 4 5 6 5 7 8 7 9 12 14 13 14 16 18 17 Off-diagonal values: 0.132317 0.885458 0.690647 0.934692 0.796236 0.805540 0.016495 0.199145 0.361797 0.283534 0.014893 0.995445 0.984375 0.733614 0.555630 0.838538 0.154905 x x - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - | | | x x - - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | x x x - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | x x x - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | x x x - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | | x x x - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | | x The error in solving: 5.551115e-17 The error in solving: 1.501112e-16 The error in solving: 2.723019e-16 The error in solving: 2.543841e-16 The error in solving: 1.359740e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.452791 0.094277 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.136397 0.150086 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.381270 0.106468 0.330957 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.455151 0.086637 0.072313 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.442358 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.288091 0.096910 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.697876 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.537318 0.590551 0.559035 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.551302 0.750640 0.987610 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.233182 0.988029 0.461516 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.058851 0.731645 0.503647 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.175547 0.529031 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.933846 0.949638 0.190355 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.213528 0.912874 0.473990 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.702729]; Dimension: 20 x 20 Off-diagonal entries: 29 (max 380) Diagonal entries: 0.452791 0.150086 0.106468 0.086637 0.442358 0.288091 0.697876 0.590551 0.750640 0.988029 0.731645 0.529031 0.736873 0.195513 0.707914 0.591241 0.764666 0.949638 0.912874 0.702729 Row indices: 0 1 2 4 6 6 7 7 9 11 13 15 17 18 20 21 23 25 27 29 29 Column indices: 1 0 1 3 2 4 6 6 8 7 9 8 10 9 11 10 12 13 12 14 15 14 16 15 17 16 18 17 19 Off-diagonal values: 0.094277 0.136397 0.381270 0.330957 0.455151 0.072313 0.096910 0.537318 0.559035 0.551302 0.987610 0.233182 0.461516 0.058851 0.503647 0.175547 0.711613 0.954115 0.764834 0.161911 0.974909 0.110963 0.198298 0.705811 0.696109 0.933846 0.190355 0.213528 0.473990 x x - - - - - - - - - - - - - - - - - - x x - - - - - - - - - - - - - - - - - - | x x x - - - - - - - - - - - - - - - - | | x x x - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | x x x - - - - - - - - - - - | | | | | | | x x x - - - - - - - - - - | | | | | | | | x x x - - - - - - - - - | | | | | | | | | x x x - - - - - - - - | | | | | | | | | | x x x - - - - - - - | | | | | | | | | | | | x x - - - - - - | | | | | | | | | | | | x x x - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | x x x - - - | | | | | | | | | | | | | | | x x x - - | | | | | | | | | | | | | | | | x x x - | | | | | | | | | | | | | | | | | x x x | | | | | | | | | | | | | | | | | | | x The error in solving: 3.855928e-16 The error in solving: 2.373467e-16 The error in solving: 5.295426e-16 The error in solving: 4.871084e-16 The error in solving: 2.803189e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.238556 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.401842 0.000000 0.534579 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.080912 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.731445 0.000000 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0.000000 0.327935]; Dimension: 20 x 20 Off-diagonal entries: 15 (max 380) Diagonal entries: 0.238556 0.401842 0.080912 0.731445 0.937968 0.836559 0.740899 0.432558 0.652370 0.035795 0.346788 0.376623 0.890933 0.263655 0.637912 0.417979 0.634525 0.043391 0.469738 0.327935 Row indices: 0 0 1 1 1 2 3 3 4 5 6 8 10 12 12 12 13 14 14 15 15 Column indices: 3 6 6 5 7 8 11 12 10 13 10 11 17 15 16 Off-diagonal values: 0.534579 0.931795 0.142567 0.773145 0.357556 0.463701 0.634147 0.071983 0.408432 0.394264 0.157004 0.540490 0.814624 0.849869 0.339329 x - - - - - - - - - - - - - - - - - - - | x - x - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | | x - - - - - - - - - - - - - - - - | | | | x - x - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | x | x - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | | x x x - - - - - - - | | | | | | | | | | x x - x - - - - - - | | | | | | | | | | x x x - - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | x - x - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | x | x - | | | | | | | | | | | | | | | | | | | x The error in solving: 1.366804e-16 The error in solving: 5.467214e-16 The error in solving: 3.002225e-16 The error in solving: 2.294037e-16 The error in solving: 2.292987e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.483490 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.206988 0.427080 0.324795 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.962103 0.255609 0.393393 0.371027 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.086150 0.155829 0.394800 0.486410 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.636519 0.000000 0.045271 0.663119 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.333156 0.948768 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.066486 0.000000 0.125831 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.230115 0.000000 0.448351 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.464396 0.519225 0.260749 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.142446 0.000000 0.497371 0.520183 0.553271 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.970305 0.864362 0.931551 0.595470 0.879006 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.196617 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.308920 0.511400 0.609145 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.502723 0.000000 0.034431 0.000000 0.578575 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.330223 0.658342 0.905796 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.882000 0.146549 0.490217 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.071919 0.000000 0.015581 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.514264 0.242186 0.236694 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.179776 0.308457 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.666179]; Dimension: 20 x 20 Off-diagonal entries: 34 (max 380) Diagonal entries: 0.483490 0.427080 0.255609 0.155829 0.045271 0.333156 0.125831 0.230115 0.260749 0.497371 0.931551 0.196617 0.609145 0.034431 0.658342 0.146549 0.015581 0.242186 0.308457 0.666179 Row indices: 0 0 2 5 8 10 11 12 13 15 18 22 22 24 26 28 30 31 33 34 34 Column indices: 0 2 1 3 4 2 4 5 2 5 6 4 9 6 7 7 10 11 8 9 11 12 10 11 11 15 13 15 14 16 14 16 18 17 Off-diagonal values: 0.206988 0.324795 0.962103 0.393393 0.371027 0.086150 0.394800 0.486410 0.636519 0.663119 0.948768 0.066486 0.448351 0.464396 0.519225 0.142446 0.520183 0.553271 0.970305 0.864362 0.595470 0.879006 0.308920 0.511400 0.502723 0.578575 0.330223 0.905796 0.882000 0.490217 0.071919 0.514264 0.236694 0.179776 x - - - - - - - - - - - - - - - - - - - x x x - - - - - - - - - - - - - - - - - | x x x x - - - - - - - - - - - - - - - | | x x x x - - - - - - - - - - - - - - | | x | x x - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | x | x - - - - - - - - - - - - - | | | | | | | x - x - - - - - - - - - - | | | | | | x x x - - - - - - - - - - - | | | | | | | x | x x x - - - - - - - - | | | | | | | | x x x x x - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | x x x - - - - - - - | | | | | | | | | | | x | x - x - - - - | | | | | | | | | | | | | x x x - - - - | | | | | | | | | | | | | | x x x - - - | | | | | | | | | | | | | | x | x - - - | | | | | | | | | | | | | | | | x x x - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | | x The error in solving: 3.925231e-16 The error in solving: 2.543841e-16 The error in solving: 4.172578e-16 The error in solving: 4.619579e-16 The error in solving: 4.089240e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.733159 0.753959 0.573423 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.907625 0.883511 0.002241 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.482827 0.082527 0.524666 0.000000 0.192376 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.375644 0.787712 0.719662 0.726953 0.448006 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.790067 0.286842 0.000000 0.404856 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.758036 0.911799 0.011569 0.000000 0.141568 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.638570 0.292548 0.265527 0.672887 0.893470 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.855611 0.848095 0.967733 0.905905 0.416959 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.799978 0.934131 0.731341 0.053317 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.686551 0.371152 0.825172 0.006888 0.604768 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.123140 0.703503 0.387011 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.806162 0.742514 0.776026 0.313224 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.446587 0.000000 0.814536 0.144386 0.592708 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.691487 0.572477 0.076504 0.548489 0.911953 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.406233 0.257225 0.610078 0.000000 0.275760 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.274206 0.528635 0.878036 0.000000 0.324357 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.713889 0.346312 0.805674 0.766164 0.325609 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.154439 0.291757 0.363773 0.653236 0.614714 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.738154 0.288007 0.198176 0.963423 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.803811 0.358293 0.270365]; Dimension: 20 x 20 Off-diagonal entries: 62 (max 380) Diagonal entries: 0.733159 0.883511 0.524666 0.719662 0.286842 0.011569 0.265527 0.967733 0.731341 0.825172 0.123140 0.742514 0.814536 0.076504 0.610078 0.878036 0.805674 0.363773 0.198176 0.270365 Row indices: 0 2 4 7 11 13 16 20 24 27 31 33 36 39 43 46 49 53 57 60 62 Column indices: 1 2 0 2 0 1 4 1 2 4 5 3 6 3 4 7 4 5 7 8 5 6 8 9 6 7 9 7 8 10 11 11 12 10 12 13 10 13 14 11 12 14 15 12 13 16 13 14 17 14 15 17 18 15 16 18 19 16 17 19 17 18 Off-diagonal values: 0.753959 0.573423 0.907625 0.002241 0.482827 0.082527 0.192376 0.375644 0.787712 0.726953 0.448006 0.790067 0.404856 0.758036 0.911799 0.141568 0.638570 0.292548 0.672887 0.893470 0.855611 0.848095 0.905905 0.416959 0.799978 0.934131 0.053317 0.686551 0.371152 0.006888 0.604768 0.703503 0.387011 0.806162 0.776026 0.313224 0.446587 0.144386 0.592708 0.691487 0.572477 0.548489 0.911953 0.406233 0.257225 0.275760 0.274206 0.528635 0.324357 0.713889 0.346312 0.766164 0.325609 0.154439 0.291757 0.653236 0.614714 0.738154 0.288007 0.963423 0.803811 0.358293 x x x - - - - - - - - - - - - - - - - - x x x - - - - - - - - - - - - - - - - - x x x - x - - - - - - - - - - - - - - - | x x x x x - - - - - - - - - - - - - - | | | x x - x - - - - - - - - - - - - - | | | x x x - x - - - - - - - - - - - - | | | | x x x x x - - - - - - - - - - - | | | | | x x x x x - - - - - - - - - - | | | | | | x x x x - - - - - - - - - - | | | | | | | x x x x x - - - - - - - - | | | | | | | | | | x x x - - - - - - - | | | | | | | | | | x x x x - - - - - - | | | | | | | | | | x | x x x - - - - - | | | | | | | | | | | x x x x x - - - - | | | | | | | | | | | | x x x - x - - - | | | | | | | | | | | | | x x x - x - - | | | | | | | | | | | | | | x x x x x - | | | | | | | | | | | | | | | x x x x x | | | | | | | | | | | | | | | | x x x x | | | | | | | | | | | | | | | | | x x x The error in solving: 5.802281e-16 The error in solving: 2.849386e-16 The error in solving: 5.795534e-16 The error in solving: 8.204343e-16 The error in solving: 4.627909e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.177308 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.124480 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 1 1 2 2 2 3 4 4 5 5 5 5 6 6 7 7 7 7 Column indices: 0 3 8 7 9 15 17 Off-diagonal values: 0.177308 0.124480 0.049445 0.123617 0.496629 0.167478 0.490865 . - - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | x . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . x - - - - - - - - - - - | | | | | | | x . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | x . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.662221e-16 The error in solving: 5.721958e-17 The error in solving: 3.376612e-16 The error in solving: 4.441028e-16 The error in solving: 1.570116e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.427276 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.695324 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.466199 0.000000 0.431565 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.083763 0.000000 0.153723 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.588543 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.416969 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.520741 0.000000 0.013814 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.698320 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.994657 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.777870 0.000000 0.348653 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.176522 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.829083 0.000000 0.822859 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.983213 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.496373 0.000000 0.222977 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.193063 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 21 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 1 1 2 4 6 7 8 10 11 12 12 14 15 17 18 20 21 21 Column indices: 1 5 4 6 5 7 8 9 8 10 9 12 12 14 15 14 16 17 16 18 17 Off-diagonal values: 0.427276 0.695324 0.466199 0.431565 0.083763 0.153723 0.588543 0.416969 0.520741 0.013814 0.698320 0.994657 0.777870 0.348653 0.176522 0.829083 0.822859 0.983213 0.496373 0.222977 0.193063 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | x . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | | x . x - - - - - - - - - - - - - | | | | | x . x - - - - - - - - - - - - | | | | | | | . x - - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | | x . x - - - - - - - - - | | | | | | | | | x . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | x . x - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | x . x - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | x . x - | | | | | | | | | | | | | | | | | x . - | | | | | | | | | | | | | | | | | | | . The error in solving: 4.005371e-16 The error in solving: 2.588868e-16 The error in solving: 8.092071e-17 The error in solving: 3.895681e-16 The error in solving: 4.079220e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.331223 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.105179 0.000000 0.850730 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.886898 0.000000 0.240248 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.138778 0.000000 0.902663 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.162905 0.000000 0.597744 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.888522 0.000000 0.328995 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.570818 0.000000 0.070882 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.144930 0.000000 0.802287 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.139815 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.543805 0.000000 0.018917 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.259365 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.810614 0.000000 0.910483 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.121859 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.020151 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.978303 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.742144 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.734498 0.000000 0.806527 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.936277 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 28 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 5 7 9 11 13 15 16 16 18 19 21 21 22 23 24 25 27 28 Column indices: 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 11 12 11 13 13 14 17 18 17 19 18 Off-diagonal values: 0.331223 0.105179 0.850730 0.886898 0.240248 0.138778 0.902663 0.162905 0.597744 0.888522 0.328995 0.570818 0.070882 0.144930 0.802287 0.139815 0.543805 0.018917 0.259365 0.810614 0.910483 0.121859 0.020151 0.978303 0.742144 0.734498 0.806527 0.936277 . x - - - - - - - - - - - - - - - - - - x . x - - - - - - - - - - - - - - - - - | x . x - - - - - - - - - - - - - - - - | | x . x - - - - - - - - - - - - - - - | | | x . x - - - - - - - - - - - - - - | | | | x . x - - - - - - - - - - - - - | | | | | x . x - - - - - - - - - - - - | | | | | | x . x - - - - - - - - - - - | | | | | | | x . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | x . x - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | x . x - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | x . - - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | | x . x | | | | | | | | | | | | | | | | | | x . The error in solving: 2.513374e-16 The error in solving: 4.510281e-16 The error in solving: 2.737128e-16 The error in solving: 4.005521e-16 The error in solving: 2.544787e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.476782 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.198790 0.000000 0.000000 0.854352 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.855302 0.000000 0.372613 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.402358 0.000000 0.000000 0.198814 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.024791 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.580149 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.700748 0.453355 0.000000 0.716501 0.973128 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.588659 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.573423 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.144876 0.000000 0.000000 0.000000 0.074515 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.579724 0.000000 0.000000 0.615045 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.984423 0.294737 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.876233 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.828773 0.000000 0.916469 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 24 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 3 5 5 7 8 9 13 14 14 15 17 19 21 22 22 22 24 24 Column indices: 2 0 3 2 4 3 6 4 9 6 7 9 10 7 10 10 14 11 14 12 13 13 17 19 Off-diagonal values: 0.476782 0.198790 0.854352 0.855302 0.372613 0.402358 0.198814 0.024791 0.580149 0.700748 0.453355 0.716501 0.973128 0.588659 0.573423 0.144876 0.074515 0.579724 0.615045 0.984423 0.294737 0.876233 0.828773 0.916469 . - x - - - - - - - - - - - - - - - - - x . - x - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | x . x - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | x | . x - - - - - - - - - - - - - | | | | x | . - - - - - - - - - - - - - | | | | | | | . - x - - - - - - - - - - | | | | | | x x . x x - - - - - - - - - | | | | | | | x | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | x | . - x - - - - - | | | | | | | | | | | x | . x - - - - - | | | | | | | | | | | | x x . - - - - - | | | | | | | | | | | | | x | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | x . x | | | | | | | | | | | | | | | | | | | . The error in solving: 2.077037e-16 The error in solving: 2.966732e-16 The error in solving: 3.140185e-16 The error in solving: 2.833924e-16 The error in solving: 2.514332e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.254461 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.208892 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.003878 0.919524 0.000000 0.000000 0.015723 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.642925 0.000000 0.000000 0.907385 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.513283 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.535532 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.972482 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.590048 0.370963 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.309231 0.000000 0.065727 0.777267 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.952775 0.000000 0.000000 0.766506 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.281579 0.000000 0.000000 0.448056 0.646157 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.076216 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.450681 0.000000 0.000000 0.770376 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.374702 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.876139 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.123525 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.473972 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.241505 0.000000 0.000000 0.000000 0.411489 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.400412 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.487722 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 31 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 5 7 8 9 10 12 15 17 20 21 23 24 25 26 27 29 30 31 Column indices: 1 2 0 1 4 1 4 5 3 8 8 9 7 9 10 8 11 8 11 12 13 10 13 11 15 17 18 15 19 19 17 Off-diagonal values: 0.254461 0.208892 0.003878 0.919524 0.015723 0.642925 0.907385 0.513283 0.535532 0.972482 0.590048 0.370963 0.309231 0.065727 0.777267 0.952775 0.766506 0.281579 0.448056 0.646157 0.076216 0.450681 0.770376 0.374702 0.876139 0.123525 0.473972 0.241505 0.411489 0.400412 0.487722 . x - - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - x x . - x - - - - - - - - - - - - - - - | x | . x - - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | x | . - - - - - - - - - - - - - - | | | | | | . - x - - - - - - - - - - - | | | | | | | . x x - - - - - - - - - - | | | | | | | x . x x - - - - - - - - - | | | | | | | | x . - x - - - - - - - - | | | | | | | | x | . x x - - - - - - - | | | | | | | | | | | . - x - - - - - - | | | | | | | | | | x | . x - - - - - - | | | | | | | | | | | x | . - - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | | . - x - - | | | | | | | | | | | | | | | | . - x - | | | | | | | | | | | | | | | x | . - x | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | x | . The error in solving: 3.848428e-16 The error in solving: 3.402182e-16 The error in solving: 3.343834e-16 The error in solving: 2.276126e-16 The error in solving: 4.720488e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.766322 0.762065 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.376558 0.000000 0.232583 0.070386 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.587895 0.667053 0.000000 0.201852 0.032908 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.591194 0.000000 0.000000 0.630949 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.652910 0.334299 0.000000 0.321668 0.738750 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.949966 0.000000 0.178836 0.248527 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.551518 0.336914 0.000000 0.539332 0.386412 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.601731 0.278435 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.229078 0.000000 0.000000 0.873201 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.798693 0.000000 0.986020 0.912888 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.720502 0.000000 0.724171 0.969059 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.718462 0.405941 0.000000 0.828319 0.105472 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.910478 0.994064 0.000000 0.557090 0.753333 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.861497 0.000000 0.000000 0.237638 0.367852 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.700181 0.610183 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.704615 0.166204 0.000000 0.867697 0.001452 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.306733 0.446542 0.000000 0.151832 0.865309 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.020992 0.759348 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.611238 0.954876 0.000000 0.268768 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.610888 0.158842 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 60 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 5 9 11 15 18 22 24 26 29 32 36 40 43 45 49 53 55 58 60 Column indices: 1 2 0 2 3 0 1 3 4 1 4 2 3 5 6 4 6 7 4 5 7 8 8 9 6 9 8 10 11 9 11 12 9 10 12 13 10 11 13 14 11 14 15 12 13 13 14 16 17 14 15 17 18 18 19 16 17 19 17 18 Off-diagonal values: 0.766322 0.762065 0.376558 0.232583 0.070386 0.587895 0.667053 0.201852 0.032908 0.591194 0.630949 0.652910 0.334299 0.321668 0.738750 0.949966 0.178836 0.248527 0.551518 0.336914 0.539332 0.386412 0.601731 0.278435 0.229078 0.873201 0.798693 0.986020 0.912888 0.720502 0.724171 0.969059 0.718462 0.405941 0.828319 0.105472 0.910478 0.994064 0.557090 0.753333 0.861497 0.237638 0.367852 0.700181 0.610183 0.704615 0.166204 0.867697 0.001452 0.306733 0.446542 0.151832 0.865309 0.020992 0.759348 0.611238 0.954876 0.268768 0.610888 0.158842 . x x - - - - - - - - - - - - - - - - - x . x x - - - - - - - - - - - - - - - - x x . x x - - - - - - - - - - - - - - - | x | . x - - - - - - - - - - - - - - - | | x x . x x - - - - - - - - - - - - - | | | | x . x x - - - - - - - - - - - - | | | | x x . x x - - - - - - - - - - - | | | | | | | . x x - - - - - - - - - - | | | | | | x | . x - - - - - - - - - - | | | | | | | | x . x x - - - - - - - - | | | | | | | | | x . x x - - - - - - - | | | | | | | | | x x . x x - - - - - - | | | | | | | | | | x x . x x - - - - - | | | | | | | | | | | x | . x x - - - - | | | | | | | | | | | | x x . - - - - - | | | | | | | | | | | | | x x . x x - - | | | | | | | | | | | | | | x x . x x - | | | | | | | | | | | | | | | | | . x x | | | | | | | | | | | | | | | | x x . x | | | | | | | | | | | | | | | | | x x . The error in solving: 4.910463e-16 The error in solving: 3.775804e-16 The error in solving: 6.206723e-16 The error in solving: 5.440730e-16 The error in solving: 5.995848e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 -0.884592 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.659872 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.762589 0.868596 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.428477 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.050598 0.000000 -0.934390 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.924427 0.395150 -0.069614 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.404805 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.546669 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.551354 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.447083 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.149874 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.897023 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.551793 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 12 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.868596 0.000000 0.000000 0.395150 -0.404805 0.000000 0.000000 0.000000 0.000000 0.000000 0.551354 0.000000 0.000000 0.897023 0.000000 0.000000 Row indices: 0 1 1 2 2 3 4 6 8 8 9 9 9 9 9 9 10 11 11 12 12 Column indices: 1 1 3 4 5 7 6 8 10 16 15 17 Off-diagonal values: -0.884592 -0.659872 -0.762589 -0.428477 0.050598 -0.934390 -0.924427 -0.069614 -0.546669 0.447083 0.149874 0.551793 . o - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | o . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | o x - - - - - - - - - - - - - - - | | | | o . - - - - - - - - - - - - - - | | | | | x . o - - - - - - - - - - - - | | | | | | o x o - - - - - - - - - - - | | | | | | | | o - - - - - - - - - - - | | | | | | | | | . o - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | x . - - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | x . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.241267e-16 The error in solving: 1.118863e-16 The error in solving: 1.361509e-16 The error in solving: 4.484587e-16 The error in solving: 1.146493e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.475304 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.205906 0.000000 -0.127307 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.004851 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.377698 0.926542 0.446436 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.687336 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.055539 -0.368333 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.867037 0.108433 0.014863 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.112687 0.976595 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.548951 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.435308 0.657696 0.594521 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.728919 0.343730 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.444411 0.272322 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.056074]; Dimension: 20 x 20 Off-diagonal entries: 20 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.926542 -0.687336 0.000000 0.055539 0.108433 -0.259061 0.000000 0.000000 0.185659 0.000000 0.976595 0.000000 0.657696 -0.728919 0.272322 0.056074 Row indices: 0 1 1 3 4 6 6 6 7 9 10 12 13 13 14 15 16 18 19 20 20 Column indices: 1 1 3 2 3 5 8 7 9 8 9 11 10 12 13 16 15 17 18 17 Off-diagonal values: 0.475304 0.205906 -0.127307 0.004851 0.377698 0.446436 -0.368333 0.867037 0.014863 0.198335 -0.287460 -0.273802 0.892699 0.675618 0.112687 0.548951 -0.435308 0.594521 0.343730 0.444411 . x - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | x . o - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | | x x x - - - - - - - - - - - - - - | | | | | o - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | x o - - - - - - - - - - - | | | | | | | x x x - - - - - - - - - - | | | | | | | | x o - - - - - - - - - - | | | | | | | | | o . o - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | x . - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | o x x - - | | | | | | | | | | | | | | | | | o x - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | | x The error in solving: 2.733607e-16 The error in solving: 3.353719e-16 The error in solving: 3.260542e-16 The error in solving: 4.980560e-16 The error in solving: 4.720488e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.750000 [ -0.172147 -0.110427 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.331920 0.778998 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.902926 -0.081126 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.976603 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.053239 0.000000 0.000000 0.000000 0.000000 0.000000 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-0.081126 -0.976603 0.053239 0.558875 0.538854 -0.491049 0.318640 -0.752628 0.733317 -0.051196 0.805142 -0.266683 0.160578 o o - - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - | o o x - - - - - - - - - - - - - - - - | | | o o - - - - - - - - - - - - - - - | | | x x x - - - - - - - - - - - - - - | | | | x o o - - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | o x - - - - - - - - - - - | | | | | | | | x o - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | o . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | x . x - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | o o - - - - | | | | | | | | | | | | | | x x o - - - | | | | | | | | | | | | | | | x o o - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | x o | | | | | | | | | | | | | | | | | | x o The error in solving: 6.686678e-16 The error in solving: 2.989367e-16 The error in solving: 5.087681e-16 The error in solving: 1.359740e-16 The error in solving: 2.779025e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.693016 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.878308 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.933771 -0.085976 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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entries: 17 (max 380) Diagonal entries: 0.000000 0.000000 0.878308 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.262591 0.000000 -0.978847 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 1 1 3 4 5 6 6 6 8 8 10 10 11 13 13 15 15 16 17 Column indices: 1 1 2 2 6 7 7 8 9 13 11 12 16 14 18 19 18 Off-diagonal values: 0.693016 0.933771 -0.085976 -0.577357 -0.674741 -0.376433 0.182562 -0.171437 -0.575660 0.398920 -0.203602 0.711063 -0.432176 -0.654709 0.683179 0.291289 0.197838 . x - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | x o . - - - - - - - - - - - - - - - - | | o | . - - - - - - - - - - - - - - - | | | | | . o - - - - - - - - - - - - - | | | | | | . o - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | x o . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | o | o - x - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | o | o - - - - - - | | | | | | | | | | | | x | . - o - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | o | . - x - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | x . The error in solving: 2.220446e-16 The error in solving: 3.152427e-16 The error in solving: 2.482534e-16 The error in solving: 1.387779e-16 The error in solving: 7.850462e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.500000 [ 0.262817 -0.980666 0.806603 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.219758 0.000000 0.980112 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.011724 0.127794 0.000000 0.000000 -0.509144 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.680769 0.000000 0.000000 0.938436 -0.135888 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.779332 -0.393721 -0.879020 -0.868004 -0.405131 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.076691 0.190460 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.219611 -0.532652 0.296145 0.904780 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.976212 0.000000 0.000000 0.000000 0.093076 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.274134 -0.507609 -0.049619 0.000000 -0.269195 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.572714 0.000000 0.195405 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.890288 0.706715 0.000000 0.034043 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.280223 0.379218 0.000000 -0.261522 -0.214691 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.626978 -0.919281 0.669687 0.000000 0.429820 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.778375 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.562405 0.629984 -0.680490 -0.272188 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.011361 0.000000 -0.270840 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.157019 0.000000 0.323720 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.700121 0.492052 0.000000 0.001343 0.118031 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.168323 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.339296 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 46 (max 380) Diagonal entries: 0.262817 -0.219758 0.000000 0.000000 -0.879020 0.000000 -0.532652 0.000000 -0.049619 0.000000 0.706715 0.000000 0.669687 0.000000 -0.680490 -0.270840 -0.157019 0.000000 0.000000 0.000000 Row indices: 0 2 3 6 9 13 15 18 20 23 25 27 31 34 35 38 39 40 44 45 46 Column indices: 1 2 3 0 1 4 1 4 5 2 3 5 6 3 4 5 7 8 5 9 6 7 10 8 10 9 12 9 10 12 13 10 11 14 14 12 13 15 13 18 15 16 18 19 17 17 Off-diagonal values: -0.980666 0.806603 0.980112 -0.011724 0.127794 -0.509144 -0.680769 0.938436 -0.135888 0.779332 -0.393721 -0.868004 -0.405131 -0.076691 0.190460 -0.219611 0.296145 0.904780 0.976212 0.093076 0.274134 -0.507609 -0.269195 -0.572714 0.195405 0.890288 0.034043 0.280223 0.379218 -0.261522 -0.214691 0.626978 -0.919281 0.429820 0.778375 -0.562405 0.629984 -0.272188 -0.011361 0.323720 -0.700121 0.492052 0.001343 0.118031 -0.168323 -0.339296 x o x - - - - - - - - - - - - - - - - - | o - x - - - - - - - - - - - - - - - - o x . - o - - - - - - - - - - - - - - - | o | . x o - - - - - - - - - - - - - - | | x o o o o - - - - - - - - - - - - - | | | o x . - - - - - - - - - - - - - - | | | | | o o x x - - - - - - - - - - - | | | | | x | . - x - - - - - - - - - - | | | | | | x o o - o - - - - - - - - - | | | | | | | | o . x - - - - - - - - - | | | | | | | | | x x - x - - - - - - - | | | | | | | | | x x . o o - - - - - - | | | | | | | | | | x o x - x - - - - - | | | | | | | | | | | | | . x - - - - - | | | | | | | | | | | | o x o o - - - - | | | | | | | | | | | | | o | o - - - - | | | | | | | | | | | | | | | | o - x - | | | | | | | | | | | | | | | o x . x x | | | | | | | | | | | | | | | | | o . - | | | | | | | | | | | | | | | | | o | . The error in solving: 4.910463e-16 The error in solving: 6.132977e-16 The error in solving: 5.986782e-16 The error in solving: 6.856526e-16 The error in solving: 5.689893e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.750000 [ -0.329559 0.000000 -0.692380 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.771531 0.722050 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.583118 0.771698 0.569059 -0.159497 -0.203087 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.830003 0.000000 0.336783 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0.000000 0.000000 0.000000 -0.213430 0.921359 -0.026894]; Dimension: 20 x 20 Off-diagonal entries: 57 (max 380) Diagonal entries: -0.329559 0.000000 0.569059 0.336783 0.892484 -0.396872 0.000000 0.706914 0.237619 -0.637378 0.000000 0.000000 -0.291530 -0.750614 -0.735307 0.000000 0.223740 0.000000 0.245853 -0.026894 Row indices: 0 1 3 7 10 13 16 18 22 26 30 33 37 39 40 43 45 49 53 55 57 Column indices: 2 2 3 0 1 3 4 1 4 5 3 5 6 3 6 7 7 8 5 6 8 9 6 7 9 10 7 8 10 11 9 11 12 9 10 12 13 10 11 15 13 15 16 14 17 14 15 17 18 15 16 18 19 16 19 17 18 Off-diagonal values: -0.692380 0.771531 0.722050 0.583118 0.771698 -0.159497 -0.203087 0.830003 -0.003270 0.188584 0.864212 0.969957 -0.866833 0.101013 -0.046198 -0.025507 -0.100602 -0.541759 0.146383 -0.926267 0.605183 -0.566323 -0.772267 -0.744127 0.645060 0.692312 0.260415 0.306148 -0.869809 -0.700530 0.872606 -0.219196 -0.064906 0.993196 0.626566 0.797406 -0.887934 0.874402 -0.542534 -0.609863 0.182028 -0.366433 0.214637 -0.115508 -0.673216 0.933548 0.205667 0.879873 -0.722520 -0.677602 0.716300 -0.612467 -0.296919 0.505693 0.024053 -0.213430 0.921359 o - o - - - - - - - - - - - - - - - - - | . x x - - - - - - - - - - - - - - - - x x x o o - - - - - - - - - - - - - - - | x | x o x - - - - - - - - - - - - - - | | | x x x o - - - - - - - - - - - - - | | | x | o o o - - - - - - - - - - - - | | | | | | . o o - - - - - - - - - - - | | | | | x o x x o - - - - - - - - - - | | | | | | o o x x x - - - - - - - - - | | | | | | | x x o o o - - - - - - - - | | | | | | | | | x . o o - - - - - - - | | | | | | | | | x x . x o - - - - - - | | | | | | | | | | x o o - - - - - - - | | | | | | | | | | | | | o - o - - - - | | | | | | | | | | | | | x o o x - - - | | | | | | | | | | | | | | o . - o - - | | | | | | | | | | | | | | x x x x o - | | | | | | | | | | | | | | | o x . o o | | | | | | | | | | | | | | | | x | x x | | | | | | | | | | | | | | | | | o x o The error in solving: 4.397310e-16 The error in solving: 5.095719e-16 The error in solving: 3.640110e-16 The error in solving: 4.510281e-16 The error in solving: 1.002376e-15 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.250000 [ -0.609670 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.551082 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.962496 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.571713 -0.188767 0.014756 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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7 (max 380) Diagonal entries: -0.609670 -0.551082 0.962496 -0.188767 -0.216175 0.273684 0.033241 0.495992 0.781921 0.506789 -0.813088 -0.294928 -0.151136 0.561367 -0.602877 0.540665 -0.961810 -0.898312 0.367940 0.752414 Row indices: 0 0 0 0 2 2 3 5 5 5 5 5 5 5 5 5 5 6 7 7 7 Column indices: 2 4 4 5 7 15 16 Off-diagonal values: 0.571713 0.014756 -0.631953 0.301502 -0.237181 0.688294 0.318271 o - - - - - - - - - - - - - - - - - - - | o - - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | x o x - - - - - - - - - - - - - - - | | | | o - - - - - - - - - - - - - - - | | | | o x - - - - - - - - - - - - - - | | | | | x x o - - - - - - - - - - - - | | | | | | | x - - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | o - - - - - - - - - | | | | | | | | | | | o - - - - - - - - | | | | | | | | | | | | o - - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | o - - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | x o - - - | | | | | | | | | | | | | | | | x o - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | x The error in solving: 0.000000e+00 The error in solving: 1.570092e-16 The error in solving: 1.243205e-16 The error in solving: 1.241267e-16 The error in solving: 1.110223e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.500000 [ -0.129679 0.814294 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.763145 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.338501 0.000000 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0.000000 0.000000 0.000000 0.000000 -0.383062 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.530808]; Dimension: 20 x 20 Off-diagonal entries: 11 (max 380) Diagonal entries: -0.129679 0.763145 -0.338501 -0.472106 0.222934 -0.316439 0.795015 -0.205554 0.908747 -0.705088 0.038632 -0.944864 0.523396 0.572874 -0.296864 -0.026610 -0.403447 0.514271 -0.383062 -0.530808 Row indices: 0 1 1 1 2 2 3 3 3 5 6 7 7 8 8 9 10 11 11 11 11 Column indices: 1 4 6 7 9 10 9 11 15 16 17 Off-diagonal values: 0.814294 -0.216316 -0.587236 0.861251 -0.697670 0.145973 -0.970158 -0.770630 0.485000 -0.114424 0.867873 o x - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | | o - - - - - - - - - - - - - - - - - | | | o o - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | o o - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | | o - - - - - - - - - - - - | | | | | | | x x o - - - - - - - - - - | | | | | | | | | o x - - - - - - - - - | | | | | | | | | o x - - - - - - - - - | | | | | | | | | | | o - - - - - - - - | | | | | | | | | | | o x - - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | o x - - - - | | | | | | | | | | | | | | | o o - - - | | | | | | | | | | | | | | | | o x - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | | o - | | | | | | | | | | | | | | | | | | | o The error in solving: 2.775558e-17 The error in solving: 5.214799e-16 The error in solving: 8.326673e-17 The error in solving: 5.551115e-17 The error in solving: 2.603704e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.037540 -0.052167 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.433771 0.576552 0.901069 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.610327 0.900034 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.514397 0.641967 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.174766 0.505799 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.669866 -0.494589 -0.578424 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.987433 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.053204 0.961936 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.022131 0.280793 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.513047]; Dimension: 20 x 20 Off-diagonal entries: 29 (max 380) Diagonal entries: 0.037540 0.576552 0.900034 -0.514397 -0.174766 -0.494589 0.904611 -0.755996 -0.825424 0.558594 0.086996 -0.332579 -0.977778 -0.347516 -0.509635 -0.200219 0.987433 0.961936 0.280793 0.513047 Row indices: 0 1 3 4 5 6 8 10 12 14 16 18 20 22 24 26 26 27 28 29 29 Column indices: 1 0 2 1 4 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 15 16 17 Off-diagonal values: -0.052167 0.433771 0.901069 0.610327 0.641967 0.505799 -0.669866 -0.578424 0.572055 -0.195253 -0.352243 -0.832538 -0.022879 -0.357670 0.529280 -0.371760 0.796984 -0.943384 0.287812 -0.051499 0.740058 -0.969006 -0.119078 -0.718665 0.769517 -0.717222 0.967096 -0.053204 0.022131 x o - - - - - - - - - - - - - - - - - - x x x - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - | | | o x - - - - - - - - - - - - - - - | | | | o x - - - - - - - - - - - - - - | | | | o o o - - - - - - - - - - - - - | | | | | x x o - - - - - - - - - - - - | | | | | | o o o - - - - - - - - - - - | | | | | | | o o o - - - - - - - - - - | | | | | | | | x x o - - - - - - - - - | | | | | | | | | x x o - - - - - - - - | | | | | | | | | | x o o - - - - - - - | | | | | | | | | | | x o o - - - - - - | | | | | | | | | | | | o o o - - - - - | | | | | | | | | | | | | x o o - - - - | | | | | | | | | | | | | | | o - - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | | o x - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | | x The error in solving: 3.188873e-16 The error in solving: 2.884444e-16 The error in solving: 3.472915e-16 The error in solving: 2.288783e-16 The error in solving: 9.029098e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.250000 [ -0.510667 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.911425 0.000000 0.882587 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.168700 -0.401373 0.029086 -0.407206 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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- - - - - - - - - | | | | o | x - o - - - - - - - - - - - | | | | | | o x - - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | o o - - - - - - - - - | | | | | | | | x | x o x - - - - - - - | | | | | | | | | | x x - o - - - - - - | | | | | | | | | | | | o x - - - - - - | | | | | | | | | | | | x o - o - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | o o - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | | o o - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | o The error in solving: 2.355139e-16 The error in solving: 2.077037e-16 The error in solving: 3.145643e-16 The error in solving: 5.770661e-16 The error in solving: 1.624353e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.500000 [ -0.467939 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8 5 6 8 6 11 8 9 11 10 13 10 11 14 12 13 15 16 13 14 15 17 18 19 16 17 19 17 Off-diagonal values: -0.067597 0.504524 -0.465525 -0.381002 -0.041589 -0.952689 -0.839648 0.721683 -0.547030 0.008338 -0.608381 0.868780 -0.031815 0.990144 -0.052956 -0.996179 0.930903 -0.468912 0.089180 0.073581 -0.474940 0.776503 -0.782559 -0.592571 0.979839 0.269136 -0.423201 -0.295738 -0.679383 0.018976 -0.415270 0.327427 0.272910 -0.071397 0.381340 0.981422 -0.882041 0.268251 0.450539 0.391924 o - o - - - - - - - - - - - - - - - - - x o o - - - - - - - - - - - - - - - - - | o o o - - - - - - - - - - - - - - - - | o | x - o - - - - - - - - - - - - - - | | | x o - o - - - - - - - - - - - - - | | | x | x o - - - - - - - - - - - - - | | | | x | o - o - - - - - - - - - - - | | | | | x o x o - - - - - - - - - - - | | | | | | x | x - - - - - - - - - - - | | | | | | | | | x - o - - - - - - - - | | | | | | | | x x x o - - - - - - - - | | | | | | | | | | x x - o - - - - - - | | | | | | | | | | o x x - x - - - - - | | | | | | | | | | | | o x - - - - - - | | | | | | | | | | | | | o o o x - - - | | | | | | | | | | | | | o x o - - - - | | | | | | | | | | | | | | | x o o - - | | | | | | | | | | | | | | | | | o x x | | | | | | | | | | | | | | | | o x x x | | | | | | | | | | | | | | | | | x | o The error in solving: 7.002441e-16 The error in solving: 3.908636e-16 The error in solving: 6.036471e-16 The error in solving: 3.906788e-16 The error in solving: 3.261280e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.750000 [ -0.790829 0.313697 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.866847 0.566991 0.022435 0.819508 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.839239 0.507363 0.855592 -0.275099 0.247004 -0.880406 0.943329 -0.581972 0.888336 0.111423 0.030375 -0.821391 -0.703002 0.006732 0.087973 -0.886655 0.907027 -0.409908 0.556946 0.968586 0.416693 0.162417 -0.478003 0.590356 -0.743604 -0.028314 0.862943 -0.414297 -0.072497 -0.274225 0.243378 0.468608 -0.275846 -0.273760 0.925498 0.793986 0.148938 -0.739536 -0.109661 0.312911 o x - - - - - - - - - - - - - - - - - - x x x x - - - - - - - - - - - - - - - - o o o - o - - - - - - - - - - - - - - - | x o o o o - - - - - - - - - - - - - - | | o o o o - - - - - - - - - - - - - - | | | x | o - x - - - - - - - - - - - - | | | | | | x x x - - - - - - - - - - - | | | | | x | x o x - - - - - - - - - - | | | | | | o x x - o - - - - - - - - - | | | | | | | x x x x o - - - - - - - - | | | | | | | | o x o x o - - - - - - - | | | | | | | | | | x x o x - - - - - - | | | | | | | | | | | | x x x - - - - - | | | | | | | | | | | x o x x - - - - - | | | | | | | | | | | | o o x - x - - - | | | | | | | | | | | | | o o x o x - - | | | | | | | | | | | | | | | x x o o - | | | | | | | | | | | | | | | | x o - x | | | | | | | | | | | | | | | | x | x o | | | | | | | | | | | | | | | | | o x o The error in solving: 4.554500e-16 The error in solving: 4.069914e-16 The error in solving: 3.779080e-16 The error in solving: 4.440892e-16 The error in solving: 3.976416e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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o - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . o - - - - - - | | | | | | | | | | | | | . o - - - - - | | | | | | | | | | | | | | . o - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 3.179801e-17 The error in solving: 1.241267e-16 The error in solving: 3.236829e-16 The error in solving: 2.254874e-16 The error in solving: 3.188873e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.598314 0.000000 0.193703 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.642897 0.000000 0.243134 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.838088 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.341410 0.000000 -0.039726 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.318521 0.000000 0.124945 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.999572 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.289398 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.225825 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.408408 0.000000 0.932616 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 14 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 2 4 4 4 5 5 7 9 9 10 11 11 11 11 12 14 14 14 Column indices: 1 3 2 4 5 7 9 8 10 12 13 17 16 18 Off-diagonal values: 0.598314 0.193703 0.642897 0.243134 -0.838088 0.341410 -0.039726 -0.318521 0.124945 -0.999572 0.289398 0.225825 -0.408408 0.932616 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | x . x - - - - - - - - - - - - - - - - | | x . x - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | o . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | x . o - - - - - - - - - - | | | | | | | | o . x - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . o - - - - - - - | | | | | | | | | | | | . x - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | o . x - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.077037e-16 The error in solving: 2.486410e-16 The error in solving: 3.376612e-16 The error in solving: 2.776425e-16 The error in solving: 2.618456e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.754551 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.350158 0.000000 0.150208 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.818224 0.000000 -0.186650 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.725640 0.000000 -0.841522 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.912101 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.685743 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000209 0.000000 0.378983 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.408979 0.000000 -0.899017 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.166196 0.000000 0.804999 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.521125 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.498218 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.906508 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.694883 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.418183 0.000000 -0.239507 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.326501 0.000000 -0.422096 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.786158 0.000000 0.670989 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.640947 0.000000 0.126719 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.854205 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 28 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 3 5 7 8 9 11 13 15 15 16 17 18 19 21 23 25 27 28 Column indices: 1 0 2 2 4 3 5 4 7 6 8 7 9 8 10 10 13 14 13 14 16 15 17 16 18 17 19 18 Off-diagonal values: 0.754551 0.350158 0.150208 -0.818224 -0.186650 -0.725640 -0.841522 0.912101 -0.685743 0.000209 0.378983 0.408979 -0.899017 0.166196 0.804999 -0.521125 0.498218 -0.906508 -0.694883 -0.418183 -0.239507 0.326501 -0.422096 0.786158 0.670989 -0.640947 0.126719 0.854205 . x - - - - - - - - - - - - - - - - - - x . x - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | o . o - - - - - - - - - - - - - - - | | | o . o - - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | | | . o - - - - - - - - - - - - | | | | | | x . x - - - - - - - - - - - | | | | | | | x . o - - - - - - - - - - | | | | | | | | x . x - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | o . - - - - - - - - | | | | | | | | | | | | . x - - - - - - | | | | | | | | | | | | | . o - - - - - | | | | | | | | | | | | | o . - - - - - | | | | | | | | | | | | | | o . o - - - | | | | | | | | | | | | | | | x . o - - | | | | | | | | | | | | | | | | x . x - | | | | | | | | | | | | | | | | | o . x | | | | | | | | | | | | | | | | | | x . The error in solving: 3.425453e-16 The error in solving: 2.224779e-16 The error in solving: 3.610893e-16 The error in solving: 3.554448e-16 The error in solving: 3.727073e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.868723 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.668031 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.134749 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.058605 0.000000 0.000000 0.000000 -0.928177 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.113043 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.571936 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.899450 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.397549 -0.614656 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.281323 0.000000 -0.345596 0.978573 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.478952 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.132862 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 15 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 2 3 5 5 5 5 6 6 7 8 10 10 13 13 13 13 14 15 Column indices: 2 0 4 2 6 7 12 9 13 14 13 15 16 17 17 Off-diagonal values: 0.868723 0.668031 0.134749 -0.058605 -0.928177 -0.113043 -0.571936 -0.899450 -0.397549 -0.614656 -0.281323 -0.345596 0.978573 -0.478952 -0.132862 . - x - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | o | . - o - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | o . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - o - - - - - - - | | | | | | | | | o | . - - - - - - - - | | | | | | | | | | | | . o o - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | o . o x - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | o . - | | | | | | | | | | | | | | | | | o | . The error in solving: 3.986091e-17 The error in solving: 1.666780e-16 The error in solving: 0.000000e+00 The error in solving: 5.667849e-16 The error in solving: 2.543841e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.745148 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.767484 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.073528 0.000000 0.258600 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.548907 0.352040 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.159393 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.616809 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.166320 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.226012 0.000000 0.000000 0.000000 0.084809 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.001634 0.000000 0.944004 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.767243 -0.614078 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.553093 0.000000 0.000000 0.000000 0.382736 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.122017 -0.475695 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.836015 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.259355 -0.517543 0.000000 0.359974 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.978768 0.685977 0.000000 0.000000 -0.041008 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.962225 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.796542 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.432937 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.067956 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.418310 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 31 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 4 6 7 8 9 11 13 15 17 19 20 23 26 27 28 29 30 31 Column indices: 2 0 1 3 4 5 6 4 5 5 9 7 9 7 8 8 12 9 10 14 11 12 14 12 13 16 14 18 16 19 18 Off-diagonal values: 0.745148 -0.767484 -0.073528 0.258600 0.548907 0.352040 -0.159393 0.616809 0.166320 0.226012 0.084809 -0.001634 0.944004 -0.767243 -0.614078 0.553093 0.382736 0.122017 -0.475695 0.836015 -0.259355 -0.517543 0.359974 -0.978768 0.685977 -0.041008 0.962225 0.796542 -0.432937 0.067956 0.418310 . - x - - - - - - - - - - - - - - - - - o . - - - - - - - - - - - - - - - - - - | o . x - - - - - - - - - - - - - - - - | | | . x x - - - - - - - - - - - - - - | | | | . - o - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | x | . - x - - - - - - - - - - | | | | | | | o . x - - - - - - - - - - | | | | | | | o o . - - - - - - - - - - | | | | | | | | x | . - x - - - - - - - | | | | | | | | | x o . - - - - - - - - | | | | | | | | | | | | . - x - - - - - | | | | | | | | | | | o o . x - - - - - | | | | | | | | | | | | o x . - o - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | | . - x - | | | | | | | | | | | | | | | | o . - - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | x . The error in solving: 3.203936e-16 The error in solving: 5.178229e-16 The error in solving: 3.565268e-16 The error in solving: 6.667479e-16 The error in solving: 7.114312e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 0.259733 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.694085 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.065584 0.000000 0.097028 0.040704 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.504597 -0.445709 0.000000 0.975308 0.472715 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.668300 0.000000 0.000000 0.047186 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.143776 0.855603 0.000000 0.000000 -0.241101 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.027889 0.132766 0.000000 0.045053 -0.999155 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.728256 0.000000 0.000000 -0.443231 0.343586 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.675407 0.479215 0.000000 -0.105319 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.889789 -0.251551 0.000000 0.205619 0.984802 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.710016 -0.721547 0.000000 -0.802011 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.790546 0.000000 -0.391310 -0.718375 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.739851 0.000000 0.000000 0.000000 0.350359 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.104611 -0.018696 0.000000 0.127195 -0.870526 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.903846 0.866296 0.000000 0.210388 0.063708 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.096599 -0.603483 0.000000 0.921244 -0.691398 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.275471 0.398791 0.000000 0.471831 -0.111851 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.051903 0.000000 0.000000 -0.167337 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.223346 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 55 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 5 9 11 14 18 21 24 28 31 34 36 36 40 44 48 52 54 55 Column indices: 2 0 1 3 4 1 2 4 5 3 6 3 4 7 4 5 7 8 5 8 9 6 7 9 7 8 10 11 8 9 11 10 12 13 10 14 12 13 15 16 13 14 16 17 14 15 17 18 15 16 18 19 16 19 18 Off-diagonal values: 0.259733 0.694085 -0.065584 0.097028 0.040704 -0.504597 -0.445709 0.975308 0.472715 -0.668300 0.047186 0.143776 0.855603 -0.241101 -0.027889 0.132766 0.045053 -0.999155 -0.728256 -0.443231 0.343586 0.675407 0.479215 -0.105319 -0.889789 -0.251551 0.205619 0.984802 0.710016 -0.721547 -0.802011 -0.790546 -0.391310 -0.718375 0.739851 0.350359 -0.104611 -0.018696 0.127195 -0.870526 -0.903846 0.866296 0.210388 0.063708 -0.096599 -0.603483 0.921244 -0.691398 0.275471 0.398791 0.471831 -0.111851 -0.051903 -0.167337 -0.223346 . - x - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | o . x x - - - - - - - - - - - - - - - | o o . x x - - - - - - - - - - - - - - | | | o . - x - - - - - - - - - - - - - | | | x x . - o - - - - - - - - - - - - | | | | o x . x o - - - - - - - - - - - | | | | | o | . o x - - - - - - - - - - | | | | | | x x . o - - - - - - - - - - | | | | | | | o o . x x - - - - - - - - | | | | | | | | x o . o - - - - - - - - | | | | | | | | | | o . o o - - - - - - | | | | | | | | | | x | . - x - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | o o . x o - - - | | | | | | | | | | | | | o x . x x - - | | | | | | | | | | | | | | o o . x o - | | | | | | | | | | | | | | | x x . x o | | | | | | | | | | | | | | | | o | . o | | | | | | | | | | | | | | | | | | o . The error in solving: 2.775558e-16 The error in solving: 7.952832e-16 The error in solving: 3.470834e-16 The error in solving: 5.474695e-16 The error in solving: 5.941574e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.437305 -0.931731 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.128094 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.815650 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- - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | x o - - - - - | | | | | | | | | | | | | | o - - - - - | | | | | | | | | | | | | | o . - - - - | | | | | | | | | | | | | | | o . - - - | | | | | | | | | | | | | | | | o . o - | | | | | | | | | | | | | | | | | o . - | | | | | | | | | | | | | | | | | | | o The error in solving: 5.467242e-16 The error in solving: 1.110223e-16 The error in solving: 4.965068e-16 The error in solving: 2.775558e-17 The error in solving: 2.777508e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.485372 0.000000 0.837166 0.000000 0.000000 0.000000 0.000000 0.000000 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-2.428370 0.884411 -0.252743 3.624333 . - - - - - - - - - - - - - - - - - - - o . x - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | | . o - - - - - - - - - - - - - - - | | | x . x - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | o . - - - - - - - - - - - - - | | | | | | o o x - - - - - - - - - - - | | | | | | | | x o - - - - - - - - - - | | | | | | | | o . o - - - - - - - - - | | | | | | | | | x o - - - - - - - - - | | | | | | | | | | | x x - - - - - - - | | | | | | | | | | | o x x - - - - - - | | | | | | | | | | | | o . x - - - - - | | | | | | | | | | | | | o . x - - - - | | | | | | | | | | | | | | o . - - - - | | | | | | | | | | | | | | | | . o - - | | | | | | | | | | | | | | | | x . - - | | | | | | | | | | | | | | | | | o x x | | | | | | | | | | | | | | | | | | | . The error in solving: 4.230450e-16 The error in solving: 6.938894e-18 The error in solving: 4.118361e-16 The error in solving: 3.436515e-16 The error in solving: 3.164623e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.750000 [ 0.423997 0.367776 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.088472 -1.412827 -0.347500 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.579399 0.000000 -1.361477 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.399245 -1.043958 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0.000000 0.000000 0.000000 0.000000 1.547318 -0.859151]; Dimension: 20 x 20 Off-diagonal entries: 30 (max 380) Diagonal entries: 0.423997 -1.412827 0.000000 -1.043958 0.000000 0.000000 0.000000 -0.320782 -0.663282 0.000000 -1.127473 -0.626576 1.206624 0.166184 0.000000 2.230563 0.617971 0.000000 0.612856 -0.859151 Row indices: 0 1 3 5 7 8 9 9 11 13 14 16 18 20 21 23 25 26 28 29 30 Column indices: 1 0 2 1 3 2 4 5 4 6 8 7 9 8 9 11 10 12 11 13 12 13 15 14 16 17 16 18 19 18 Off-diagonal values: 0.367776 0.088472 -0.347500 -1.579399 -1.361477 0.399245 -0.413652 1.857008 0.006970 0.034370 -0.063748 -0.311572 0.207595 -0.676130 -1.380915 -1.228560 0.551745 1.229696 -0.524828 -0.193746 0.965952 -0.162842 -0.819427 0.470525 -1.336306 1.823508 0.021681 -1.676486 1.607814 1.547318 x x - - - - - - - - - - - - - - - - - - x o o - - - - - - - - - - - - - - - - - | o . o - - - - - - - - - - - - - - - - | | x o o - - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | x o o - - - - - - - - - - - | | | | | | | o o x - - - - - - - - - - | | | | | | | | o . - - - - - - - - - - | | | | | | | | | o o o - - - - - - - - | | | | | | | | | | x o x - - - - - - - | | | | | | | | | | | o x o - - - - - - | | | | | | | | | | | | x x - - - - - - | | | | | | | | | | | | | o . o - - - - | | | | | | | | | | | | | | x x o - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | x . o - | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | x o The error in solving: 1.570092e-16 The error in solving: 4.560706e-16 The error in solving: 4.619448e-16 The error in solving: 2.254874e-16 The error in solving: 2.509540e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.250000 [ 1.745276 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.345505 0.000000 -0.215629 0.000000 -0.871563 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.082128 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.671123 0.000000 0.718300 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.145649 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.606980 0.000000 0.000000 0.000000 0.467629 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.875817 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 17 (max 380) Diagonal entries: 1.745276 0.000000 0.000000 0.000000 0.000000 -1.473289 -0.215629 -0.082128 0.000000 0.718300 1.145649 0.000000 0.000000 -0.669793 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 2 3 3 5 5 7 7 7 8 8 9 9 10 12 14 16 17 17 17 Column indices: 0 2 3 3 5 4 8 7 9 12 12 13 16 17 14 18 18 Off-diagonal values: 0.263006 -0.621667 -0.362927 -0.340312 -0.138133 0.345505 -0.871563 -2.671123 2.059193 0.217439 -0.305585 -0.703464 1.493595 0.170570 0.606980 0.467629 -1.875817 x - - - - - - - - - - - - - - - - - - - x . o - - - - - - - - - - - - - - - - - | | . o - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | o . o - - - - - - - - - - - - - - | | | | | o - - - - - - - - - - - - - - | | | | x | o - o - - - - - - - - - - - | | | | | | | o - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | o | x - - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | x | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | x o - - - - - - | | | | | | | | | | | | o o . - - - - - | | | | | | | | | | | | | | | . x x - - | | | | | | | | | | | | | | x | . - x - | | | | | | | | | | | | | | | | | . o - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.241267e-16 The error in solving: 3.330669e-16 The error in solving: 1.942890e-16 The error in solving: 2.603704e-16 The error in solving: 2.775558e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.500000 [ 0.000000 -1.218485 -1.755688 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.332155 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.004654 -0.797309 0.000000 -1.186180 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.144424 0.000000 0.631980 0.000000 -0.386283 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.067160 1.043183 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.364652 0.241091 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.071593 0.000000 0.510704 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.847115 0.083107 0.000000 -0.529079 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.902637 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.196502 0.000000 -0.677043 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.033405 1.046705 1.418609 0.000000 0.212103 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.169385 0.000000 0.000000 0.000000 -0.738487 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.022176 0.000000 0.000000 -1.112637 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.774732 0.273879 0.478740]; Dimension: 20 x 20 Off-diagonal entries: 33 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 -0.797309 0.631980 -0.067160 0.241091 0.510704 0.083107 -0.109343 0.000000 1.133948 0.000000 0.000000 0.902637 0.000000 1.418609 0.000000 0.000000 0.478740 Row indices: 0 2 3 3 5 7 8 9 10 12 13 14 17 21 22 22 24 27 29 31 33 Column indices: 1 2 2 2 5 2 6 6 5 5 7 10 11 8 9 10 13 10 11 13 14 15 14 16 14 15 18 15 19 16 19 17 18 Off-diagonal values: -1.218485 -1.755688 0.332155 -2.004654 -1.186180 -1.144424 -0.386283 1.043183 -2.364652 1.071593 0.847115 -0.529079 0.405247 0.472681 -0.018001 0.139009 -0.307008 -1.122324 -0.867360 1.043276 0.461410 0.149760 1.196502 -0.677043 0.033405 1.046705 0.212103 0.169385 -0.738487 -0.022176 -1.112637 -0.774732 0.273879 . o o - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | o o - o - - - - - - - - - - - - - - | | o | x - o - - - - - - - - - - - - - | | | | | o x - - - - - - - - - - - - - | | | | | o x - - - - - - - - - - - - - | | | | | x | x - - - - - - - - - - - - | | | | | | | x x - o - - - - - - - - - | | | | | | | | | o - x - - - - - - - - | | | | | | | | x | . - - - - - - - - - | | | | | | | | | o x x - o - - - - - - | | | | | | | | | | o o . x x - - - - - | | | | | | | | | | | | | . - x - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | x . o - - - | | | | | | | | | | | | | | x x x - x - | | | | | | | | | | | | | | | x | . - o | | | | | | | | | | | | | | | | o | . o | | | | | | | | | | | | | | | | | o x x The error in solving: 3.188873e-16 The error in solving: 1.924527e-16 The error in solving: 3.964289e-16 The error in solving: 4.302114e-16 The error in solving: 3.153191e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.750000 [ 0.000000 0.241861 -0.718194 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.184431 -1.425244 -2.299702 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.124383 0.675444 -0.542587 0.559354 1.591779 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.182843 0.248969 -0.695510 0.145422 0.951157 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.640672 0.000000 0.298115 0.653357 0.913818 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.119127 1.922351 0.708405 0.120231 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.069996 -1.843576 -0.447815 -0.207023 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.950914 1.578652 0.791762 -0.695280 0.268428 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.220197 0.000000 -0.052715 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.228112 -1.528637 1.508346]; Dimension: 20 x 20 Off-diagonal entries: 61 (max 380) Diagonal entries: 0.000000 -0.184431 -0.542587 -0.695510 0.298115 0.708405 -0.313775 -0.066420 0.657458 -0.312702 -1.106815 0.000000 0.000000 -0.141891 0.000000 1.323631 -0.447815 0.791762 -0.052715 1.508346 Row indices: 0 2 4 8 12 15 19 23 25 29 33 36 40 41 44 48 51 54 58 59 61 Column indices: 1 2 2 3 0 1 3 4 1 2 4 5 2 5 6 3 4 6 7 4 5 7 8 5 9 6 7 9 10 7 8 10 11 9 11 12 9 10 12 13 13 11 12 14 12 13 15 16 13 16 17 14 15 17 15 16 18 19 16 17 18 Off-diagonal values: 0.241861 -0.718194 -1.425244 -2.299702 -1.124383 0.675444 0.559354 1.591779 -0.182843 0.248969 0.145422 0.951157 -0.640672 0.653357 0.913818 -1.119127 1.922351 0.120231 -1.102451 -0.769013 -0.203279 0.976313 -0.261331 0.559313 1.230821 0.725379 -0.841688 -0.113422 -0.194447 -1.078439 -0.714907 -0.777385 -0.108374 -0.077619 -0.619605 0.595127 -0.424411 0.229114 1.096703 1.534083 0.718740 -0.496344 1.507433 0.169573 -0.970068 0.368933 -0.147111 -0.006680 -1.278305 -1.102511 2.783755 -1.069996 -1.843576 -0.207023 -1.950914 1.578652 -0.695280 0.268428 0.220197 0.228112 -1.528637 . x o - - - - - - - - - - - - - - - - - | o o o - - - - - - - - - - - - - - - - o x o x x - - - - - - - - - - - - - - - | o x o x x - - - - - - - - - - - - - - | | o | x x x - - - - - - - - - - - - - | | | o x x x o - - - - - - - - - - - - | | | | o o o x o - - - - - - - - - - - | | | | | x | o - x - - - - - - - - - - | | | | | | x o x o o - - - - - - - - - | | | | | | | o o o o o - - - - - - - - | | | | | | | | | o o o x - - - - - - - | | | | | | | | | o x . x x - - - - - - | | | | | | | | | | | | . x - - - - - - | | | | | | | | | | | o x o x - - - - - | | | | | | | | | | | | o x . o o - - - | | | | | | | | | | | | | o | x o x - - | | | | | | | | | | | | | | o o o o - - | | | | | | | | | | | | | | | o x x o x | | | | | | | | | | | | | | | | x | o - | | | | | | | | | | | | | | | | | x o x The error in solving: 3.767506e-16 The error in solving: 3.831226e-16 The error in solving: 4.878985e-16 The error in solving: 4.779785e-16 The error in solving: 3.532878e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.250000 [ 1.412840 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.392657 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.812519 -1.589983 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.848237 -0.281688 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.599123 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.789580 0.559302 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.003278 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.346538 0.248891 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.876019 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.676054 0.297491 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.000799 0.941007 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.809067 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.947414 -0.484107 -0.947370 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.533766 -0.508392 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.903385 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.361553 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.051084 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.553755 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.573886 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.531602 -2.626461]; Dimension: 20 x 20 Off-diagonal entries: 10 (max 380) Diagonal entries: 1.412840 0.392657 -1.589983 -0.848237 1.599123 -0.789580 -1.003278 0.248891 0.876019 -2.676054 -1.000799 1.809067 -0.484107 1.533766 0.903385 -0.361553 0.051084 -0.553755 2.573886 -2.626461 Row indices: 0 0 0 1 2 2 3 3 4 4 5 6 6 8 9 9 9 9 9 9 10 Column indices: 1 4 6 6 10 11 11 13 14 18 Off-diagonal values: 0.812519 -0.281688 0.559302 -0.346538 0.297491 0.941007 0.947414 -0.947370 -0.508392 0.531602 x - - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | x o - - - - - - - - - - - - - - - - - | | | o o - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | o x - - - - - - - - - - - - - | | | | | | o - - - - - - - - - - - - - | | | | | | o x - - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | | o x - - - - - - - - - | | | | | | | | | | o x - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | x o o - - - - - - | | | | | | | | | | | | | x o - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | o - - - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | | | o - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | x o The error in solving: 6.798700e-17 The error in solving: 1.594814e-16 The error in solving: 5.561947e-17 The error in solving: 2.498002e-16 The error in solving: 2.255941e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.500000 [ 0.596915 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.959066 -0.311192 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.516828 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.496792 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.920572 -1.243701 -0.903419 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.099990 -0.058813 -0.665946 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.926273 2.272500 1.568832 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.078980 -0.293716 -1.309000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.966691 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.453766 1.080883 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.265224 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.749605 -0.433695 0.239442 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.772309 -0.083936 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.081601 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.481852 -0.003565 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.903303 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.023483 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.162737 -0.821768 0.580455 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.004635 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.617488 1.197405]; Dimension: 20 x 20 Off-diagonal entries: 17 (max 380) Diagonal entries: 0.596915 0.959066 -1.516828 -0.496792 -1.243701 -0.058813 2.272500 -0.293716 -0.966691 1.453766 0.265224 -0.433695 1.772309 -0.081601 -0.003565 -1.903303 -0.023483 -0.821768 -2.004635 1.197405 Row indices: 0 0 1 1 1 3 5 7 9 9 10 10 12 13 13 14 14 14 16 16 17 Column indices: 2 3 5 4 6 5 7 6 8 10 10 12 13 13 16 18 18 Off-diagonal values: -0.311192 -0.920572 -0.903419 -0.099990 -0.665946 -0.926273 1.568832 0.078980 -1.309000 1.080883 1.749605 0.239442 -0.083936 -1.481852 0.162737 0.580455 0.617488 x - - - - - - - - - - - - - - - - - - - | x o - - - - - - - - - - - - - - - - - | | o - - - - - - - - - - - - - - - - - | | | o - - - - - - - - - - - - - - - - | | | o o o - - - - - - - - - - - - - - | | | | o o o - - - - - - - - - - - - - | | | | | o x x - - - - - - - - - - - - | | | | | | x o o - - - - - - - - - - - | | | | | | | | o - - - - - - - - - - - | | | | | | | | | x x - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | x o x - - - - - - - | | | | | | | | | | | | x o - - - - - - | | | | | | | | | | | | | o - - - - - - | | | | | | | | | | | | | o o - - - - - | | | | | | | | | | | | | | | o - - - - | | | | | | | | | | | | | | | | o - - - | | | | | | | | | | | | | | | | x o x - | | | | | | | | | | | | | | | | | | o - | | | | | | | | | | | | | | | | | | x x The error in solving: 2.950458e-16 The error in solving: 2.505700e-16 The error in solving: 5.095246e-16 The error in solving: 1.600465e-16 The error in solving: 4.002966e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.750000 [ -2.193666 0.942970 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.415684 0.809589 0.763558 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.516431 -0.401454 -0.083956 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.248069 1.009067 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.608541 0.428087 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.773675 -0.279918 1.521964 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.582790 0.027710 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 -0.898794 -0.049327 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.222651 0.139848 -0.237668 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.007770 0.549808 -1.645844 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.579876 -0.074811 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.042722 -0.051923 1.222010 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.716510 -0.338452 -0.578808 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.929770 0.637932 0.403211 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.095735 -0.174801]; Dimension: 20 x 20 Off-diagonal entries: 31 (max 380) Diagonal entries: -2.193666 0.809589 -0.401454 0.248069 0.608541 -0.279918 0.582790 0.972094 -1.144014 0.200017 -0.644005 0.206608 -0.898794 0.139848 0.549808 -0.074811 -0.051923 -0.338452 0.637932 -0.174801 Row indices: 0 1 3 5 6 7 9 10 11 13 15 16 18 19 21 23 24 26 28 30 31 Column indices: 1 0 2 1 3 4 5 4 6 7 8 7 9 8 10 11 10 12 13 12 14 13 15 14 15 17 16 18 17 19 18 Off-diagonal values: 0.942970 -1.415684 0.763558 0.516431 -0.083956 1.009067 0.428087 1.773675 1.521964 0.027710 -0.816989 0.256206 2.425491 -1.061845 -0.755816 -0.806150 -1.041633 -1.155340 -0.049327 0.222651 -0.237668 0.007770 -1.645844 2.579876 1.042722 1.222010 1.716510 -0.578808 0.929770 0.403211 -1.095735 o x - - - - - - - - - - - - - - - - - - o x x - - - - - - - - - - - - - - - - - | x o o - - - - - - - - - - - - - - - - | | | x x - - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | | | | x o x - - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | x o - - - - - - - - - - - | | | | | | | x o x - - - - - - - - - - | | | | | | | | o x o - - - - - - - - - | | | | | | | | | | o o - - - - - - - - | | | | | | | | | | o x o - - - - - - - | | | | | | | | | | | | o o - - - - - - | | | | | | | | | | | | x x o - - - - - | | | | | | | | | | | | | x x o - - - - | | | | | | | | | | | | | | x o - - - - | | | | | | | | | | | | | | | x o x - - | | | | | | | | | | | | | | | | x o o - | | | | | | | | | | | | | | | | | x x x | | | | | | | | | | | | | | | | | | o o The error in solving: 5.743795e-16 The error in solving: 3.422333e-16 The error in solving: 6.758924e-16 The error in solving: 3.040471e-16 The error in solving: 2.540052e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.250000 [ 0.617411 0.000000 -0.004066 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.651177 -0.908050 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.064985 0.000000 -0.542192 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.362108 -0.824112 0.150100 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.193530 0.423558 0.000000 -0.204882 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.789416 0.000000 0.738107 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.559062 0.448822 0.856167 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.630223 -0.019994 -0.312492 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.304513 0.000000 0.119527 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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entries: 21 (max 380) Diagonal entries: 0.617411 -0.908050 -0.064985 -0.824112 0.423558 -0.789416 1.559062 -0.630223 0.119527 1.644380 -1.783593 -0.323092 -1.770161 -0.096544 -0.855080 -1.417437 -0.183045 -0.706003 0.536573 1.151070 Row indices: 0 1 2 3 5 7 8 10 12 13 14 15 16 17 18 19 20 20 21 21 21 Column indices: 2 0 4 2 4 3 6 7 7 8 8 9 6 8 12 10 13 11 13 17 15 Off-diagonal values: -0.004066 0.651177 -0.542192 0.362108 0.150100 0.193530 -0.204882 0.738107 0.448822 0.856167 -0.019994 -0.312492 0.304513 0.554400 -0.066127 0.596470 0.661965 -1.206965 0.208989 -2.229271 -0.330948 x - o - - - - - - - - - - - - - - - - - x o - - - - - - - - - - - - - - - - - - | | o - o - - - - - - - - - - - - - - - | | x o x - - - - - - - - - - - - - - - | | | x x - o - - - - - - - - - - - - - | | | | | o - x - - - - - - - - - - - - | | | | | | x x x - - - - - - - - - - - | | | | | | | o o o - - - - - - - - - - | | | | | | x | x - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | | o - o - - - - - - - | | | | | | | | | | x o - - - - - - - - | | | | | | | | | | | | o x - - - - - - | | | | | | | | | | | o | o - - - - - - | | | | | | | | | | | | | x o - - - - - | | | | | | | | | | | | | | | o - o - - | | | | | | | | | | | | | | | | o - - - | | | | | | | | | | | | | | | o | o - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | x The error in solving: 2.733607e-16 The error in solving: 2.149938e-16 The error in solving: 2.775558e-16 The error in solving: 2.603704e-16 The error in solving: 2.884444e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.500000 [ -0.533479 -0.626236 -0.174410 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.445673 0.855707 -0.219441 1.870750 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.173518 0.000000 0.218470 -0.194846 -0.084421 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.664423 0.136323 0.247905 -1.014953 0.728194 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.278718 -0.976651 -0.163136 0.584350 0.834149 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.894557 0.000000 0.963327 0.556626 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.549718 0.000000 0.289717 0.036627 0.104337 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.280937 0.980277 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.098943 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.270024 0.000000 0.203841 0.000000 0.086107 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.488361 -0.038814 0.000000 0.266627 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.342245 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.955670 0.000000 -1.219417 -0.345864 1.860351 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.437567 0.000000 -1.398647 1.019552 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.998741 0.415382 1.123029 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.033051 1.876873 -0.972355 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.074061 0.000000 -0.706582 -0.993811 -0.937384 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.018266 1.730035 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.240937 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.263777]; Dimension: 20 x 20 Off-diagonal entries: 39 (max 380) Diagonal entries: -0.533479 0.855707 0.218470 0.247905 -0.163136 0.963327 0.289717 0.980277 0.098943 0.203841 -0.038814 -0.342245 -1.219417 -1.398647 0.415382 -0.972355 -0.706582 1.730035 1.240937 2.263777 Row indices: 0 2 5 8 12 16 18 21 22 22 24 26 26 29 31 33 35 38 39 39 39 Column indices: 1 2 0 2 3 0 3 4 1 2 4 5 2 3 5 6 3 6 4 7 8 6 7 11 9 12 10 13 14 11 14 13 15 13 14 14 17 18 16 Off-diagonal values: -0.626236 -0.174410 1.445673 -0.219441 1.870750 0.173518 -0.194846 -0.084421 0.664423 0.136323 -1.014953 0.728194 -1.278718 -0.976651 0.584350 0.834149 -0.894557 0.556626 -0.549718 0.036627 0.104337 0.280937 0.270024 0.086107 1.488361 0.266627 2.955670 -0.345864 1.860351 -0.437567 1.019552 -0.998741 1.123029 2.033051 1.876873 -2.074061 -0.993811 -0.937384 0.018266 o o o - - - - - - - - - - - - - - - - - x x o x - - - - - - - - - - - - - - - - x | x o o - - - - - - - - - - - - - - - | x x x o x - - - - - - - - - - - - - - | | o o o x x - - - - - - - - - - - - - | | | o | x x - - - - - - - - - - - - - | | | | o | x x x - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | x | x - x - - - - - - - - | | | | | | | | | x o - x - - - - - - - | | | | | | | | | | | o - - - - - - - - | | | | | | | | | | x | o o x - - - - - | | | | | | | | | | | o | o x - - - - - | | | | | | | | | | | | | o x x - - - - | | | | | | | | | | | | | x x o - - - - | | | | | | | | | | | | | | o | o o o - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | x The error in solving: 3.411412e-16 The error in solving: 3.692802e-16 The error in solving: 5.467242e-16 The error in solving: 5.125396e-16 The error in solving: 5.559782e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.750000 [ -0.150910 -1.518028 -0.616851 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.060829 0.895069 -0.867699 1.187683 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.756008 -0.895713 -0.263223 -0.047208 -1.420829 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.285615 0.199519 0.582045 -0.840971 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.442906 0.001873 -2.090315 0.048392 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.543672 0.092501 -1.073626 -1.233072 0.394706 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.338767 0.000000 -0.583336 0.916190 -0.791498 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.975456 -1.378614 1.018079 0.573455 0.272327 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.802992 1.317226 0.000000 -2.037859 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.353723 -0.243207 0.177659 -0.803389 -1.219052 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.421687 -1.819427 -0.316267 -0.245510 -0.273056 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.635855 0.000000 1.228562 0.560572 -0.474054 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.669530 -0.502874 -0.461425 -0.322464 0.530383 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.765146 0.000000 0.571144 0.000000 -0.252526 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.639357 -0.711414 1.226217 0.272311 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.706937 0.224128 -0.534128 0.309927 -0.178099 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.293486 0.518531 -0.597118 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.660321 -1.855050 0.091526 1.767052 -0.883565 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.954354 0.631342 0.197286 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.186375 0.387102 -1.074199]; Dimension: 20 x 20 Off-diagonal entries: 62 (max 380) Diagonal entries: -0.150910 0.895069 -0.263223 0.199519 0.001873 -1.073626 -0.583336 1.018079 1.317226 0.177659 -0.316267 1.228562 -0.461425 0.571144 1.226217 -0.534128 -0.597118 0.091526 0.631342 -1.074199 Row indices: 0 2 5 9 12 15 19 22 26 28 32 36 39 43 45 48 52 54 58 60 62 Column indices: 1 2 0 2 3 0 1 3 4 2 4 5 3 5 6 3 4 6 7 4 7 8 5 6 8 9 7 10 7 8 10 11 8 9 11 12 9 12 13 10 11 13 14 11 15 12 13 15 13 14 16 17 14 15 15 16 18 19 17 19 17 18 Off-diagonal values: -1.518028 -0.616851 -1.060829 -0.867699 1.187683 -0.756008 -0.895713 -0.047208 -1.420829 0.285615 0.582045 -0.840971 -0.442906 -2.090315 0.048392 -1.543672 0.092501 -1.233072 0.394706 -0.338767 0.916190 -0.791498 -0.975456 -1.378614 0.573455 0.272327 0.802992 -2.037859 0.353723 -0.243207 -0.803389 -1.219052 -1.421687 -1.819427 -0.245510 -0.273056 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x x | | | | | | | | | | | | | | | | | x x o The error in solving: 3.966717e-16 The error in solving: 3.910486e-16 The error in solving: 7.087189e-16 The error in solving: 6.784482e-16 The error in solving: 6.503339e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.204334 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 13 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 1 1 1 1 1 3 4 5 6 7 9 10 11 11 11 12 13 13 Column indices: 3 6 8 7 8 9 10 11 13 14 13 16 17 Off-diagonal values: -0.204334 0.077873 1.760483 -0.543093 -0.352839 0.768618 0.792038 -1.432605 -2.000074 1.392364 -1.541114 0.563144 0.736790 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . o - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | x . x - - - - - - - - - - - | | | | | | | o . - - - - - - - - - - - | | | | | | | | o . - - - - - - - - - - | | | | | | | | | x . - - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | | o . o - - - - - - | | | | | | | | | | | | | . x - - - - - | | | | | | | | | | | | | o . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | x . - - | | | | | | | | | | | | | | | | | x . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.962616e-16 The error in solving: 2.498002e-16 The error in solving: 3.510833e-16 The error in solving: 3.469447e-18 The error in solving: 2.482534e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.980807 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.469846 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.261000 0.000000 1.942834 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.305742 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.620663 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.199259 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.356694 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.863327 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.382752 0.000000 -0.181661 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.288905 0.000000 0.772227 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.891171 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 14 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 1 2 4 4 4 5 5 6 7 8 8 9 11 13 13 13 14 Column indices: 2 3 4 6 9 9 10 11 15 14 16 15 17 18 Off-diagonal values: 0.980807 0.469846 -0.261000 1.942834 -1.305742 0.620663 -0.199259 0.356694 0.863327 -0.382752 -0.181661 -0.288905 0.772227 -1.891171 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | | x . - - - - - - - - - - - - - - - | | | | o . x - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . o - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | x . - - - - - - - - - | | | | | | | | | | o . - - - - - - - - | | | | | | | | | | | x . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | o . o - - - | | | | | | | | | | | | | | | o . x - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | o . The error in solving: 2.603704e-16 The error in solving: 2.482534e-16 The error in solving: 1.570092e-16 The error in solving: 1.387779e-17 The error in solving: 1.570092e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 1-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.392724 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.255909 0.000000 -0.834077 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.081279 0.000000 1.443974 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.037796 0.000000 0.557620 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.909485 0.000000 -0.836751 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.786883 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.058165 0.000000 -0.619523 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.271804 0.000000 1.225398 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.215679 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.832991 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.024894 0.000000 -0.078014 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.469740 0.000000 -0.050776 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.368134 0.000000 0.922889 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.403753 0.000000 -1.084728 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.033281 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.044447 0.000000 -0.915367 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 27 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 3 5 7 9 10 10 12 14 15 16 18 20 20 22 24 25 27 27 Column indices: 0 1 3 2 4 3 5 4 6 7 7 9 8 10 9 10 11 13 12 14 14 16 15 17 18 17 19 Off-diagonal values: 1.392724 -1.255909 -0.834077 0.081279 1.443974 0.037796 0.557620 0.909485 -0.836751 0.786883 0.058165 -0.619523 -1.271804 1.225398 0.215679 0.832991 0.024894 -0.078014 -0.469740 -0.050776 -0.368134 0.922889 -1.403753 -1.084728 1.033281 1.044447 -0.915367 . - - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | o . o - - - - - - - - - - - - - - - - | | x . x - - - - - - - - - - - - - - - | | | x . x - - - - - - - - - - - - - - | | | | x . o - - - - - - - - - - - - - | | | | | | . x - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | x . o - - - - - - - - - - | | | | | | | | o . x - - - - - - - - - | | | | | | | | | x . - - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | | x . o - - - - - - | | | | | | | | | | | | o . o - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | o . x - - - | | | | | | | | | | | | | | | o . o - - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | | x . o | | | | | | | | | | | | | | | | | | | . The error in solving: 3.327777e-17 The error in solving: 3.390844e-16 The error in solving: 3.336446e-16 The error in solving: 2.603704e-16 The error in solving: 4.980560e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 -0.858142 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.614293 0.000000 0.000000 -1.684910 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.329714 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.302971 0.000000 0.000000 0.043925 -0.210268 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.118252 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.078100 0.000000 0.000000 -0.033098 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.526286 0.000000 0.000000 -1.338868 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.771003 0.000000 0.000000 0.000000 0.550867 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.122925 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.021682 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.279355 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.217596 0.000000 -0.934207 0.248429 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.433257 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 21 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 3 4 7 7 8 10 12 12 12 12 14 15 16 16 17 20 21 21 Column indices: 2 0 3 5 2 5 6 4 6 9 6 9 10 14 15 12 17 16 18 19 16 Off-diagonal values: -0.858142 -0.614293 -1.684910 1.329714 -0.302971 0.043925 -0.210268 -0.118252 -1.078100 -0.033098 -0.526286 -1.338868 -1.771003 0.550867 -1.122925 -0.021682 1.279355 1.217596 -0.934207 0.248429 1.433257 . - o - - - - - - - - - - - - - - - - - o . - o - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - x - - - - - - - - - - - - - - | | o | . x o - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | o | . - - - - - - - - - - - - - | | | | | | o . - o - - - - - - - - - - | | | | | | o | . o - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | o | . - x - - - - - | | | | | | | | | | | | | . - o - - - - | | | | | | | | | | | | o | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | x . o x | | | | | | | | | | | | | | | | x | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 4.241248e-16 The error in solving: 3.191891e-16 The error in solving: 2.558938e-16 The error in solving: 1.273812e-16 The error in solving: 3.535816e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.665096 0.000000 0.081521 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.571474 0.010065 0.000000 0.000000 1.056644 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.822518 0.000000 0.000000 1.308752 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.926028 0.200588 0.000000 -0.930433 1.863588 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.844168 0.000000 0.749235 0.446214 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.037626 0.524635 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.253850 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.905278 0.000000 -1.841561 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.128143 0.632223 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.113689 0.000000 0.000000 0.000000 -1.107300 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.861156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.902311 -0.926766 0.000000 0.000000 0.172687 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.193904 -1.732333 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.017919 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.377898 -0.704666 0.000000 0.273459 0.421311 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.195622 -0.318493 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.545098 0.758852 0.000000 0.975508 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.181737 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 40 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 2 5 7 11 14 16 17 19 21 23 24 27 29 30 34 36 39 40 Column indices: 1 3 1 2 5 2 5 3 4 6 7 5 7 8 5 6 6 8 10 8 9 9 13 14 11 12 15 15 16 13 14 15 17 18 18 19 16 17 19 18 Off-diagonal values: 0.665096 0.081521 -0.571474 0.010065 1.056644 -0.822518 1.308752 -0.926028 0.200588 -0.930433 1.863588 -1.844168 0.749235 0.446214 1.037626 0.524635 0.253850 -0.905278 -1.841561 0.128143 0.632223 1.113689 -1.107300 -0.861156 -0.902311 -0.926766 0.172687 1.193904 -1.732333 -0.017919 0.377898 -0.704666 0.273459 0.421311 2.195622 -0.318493 -1.545098 0.758852 0.975508 -1.181737 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | x . x - - - - - - - - - - - - - - - - | o x . - x - - - - - - - - - - - - - - | | o | . x - - - - - - - - - - - - - - | | | o x . o x - - - - - - - - - - - - | | | | | o . x x - - - - - - - - - - - | | | | | x x . - - - - - - - - - - - - | | | | | | x | . - - - - - - - - - - - | | | | | | | | o . o - - - - - - - - - | | | | | | | | x x . - - - - - - - - - | | | | | | | | | x | . - o - - - - - - | | | | | | | | | | | | . - o - - - - - | | | | | | | | | | | o o . - x - - - - | | | | | | | | | | | | | | . x o - - - | | | | | | | | | | | | | o | . - - - - | | | | | | | | | | | | | | x o . x x - | | | | | | | | | | | | | | | | | . x o | | | | | | | | | | | | | | | | o x . x | | | | | | | | | | | | | | | | | | o . The error in solving: 6.826969e-16 The error in solving: 4.209341e-16 The error in solving: 2.482777e-16 The error in solving: 4.154074e-16 The error in solving: 6.151790e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A 2-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000301 0.536104 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.177699 0.000000 0.000000 0.445308 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.722012 0.000000 0.000000 -0.450389 0.173978 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.106549 1.648302 0.000000 0.000000 1.776066 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.937769 1.551563 0.000000 1.959600 1.788530 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.833352 0.000000 0.000000 1.857505 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.994808 0.834718 0.000000 0.000000 1.865776 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.152426 -1.154336 0.000000 -1.400049 -0.944324 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.162819 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.461182 0.261736 0.000000 0.028004 0.831289 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.568015 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.912412 0.000000 0.966413 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.570214 0.000000 0.000000 -0.672942 -1.436911 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.293290 0.000000 0.000000 -0.631962 1.628536 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.426011 0.000000 0.000000 0.000000 -0.482238 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.722393 -2.258324 0.000000 -0.106167 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.401082 -1.231146 0.000000 -0.927539 -1.062876 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.948440 0.000000 0.288960 -0.309060 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.402252 2.074896 0.000000 0.419152 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.919079 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 53 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 4 7 10 14 16 19 23 24 28 29 31 34 37 39 42 46 49 52 53 Column indices: 1 2 0 3 0 3 4 1 2 5 2 3 5 6 4 7 4 5 8 5 6 8 9 10 7 8 10 11 8 10 12 10 13 14 11 14 15 12 16 13 14 16 14 15 17 18 16 18 19 16 17 19 18 Off-diagonal values: 0.000301 0.536104 0.177699 0.445308 -0.722012 -0.450389 0.173978 0.106549 1.648302 1.776066 0.937769 1.551563 1.959600 1.788530 0.833352 1.857505 0.994808 0.834718 1.865776 2.152426 -1.154336 -1.400049 -0.944324 -0.162819 1.461182 0.261736 0.028004 0.831289 -0.568015 -0.912412 0.966413 0.570214 -0.672942 -1.436911 -0.293290 -0.631962 1.628536 -1.426011 -0.482238 0.722393 -2.258324 -0.106167 -0.401082 -1.231146 -0.927539 -1.062876 1.948440 0.288960 -0.309060 1.402252 2.074896 0.419152 -0.919079 . x x - - - - - - - - - - - - - - - - - x . - x - - - - - - - - - - - - - - - - o | . o x - - - - - - - - - - - - - - - | x x . - x - - - - - - - - - - - - - - | | x x . x x - - - - - - - - - - - - - | | | | x . - x - - - - - - - - - - - - | | | | x x . - x - - - - - - - - - - - | | | | | x o . o o - - - - - - - - - - | | | | | | | | . - o - - - - - - - - - | | | | | | | x x . x x - - - - - - - - | | | | | | | | o | . - - - - - - - - - | | | | | | | | | | o . x - - - - - - - | | | | | | | | | | x | . o o - - - - - | | | | | | | | | | | o | . o x - - - - | | | | | | | | | | | | o | . - o - - - | | | | | | | | | | | | | x o . o - - - | | | | | | | | | | | | | | o o . o o - | | | | | | | | | | | | | | | | x . x o | | | | | | | | | | | | | | | | x x . x | | | | | | | | | | | | | | | | | | o . The error in solving: 7.120485e-16 The error in solving: 3.869794e-16 The error in solving: 3.480704e-16 The error in solving: 4.930644e-16 The error in solving: 4.349177e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.183088 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.122858 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.212331 0.001898 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.458765 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.444571 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.074014 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.465442 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.624945 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 5 (max 380) Diagonal entries: 0.000000 0.000000 0.183088 0.000000 0.122858 0.000000 0.000000 0.000000 0.212331 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.465442 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 0 0 0 0 0 1 2 2 3 3 4 4 4 5 5 5 5 Column indices: 9 10 12 14 17 Off-diagonal values: 0.001898 0.458765 0.444571 0.074014 0.624945 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | . x - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . x - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 0.000000e+00 The error in solving: 2.558938e-16 The error in solving: 2.482534e-16 The error in solving: 2.220446e-16 The error in solving: 2.288783e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.500000 [ 0.238358 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.987519 0.181495 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.606999 0.086084 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.899978 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.682784 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.862950 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.440944 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.297687 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.829025 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.136061 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.759030 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.283617 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.452758 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.243007 0.433944 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 11 (max 380) Diagonal entries: 0.238358 0.000000 0.000000 0.987519 0.606999 0.000000 0.682784 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.136061 0.000000 0.000000 0.000000 0.000000 0.243007 0.000000 Row indices: 0 0 0 0 1 2 3 3 4 4 5 6 7 7 7 8 9 10 10 11 11 Column indices: 4 5 6 8 10 11 12 15 16 17 19 Off-diagonal values: 0.181495 0.086084 0.899978 0.862950 0.440944 0.297687 0.829025 0.759030 0.283617 0.452758 0.433944 x - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | x x - - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | | . x - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . x - - - - - - - - - | | | | | | | | | | . x - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | | . The error in solving: 6.206335e-17 The error in solving: 2.789401e-16 The error in solving: 2.559173e-16 The error in solving: 1.110223e-16 The error in solving: 1.570092e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.750000 [ 0.175198 0.586694 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.541020 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.430893 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.640212]; Dimension: 20 x 20 Off-diagonal entries: 9 (max 380) Diagonal entries: 0.175198 0.541020 0.430893 0.000000 0.000000 0.649433 0.278491 0.061732 0.661006 0.526432 0.208397 0.000000 0.574016 0.588753 0.226438 0.000000 0.000000 0.000000 0.866471 0.640212 Row indices: 0 1 1 1 1 1 2 3 4 4 4 5 5 6 6 7 8 9 9 9 9 Column indices: 1 6 7 8 11 13 15 16 17 Off-diagonal values: 0.586694 0.255203 0.268294 0.906158 0.760378 0.295030 0.884015 0.435355 0.678740 x x - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | x x - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | x The error in solving: 0.000000e+00 The error in solving: 1.359740e-16 The error in solving: 1.394700e-16 The error in solving: 8.441529e-17 The error in solving: 3.104380e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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- | | | | | | . - - - - - - - - - - - - - | | | | | | | x - x - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | . - x - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | | . - x - - - - | | | | | | | | | | | | | | . x x - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 0.000000e+00 The error in solving: 6.947161e-18 The error in solving: 3.103168e-17 The error in solving: 0.000000e+00 The error in solving: 2.791126e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 0.253424 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.529698 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.441743 0.044940 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.743205 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.146368 0.656224 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.495434 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.868304 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.559573 0.360632 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.164045]; Dimension: 20 x 20 Off-diagonal entries: 21 (max 380) Diagonal entries: 0.000000 0.529698 0.000000 0.000000 0.000000 0.000000 0.000000 0.540435 0.000000 0.713294 0.848168 0.000000 0.434836 0.000000 0.743205 0.146368 0.000000 0.000000 0.559573 0.164045 Row indices: 0 1 1 3 5 6 8 9 10 11 13 14 15 15 17 17 18 19 20 21 21 Column indices: 2 3 4 4 5 6 6 7 7 8 10 10 11 12 13 14 15 16 18 18 19 Off-diagonal values: 0.253424 0.441743 0.044940 0.640582 0.181789 0.307832 0.874601 0.897854 0.712677 0.990209 0.265061 0.322572 0.645506 0.329878 0.623222 0.396197 0.693767 0.656224 0.495434 0.868304 0.360632 . - x - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | | . x x - - - - - - - - - - - - - - - | | | . x x - - - - - - - - - - - - - - | | | | . - x - - - - - - - - - - - - - | | | | | . x x - - - - - - - - - - - - | | | | | | . x - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | . - x - - - - - - - - - | | | | | | | | | x x x - - - - - - - - | | | | | | | | | | x - x - - - - - - - | | | | | | | | | | | . - x - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | | . x x - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | | . - x - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | | x The error in solving: 2.001483e-16 The error in solving: 4.518280e-16 The error in solving: 3.188873e-16 The error in solving: 1.241267e-16 The error in solving: 5.721958e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.750000 [ 0.000000 0.913019 0.336965 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.713689 0.323223 0.338660 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.803617 0.788085 0.909892 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.719156 0.919011 0.409004 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.312731 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.380641 0.596889 0.511852 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.726411 0.376634 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.297779 0.551209 0.166323 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.486367 0.946978 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.421643 0.855568 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.730549 0.510055 0.190252 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.620690 0.386948 0.606776 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.743196 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.551903 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.098147 0.146767 0.494432 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.093818 0.166452 0.428949 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.412964 0.266474 0.161475 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.532606 0.879440 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.042430 0.926953 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.998464]; Dimension: 20 x 20 Off-diagonal entries: 31 (max 380) Diagonal entries: 0.000000 0.713689 0.803617 0.719156 0.000000 0.380641 0.726411 0.297779 0.486367 0.421643 0.730549 0.620690 0.000000 0.000000 0.098147 0.093818 0.412964 0.000000 0.042430 0.998464 Row indices: 0 2 4 6 8 9 11 12 14 15 16 18 20 21 22 24 26 28 30 31 31 Column indices: 1 2 2 3 3 4 4 5 6 6 7 7 8 9 9 10 11 12 12 13 13 15 15 16 16 17 17 18 18 19 19 Off-diagonal values: 0.913019 0.336965 0.323223 0.338660 0.788085 0.909892 0.919011 0.409004 0.312731 0.596889 0.511852 0.376634 0.551209 0.166323 0.946978 0.855568 0.510055 0.190252 0.386948 0.606776 0.743196 0.551903 0.146767 0.494432 0.166452 0.428949 0.266474 0.161475 0.532606 0.879440 0.926953 . x x - - - - - - - - - - - - - - - - - | x x x - - - - - - - - - - - - - - - - | | x x x - - - - - - - - - - - - - - - | | | x x x - - - - - - - - - - - - - - | | | | . - x - - - - - - - - - - - - - | | | | | x x x - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | x x x - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | x x - - - - - - - - - | | | | | | | | | | x x x - - - - - - - | | | | | | | | | | | x x x - - - - - - | | | | | | | | | | | | . x - - - - - - | | | | | | | | | | | | | . - x - - - - | | | | | | | | | | | | | | x x x - - - | | | | | | | | | | | | | | | x x x - - | | | | | | | | | | | | | | | | x x x - | | | | | | | | | | | | | | | | | . x x | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | | x The error in solving: 2.237726e-16 The error in solving: 2.633125e-16 The error in solving: 2.543841e-16 The error in solving: 5.087681e-16 The error in solving: 3.236829e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.708103 0.542916 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.543166 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.861660 0.210827 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.061791 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0.000000 0.000000 0.970139]; Dimension: 20 x 20 Off-diagonal entries: 9 (max 380) Diagonal entries: 0.708103 0.543166 0.861660 0.061791 0.967793 0.370425 0.865937 0.072255 0.365871 0.518365 0.530801 0.585605 0.685767 0.949716 0.817570 0.403568 0.606150 0.314819 0.639990 0.970139 Row indices: 0 1 1 2 3 3 3 4 4 5 6 6 6 6 7 8 8 8 9 9 9 Column indices: 1 3 4 7 9 10 14 15 18 Off-diagonal values: 0.542916 0.210827 0.647338 0.861827 0.018830 0.406824 0.900758 0.215171 0.192750 x x - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | | x x - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | x - - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | x x - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | x The error in solving: 3.925231e-17 The error in solving: 1.241267e-16 The error in solving: 3.388000e-16 The error in solving: 2.558938e-16 The error in solving: 7.850462e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.355986 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.523328 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.278629 0.085037 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.221859 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.233421 0.002798 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.876949 0.895087 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.001858 0.900058 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.537780 0.879092 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.484718]; Dimension: 20 x 20 Off-diagonal entries: 10 (max 380) Diagonal entries: 0.355986 0.523328 0.303338 0.730125 0.546086 0.914381 0.527477 0.426384 0.623668 0.210459 0.051061 0.914361 0.212788 0.278629 0.221859 0.233421 0.876949 0.001858 0.537780 0.484718 Row indices: 0 0 0 1 2 2 3 3 4 4 4 4 4 5 6 6 7 8 9 10 10 Column indices: 3 4 6 8 13 14 16 17 18 19 Off-diagonal values: 0.411265 0.419726 0.659761 0.312572 0.010258 0.085037 0.002798 0.895087 0.900058 0.879092 x - - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | | x x - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | | x x - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | | x The error in solving: 6.938894e-18 The error in solving: 1.110359e-16 The error in solving: 1.387779e-17 The error in solving: 2.220446e-16 The error in solving: 1.570092e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.514793 0.041001 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.551818 0.026208 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.286721 0.613939 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.876510 0.239036 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.468807 0.602273 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.683292 0.325620 0.000000 0.000000 0.000000 0.000000 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values: 0.041001 0.026208 0.613939 0.239036 0.602273 0.325620 0.060418 0.187581 0.718054 0.291979 0.223488 0.457356 0.597819 0.150001 0.856887 0.011981 0.346399 0.540833 x x - - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | | x x - - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | x - - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | x x - - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | | x x - - - - - - - | | | | | | | | | | | | x x - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | | x The error in solving: 2.237726e-16 The error in solving: 1.241388e-16 The error in solving: 6.208759e-17 The error in solving: 2.482534e-16 The error in solving: 2.096433e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.243600 0.022617 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.901803 0.169535 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.509401 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.139541 0.000000 0.000000 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0.226431]; Dimension: 20 x 20 Off-diagonal entries: 8 (max 380) Diagonal entries: 0.243600 0.901803 0.509401 0.139541 0.869349 0.377924 0.541853 0.771118 0.932510 0.003604 0.656471 0.943122 0.444293 0.511762 0.492703 0.257931 0.536357 0.844601 0.858351 0.226431 Row indices: 0 1 2 2 2 2 3 5 6 7 7 7 7 7 7 8 8 8 8 8 8 Column indices: 1 2 7 7 8 9 10 16 Off-diagonal values: 0.022617 0.169535 0.194934 0.223841 0.283967 0.486558 0.396654 0.231398 x x - - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | | x - - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | x - x - - - - - - - - - - - - | | | | | | x x x - - - - - - - - - - - | | | | | | | x - x - - - - - - - - - - | | | | | | | | x - x - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | x - x - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | x The error in solving: 1.241267e-16 The error in solving: 2.482534e-16 The error in solving: 1.271920e-16 The error in solving: 6.206335e-17 The error in solving: 2.288783e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.440721 0.272591 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.661760 0.406343 0.458522 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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- - | | | | x - - - - - - - - - - - - - - - | | | | | x - x - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | x - x - - - - - - - - - | | | | | | | | | x x x - - - - - - - - | | | | | | | | | | x - x - - - - - - - | | | | | | | | | | | x - x - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | x - x | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | | x The error in solving: 1.922963e-16 The error in solving: 2.775774e-16 The error in solving: 1.361509e-16 The error in solving: 3.152618e-16 The error in solving: 5.551115e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform 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Column indices: 1 2 3 3 4 5 5 6 8 8 9 9 10 11 11 14 15 15 17 17 19 19 Off-diagonal values: 0.236813 0.765466 0.778543 0.014198 0.303552 0.841249 0.783580 0.857544 0.780522 0.391472 0.588710 0.070995 0.809835 0.766028 0.035942 0.057889 0.253003 0.466755 0.193777 0.902817 0.577702 0.551741 x x x - - - - - - - - - - - - - - - - - | x - x - - - - - - - - - - - - - - - - | | x x x - - - - - - - - - - - - - - - | | | x - x - - - - - - - - - - - - - - | | | | x x x - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | x - x - - - - - - - - - - - | | | | | | | x x x - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | x x x - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | | x - x - - - - - | | | | | | | | | | | | | x - x - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | x - x - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | x - x | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | | x The error in solving: 2.355139e-16 The error in solving: 2.733662e-16 The error in solving: 1.144392e-16 The error in solving: 2.618456e-16 The error in solving: 3.330669e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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- - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | | . The error in solving: 3.345274e-16 The error in solving: 0.000000e+00 The error in solving: 5.551115e-17 The error in solving: 1.249001e-16 The error in solving: 1.576214e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.719049 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.573728 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.444564 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.761028 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.165940 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.683188 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 6 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 0 0 1 1 1 2 3 3 3 3 4 4 5 5 6 6 6 Column indices: 6 9 10 14 16 18 Off-diagonal values: 0.719049 0.573728 0.444564 0.761028 0.165940 0.683188 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | | | . x - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . x - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.775558e-17 The error in solving: 1.110223e-16 The error in solving: 0.000000e+00 The error in solving: 1.390487e-17 The error in solving: 2.603704e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.519162 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.387959 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.245450 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.822554 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.841697 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.446732 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.051591 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.208150 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.441192 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.969213 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.743869 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.156625 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.629671 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.366400 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.113802 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.516756 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 16 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 1 2 3 3 4 5 6 7 8 8 9 10 11 12 13 14 15 16 16 Column indices: 1 3 4 6 7 8 9 10 12 13 14 15 16 17 18 19 Off-diagonal values: 0.519162 0.387959 0.245450 0.822554 0.841697 0.446732 0.051591 0.208150 0.441192 0.969213 0.743869 0.156625 0.629671 0.366400 0.113802 0.516756 . x - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . x - - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | | | . x - - - - - - - - - - - - | | | | | | | . x - - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | | | . x - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | | . x - - - - - - | | | | | | | | | | | | | . x - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | | . The error in solving: 0.000000e+00 The error in solving: 2.224779e-16 The error in solving: 1.152776e-16 The error in solving: 2.288783e-16 The error in solving: 1.922963e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.206721 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.314732 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.341078 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.165791 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.317467 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.040740 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.918519 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.268358 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 8 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 1 1 1 2 2 3 3 3 4 4 4 4 5 6 6 6 7 8 8 Column indices: 1 6 7 10 15 15 19 19 Off-diagonal values: 0.206721 0.314732 0.341078 0.165791 0.317467 0.040740 0.918519 0.268358 . x - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - x - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . x - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . x - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - x - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - x | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | | . The error in solving: 1.144392e-16 The error in solving: 1.570476e-16 The error in solving: 2.558938e-16 The error in solving: 0.000000e+00 The error in solving: 1.570092e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.771770 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.996289 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.239833 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.297637 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.763248 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.138492 0.697670 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.226679 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.539602 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.555163 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.818263 0.398748 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.461892 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.112812 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 14 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 3 3 4 5 7 7 8 9 9 9 9 9 10 12 13 14 14 14 Column indices: 1 3 3 5 7 7 8 9 11 15 16 17 17 18 Off-diagonal values: 0.771770 0.996289 0.239833 0.297637 0.763248 0.138492 0.697670 0.226679 0.539602 0.555163 0.818263 0.398748 0.461892 0.112812 . x - - - - - - - - - - - - - - - - - - | . - x - - - - - - - - - - - - - - - - | | . x - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | | | . - x - - - - - - - - - - - - | | | | | | . x x - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | | | . - x - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | | . x x - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.144392e-16 The error in solving: 1.249001e-16 The error in solving: 2.719480e-16 The error in solving: 1.570092e-16 The error in solving: 1.118863e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.530960 0.970175 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.059161 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.822537 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.926981 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.483660 0.312238 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.363268 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.161370 0.619683 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.566746 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.962337 0.183967 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.690792 0.595578 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.266989 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.322255 0.311552 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.903926 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.837167 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.662427 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.606267 0.781645 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.060799 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 24 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 3 4 5 7 8 10 11 13 15 16 18 18 19 19 20 21 23 24 24 Column indices: 1 2 2 3 5 5 6 7 7 8 9 9 10 10 11 11 12 13 15 16 18 18 19 19 Off-diagonal values: 0.530960 0.970175 0.059161 0.822537 0.926981 0.483660 0.312238 0.363268 0.161370 0.619683 0.566746 0.962337 0.183967 0.690792 0.595578 0.266989 0.322255 0.311552 0.903926 0.837167 0.662427 0.606267 0.781645 0.060799 . x x - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | | . x - - - - - - - - - - - - - - - - | | | . - x - - - - - - - - - - - - - - | | | | . x x - - - - - - - - - - - - - | | | | | . - x - - - - - - - - - - - - | | | | | | . x x - - - - - - - - - - - | | | | | | | . - x - - - - - - - - - - | | | | | | | | . x x - - - - - - - - - | | | | | | | | | . x x - - - - - - - - | | | | | | | | | | . x - - - - - - - - | | | | | | | | | | | . x x - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - x - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | | . - x - | | | | | | | | | | | | | | | | | . x x | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | | . The error in solving: 5.551115e-17 The error in solving: 2.498980e-16 The error in solving: 3.888413e-16 The error in solving: 1.570092e-16 The error in solving: 6.216025e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 -0.014821 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.519493 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.039262 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.219734 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.653509 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.191847 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.937672 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.821340 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.729413 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.860599 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.455812 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 7 (max 380) Diagonal entries: 0.000000 -0.519493 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.191847 0.000000 -0.821340 0.729413 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 1 1 2 2 2 2 3 3 3 4 4 4 5 5 5 6 7 7 7 Column indices: 1 4 8 11 14 17 18 Off-diagonal values: -0.014821 0.039262 0.219734 0.653509 0.937672 -0.860599 0.455812 . o - - - - - - - - - - - - - - - - - - | o - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . x - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . x - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | o - - - - - - - | | | | | | | | | | | | | . x - - - - - | | | | | | | | | | | | | | o - - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | | . o - - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.220446e-16 The error in solving: 1.594436e-16 The error in solving: 2.543841e-16 The error in solving: 1.361509e-16 The error in solving: 2.288783e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.339119 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.361379 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.547687 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.905719 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.279178 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.756761 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.212471 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.042626 -0.129076 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.105195 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.324145 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.697569 -0.659977 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.389180 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.328496 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.171469 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.856040 -0.734961 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.642366 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.064116 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 9 (max 380) Diagonal entries: 0.000000 -0.361379 0.000000 0.000000 0.905719 0.000000 -0.756761 0.212471 0.042626 -0.105195 0.000000 0.000000 -0.697569 0.000000 0.328496 0.000000 0.856040 0.642366 -0.064116 0.000000 Row indices: 0 1 1 1 2 2 3 3 3 4 4 4 5 6 7 7 8 9 9 9 9 Column indices: 1 4 6 9 12 13 14 16 17 Off-diagonal values: 0.339119 0.547687 -0.279178 -0.129076 0.324145 -0.659977 -0.389180 -0.171469 -0.734961 . x - - - - - - - - - - - - - - - - - - | o - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | . o - - - - - - - - - - - - - | | | | | | o - - - - - - - - - - - - - | | | | | | | x - - - - - - - - - - - - | | | | | | | | x o - - - - - - - - - - | | | | | | | | | o - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | | o o - - - - - - | | | | | | | | | | | | | . o - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | . o - - - | | | | | | | | | | | | | | | | x o - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | | o - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.224779e-16 The error in solving: 5.561947e-17 The error in solving: 1.110223e-16 The error in solving: 2.288783e-16 The error in solving: 3.858424e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.750000 [ -0.936171 0.325603 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.988407 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.889866 0.952278 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.324532 0.381167 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.983323 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.141023 0.829275 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.406786 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.219296 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.726325 0.593231 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.269984 -0.339673 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.142644 0.331503 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.435490 0.840480 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.929123 0.714113 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.152910 0.614270 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.403703 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.651577 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.474293 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.732908 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.821095 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 14 (max 380) Diagonal entries: -0.936171 0.000000 -0.889866 0.324532 0.000000 0.141023 -0.406786 -0.219296 0.726325 0.269984 -0.142644 -0.435490 0.929123 -0.152910 0.000000 0.000000 -0.474293 0.732908 -0.821095 0.000000 Row indices: 0 1 2 3 4 5 6 6 6 7 8 9 10 11 12 13 14 14 14 14 14 Column indices: 1 2 3 4 5 6 9 10 11 12 13 14 15 16 Off-diagonal values: 0.325603 -0.988407 0.952278 0.381167 -0.983323 0.829275 0.593231 -0.339673 0.331503 0.840480 0.714113 0.614270 0.403703 0.651577 o x - - - - - - - - - - - - - - - - - - | . o - - - - - - - - - - - - - - - - - | | o x - - - - - - - - - - - - - - - - | | | x x - - - - - - - - - - - - - - - | | | | . o - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | o - - - - - - - - - - - - - | | | | | | | o - - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | x o - - - - - - - - - | | | | | | | | | | o x - - - - - - - - | | | | | | | | | | | o x - - - - - - - | | | | | | | | | | | | x x - - - - - - | | | | | | | | | | | | | o x - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | | o - - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | | o - | | | | | | | | | | | | | | | | | | | . The error in solving: 6.938894e-18 The error in solving: 2.779241e-16 The error in solving: 1.666780e-16 The error in solving: 2.860979e-17 The error in solving: 1.595946e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.527390 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.566324 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.725819 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.341438 -0.557951 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.981530 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.890196 0.091439 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.285716 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.695737 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.594322 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.890752 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.154164 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 12 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.594322 0.000000 0.000000 0.000000 Row indices: 0 0 0 1 2 2 3 3 3 5 6 6 8 8 9 9 10 10 11 12 12 Column indices: 4 4 7 9 10 11 12 13 14 17 19 19 Off-diagonal values: -0.527390 -0.566324 0.725819 -0.341438 -0.557951 0.981530 0.890196 0.091439 0.285716 -0.695737 0.890752 -0.154164 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - o - - - - - - - - - - - - - - - | | | . o - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - x - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . o o - - - - - - - - - | | | | | | | | | . - x - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . x x - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . x - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - o - - | | | | | | | | | | | | | | | | o - - - | | | | | | | | | | | | | | | | | . - x | | | | | | | | | | | | | | | | | | . o | | | | | | | | | | | | | | | | | | | . The error in solving: 2.559878e-16 The error in solving: 1.594436e-16 The error in solving: 3.251670e-16 The error in solving: 1.110223e-16 The error in solving: 1.249001e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 -0.938448 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.061178 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.988244 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.050528 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.519881 0.910312 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.523984 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.864831 -0.948825 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.277295 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.008879 -0.252368 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.445146 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.521539 -0.769456 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.032161 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.460457 0.173586 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.742015 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.933394 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.696909 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 16 (max 380) Diagonal entries: 0.000000 -0.061178 0.000000 0.050528 0.000000 0.000000 0.000000 0.864831 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.460457 0.742015 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 1 2 2 4 5 5 6 7 9 10 10 12 13 14 14 15 16 16 16 Column indices: 2 3 5 6 6 8 9 10 11 12 13 14 15 15 18 18 Off-diagonal values: -0.938448 0.988244 0.519881 0.910312 0.523984 -0.948825 -0.277295 0.008879 -0.252368 -0.445146 0.521539 -0.769456 -0.032161 0.173586 -0.933394 0.696909 . - o - - - - - - - - - - - - - - - - - | o - - - - - - - - - - - - - - - - - - | | . x - - - - - - - - - - - - - - - - | | | x - - - - - - - - - - - - - - - - | | | | . x x - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | x o - - - - - - - - - - - | | | | | | | | . o - - - - - - - - - - | | | | | | | | | . x o - - - - - - - - | | | | | | | | | | . - o - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . x o - - - - - | | | | | | | | | | | | | . - o - - - - | | | | | | | | | | | | | | o x - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | | . - o - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.118997e-16 The error in solving: 2.498002e-16 The error in solving: 2.254874e-16 The error in solving: 3.140233e-16 The error in solving: 3.189628e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.750000 [ 0.253295 0.054161 -0.894240 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.613665 -0.054922 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.667801 -0.388926 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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- - - - - - | | | | | o x o - - - - - - - - - - - - | | | | | | o o - - - - - - - - - - - - | | | | | | | x - - - - - - - - - - - - | | | | | | | | x o x - - - - - - - - - | | | | | | | | | o x o - - - - - - - - | | | | | | | | | | x o - - - - - - - - | | | | | | | | | | | x x x - - - - - - | | | | | | | | | | | | o o - - - - - - | | | | | | | | | | | | | . o o - - - - | | | | | | | | | | | | | | x o o - - - | | | | | | | | | | | | | | | . - o - - | | | | | | | | | | | | | | | | . x o - | | | | | | | | | | | | | | | | | x o o | | | | | | | | | | | | | | | | | | . o | | | | | | | | | | | | | | | | | | | o The error in solving: 6.397344e-17 The error in solving: 8.326673e-17 The error in solving: 1.301852e-16 The error in solving: 1.665335e-16 The error in solving: 1.570092e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.250000 [ -0.855896 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.615602 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.808659 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.995889 -0.343915 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.390115 0.639314 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.195963 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11 18 Off-diagonal values: -0.343915 0.639314 -0.933653 0.566910 -0.964050 o - - - - - - - - - - - - - - - - - - - | o - - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | | x o - - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | | o - - - - - - - - - - - - | | | | | | | | o o - - - - - - - - - - | | | | | | | | | o - - - - - - - - - - | | | | | | | | | | o x - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | | o - - - - - - - | | | | | | | | | | | | | o - - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | | | x o - | | | | | | | | | | | | | | | | | | o - | | | | | | | | | | | | | | | | | | | o The error in solving: 2.292987e-16 The error in solving: 2.482534e-16 The error in solving: 2.498002e-16 The error in solving: 1.112389e-16 The error in solving: 3.152427e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.168265 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.289304 -0.435667 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.159090 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.138080 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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entries: 0.168265 -0.289304 -0.159090 0.138080 -0.129666 0.328770 0.132084 -0.304696 0.066634 0.004804 0.760781 0.442963 -0.770763 0.156343 0.789277 0.207675 -0.106610 -0.193542 -0.694252 0.466139 Row indices: 0 0 1 1 1 1 1 1 1 1 1 2 3 4 4 4 5 6 7 8 8 Column indices: 2 11 12 13 16 17 18 19 Off-diagonal values: -0.435667 0.517554 -0.528966 -0.164744 0.621403 -0.342025 -0.734001 0.242601 x - - - - - - - - - - - - - - - - - - - | o o - - - - - - - - - - - - - - - - - | | o - - - - - - - - - - - - - - - - - | | | x - - - - - - - - - - - - - - - - | | | | o - - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | | o - - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | | x o - - - - - - - | | | | | | | | | | | | o o - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | | o o - - | | | | | | | | | | | | | | | | | o o - | | | | | | | | | | | | | | | | | | o x | | | | | | | | | | | | | | | | | | | x The error in solving: 1.594436e-16 The error in solving: 6.206335e-17 The error in solving: 5.551115e-17 The error in solving: 1.241267e-16 The error in solving: 7.850462e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.813586 0.816104 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.197374 -0.834807 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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- - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | | o o - - - - - - - - - - - | | | | | | | | x o - - - - - - - - - - | | | | | | | | | o - - - - - - - - - - | | | | | | | | | | x o - - - - - - - - | | | | | | | | | | | o x - - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | | o o - - - - - | | | | | | | | | | | | | | x o - - - - | | | | | | | | | | | | | | | o o - - - | | | | | | | | | | | | | | | | o x - - | | | | | | | | | | | | | | | | | o - - | | | | | | | | | | | | | | | | | | o - | | | | | | | | | | | | | | | | | | | x The error in solving: 2.482534e-16 The error in solving: 2.077037e-16 The error in solving: 1.110223e-16 The error in solving: 2.775558e-16 The error in solving: 3.146312e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.396472 0.254669 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.413882 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.832893 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.474955 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.022773 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.017184 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.566405 0.000000 -0.610129 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.382259 0.298757 -0.670556 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.697946 -0.842123 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.678545]; Dimension: 20 x 20 Off-diagonal entries: 9 (max 380) Diagonal entries: 0.396472 -0.413882 -0.832893 -0.474955 -0.022773 0.017184 0.652725 -0.010375 -0.339048 -0.575280 -0.734172 -0.679771 0.827729 0.036175 0.201319 -0.450230 -0.566405 -0.382259 -0.697946 -0.678545 Row indices: 0 1 1 1 1 1 1 2 2 2 2 2 2 3 5 5 5 6 8 9 9 Column indices: 1 8 13 14 15 18 18 19 19 Off-diagonal values: 0.254669 0.393051 -0.945726 -0.841739 0.486536 -0.610129 0.298757 -0.670556 -0.842123 x x - - - - - - - - - - - - - - - - - - | o - - - - - - - - - - - - - - - - - - | | o - - - - - - - - - - - - - - - - - | | | o - - - - - - - - - - - - - - - - | | | | o - - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | x - x - - - - - - - - - - - | | | | | | | o - - - - - - - - - - - - | | | | | | | | o - - - - - - - - - - - | | | | | | | | | o - - - - - - - - - - | | | | | | | | | | o - - - - - - - - - | | | | | | | | | | | o - - - - - - - - | | | | | | | | | | | | x o - - - - - - | | | | | | | | | | | | | x o x - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | o - - - - | | | | | | | | | | | | | | | | o - o - | | | | | | | | | | | | | | | | | o x o | | | | | | | | | | | | | | | | | | o o | | | | | | | | | | | | | | | | | | | o The error in solving: 2.719480e-16 The error in solving: 1.665696e-16 The error in solving: 2.237726e-16 The error in solving: 1.301852e-16 The error in solving: 5.551115e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.500000 [ -0.768058 -0.385727 -0.365546 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.091288 0.000000 0.636883 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.957297 0.509997 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.574547 -0.289760 0.289493 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.605767 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.320403 -0.147263 0.223623 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.451435 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.608418 0.962898 -0.499192 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.150700 0.000000 -0.152757 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.073670 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.459765 0.096599 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.737690 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.221179 0.000000 -0.210313 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.539012 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.290763 -0.123233 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.422952 0.726622 -0.602417 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.064562 0.696670 0.808778 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.655281 0.000000 -0.340388 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.393566 -0.452072 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.330363]; Dimension: 20 x 20 Off-diagonal entries: 20 (max 380) Diagonal entries: -0.768058 -0.091288 0.957297 0.574547 0.605767 -0.320403 -0.451435 -0.608418 0.150700 -0.073670 -0.459765 0.737690 -0.221179 0.539012 -0.290763 -0.422952 0.064562 -0.655281 0.393566 0.330363 Row indices: 0 2 3 4 6 6 8 8 10 11 11 12 12 13 13 14 16 18 19 20 20 Column indices: 1 2 3 3 4 5 6 7 8 9 10 11 14 15 16 17 17 18 19 19 Off-diagonal values: -0.385727 -0.365546 0.636883 0.509997 -0.289760 0.289493 -0.147263 0.223623 0.962898 -0.499192 -0.152757 0.096599 -0.210313 -0.123233 0.726622 -0.602417 0.696670 0.808778 -0.340388 -0.452072 o o o - - - - - - - - - - - - - - - - - | o - x - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | | x o x - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | o o x - - - - - - - - - - - - | | | | | | o - - - - - - - - - - - - - | | | | | | | o x o - - - - - - - - - - | | | | | | | | x - o - - - - - - - - - | | | | | | | | | o - - - - - - - - - - | | | | | | | | | | o x - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | | o - o - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | o o - - - - | | | | | | | | | | | | | | | o x o - - | | | | | | | | | | | | | | | | x x x - | | | | | | | | | | | | | | | | | o - o | | | | | | | | | | | | | | | | | | x o | | | | | | | | | | | | | | | | | | | x The error in solving: 2.737128e-16 The error in solving: 1.597830e-16 The error in solving: 1.756788e-16 The error in solving: 2.989568e-16 The error in solving: 5.721958e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.750000 [ -0.885341 -0.787739 -0.140159 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.417233 -0.378732 -0.324101 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.969910 0.054071 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.550122 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.092499 0.089585 -0.159241 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.910385 -0.078158 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.443721 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.524410 0.824440 -0.745399 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.262854 -0.308299 -0.978175 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.956226 0.398664 -0.986392 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.606622 0.258772 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.407522 0.649947 -0.692512 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.984712 0.375535 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.778017 0.277035 0.973550 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.893828 0.000000 0.107933 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.056570 -0.815296 0.177277 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.701057 0.074545 -0.821163 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.854677 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.787790 -0.004224 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.042004]; Dimension: 20 x 20 Off-diagonal entries: 26 (max 380) Diagonal entries: -0.885341 0.417233 -0.969910 -0.550122 0.092499 0.910385 -0.443721 0.524410 -0.262854 -0.956226 0.606622 0.407522 0.984712 -0.778017 -0.893828 0.056570 0.701057 0.854677 -0.787790 -0.042004 Row indices: 0 2 4 5 5 7 8 8 10 12 14 15 17 18 20 21 23 25 25 26 26 Column indices: 1 2 2 3 3 5 6 6 8 9 9 10 10 11 11 12 13 13 14 15 16 16 17 17 18 19 Off-diagonal values: -0.787739 -0.140159 -0.378732 -0.324101 0.054071 0.089585 -0.159241 -0.078158 0.824440 -0.745399 -0.308299 -0.978175 0.398664 -0.986392 0.258772 0.649947 -0.692512 0.375535 0.277035 0.973550 0.107933 -0.815296 0.177277 0.074545 -0.821163 -0.004224 o o o - - - - - - - - - - - - - - - - - | x o o - - - - - - - - - - - - - - - - | | o x - - - - - - - - - - - - - - - - | | | o - - - - - - - - - - - - - - - - | | | | x x o - - - - - - - - - - - - - | | | | | x o - - - - - - - - - - - - - | | | | | | o - - - - - - - - - - - - - | | | | | | | x x o - - - - - - - - - - | | | | | | | | o o o - - - - - - - - - | | | | | | | | | o x o - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | | x x o - - - - - - | | | | | | | | | | | | x x - - - - - - | | | | | | | | | | | | | o x x - - - - | | | | | | | | | | | | | | o - x - - - | | | | | | | | | | | | | | | x o x - - | | | | | | | | | | | | | | | | x x o - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | | o o | | | | | | | | | | | | | | | | | | | o The error in solving: 3.764949e-16 The error in solving: 1.144392e-16 The error in solving: 2.305551e-16 The error in solving: 1.152776e-16 The error in solving: 1.110223e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.368896 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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Off-diagonal entries: 3 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3 3 Column indices: 2 13 17 Off-diagonal values: -0.368896 -0.208091 -0.592715 . - - - - - - - - - - - - - - - - - - - | . o - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . o - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - 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The error in solving: 0.000000e+00 The error in solving: 6.798700e-17 The error in solving: 5.721958e-17 The error in solving: 1.110223e-16 The error in solving: 2.482534e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.210702 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.119143 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.124709 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.400817 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.399942 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.592365 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 6 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 1 1 1 2 2 3 3 4 4 4 5 5 5 6 6 6 6 6 Column indices: 2 6 8 10 13 16 Off-diagonal values: 0.210702 0.119143 -0.124709 -0.400817 -0.399942 -0.592365 . - - - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . o - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . o - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . o - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . o - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.179612e-16 The error in solving: 1.367244e-16 The error in solving: 2.305551e-16 The error in solving: 1.570092e-16 The error in solving: 2.498002e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.253524 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.601264 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.280293 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.914604 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.808848 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.177341 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.336485 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.233574 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.342115 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.639387 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.033894 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.903675 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.287975 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.012804 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 14 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 3 3 4 4 4 4 5 6 7 8 9 9 10 11 12 13 14 14 Column indices: 1 2 3 5 9 10 11 12 13 15 16 17 18 19 Off-diagonal values: 0.253524 -0.601264 -0.280293 0.914604 0.808848 0.177341 0.336485 0.233574 0.342115 -0.639387 0.033894 0.903675 0.287975 0.012804 . x - - - - - - - - - - - - - - - - - - | . o - - - - - - - - - - - - - - - - - | | . o - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | | | . x - - - - - - - - - | | | | | | | | | | . x - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | | . x - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . o - - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | | . The error in solving: 2.355139e-16 The error in solving: 1.301852e-16 The error in solving: 8.777084e-17 The error in solving: 1.594436e-16 The error in solving: 2.789401e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.247057 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.920364 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.240732 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.453452 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.304724 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.096070 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.436746 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.354534 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.473939 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.709990 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.677558 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.902450 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.025798 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.511520 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 14 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 3 4 5 6 7 8 8 9 9 9 10 11 12 12 13 13 14 14 Column indices: 2 3 4 5 5 7 7 8 10 14 14 15 18 19 Off-diagonal values: 0.247057 -0.920364 0.240732 -0.453452 0.304724 -0.096070 0.436746 -0.354534 -0.473939 -0.709990 0.677558 0.902450 -0.025798 -0.511520 . - x - - - - - - - - - - - - - - - - - | . - o - - - - - - - - - - - - - - - - | | . - x - - - - - - - - - - - - - - - | | | . - o - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | | | . - o - - - - - - - - - - - - | | | | | | . x - - - - - - - - - - - - | | | | | | | . o - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . o - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - o - - - - - | | | | | | | | | | | | | . x - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - o - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . o | | | | | | | | | | | | | | | | | | | . The error in solving: 1.110231e-16 The error in solving: 1.110223e-16 The error in solving: 6.992894e-18 The error in solving: 0.000000e+00 The error in solving: 3.342214e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.834236 0.506512 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.877783 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.834105 -0.258775 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.371328 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.991858 -0.031588 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.973476 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.074124 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.266128 -0.839222 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.543493 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.505630 -0.936623 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.862803 -0.103017 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.533937 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.925523 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.268404 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.962863 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 21 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 3 5 6 8 9 9 10 10 12 13 15 17 17 18 19 20 21 21 21 Column indices: 1 2 3 3 4 4 5 6 7 8 10 11 11 12 13 13 14 15 17 17 19 Off-diagonal values: 0.834236 0.506512 -0.877783 -0.834105 -0.258775 -0.371328 0.991858 -0.031588 0.973476 -0.074124 0.266128 -0.839222 -0.543493 -0.505630 -0.936623 -0.862803 -0.103017 0.533937 -0.925523 -0.268404 -0.962863 . x x - - - - - - - - - - - - - - - - - | . - o - - - - - - - - - - - - - - - - | | . o o - - - - - - - - - - - - - - - | | | . o - - - - - - - - - - - - - - - | | | | . x o - - - - - - - - - - - - - | | | | | . - x - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . o - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . x o - - - - - - - - | | | | | | | | | | . o - - - - - - - - | | | | | | | | | | | . o o - - - - - - | | | | | | | | | | | | . o o - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | | . - o - - | | | | | | | | | | | | | | | | . o - - | | | | | | | | | | | | | | | | | . - o | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.145734e-17 The error in solving: 0.000000e+00 The error in solving: 2.220446e-16 The error in solving: 2.237995e-16 The error in solving: 3.284130e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.664737 0.368627 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.617532 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.141224 -0.087784 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.113635 0.804882 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.521823 -0.638868 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.403785 -0.877303 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.027635 -0.135778 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.012788 -0.349246 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.181233 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.787691 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.812621 0.549509 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.121637 -0.314791 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.275419 -0.952564 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.539701 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.389173 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.065992 0.884302 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.858821 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 28 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 3 5 7 9 11 13 15 16 17 19 21 21 23 24 25 25 27 28 28 Column indices: 1 2 2 3 4 4 5 5 6 6 7 7 8 8 9 10 10 11 12 12 13 14 15 16 16 18 19 19 Off-diagonal values: 0.664737 0.368627 0.617532 -0.141224 -0.087784 -0.113635 0.804882 -0.521823 -0.638868 -0.403785 -0.877303 -0.027635 -0.135778 0.012788 -0.349246 0.181233 -0.787691 -0.812621 0.549509 -0.121637 -0.314791 0.275419 -0.952564 0.539701 -0.389173 -0.065992 0.884302 -0.858821 . x x - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | | . o o - - - - - - - - - - - - - - - | | | . o x - - - - - - - - - - - - - - | | | | . o o - - - - - - - - - - - - - | | | | | . o o - - - - - - - - - - - - | | | | | | . o o - - - - - - - - - - - | | | | | | | . x o - - - - - - - - - - | | | | | | | | . - x - - - - - - - - - | | | | | | | | | . o - - - - - - - - - | | | | | | | | | | . o x - - - - - - - | | | | | | | | | | | . o o - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . x o - - - - | | | | | | | | | | | | | | . - x - - - | | | | | | | | | | | | | | | . o - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . o x | | | | | | | | | | | | | | | | | | . o | | | | | | | | | | | | | | | | | | | . The error in solving: 1.110223e-16 The error in solving: 2.482534e-16 The error in solving: 1.279469e-16 The error in solving: 1.110223e-16 The error in solving: 2.498002e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.970805 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.736098 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.933340 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.647584 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.585055 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.052264 -0.540703 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.308771 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.339715 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.031108 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 6 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.933340 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.052264 0.000000 0.000000 0.000000 0.339715 1.031108 0.000000 0.000000 Row indices: 0 0 0 1 2 2 2 2 2 2 2 3 4 5 5 6 6 6 6 6 6 Column indices: 3 4 11 12 13 15 Off-diagonal values: -0.970805 1.736098 -0.647584 -1.585055 -0.540703 1.308771 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . o - - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . o - - - - - - - - | | | | | | | | | | | . o - - - - - - - | | | | | | | | | | | | x o - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.279469e-16 The error in solving: 2.482534e-16 The error in solving: 2.558938e-16 The error in solving: 7.850462e-17 The error in solving: 2.220463e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.746710 -0.356064 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.038626 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.143575 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.033355 2.558716 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.872901 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.100376 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.625205 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.975959 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.354490 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.018395 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.621304 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.028503 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.076965 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.657816 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.344734 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.624040 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 10 (max 380) Diagonal entries: 0.000000 -0.746710 0.000000 -0.143575 0.033355 0.000000 0.000000 0.000000 0.975959 0.000000 0.000000 0.000000 -0.621304 -2.028503 0.076965 0.000000 0.000000 -0.624040 0.000000 0.000000 Row indices: 0 0 1 2 2 3 4 5 6 6 6 7 8 8 8 8 9 10 10 10 10 Column indices: 2 3 5 6 7 8 11 12 16 17 Off-diagonal values: -0.356064 -1.038626 2.558716 -0.872901 0.100376 0.625205 -0.354490 0.018395 -1.657816 0.344734 . - - - - - - - - - - - - - - - - - - - | o o - - - - - - - - - - - - - - - - - | | . o - - - - - - - - - - - - - - - - | | | o - - - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | | | | | . o - - - - - - - - - - - - - | | | | | | . x - - - - - - - - - - - - | | | | | | | . x - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . o - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | | o - - - - - - - | | | | | | | | | | | | | o - - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | . o - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | | o - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.483504e-16 The error in solving: 1.256687e-16 The error in solving: 1.570092e-16 The error in solving: 1.177569e-16 The error in solving: 2.558938e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.750000 [ -0.898998 -0.048855 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.046034 -0.463201 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.393106 1.721896 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.717320 -1.883448 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.732783 -0.456772 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.254650 0.717087 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.832370 -0.373808 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.310428 0.392318 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.248820 -0.710365 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.507648 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.083611 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.484445 0.213748 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.476570 -0.044617 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.826304 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.501254 -0.266405 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.672684 0.162989 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.620824 1.322411 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.638348 0.724170 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.243065]; Dimension: 20 x 20 Off-diagonal entries: 17 (max 380) Diagonal entries: -0.898998 1.046034 -0.393106 0.717320 -1.732783 0.254650 0.000000 -0.832370 1.310428 -0.248820 0.000000 -0.083611 0.484445 0.476570 0.000000 0.501254 1.672684 0.620824 0.638348 0.243065 Row indices: 0 1 2 3 4 5 6 6 7 8 9 10 10 11 12 13 14 15 16 17 17 Column indices: 1 2 3 4 5 6 8 9 10 11 13 14 15 16 17 18 19 Off-diagonal values: -0.048855 -0.463201 1.721896 -1.883448 -0.456772 0.717087 -0.373808 0.392318 -0.710365 -0.507648 0.213748 -0.044617 0.826304 -0.266405 0.162989 1.322411 0.724170 o o - - - - - - - - - - - - - - - - - - | x o - - - - - - - - - - - - - - - - - | | o x - - - - - - - - - - - - - - - - | | | x o - - - - - - - - - - - - - - - | | | | o o - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | o o - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | o o - - - - - - - - - | | | | | | | | | | . o - - - - - - - - | | | | | | | | | | | o - - - - - - - - | | | | | | | | | | | | x x - - - - - - | | | | | | | | | | | | | x o - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | | x o - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | | x The error in solving: 1.118863e-16 The error in solving: 1.570476e-16 The error in solving: 2.220514e-16 The error in solving: 2.224779e-16 The error in solving: 5.553825e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.250000 [ -0.330009 1.847804 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.078594 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.331874 -0.108805 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 11 (max 380) Diagonal entries: -0.330009 1.078594 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.835331 0.000000 0.000000 0.000000 0.331874 0.000000 Row indices: 0 1 1 1 1 1 1 2 3 3 4 4 5 6 6 7 8 10 10 11 11 Column indices: 1 8 8 10 12 13 15 17 17 18 19 Off-diagonal values: 1.847804 0.428597 -0.055342 -0.657841 -1.571777 0.728141 0.092338 -0.901844 -0.371429 -0.688577 -0.108805 o x - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - x - - - - - - - - - - - | | | | | | | . o - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . o - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . o - - - - - - - | | | | | | | | | | | | . x - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | o x - - - - | | | | | | | | | | | | | | | . - o - - | | | | | | | | | | | | | | | | . o o - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | x o | | | | | | | | | | | | | | | | | | | . The error in solving: 1.841097e-16 The error in solving: 1.146493e-16 The error in solving: 2.244440e-16 The error in solving: 1.570092e-16 The error in solving: 2.775558e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.083951 -1.041430 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.262826 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.887660 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.398721 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.581694 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.062994 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.618093 -0.281130 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.868864 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.470422 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.870157 -0.718572 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.568476 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.534406 0.549104 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.715477 0.000000 -0.380983 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.138633 -0.473985 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 14 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 1.887660 0.000000 -1.398721 0.000000 0.000000 0.618093 0.000000 0.000000 0.000000 0.000000 -2.568476 0.000000 -1.715477 -2.138633 0.000000 0.000000 Row indices: 0 0 2 3 3 3 3 3 4 5 6 6 7 8 10 10 12 13 14 14 14 Column indices: 2 3 3 9 10 10 13 14 14 15 16 17 18 18 Off-diagonal values: 1.083951 -1.041430 -0.262826 -1.581694 2.062994 -0.281130 -0.868864 0.470422 -0.870157 -0.718572 0.534406 0.549104 -0.380983 -0.473985 . - - - - - - - - - - - - - - - - - - - | . x o - - - - - - - - - - - - - - - - | | . o - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | o - - - - - - - - - - - - - | | | | | | | . - o - - - - - - - - - - | | | | | | | | . - x - - - - - - - - - | | | | | | | | | x o - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - o - - - - - - | | | | | | | | | | | | . - x - - - - - | | | | | | | | | | | | | . o o - - - - | | | | | | | | | | | | | | o - - - - - | | | | | | | | | | | | | | | . x x - - | | | | | | | | | | | | | | | | o - o - | | | | | | | | | | | | | | | | | o o - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.624353e-16 The error in solving: 2.482534e-16 The error in solving: 2.482534e-16 The error in solving: 2.237726e-16 The error in solving: 1.359768e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.750000 [ 1.306720 -0.238037 1.186808 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.645083 0.594515 1.111148 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.556682 0.000000 -0.889315 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.191286 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.561233 -1.065011 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.230192 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.512608 -0.528682 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.111123 0.000000 -1.076591 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.627517 1.911463 -0.893889 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.646753 0.481624 0.025577 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.302244 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.189232 -1.214846 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.445144 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.433469 0.441797 0.790728 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.032626 -1.151609 -0.844622 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.700964 0.000000 0.000289 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.223511 0.706388 -0.072501 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.068304 0.299689 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.637572 0.315710 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.430855]; Dimension: 20 x 20 Off-diagonal entries: 27 (max 380) Diagonal entries: 1.306720 0.645083 0.556682 0.000000 -0.561233 0.000000 0.000000 -0.111123 0.627517 -1.646753 0.000000 0.000000 1.445144 1.433469 1.032626 0.700964 0.223511 1.068304 0.637572 -0.430855 Row indices: 0 2 4 5 6 7 8 10 11 13 15 16 18 18 20 22 23 25 26 27 27 Column indices: 1 2 2 3 4 5 5 7 7 8 9 9 10 10 11 12 12 13 14 15 15 16 17 17 18 18 19 Off-diagonal values: -0.238037 1.186808 0.594515 1.111148 -0.889315 -0.191286 -1.065011 0.230192 0.512608 -0.528682 -1.076591 1.911463 -0.893889 0.481624 0.025577 0.302244 -0.189232 -1.214846 0.441797 0.790728 -1.151609 -0.844622 0.000289 0.706388 -0.072501 0.299689 0.315710 x o x - - - - - - - - - - - - - - - - - | x x x - - - - - - - - - - - - - - - - | | x - o - - - - - - - - - - - - - - - | | | . - o - - - - - - - - - - - - - - | | | | o o - - - - - - - - - - - - - - | | | | | . - x - - - - - - - - - - - - | | | | | | . x o - - - - - - - - - - - | | | | | | | o - o - - - - - - - - - - | | | | | | | | x x o - - - - - - - - - | | | | | | | | | o x x - - - - - - - - | | | | | | | | | | . - x - - - - - - - | | | | | | | | | | | . o o - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | | x x x - - - - | | | | | | | | | | | | | | x o o - - - | | | | | | | | | | | | | | | x - x - - | | | | | | | | | | | | | | | | x x o - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | | o The error in solving: 1.001681e-16 The error in solving: 7.972182e-17 The error in solving: 1.594436e-16 The error in solving: 2.238802e-16 The error in solving: 5.721958e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.250000 [ -2.174552 -0.383573 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.666162 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.168070 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.461448 -0.751260 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.236580 -0.195407 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.809793 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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-0.195407 -0.529958 0.938688 -0.355157 o o - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | | o o - - - - - - - - - - - - - - - | | | | x o - - - - - - - - - - - - - - | | | | | o - - - - - - - - - - - - - - | | | | | | o - - - - - - - - - - - - - | | | | | | | o - - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | | o - - - - - - - - | | | | | | | | | | | | o - - - - - - - | | | | | | | | | | | | | o o - - - - - | | | | | | | | | | | | | | o - - - - - | | | | | | | | | | | | | | | o - - - - | | | | | | | | | | | | | | | | o x - - | | | | | | | | | | | | | | | | | o - - | | | | | | | | | | | | | | | | | | x o | | | | | | | | | | | | | | | | | | | o The error in solving: 1.110223e-16 The error in solving: 2.355139e-16 The error in solving: 0.000000e+00 The error in solving: 1.241267e-16 The error in solving: 2.482777e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.500000 [ 0.000803 0.059498 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.256750 -0.562105 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.747374 -0.887271 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.308007 1.088301 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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1.082181 0.424222 1.127488 -0.040314 0.635119 1.972207 1.788072 1.643305 0.036914 0.532925 -1.190529 -0.423943 1.276882 -0.853373 -1.067574 1.311080 Row indices: 0 1 2 3 4 5 5 5 6 6 6 6 7 8 9 10 10 10 10 11 11 Column indices: 1 2 3 4 5 8 12 13 14 15 19 Off-diagonal values: 0.059498 -0.562105 -0.887271 1.088301 1.285432 -0.187949 0.387373 -1.829906 -0.977901 -1.578671 0.549265 x x - - - - - - - - - - - - - - - - - - | x o - - - - - - - - - - - - - - - - - | | o o - - - - - - - - - - - - - - - - | | | x x - - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | | o o - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | | x x - - - - - - - | | | | | | | | | | | | x o - - - - - - | | | | | | | | | | | | | x o - - - - - | | | | | | | | | | | | | | o o - - - - | | | | | | | | | | | | | | | o - - - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | | | o - - | | | | | | | | | | | | | | | | | | o x | | | | | | | | | | | | | | | | | | | x The error in solving: 1.241388e-16 The error in solving: 2.254874e-16 The error in solving: 1.110223e-16 The error in solving: 7.972182e-17 The error in solving: 3.041263e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.750000 [ -0.111611 0.121224 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.062357 -0.243246 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.924975 -0.876421 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.238452 -1.114281 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.286987 -0.234839 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.869509 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.423261 0.406849 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.151075 -1.589796 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.539901 0.723538 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.620028 0.162178 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.066182 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.107946 -2.179043 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.298618 0.608269 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 3.745254 1.228245 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.754873]; Dimension: 20 x 20 Off-diagonal entries: 16 (max 380) Diagonal entries: -0.111611 -1.062357 -0.924975 0.238452 -0.286987 0.869509 0.423261 -0.151075 0.055941 -1.830467 0.069890 0.823769 -0.392388 0.539901 0.620028 1.066182 0.107946 0.298618 3.745254 -0.754873 Row indices: 0 1 2 3 4 5 5 6 7 7 8 9 10 11 12 13 13 14 15 16 16 Column indices: 1 2 3 4 5 7 8 10 11 12 13 14 15 17 18 19 Off-diagonal values: 0.121224 -0.243246 -0.876421 -1.114281 -0.234839 0.406849 -1.589796 -0.338648 1.337489 0.006081 -0.989730 0.723538 0.162178 -2.179043 0.608269 1.228245 o x - - - - - - - - - - - - - - - - - - | o o - - - - - - - - - - - - - - - - - | | o o - - - - - - - - - - - - - - - - | | | x o - - - - - - - - - - - - - - - | | | | o o - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | o o - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | | o o - - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | | x x - - - - - - - | | | | | | | | | | | | o o - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | | x o - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | | o The error in solving: 5.088746e-16 The error in solving: 3.164623e-16 The error in solving: 2.775558e-17 The error in solving: 2.482534e-16 The error in solving: 3.480921e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.250000 [ 0.515631 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.061653 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.377752 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.645809 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.060611 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.640975 0.388303 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.146283 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.693746 0.282427 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.982804 -1.152798 0.294095 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.055021 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.630348 -0.773279 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.531804 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.834534 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.159788 0.000000 -1.765208 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.669453 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.996788 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.425107 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.384117 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.103823 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.263753]; Dimension: 20 x 20 Off-diagonal entries: 6 (max 380) Diagonal entries: 0.515631 1.061653 -0.377752 0.645809 -0.060611 0.640975 0.146283 0.693746 -2.982804 -0.055021 -0.630348 0.531804 0.834534 0.159788 -0.669453 0.996788 0.425107 1.384117 0.103823 -0.263753 Row indices: 0 0 0 0 0 0 1 1 2 4 4 5 5 5 6 6 6 6 6 6 6 Column indices: 6 8 9 10 11 15 Off-diagonal values: 0.388303 0.282427 -1.152798 0.294095 -0.773279 -1.765208 x - - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | | o - - - - - - - - - - - - - - - - - | | | x - - - - - - - - - - - - - - - - | | | | o - - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | o o x - - - - - - - - - | | | | | | | | | o - - - - - - - - - - | | | | | | | | | | o o - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | | x - o - - - - | | | | | | | | | | | | | | o - - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | o The error in solving: 2.220446e-16 The error in solving: 2.719480e-16 The error in solving: 3.140185e-16 The error in solving: 2.543841e-16 The error in solving: 1.110223e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.500000 [ 0.382246 -1.373960 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.094753 0.000000 -0.523057 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.168303 -0.482515 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.320594 1.471100 -0.142352 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.789476 -0.607029 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.667375 -0.339142 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.144361 -0.243136 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.610349 1.697480 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.316453 0.000000 2.320063 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.467121 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.563820 0.731787 -0.609955 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.008221 -1.820004 0.827023 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.605616 0.000000 0.590926 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.752894 0.000000 0.308373 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.810497 0.000000 0.826880 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.293549 0.000000 -0.295701 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.083178 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.519332 -0.634311 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.258850 -2.176041 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.383085]; Dimension: 20 x 20 Off-diagonal entries: 20 (max 380) Diagonal entries: 0.382246 0.094753 0.168303 1.320594 -0.789476 -0.667375 1.144361 -0.610349 -0.316453 -1.467121 -0.563820 -0.008221 1.605616 0.752894 -2.810497 0.293549 -0.083178 1.519332 -1.258850 -0.383085 Row indices: 0 1 2 3 5 6 7 8 9 10 10 12 14 15 16 17 18 18 19 20 20 Column indices: 1 3 3 4 5 5 6 7 8 10 11 12 12 13 14 15 16 17 18 19 Off-diagonal values: -1.373960 -0.523057 -0.482515 1.471100 -0.142352 -0.607029 -0.339142 -0.243136 1.697480 2.320063 0.731787 -0.609955 -1.820004 0.827023 0.590926 0.308373 0.826880 -0.295701 -0.634311 -2.176041 x o - - - - - - - - - - - - - - - - - - | x - o - - - - - - - - - - - - - - - - | | x o - - - - - - - - - - - - - - - - | | | x x o - - - - - - - - - - - - - - | | | | o o - - - - - - - - - - - - - - | | | | | o o - - - - - - - - - - - - - | | | | | | x o - - - - - - - - - - - - | | | | | | | o x - - - - - - - - - - - | | | | | | | | o - x - - - - - - - - - | | | | | | | | | o - - - - - - - - - - | | | | | | | | | | o x o - - - - - - - | | | | | | | | | | | o o x - - - - - - | | | | | | | | | | | | x - x - - - - - | | | | | | | | | | | | | x - x - - - - | | | | | | | | | | | | | | o - x - - - | | | | | | | | | | | | | | | x - o - - | | | | | | | | | | | | | | | | o - - - | | | | | | | | | | | | | | | | | x o - | | | | | | | | | | | | | | | | | | o o | | | | | | | | | | | | | | | | | | | o The error in solving: 2.830524e-16 The error in solving: 2.501854e-16 The error in solving: 2.720365e-16 The error in solving: 2.371691e-16 The error in solving: 1.110223e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.750000 [ -0.221515 0.048618 -0.436790 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.854903 1.064991 1.080496 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0.458540 -0.966344 -2.094989 -1.389936 -0.990413 0.724538 -0.491486 1.682200 -0.999214 0.509078 -1.720982 0.257400 o x o - - - - - - - - - - - - - - - - - | o x x - - - - - - - - - - - - - - - - | | o x o - - - - - - - - - - - - - - - | | | o - - - - - - - - - - - - - - - - | | | | o o o - - - - - - - - - - - - - | | | | | o x - - - - - - - - - - - - - | | | | | | x o x - - - - - - - - - - - | | | | | | | o x - - - - - - - - - - - | | | | | | | | x x o - - - - - - - - - | | | | | | | | | o x x - - - - - - - - | | | | | | | | | | x o - - - - - - - - | | | | | | | | | | | x o - - - - - - - | | | | | | | | | | | | x o o - - - - - | | | | | | | | | | | | | o - x - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | x - o - - | | | | | | | | | | | | | | | | o x o - | | | | | | | | | | | | | | | | | o x o | | | | | | | | | | | | | | | | | | o x | | | | | | | | | | | | | | | | | | | o The error in solving: 3.342934e-16 The error in solving: 1.301852e-16 The error in solving: 4.163336e-17 The error in solving: 6.245005e-17 The error in solving: 1.110223e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.495026 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 Column indices: 4 9 Off-diagonal values: 0.495026 1.188102 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.775558e-17 The error in solving: 2.305551e-16 The error in solving: 2.792851e-16 The error in solving: 1.361509e-16 The error in solving: 1.110223e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.295090 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.042147 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.044731 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.809095 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.976337 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.585302 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.022455 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.470470 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.549080 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.905648 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.927223 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.636071 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.084232 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.651096 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 14 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 1 2 3 4 4 5 6 7 8 9 10 11 12 13 13 14 14 14 Column indices: 3 4 5 6 8 9 10 11 12 13 14 15 16 18 Off-diagonal values: -1.295090 -0.042147 -0.044731 -0.809095 0.976337 0.585302 0.022455 0.470470 -1.549080 0.905648 -1.927223 -0.636071 -0.084232 -0.651096 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . o - - - - - - - - - - - - - - - - | | | . o - - - - - - - - - - - - - - - | | | | . o - - - - - - - - - - - - - - | | | | | . o - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . x - - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | | | . x - - - - - - - - - | | | | | | | | | | . x - - - - - - - - | | | | | | | | | | | . o - - - - - - - | | | | | | | | | | | | . x - - - - - - | | | | | | | | | | | | | . o - - - - - | | | | | | | | | | | | | | . o - - - - | | | | | | | | | | | | | | | . o - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . o - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.720365e-16 The error in solving: 5.575456e-17 The error in solving: 3.421937e-16 The error in solving: 2.288783e-16 The error in solving: 2.486410e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 1-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.637121 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.575941 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.173097 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.284552 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.208966 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.808676 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.195391 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.250511 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.877601 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.980032 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.003665 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.045293 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.620131 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.588638 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 14 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 1 2 3 3 4 5 6 7 8 8 9 10 11 11 12 13 13 14 14 Column indices: 1 3 4 6 7 8 9 10 12 13 14 16 17 19 Off-diagonal values: 0.637121 0.575941 0.173097 -0.284552 -0.208966 -0.808676 -1.195391 -0.250511 -0.877601 -0.980032 2.003665 1.045293 -0.620131 -0.588638 . x - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . x - - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . o - - - - - - - - - - - - - | | | | | | . o - - - - - - - - - - - - | | | | | | | . o - - - - - - - - - - - | | | | | | | | . o - - - - - - - - - - | | | | | | | | | . o - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . o - - - - - - - | | | | | | | | | | | | . o - - - - - - | | | | | | | | | | | | | . x - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | | . o - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . o | | | | | | | | | | | | | | | | | | | . The error in solving: 2.989370e-16 The error in solving: 4.163336e-16 The error in solving: 1.279939e-16 The error in solving: 2.371437e-16 The error in solving: 7.850462e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.684079 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.714741 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.394772 1.016137 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.564847 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.733717 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 6 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 1 1 2 2 2 2 2 2 2 2 2 2 4 5 5 6 6 6 Column indices: 4 6 15 16 17 19 Off-diagonal values: -0.684079 0.714741 -1.394772 1.016137 -1.564847 2.733717 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - o - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - x - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . o x - - - | | | | | | | | | | | | | | | . - o - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - x | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 0.000000e+00 The error in solving: 1.579670e-16 The error in solving: 1.671107e-16 The error in solving: 2.288783e-16 The error in solving: 1.110359e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.500000 [ 0.000000 -1.508858 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.414539 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.348562 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.797834 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.810522 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.165395 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.960614 0.344423 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.412081 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.368777 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.447300 2.666831 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.013419 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.975335 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.265298 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.192929 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.822934 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.569355 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 18 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 3 4 4 5 6 8 9 10 12 13 14 15 16 16 17 18 18 18 Column indices: 1 3 4 4 7 7 8 9 10 10 11 12 12 14 15 15 17 19 Off-diagonal values: -1.508858 -0.414539 -0.348562 1.797834 1.810522 0.165395 2.960614 0.344423 -0.412081 -0.368777 -1.447300 2.666831 1.013419 -0.975335 0.265298 -1.192929 0.822934 0.569355 . o - - - - - - - - - - - - - - - - - - | . - o - - - - - - - - - - - - - - - - | | . - o - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - x - - - - - - - - - - - - | | | | | | . x - - - - - - - - - - - - | | | | | | | . x x - - - - - - - - - - | | | | | | | | . - o - - - - - - - - - | | | | | | | | | . o - - - - - - - - - | | | | | | | | | | . o x - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | | . - o - - - - - | | | | | | | | | | | | | . - x - - - - | | | | | | | | | | | | | | . o - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | | . - x | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.220734e-16 The error in solving: 1.241267e-16 The error in solving: 1.570092e-16 The error in solving: 5.594483e-17 The error in solving: 1.755417e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A upper-triangular 2-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.750000 [ 0.000000 1.200396 1.031189 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.645600 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.290982 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.084845 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.180704 -1.362611 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.275774 -1.131994 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.417299 -0.851815 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.840130 -0.425925 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.142096 1.048548 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.329938 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.749882 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.409274 2.934881 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.258574 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.440093 -1.219152 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.536816 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.337721 -0.183903 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.098953 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.351417 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.751508 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 28 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 3 4 5 7 9 11 13 15 16 17 19 20 22 23 25 26 27 28 28 Column indices: 1 2 2 4 4 5 6 6 7 7 8 8 9 9 10 11 12 12 13 13 14 15 15 16 17 17 18 19 Off-diagonal values: 1.200396 1.031189 0.645600 -0.290982 -1.084845 2.180704 -1.362611 0.275774 -1.131994 -0.417299 -0.851815 1.840130 -0.425925 0.142096 1.048548 -0.329938 -0.749882 -0.409274 2.934881 -0.258574 -0.440093 -1.219152 0.536816 -1.337721 -0.183903 -1.098953 -1.351417 0.751508 . x x - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | | . - o - - - - - - - - - - - - - - - | | | . o - - - - - - - - - - - - - - - | | | | . x o - - - - - - - - - - - - - | | | | | . x o - - - - - - - - - - - - | | | | | | . o o - - - - - - - - - - - | | | | | | | . x o - - - - - - - - - - | | | | | | | | . x x - - - - - - - - - | | | | | | | | | . - o - - - - - - - - | | | | | | | | | | . - o - - - - - - - | | | | | | | | | | | . o x - - - - - - | | | | | | | | | | | | . o - - - - - - | | | | | | | | | | | | | . o o - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | | . o o - - | | | | | | | | | | | | | | | | . o - - | | | | | | | | | | | | | | | | | . o - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | | . The error in solving: 7.858125e-17 The error in solving: 3.179801e-17 The error in solving: 2.419675e-16 The error in solving: 4.166949e-17 The error in solving: 1.665335e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.250000 [ 0.384807 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.011269 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.414587 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.515350]; Dimension: 20 x 20 Off-diagonal entries: 5 (max 380) Diagonal entries: 0.384807 0.011269 0.000000 0.000000 0.226165 0.000000 0.773858 0.000000 0.000000 0.000000 0.000000 0.000000 0.190580 0.000000 0.000000 0.638665 0.000000 0.293893 0.000000 0.515350 Row indices: 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 4 4 4 5 5 5 Column indices: 1 6 11 13 16 Off-diagonal values: 0.414587 0.349692 0.666859 0.699657 0.802515 x - - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | x . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | x x - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | x . - - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | x The error in solving: 1.778578e-16 The error in solving: 1.118863e-16 The error in solving: 2.482534e-16 The error in solving: 0.000000e+00 The error in solving: 1.241267e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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The error in solving: 1.241267e-16 The error in solving: 1.665335e-16 The error in solving: 3.103168e-17 The error in solving: 6.938894e-18 The error in solving: 3.330669e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.750000 [ 0.884995 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.927755 0.399502 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.012840 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.974953 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| | x x - - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | | x x - - - - - - - | | | | | | | | | | | | x x - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | x x The error in solving: 2.221530e-16 The error in solving: 3.510833e-16 The error in solving: 3.376612e-16 The error in solving: 1.594436e-16 The error in solving: 3.330669e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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- - | x . - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | x | . - - - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | x | . - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | x | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | x x . - - - - - - - - | | | | | | | | | | x x . - - - - - - - | | | | | | | | | | | x | x - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | x . - - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | x The error in solving: 1.241267e-16 The error in solving: 3.421937e-16 The error in solving: 5.553825e-17 The error in solving: 1.110223e-16 The error in solving: 2.355139e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.500000 [ 0.584229 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.664330 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.931922 0.686022 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.873514 0.000000 0.000000 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0.000000 0.000000 0.795124 0.697690 0.000000 0.000000 0.826297 0.000000 0.000000 0.155706 Row indices: 0 0 1 2 2 3 5 6 7 8 8 9 11 12 14 15 16 17 18 19 21 Column indices: 0 1 2 3 4 5 5 7 8 9 10 10 11 12 13 13 14 16 16 17 18 Off-diagonal values: 0.664330 0.931922 0.873514 0.244898 0.711084 0.473707 0.796441 0.720694 0.807660 0.667897 0.853082 0.753890 0.171374 0.885773 0.561380 0.352533 0.458889 0.823516 0.361682 0.660299 0.562646 x - - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | x | . - - - - - - - - - - - - - - - | | | x x x - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | x | . - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | x | . - - - - - - - - - | | | | | | | | | x x . - - - - - - - - | | | | | | | | | | x | x - - - - - - - | | | | | | | | | | | x x x - - - - - - | | | | | | | | | | | | | x . - - - - - | | | | | | | | | | | | | x | . - - - - | | | | | | | | | | | | | | x | x - - - | | | | | | | | | | | | | | | | x . - - | | | | | | | | | | | | | | | | x | . - | | | | | | | | | | | | | | | | | x x x The error in solving: 3.330669e-16 The error in solving: 2.288783e-16 The error in solving: 2.001483e-16 The error in solving: 2.789414e-16 The error in solving: 2.305551e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.750000 [ 0.843033 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.935161 0.878275 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.164655 0.950109 0.837253 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.120270 0.036072 0.763981 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.647267 0.635508 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.367114 0.703917 0.557796 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.784312 0.000000 0.855770 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.758652 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.656203 0.477791 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.126568]; Dimension: 20 x 20 Off-diagonal entries: 30 (max 380) Diagonal entries: 0.843033 0.878275 0.837253 0.763981 0.000000 0.557796 0.855770 0.758652 0.559814 0.267063 0.801990 0.779350 0.888996 0.936198 0.513958 0.000000 0.034892 0.276095 0.000000 0.126568 Row indices: 0 0 1 3 5 7 9 10 10 12 14 16 17 19 21 23 25 26 28 30 30 Column indices: 0 0 1 1 2 2 3 3 4 4 6 7 7 8 8 9 10 10 11 11 12 12 13 13 14 15 15 16 16 17 Off-diagonal values: 0.935161 0.164655 0.950109 0.120270 0.036072 0.647267 0.635508 0.367114 0.703917 0.784312 0.472667 0.369404 0.871053 0.670472 0.193634 0.600042 0.474663 0.713742 0.263342 0.630199 0.742307 0.364795 0.190918 0.315980 0.791636 0.673601 0.056588 0.426596 0.656203 0.477791 x - - - - - - - - - - - - - - - - - - - x x - - - - - - - - - - - - - - - - - - x x x - - - - - - - - - - - - - - - - - | x x x - - - - - - - - - - - - - - - - | | x x . - - - - - - - - - - - - - - - | | | x x x - - - - - - - - - - - - - - | | | | x | x - - - - - - - - - - - - - | | | | | | | x - - - - - - - - - - - - | | | | | | x x x - - - - - - - - - - - | | | | | | | x x x - - - - - - - - - - | | | | | | | | x x x - - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | x x x - - - - - - - | | | | | | | | | | | x x x - - - - - - | | | | | | | | | | | | x x x - - - - - | | | | | | | | | | | | | x x . - - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | x x x - - | | | | | | | | | | | | | | | | x x . - | | | | | | | | | | | | | | | | | | | x The error in solving: 2.359224e-16 The error in solving: 2.733607e-16 The error in solving: 3.330670e-16 The error in solving: 2.002685e-16 The error in solving: 3.682234e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.408401 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.091688 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.540754 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.074872 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.051664 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0.362031 0.448985 0.556725 0.690422 0.915979 0.564489 0.137377 0.075060 0.543181 0.449418 Row indices: 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 2 2 2 2 3 Column indices: 6 14 18 Off-diagonal values: 0.263161 0.693790 0.182043 x - - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | | x - - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | x x The error in solving: 8.326673e-17 The error in solving: 2.220446e-16 The error in solving: 5.721958e-17 The error in solving: 1.388212e-16 The error in solving: 2.237726e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.065476 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.025859 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.270381 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.527061 0.790816 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.956155 0.973347 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.898927 0.512178 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.167279 0.585607 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.837107 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.007977 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.914523 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.443172 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.462311 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.623436 0.196931 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.448840]; Dimension: 20 x 20 Off-diagonal entries: 9 (max 380) Diagonal entries: 0.065476 0.025859 0.270381 0.992511 0.285774 0.246463 0.877201 0.253660 0.112077 0.790816 0.973347 0.512178 0.585607 0.837107 0.007977 0.914523 0.443172 0.462311 0.196931 0.448840 Row indices: 0 0 0 0 1 2 2 3 3 4 5 6 7 8 8 8 8 8 8 9 9 Column indices: 2 3 5 7 8 9 10 11 17 Off-diagonal values: 0.987473 0.602751 0.269428 0.952222 0.527061 0.956155 0.898927 0.167279 0.623436 x - - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | | x x - - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | | x - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | x x - - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | | x x - - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | | x The error in solving: 2.733607e-16 The error in solving: 0.000000e+00 The error in solving: 3.248707e-16 The error in solving: 2.359224e-16 The error in solving: 1.570092e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.014896 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.329731 0.308626 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.726431 0.971089 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.757874 0.657847 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.211832 0.282382 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.240463 0.721001 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.913760 0.006621 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.057509 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.776368 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.284828 0.309523 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.224346 0.642419 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.382818 0.641286 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.034570 0.890893 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.768632 0.762462 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.934761 0.050106 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.988764 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.765398 0.412593 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.958023 0.928058 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.834736 0.223821 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.145648 0.410884]; Dimension: 20 x 20 Off-diagonal entries: 16 (max 380) Diagonal entries: 0.014896 0.308626 0.971089 0.657847 0.282382 0.721001 0.006621 0.057509 0.776368 0.309523 0.642419 0.641286 0.890893 0.762462 0.050106 0.988764 0.412593 0.928058 0.223821 0.410884 Row indices: 0 0 1 2 3 4 5 6 6 6 7 8 9 10 11 12 12 13 14 15 16 Column indices: 0 1 2 3 4 5 8 9 10 11 12 13 15 16 17 18 Off-diagonal values: 0.329731 0.726431 0.757874 0.211832 0.240463 0.913760 0.284828 0.224346 0.382818 0.034570 0.768632 0.934761 0.765398 0.958023 0.834736 0.145648 x - - - - - - - - - - - - - - - - - - - x x - - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | | x x - - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | | x - - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | x x - - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | | x x - - - - - - - | | | | | | | | | | | | x x - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | x x The error in solving: 6.359601e-17 The error in solving: 2.937374e-16 The error in solving: 2.780973e-17 The error in solving: 9.837580e-17 The error in solving: 1.761236e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.882683 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.067222 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.509546 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.483454 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.387552 0.796571 0.144945 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.781692 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.539478 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.728526 0.000000 0.312295 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.955391 0.783865 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.580749 0.664528 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.496014 0.000000 0.409952 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.219344 0.354990 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.007098 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.412167 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.160357 0.000000 0.630731]; Dimension: 20 x 20 Off-diagonal entries: 10 (max 380) Diagonal entries: 0.882683 0.067222 0.509546 0.483454 0.144945 0.781692 0.539478 0.312295 0.783865 0.664528 0.409952 0.981653 0.531483 0.849679 0.994728 0.138011 0.354990 0.007098 0.412167 0.630731 Row indices: 0 0 0 0 0 2 2 2 3 4 5 6 6 7 7 8 8 9 9 9 10 Column indices: 2 3 5 7 8 8 11 13 15 17 Off-diagonal values: 0.387552 0.796571 0.728526 0.955391 0.580749 0.496014 0.200012 0.922526 0.219344 0.160357 x - - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | | x - - - - - - - - - - - - - - - - | | x x x - - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | x | x - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | x | x - - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | x x - - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | x | x The error in solving: 1.272393e-16 The error in solving: 2.100090e-16 The error in solving: 2.242092e-16 The error in solving: 1.152776e-16 The error in solving: 6.245005e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.965001 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.537492 0.071430 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.659080 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.822934 0.699306 0.000000 0.000000 0.000000 0.000000 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Dimension: 20 x 20 Off-diagonal entries: 19 (max 380) Diagonal entries: 0.965001 0.071430 0.659080 0.699306 0.798553 0.180969 0.111163 0.222919 0.927957 0.053525 0.753865 0.865979 0.916567 0.259210 0.468142 0.315029 0.883739 0.451049 0.012371 0.659417 Row indices: 0 0 1 1 2 2 3 5 7 9 10 11 13 15 16 17 18 18 19 19 19 Column indices: 0 2 3 4 5 5 6 6 7 7 8 9 10 10 11 11 13 13 15 Off-diagonal values: 0.537492 0.822934 0.167959 0.339038 0.702781 0.154018 0.771751 0.739769 0.372464 0.351680 0.711209 0.650662 0.492881 0.408819 0.288611 0.237337 0.894892 0.944830 0.368483 x - - - - - - - - - - - - - - - - - - - x x - - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | x | x - - - - - - - - - - - - - - | | | | x x x - - - - - - - - - - - - - | | | | | x x x - - - - - - - - - - - - | | | | | | x x x - - - - - - - - - - - | | | | | | | x | x - - - - - - - - - - | | | | | | | | x | x - - - - - - - - - | | | | | | | | | x x x - - - - - - - - | | | | | | | | | | x x x - - - - - - - | | | | | | | | | | | x | x - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | x | x - - - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | x | x - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | x The error in solving: 1.665335e-16 The error in solving: 1.665335e-16 The error in solving: 1.241267e-16 The error in solving: 1.273812e-16 The error in solving: 1.600465e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.346110 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.430020 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0.793556 0.206422 0.172740 0.107574 0.727220 0.545481 x - - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - x | x - - - - - - - - - - - - - - - - - | x x x - - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | x x x - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | x | x - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | x x x - - - - - - - - - - | | | | | | | | x x x - - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | | x x - - - - - - - | | | | | | | | | | | x x x - - - - - - | | | | | | | | | | | | x x x - - - - - | | | | | | | | | | | | | x x x - - - - | | | | | | | | | | | | | | x x x - - - | | | | | | | | | | | | | | | x x x - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | | x The error in solving: 2.775558e-16 The error in solving: 1.241752e-16 The error in solving: 2.775558e-17 The error in solving: 2.789401e-16 The error in solving: 3.692802e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.486859 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.712800 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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| | | | | | | | | . - - | | | | | | | | | | | | | | | | | x . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.665335e-16 The error in solving: 3.940534e-17 The error in solving: 2.775558e-16 The error in solving: 4.191000e-16 The error in solving: 6.359601e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.019556 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.888444 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.349783 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.917975 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.441956 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.939206 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.679164 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.431395 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.436742 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.160279 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.478755 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 11 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 1 2 3 4 5 6 7 7 7 7 7 7 8 9 9 10 10 11 Column indices: 0 2 3 4 5 6 7 13 14 16 18 Off-diagonal values: 0.019556 0.888444 0.349783 0.917975 0.441956 0.939206 0.679164 0.431395 0.436742 0.160279 0.478755 . - - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | | x . - - - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | | x . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | x . - - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | x . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | x . The error in solving: 1.110223e-16 The error in solving: 1.665335e-16 The error in solving: 1.118863e-16 The error in solving: 0.000000e+00 The error in solving: 4.577567e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.948520 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.731070 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.253880 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.154875 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.831604 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.769359 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.411463 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.053072 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.395457 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.733328 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.536518 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.637932 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.348760 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.062260 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.937044 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.518128 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.874886 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 17 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 2 2 3 4 5 6 6 7 8 9 10 11 12 13 14 15 16 17 Column indices: 0 1 3 4 5 6 8 9 10 11 12 13 14 15 16 17 18 Off-diagonal values: 0.948520 0.731070 0.253880 0.154875 0.831604 0.769359 0.411463 0.053072 0.395457 0.733328 0.536518 0.637932 0.348760 0.062260 0.937044 0.518128 0.874886 . - - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | x . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | x . - - - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | x . - - - - - - - - - - | | | | | | | | | x . - - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | | x . - - - - - - - | | | | | | | | | | | | x . - - - - - - | | | | | | | | | | | | | x . - - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | x . - - - | | | | | | | | | | | | | | | | x . - - | | | | | | | | | | | | | | | | | x . - | | | | | | | | | | | | | | | | | | x . The error in solving: 7.888701e-17 The error in solving: 6.798700e-17 The error in solving: 2.220717e-16 The error in solving: 1.594436e-16 The error in solving: 2.263399e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.418890 0.349004 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.853443 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.820089 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.337250 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.934401 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.388569 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 7 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 2 3 3 3 3 4 4 5 5 6 6 6 6 6 6 7 7 7 Column indices: 0 1 1 5 7 10 15 Off-diagonal values: 0.418890 0.349004 0.853443 0.820089 0.337250 0.934401 0.388569 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - x x . - - - - - - - - - - - - - - - - - | x | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | x | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | x | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | x | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.144392e-16 The error in solving: 2.305551e-16 The error in solving: 2.775558e-17 The error in solving: 2.237726e-16 The error in solving: 1.144392e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.357915 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.929696 0.415318 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.972791 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.395179 0.726982 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.593098 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.949034 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.437914 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.996003 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.615066 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.510943 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.804997 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.185176 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.783118 0.906754 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.633815 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.759037 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.712274 0.987401 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 20 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 1 3 4 6 6 7 8 8 9 10 11 12 13 14 16 17 18 20 Column indices: 0 1 2 2 3 4 5 7 8 10 11 12 13 14 14 15 15 17 17 18 Off-diagonal values: 0.357915 0.929696 0.415318 0.972791 0.395179 0.726982 0.593098 0.949034 0.437914 0.996003 0.615066 0.510943 0.804997 0.185176 0.783118 0.906754 0.633815 0.759037 0.712274 0.987401 . - - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | x x . - - - - - - - - - - - - - - - - | | x | . - - - - - - - - - - - - - - - | | | x x . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | x | . - - - - - - - - - - - - | | | | | | | x . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | x | . - - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | | x . - - - - - - - | | | | | | | | | | | | x . - - - - - - | | | | | | | | | | | | | x . - - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | x x . - - - | | | | | | | | | | | | | | | x | . - - | | | | | | | | | | | | | | | | | x . - | | | | | | | | | | | | | | | | | x x . The error in solving: 3.342214e-16 The error in solving: 1.110359e-16 The error in solving: 2.544787e-16 The error in solving: 2.532459e-16 The error in solving: 2.775558e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.136086 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.766078 0.823898 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.397505 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.706424 0.410673 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.639374 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.822647 0.488726 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.006619 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.207125 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.908340 0.825809 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.733474 0.453388 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.491448 0.957619 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.403530 0.415417 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.878956 0.198934 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.748545 0.895934 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.504540 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.606545 0.028924 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.009183 0.325207 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.982611 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.740825 0.248688 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 31 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 3 4 6 7 9 10 11 13 15 17 19 21 23 24 26 28 29 31 Column indices: 0 0 1 1 2 3 4 4 5 6 6 7 8 8 9 9 10 10 11 11 12 12 13 13 14 15 15 16 16 17 18 Off-diagonal values: 0.136086 0.766078 0.823898 0.397505 0.706424 0.410673 0.639374 0.822647 0.488726 0.006619 0.207125 0.908340 0.825809 0.733474 0.453388 0.491448 0.957619 0.403530 0.415417 0.878956 0.198934 0.748545 0.895934 0.504540 0.606545 0.028924 0.009183 0.325207 0.982611 0.740825 0.248688 . - - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - x x . - - - - - - - - - - - - - - - - - | x | . - - - - - - - - - - - - - - - - | | x x . - - - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | x x . - - - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | x | . - - - - - - - - - - - | | | | | | | x x . - - - - - - - - - - | | | | | | | | x x . - - - - - - - - - | | | | | | | | | x x . - - - - - - - - | | | | | | | | | | x x . - - - - - - - | | | | | | | | | | | x x . - - - - - - | | | | | | | | | | | | x x . - - - - - | | | | | | | | | | | | | x | . - - - - | | | | | | | | | | | | | | x x . - - - | | | | | | | | | | | | | | | x x . - - | | | | | | | | | | | | | | | | x | . - | | | | | | | | | | | | | | | | | x x . The error in solving: 3.140185e-16 The error in solving: 3.330714e-16 The error in solving: 1.154862e-16 The error in solving: 2.237726e-16 The error in solving: 1.193812e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.250000 [ -0.232244 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.890461 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.403980 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.733567 -0.146226 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.719228 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.459088 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.394433 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 5 (max 380) Diagonal entries: -0.232244 0.890461 0.000000 0.000000 0.000000 0.000000 0.000000 -0.146226 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 0 1 1 1 2 2 2 3 3 3 3 3 3 3 3 4 5 Column indices: 3 6 9 17 18 Off-diagonal values: -0.403980 -0.733567 0.719228 0.459088 0.394433 o - - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | o . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | o o - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | x . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | x . - | | | | | | | | | | | | | | | | | | x . The error in solving: 2.237726e-16 The error in solving: 1.110765e-16 The error in solving: 3.103168e-17 The error in solving: 3.477764e-16 The error in solving: 2.547623e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.500000 [ -0.057328 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.301396 -0.625887 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.091444 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.981075 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.533352 -0.552267 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.016898 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.091239 0.435823 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.424040 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.563648 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.409966 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.437633 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.314783 -0.295047 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.204315 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.486126 0.230868 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 8 (max 380) Diagonal entries: -0.057328 -0.625887 -0.091444 0.000000 0.000000 0.000000 -0.552267 0.000000 0.435823 0.000000 0.424040 0.563648 0.000000 0.000000 0.437633 -0.295047 -0.204315 0.000000 0.230868 0.000000 Row indices: 0 0 1 1 1 2 2 3 4 5 5 5 5 5 6 6 7 7 7 8 8 Column indices: 0 3 5 6 7 12 14 17 Off-diagonal values: -0.301396 -0.981075 0.533352 -0.016898 -0.091239 -0.409966 -0.314783 -0.486126 o - - - - - - - - - - - - - - - - - - - o o - - - - - - - - - - - - - - - - - - | | o - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | o . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | x o - - - - - - - - - - - - - | | | | | | o . - - - - - - - - - - - - | | | | | | | o x - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | o . - - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | o o - - - - | | | | | | | | | | | | | | | | o - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | o x - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.775558e-17 The error in solving: 2.482549e-16 The error in solving: 5.551115e-17 The error in solving: 3.152427e-16 The error in solving: 6.206335e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.750000 [ -0.224006 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.927994 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.591790 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.081752 0.232384 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.329453 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.796171 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.100565 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.545652 -0.364986 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.904080 -0.204112 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.320264 -0.136269 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.470307 0.132818 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.024488 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.138772 -0.540203 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.903061 0.035123 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.578009 0.936957 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.381009 0.228186 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.549193 -0.849823 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.284948 0.457960 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.504141 0.810712 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 15 (max 380) Diagonal entries: -0.224006 0.000000 -0.591790 0.232384 0.000000 0.000000 0.100565 -0.364986 -0.204112 -0.136269 0.132818 0.024488 -0.540203 0.035123 0.936957 0.228186 -0.849823 0.457960 0.810712 0.000000 Row indices: 0 0 1 1 2 3 4 4 5 6 7 8 8 9 10 11 12 13 14 15 15 Column indices: 0 2 3 4 6 7 8 9 11 12 13 14 15 16 17 Off-diagonal values: -0.927994 0.081752 0.329453 -0.796171 0.545652 -0.904080 0.320264 -0.470307 0.138772 0.903061 0.578009 0.381009 0.549193 0.284948 0.504141 o - - - - - - - - - - - - - - - - - - - o . - - - - - - - - - - - - - - - - - - | | o - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | | x . - - - - - - - - - - - - - - - | | | | o . - - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | x o - - - - - - - - - - - - | | | | | | | o o - - - - - - - - - - - | | | | | | | | x o - - - - - - - - - - | | | | | | | | | o x - - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | x o - - - - - - - | | | | | | | | | | | | x x - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | x o - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.288783e-16 The error in solving: 1.572032e-16 The error in solving: 5.551115e-17 The error in solving: 2.775558e-17 The error in solving: 5.594315e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.250000 [ 0.076496 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.621151 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.642605 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.990968 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.532853 0.000000 -0.155381 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.766043 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.056206 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.194971 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.763948 0.000000 0.433080 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.829760 -0.915748 -0.240537 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.843895 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.313534 0.000000 0.968246 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 12 (max 380) Diagonal entries: 0.076496 0.000000 0.000000 0.000000 -0.155381 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.433080 0.000000 0.000000 -0.240537 0.000000 0.968246 0.000000 Row indices: 0 0 1 2 3 4 5 6 6 7 7 7 7 7 8 8 8 10 11 12 12 Column indices: 0 0 1 2 3 4 6 11 14 15 15 16 Off-diagonal values: -0.621151 -0.642605 -0.990968 0.532853 -0.766043 -0.056206 -0.194971 0.763948 0.829760 -0.915748 -0.843895 0.313534 x - - - - - - - - - - - - - - - - - - - o . - - - - - - - - - - - - - - - - - - o | . - - - - - - - - - - - - - - - - - | o | . - - - - - - - - - - - - - - - - | | x | o - - - - - - - - - - - - - - - | | | o | . - - - - - - - - - - - - - - | | | | o | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | o | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | x | x - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | x o o - - - | | | | | | | | | | | | | | | o | . - - | | | | | | | | | | | | | | | | x | x - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.498002e-16 The error in solving: 3.469447e-17 The error in solving: 5.561947e-17 The error in solving: 1.135946e-16 The error in solving: 1.570188e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.500000 [ -0.172117 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.741455 0.965580 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.654942 0.754729 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.323334 0.991530 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.387516 -0.092637 0.187374 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.158947 0.000000 0.681967 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.387880 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.551620 0.000000 0.697534]; Dimension: 20 x 20 Off-diagonal entries: 22 (max 380) Diagonal entries: -0.172117 0.000000 0.965580 0.000000 -0.480775 0.156037 0.000000 0.598208 0.000000 0.000000 0.000000 -0.651208 0.000000 0.468114 0.991530 0.187374 0.681967 0.000000 0.000000 0.697534 Row indices: 0 0 0 1 3 5 6 6 6 8 9 11 13 14 16 17 19 20 20 21 22 Column indices: 1 1 2 2 3 3 6 7 7 8 9 9 10 10 11 12 13 13 14 14 17 17 Off-diagonal values: 0.741455 0.654942 0.754729 -0.481270 0.554213 -0.163613 -0.398993 -0.975836 -0.258928 -0.006560 -0.589573 -0.179374 -0.649023 -0.040211 -0.153186 -0.426760 -0.323334 -0.387516 -0.092637 -0.158947 -0.387880 -0.551620 o - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - | x x . - - - - - - - - - - - - - - - - | | o x o - - - - - - - - - - - - - - - | | | o | x - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | x - - - - - - - - - - - - | | | | | | o o . - - - - - - - - - - - | | | | | | | o | . - - - - - - - - - - | | | | | | | | o o . - - - - - - - - - | | | | | | | | | o o o - - - - - - - - | | | | | | | | | | o | . - - - - - - - | | | | | | | | | | | o o x - - - - - - | | | | | | | | | | | | | o x - - - - - | | | | | | | | | | | | | o o x - - - - | | | | | | | | | | | | | | o | x - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | o . - | | | | | | | | | | | | | | | | | o | x The error in solving: 1.243205e-16 The error in solving: 3.140185e-16 The error in solving: 2.482534e-16 The error in solving: 3.103168e-17 The error in solving: 2.240145e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.750000 [ -0.706018 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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values: 0.139171 -0.201519 -0.442416 0.111957 0.723296 0.612721 0.380702 -0.996617 0.029375 0.805942 -0.896111 0.180016 0.008954 -0.896781 -0.906858 0.444244 -0.663702 -0.083773 0.607621 -0.164867 0.618835 0.586575 0.384181 -0.186088 0.363699 0.088040 0.323869 -0.079825 -0.537684 0.712003 o - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - x | x - - - - - - - - - - - - - - - - - | o | o - - - - - - - - - - - - - - - - | | | o . - - - - - - - - - - - - - - - | | | x x o - - - - - - - - - - - - - - | | | | x x o - - - - - - - - - - - - - | | | | | o x . - - - - - - - - - - - - | | | | | | x o . - - - - - - - - - - - | | | | | | | x | o - - - - - - - - - - | | | | | | | | x o x - - - - - - - - - | | | | | | | | | | o x - - - - - - - - | | | | | | | | | | x o x - - - - - - - | | | | | | | | | | | o x o - - - - - - | | | | | | | | | | | | o x o - - - - - | | | | | | | | | | | | | x x x - - - - | | | | | | | | | | | | | | o x . - - - | | | | | | | | | | | | | | | x x o - - | | | | | | | | | | | | | | | | | o . - | | | | | | | | | | | | | | | | | o x . The error in solving: 2.563637e-16 The error in solving: 2.719480e-16 The error in solving: 1.110223e-16 The error in solving: 3.103168e-17 The error in solving: 1.570092e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.250000 [ -0.624692 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.860190 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.813774 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.320901]; Dimension: 20 x 20 Off-diagonal entries: 6 (max 380) Diagonal entries: -0.624692 -0.860190 0.813774 -0.335945 0.807307 0.056929 0.857559 -0.639955 0.198206 -0.879167 -0.433302 0.495881 -0.266411 0.909183 -0.503699 -0.551096 0.290371 -0.294493 -0.890416 0.320901 Row indices: 0 0 0 0 0 0 0 1 1 1 1 2 2 3 3 4 4 5 5 6 6 Column indices: 5 9 11 13 15 17 Off-diagonal values: 0.029369 -0.605161 -0.955060 -0.799428 -0.197238 -0.793181 o - - - - - - - - - - - - - - - - - - - | o - - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | | o - - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | | o - - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | | o - - - - - - - - - - | | | | | | | | | o o - - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | o o - - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | o o - - - - - | | | | | | | | | | | | | | | o - - - - | | | | | | | | | | | | | | | o x - - - | | | | | | | | | | | | | | | | | o - - | | | | | | | | | | | | | | | | | o o - | | | | | | | | | | | | | | | | | | | x The error in solving: 2.719480e-16 The error in solving: 1.271920e-16 The error in solving: 2.950458e-16 The error in solving: 2.775558e-16 The error in solving: 1.570092e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.500000 [ -0.789113 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.314575 -0.684885 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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- - - | | | o o - - - - - - - - - - - - - - - | | | | o x - - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | | x - - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | o x - - - - - - - - - - | | | | | | | | | x x - - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | x o - - - - - - | | | | | | | | | | | | | o o - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | o o - | | | | | | | | | | | | | | | | | | x x The error in solving: 8.673617e-19 The error in solving: 5.551115e-17 The error in solving: 3.140185e-16 The error in solving: 0.000000e+00 The error in solving: 3.376612e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a 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10 11 12 13 14 15 16 17 18 Column indices: 0 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 Off-diagonal values: 0.727284 -0.495183 0.659599 -0.981054 0.348156 -0.324950 0.478845 -0.123813 -0.635312 0.494505 0.152195 0.182174 0.979256 -0.597661 -0.445236 0.505214 0.553372 -0.180345 o - - - - - - - - - - - - - - - - - - - x x - - - - - - - - - - - - - - - - - - | o x - - - - - - - - - - - - - - - - - | | x o - - - - - - - - - - - - - - - - | | | o o - - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | | | | | o x - - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | o x - - - - - - - - - - - | | | | | | | | o o - - - - - - - - - - | | | | | | | | | x x - - - - - - - - - | | | | | | | | | | | o - - - - - - - - | | | | | | | | | | | x x - - - - - - - | | | | | | | | | | | | x x - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | o x - - - - | | | | | | | | | | | | | | | o x - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | o x The error in solving: 2.220446e-16 The error in solving: 1.594436e-16 The error in solving: 1.241267e-16 The error in solving: 2.482534e-16 The error in solving: 2.306595e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.250000 [ -0.768853 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.857557 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.283401 -0.165007 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.662353]; Dimension: 20 x 20 Off-diagonal entries: 12 (max 380) Diagonal entries: -0.768853 -0.857557 -0.165007 0.326485 0.435562 0.118492 -0.057738 0.212771 0.464269 0.506307 0.593283 0.604618 0.746526 -0.993415 -0.492112 0.509222 -0.986904 0.632242 0.578564 -0.662353 Row indices: 0 0 0 1 1 2 2 4 4 5 5 5 5 7 8 8 10 11 11 12 12 Column indices: 1 2 4 5 7 10 11 12 13 14 14 17 Off-diagonal values: -0.283401 0.503075 0.976130 0.560947 0.672940 0.738814 -0.271478 -0.535111 0.633645 -0.828263 -0.421494 0.378791 o - - - - - - - - - - - - - - - - - - - | o - - - - - - - - - - - - - - - - - - | o o - - - - - - - - - - - - - - - - - | | | x - - - - - - - - - - - - - - - - | | x | x - - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | x x o - - - - - - - - - - - - - | | | | | | | x - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | x o x - - - - - - - | | | | | | | | | | | | o o - - - - - - | | | | | | | | | | | | | | o - - - - - | | | | | | | | | | | | | x o x - - - - | | | | | | | | | | | | | | o | o - - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | | o The error in solving: 2.224779e-16 The error in solving: 1.576214e-16 The error in solving: 8.326673e-17 The error in solving: 2.305551e-16 The error in solving: 2.604628e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.121917 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.333361 0.726849 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.642508 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.554977 0.858605 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.604622 -0.115237 -0.302258 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.255400 0.000000 0.148434 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.800154 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.222016 -0.607709 -0.664276 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.516630 0.000000 -0.650082 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.844716 -0.786914 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.944436 -0.928715 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.040799 -0.456982 -0.936288 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.442619 0.000000 0.039520 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.246084 0.101073 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.486069 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.325695 0.611780 0.836105 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.629668 0.000000 0.861653 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.235283 0.000000 -0.788268 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.243266 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.299478 0.000000 0.646064]; Dimension: 20 x 20 Off-diagonal entries: 19 (max 380) Diagonal entries: 0.121917 0.726849 -0.642508 0.858605 -0.302258 0.148434 -0.800154 -0.664276 -0.650082 -0.786914 -0.928715 -0.936288 0.039520 0.101073 0.486069 0.836105 0.861653 -0.788268 -0.243266 0.646064 Row indices: 0 0 1 1 2 4 5 5 7 8 9 10 12 13 14 14 16 17 18 18 19 Column indices: 0 2 2 3 3 5 6 6 8 9 9 10 10 12 13 14 14 15 17 Off-diagonal values: 0.333361 0.554977 0.604622 -0.115237 -0.255400 -0.222016 -0.607709 -0.516630 0.844716 0.944436 -0.040799 -0.456982 0.442619 -0.246084 0.325695 0.611780 0.629668 -0.235283 -0.299478 x - - - - - - - - - - - - - - - - - - - x x - - - - - - - - - - - - - - - - - - | | o - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | x o o - - - - - - - - - - - - - - - | | | o | x - - - - - - - - - - - - - - | | | | | | o - - - - - - - - - - - - - | | | | | o o o - - - - - - - - - - - - | | | | | | o | o - - - - - - - - - - - | | | | | | | | x o - - - - - - - - - - | | | | | | | | | x o - - - - - - - - - | | | | | | | | | o o o - - - - - - - - | | | | | | | | | | x | x - - - - - - - | | | | | | | | | | | | o x - - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | x x x - - - - | | | | | | | | | | | | | | x | x - - - | | | | | | | | | | | | | | | o | o - - | | | | | | | | | | | | | | | | | | o - | | | | | | | | | | | | | | | | | o | x The error in solving: 2.355139e-16 The error in solving: 2.611090e-16 The error in solving: 1.782634e-16 The error in solving: 4.220764e-17 The error in solving: 5.551115e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.359187 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.075328 0.112858 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.652328 0.107827 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.800869 0.702756 0.435720 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.141772 0.112699 0.410489 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.974623 0.000000 -0.684799 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.404172 -0.349126 -0.232831 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.895363 0.000000 0.887703 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.386063 -0.385778]; Dimension: 20 x 20 Off-diagonal entries: 24 (max 380) Diagonal entries: 0.359187 0.112858 0.107827 0.435720 -0.378961 -0.711345 0.436046 -0.109231 -0.783967 0.421542 -0.598028 0.524959 0.006268 -0.651865 -0.656243 0.410489 -0.684799 -0.232831 0.887703 -0.385778 Row indices: 0 0 1 2 4 5 6 8 9 11 11 12 13 15 16 17 19 20 22 23 24 Column indices: 0 1 1 2 3 3 4 5 6 6 7 8 9 10 11 11 13 13 14 14 15 16 16 18 Off-diagonal values: -0.075328 0.652328 0.800869 0.702756 -0.788685 -0.262169 -0.508152 0.564401 -0.548547 -0.948790 0.699175 0.608653 0.307645 0.960597 0.132120 0.864149 0.779758 0.141772 0.112699 0.974623 0.404172 -0.349126 -0.895363 -0.386063 x - - - - - - - - - - - - - - - - - - - o x - - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - | x x x - - - - - - - - - - - - - - - - | | | o o - - - - - - - - - - - - - - - | | | o | o - - - - - - - - - - - - - - | | | | o x x - - - - - - - - - - - - - | | | | | | o o - - - - - - - - - - - - | | | | | | o x o - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | x | o - - - - - - - - - | | | | | | | | | x | x - - - - - - - - | | | | | | | | | | x x x - - - - - - - | | | | | | | | | | | x | o - - - - - - | | | | | | | | | | | | | x o - - - - - | | | | | | | | | | | | | x x x - - - - | | | | | | | | | | | | | | x | o - - - | | | | | | | | | | | | | | | x o o - - | | | | | | | | | | | | | | | | o | x - | | | | | | | | | | | | | | | | | | o o The error in solving: 2.775558e-17 The error in solving: 1.243225e-16 The error in solving: 1.387779e-17 The error in solving: 2.004188e-16 The error in solving: 2.355139e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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- - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | x . - - - - - - - - - - - | | | | | | | | x . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 6.206335e-17 The error in solving: 0.000000e+00 The error in solving: 1.110223e-16 The error in solving: 1.422050e-16 The error in solving: 3.191891e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.661439 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.327877 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.422611 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.961273 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.304865 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.721479 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.408901 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.462379 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.134839 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 9 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 1 1 1 1 2 2 3 3 3 3 3 4 5 6 7 7 8 9 Column indices: 1 5 7 12 13 14 15 17 18 Off-diagonal values: 0.661439 0.327877 0.422611 0.961273 -0.304865 -0.721479 -0.408901 -0.462379 0.134839 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | x . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | x . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | x . - - - - - - | | | | | | | | | | | | | o . - - - - - | | | | | | | | | | | | | | o . - - - - | | | | | | | | | | | | | | | o . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | o . - | | | | | | | | | | | | | | | | | | x . The error in solving: 6.359601e-17 The error in solving: 3.402182e-16 The error in solving: 2.775558e-16 The error in solving: 2.618456e-16 The error in solving: 2.154412e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.152174 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.555536 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.918964 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.544929 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.238607 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.614969 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.988730 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.912976 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.065955 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.546528 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.535261 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 11 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 1 2 2 3 4 5 6 6 6 7 8 8 8 9 9 10 11 Column indices: 2 3 5 6 7 8 11 12 15 17 18 Off-diagonal values: -0.152174 0.555536 0.918964 0.544929 0.238607 -0.614969 0.988730 -0.912976 -0.065955 -0.546528 0.535261 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | o . - - - - - - - - - - - - - - - - | | | x . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | | x . - - - - - - - - - - - | | | | | | | | o . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | x . - - - - - - - | | | | | | | | | | | | o . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | o . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | o . - | | | | | | | | | | | | | | | | | | x . The error in solving: 2.220446e-16 The error in solving: 2.603704e-16 The error in solving: 1.118997e-16 The error in solving: 1.570476e-16 The error in solving: 1.577740e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.311032 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.604782 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.749047 0.313792 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.277631 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.874771 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.526613 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.866684 -0.551124 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.760059 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.628212 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.342614 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.311738 0.820702 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 14 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 1 2 4 5 6 7 9 10 11 12 12 12 12 12 12 12 14 14 Column indices: 1 2 2 3 3 5 5 6 7 8 9 10 16 17 Off-diagonal values: 0.311032 -0.604782 -0.749047 0.313792 0.277631 0.874771 0.526613 0.866684 -0.551124 -0.760059 0.628212 -0.342614 -0.311738 0.820702 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | x . - - - - - - - - - - - - - - - - - | | o . - - - - - - - - - - - - - - - - | | o x . - - - - - - - - - - - - - - - | | | x | . - - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | x | . - - - - - - - - - - - - | | | | | | x o . - - - - - - - - - - - | | | | | | | | o . - - - - - - - - - - | | | | | | | | | x . - - - - - - - - - | | | | | | | | | | o . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | o x . - | | | | | | | | | | | | | | | | | | | . The error in solving: 3.511519e-16 The error in solving: 1.571649e-16 The error in solving: 1.387779e-17 The error in solving: 2.224846e-16 The error in solving: 2.483504e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.653692 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.185774 -0.824636 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.610442 0.227146 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.201539 -0.734955 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.377679 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.164926 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.967589 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.840217 0.337091 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.170266 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.087801 -0.483277 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.242288 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.932725 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.185069 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.356739 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.104705 0.171917 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.104350 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.668323 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 23 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 3 5 7 8 9 10 10 12 13 15 16 17 18 19 21 22 23 23 Column indices: 0 0 1 1 2 2 3 4 5 6 7 8 9 9 10 11 11 13 13 14 15 15 16 Off-diagonal values: -0.653692 -0.185774 -0.824636 0.610442 0.227146 0.201539 -0.734955 -0.377679 -0.164926 0.967589 -0.840217 0.337091 -0.170266 -0.087801 -0.483277 -0.242288 -0.932725 0.185069 0.356739 0.104705 0.171917 0.104350 0.668323 . - - - - - - - - - - - - - - - - - - - o . - - - - - - - - - - - - - - - - - - o o . - - - - - - - - - - - - - - - - - | x x . - - - - - - - - - - - - - - - - | | x o . - - - - - - - - - - - - - - - | | | | o . - - - - - - - - - - - - - - | | | | | o . - - - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | o x . - - - - - - - - - - | | | | | | | | | o . - - - - - - - - - | | | | | | | | | o o . - - - - - - - - | | | | | | | | | | | o . - - - - - - - | | | | | | | | | | | o | . - - - - - - | | | | | | | | | | | | | x . - - - - - | | | | | | | | | | | | | x | . - - - - | | | | | | | | | | | | | | x x . - - - | | | | | | | | | | | | | | | x | . - - | | | | | | | | | | | | | | | | x | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.292987e-16 The error in solving: 1.110223e-16 The error in solving: 2.288783e-16 The error in solving: 8.002323e-17 The error in solving: 3.521788e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.106663 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.728312 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.027219 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.809823 -0.926922 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.461650 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.503565 0.476084 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.091755 0.812887 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.134698 -0.867268 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.213504 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.165241 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.306807 -0.606352 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.512430 0.426014 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.147371 0.429667 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.568876 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.343316 0.474349 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.878572 -0.090925 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.595968 -0.805881 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.628952 -0.448152 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.919818 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 30 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 2 3 5 6 8 10 12 13 14 16 18 20 21 23 25 27 29 30 Column indices: 0 0 2 2 3 3 4 5 5 6 6 7 7 8 9 10 10 11 11 12 12 13 14 14 15 15 16 16 17 18 Off-diagonal values: 0.106663 -0.728312 0.027219 0.809823 -0.926922 -0.461650 0.503565 0.476084 -0.091755 0.812887 0.134698 -0.867268 -0.213504 0.165241 -0.306807 -0.606352 -0.512430 0.426014 -0.147371 0.429667 -0.568876 0.343316 0.474349 0.878572 -0.090925 0.595968 -0.805881 -0.628952 -0.448152 0.919818 . - - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - o | . - - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | x o . - - - - - - - - - - - - - - - | | | o | . - - - - - - - - - - - - - - | | | | x x . - - - - - - - - - - - - - | | | | | o x . - - - - - - - - - - - - | | | | | | x o . - - - - - - - - - - - | | | | | | | o | . - - - - - - - - - - | | | | | | | | x | . - - - - - - - - - | | | | | | | | | o o . - - - - - - - - | | | | | | | | | | o x . - - - - - - - | | | | | | | | | | | o x . - - - - - - | | | | | | | | | | | | o | . - - - - - | | | | | | | | | | | | | x x . - - - - | | | | | | | | | | | | | | x o . - - - | | | | | | | | | | | | | | | x o . - - | | | | | | | | | | | | | | | | o o . - | | | | | | | | | | | | | | | | | | x . The error in solving: 5.721958e-17 The error in solving: 1.110223e-16 The error in solving: 7.152448e-18 The error in solving: 1.144392e-16 The error in solving: 1.363276e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.696574 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.618400 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.095077 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.190465 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.180612 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.127158 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.373372 -0.162277 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.477128 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.350922 1.374928 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.934427 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.412940 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 8 (max 380) Diagonal entries: 0.000000 0.000000 -1.618400 0.000000 0.000000 0.000000 0.000000 0.000000 1.127158 -0.162277 -0.477128 0.000000 0.000000 1.374928 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 1 2 2 3 3 4 4 5 5 5 5 6 6 6 7 8 8 8 Column indices: 0 2 4 6 8 12 15 16 Off-diagonal values: 0.696574 -1.095077 1.190465 -0.180612 -0.373372 -0.350922 0.934427 -0.412940 . - - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | | o - - - - - - - - - - - - - - - - - | | o . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | o . - - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | o o - - - - - - - - - - | | | | | | | | | | o - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | o x - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | x . - - - | | | | | | | | | | | | | | | | o . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.594436e-16 The error in solving: 2.498965e-16 The error in solving: 6.938894e-18 The error in solving: 1.309228e-16 The error in solving: 1.241267e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.500000 [ -0.272505 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.457188 -1.011041 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.140480 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.067459 0.902287 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.423649 -1.352425 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.176993 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.268754 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.344239 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.453790 0.818316 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.714511 -0.821446 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.384928 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.205195 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.342183 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 11 (max 380) Diagonal entries: -0.272505 -1.011041 0.000000 0.902287 -1.352425 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.818316 -0.821446 0.000000 0.000000 0.000000 0.000000 0.000000 -2.342183 0.000000 Row indices: 0 0 1 2 3 4 5 6 6 6 6 7 8 9 9 10 11 11 11 11 11 Column indices: 0 1 2 3 4 5 9 10 11 13 14 Off-diagonal values: -0.457188 1.140480 1.067459 -0.423649 0.176993 2.268754 -0.344239 -1.453790 -0.714511 -0.384928 -1.205195 o - - - - - - - - - - - - - - - - - - - o o - - - - - - - - - - - - - - - - - - | x . - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | | o o - - - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | o . - - - - - - - - - | | | | | | | | | | o x - - - - - - - - | | | | | | | | | | | o o - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | o . - - - - - | | | | | | | | | | | | | | o . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | o - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.576214e-16 The error in solving: 2.558943e-16 The error in solving: 3.143250e-16 The error in solving: 2.439492e-16 The error in solving: 2.288783e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.750000 [ 0.908992 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.261789 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.296498 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.966831 -0.476037 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.431725 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.942845 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.586283 -0.857249 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.195089 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 -0.075849 1.030271]; Dimension: 20 x 20 Off-diagonal entries: 16 (max 380) Diagonal entries: 0.908992 0.000000 0.000000 -0.641126 -1.152485 -0.641778 0.114120 0.000000 0.528339 -0.476037 0.000000 0.000000 -0.857249 0.000000 -0.498172 0.000000 -0.667434 -0.554527 0.672552 1.030271 Row indices: 0 0 1 2 2 3 4 5 6 7 8 9 10 11 12 13 13 14 14 15 16 Column indices: 0 1 3 4 5 6 7 8 9 10 11 12 13 15 17 18 Off-diagonal values: 0.261789 -0.296498 0.631044 -1.092417 0.283076 0.403610 -0.055706 1.966831 -1.431725 0.942845 1.586283 1.195089 0.742659 1.259655 0.396485 -0.075849 x - - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | o . - - - - - - - - - - - - - - - - - | | | o - - - - - - - - - - - - - - - - | | | x o - - - - - - - - - - - - - - - | | | | o o - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | | o x - - - - - - - - - - - | | | | | | | | x o - - - - - - - - - - | | | | | | | | | o . - - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | | x o - - - - - - - | | | | | | | | | | | | x . - - - - - - | | | | | | | | | | | | | x o - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | x o - - - | | | | | | | | | | | | | | | | | o - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | o x The error in solving: 5.721958e-17 The error in solving: 2.289116e-16 The error in solving: 3.723801e-16 The error in solving: 2.288783e-16 The error in solving: 2.288783e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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- - - - - | . - - - - - - - - - - - - - - - - - - | | o - - - - - - - - - - - - - - - - - | | | x - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | o o x - - - - - - - - - - - - - - | | | | o x . - - - - - - - - - - - - - | | | | | x x . - - - - - - - - - - - - | | | | | | o | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | x x - - - - - - - - - | | | | | | | | | o | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | o . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | o . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | o | o - | | | | | | | | | | | | | | | | | | x . The error in solving: 2.305551e-16 The error in solving: 1.129570e-16 The error in solving: 2.723019e-16 The error in solving: 2.276126e-16 The error in solving: 2.309724e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.500000 [ 0.398989 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.186304 -0.888089 -0.105828 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.727736 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0.000000 0.000000 0.000000 0.000000 2.030519 0.000000 3.224037]; Dimension: 20 x 20 Off-diagonal entries: 20 (max 380) Diagonal entries: 0.398989 0.000000 -0.105828 0.649048 -0.544404 0.000000 0.000000 0.496740 -0.222572 0.085507 0.583609 0.181382 0.000000 -0.260334 0.943652 0.000000 -0.491801 2.883634 -1.316766 3.224037 Row indices: 0 0 0 2 3 4 6 8 9 10 12 13 14 14 14 14 14 16 18 19 20 Column indices: 0 1 2 2 3 4 4 5 5 7 7 8 9 9 14 15 15 16 17 17 Off-diagonal values: 2.186304 -0.888089 0.727736 -3.170666 0.449223 -1.117903 2.099574 0.802630 0.270650 2.236932 -0.258389 -0.244007 -1.061404 -0.321779 -1.111923 2.167218 1.805002 1.947056 1.432663 2.030519 x - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - x o o - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | o | o - - - - - - - - - - - - - - - | | | x o . - - - - - - - - - - - - - - | | | | x x . - - - - - - - - - - - - - | | | | | x | x - - - - - - - - - - - - | | | | | | | x o - - - - - - - - - - - | | | | | | | o o x - - - - - - - - - - | | | | | | | | | o x - - - - - - - - - | | | | | | | | | o | x - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | o - - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | o x o - - - | | | | | | | | | | | | | | | x x x - - | | | | | | | | | | | | | | | | | x o - | | | | | | | | | | | | | | | | | x | x The error in solving: 2.355139e-16 The error in solving: 5.551115e-17 The error in solving: 1.755502e-16 The error in solving: 2.240145e-16 The error in solving: 2.562698e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.750000 [ 1.281509 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.426607 -0.209437 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.241472 0.648451 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.629632 -1.678646 -1.079386 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.614257 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.096187 0.391618 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.546679 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.800011 -0.763157 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.075407 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.412661 -0.041396 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.521031 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.920620 -0.678849 -1.237932 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.293110 -0.427411 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.196263 -0.034868 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.661616 1.415142 0.285226 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.048642 0.517601 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.085661 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.045327 3.073049 0.844236 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.343224 0.130170 2.168476 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.463755 0.312596 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 27 (max 380) Diagonal entries: 1.281509 -0.209437 0.000000 -1.079386 0.614257 0.000000 0.000000 0.000000 0.075407 -0.041396 -0.521031 -1.237932 0.000000 -0.034868 0.285226 0.000000 0.000000 0.844236 2.168476 0.000000 Row indices: 0 0 1 3 5 5 7 8 10 10 11 11 13 15 16 18 20 21 23 25 27 Column indices: 0 0 1 1 2 3 4 5 5 6 8 9 10 10 11 12 12 13 13 14 14 15 16 16 17 17 18 Off-diagonal values: 0.426607 -1.241472 0.648451 0.629632 -1.678646 0.096187 0.391618 -0.546679 -1.800011 -0.763157 0.412661 1.920620 -0.678849 -1.293110 -0.427411 0.196263 -1.661616 1.415142 -1.048642 0.517601 -1.085661 1.045327 3.073049 -0.343224 0.130170 0.463755 0.312596 x - - - - - - - - - - - - - - - - - - - x o - - - - - - - - - - - - - - - - - - o x . - - - - - - - - - - - - - - - - - | x o o - - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | x x . - - - - - - - - - - - - - - | | | | | o . - - - - - - - - - - - - - | | | | | o o . - - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | x o - - - - - - - - - - | | | | | | | | | | o - - - - - - - - - | | | | | | | | | x o o - - - - - - - - | | | | | | | | | | o o . - - - - - - - | | | | | | | | | | | | x o - - - - - - | | | | | | | | | | | | o x x - - - - - | | | | | | | | | | | | | o x . - - - - | | | | | | | | | | | | | | o | . - - - | | | | | | | | | | | | | | | x x x - - | | | | | | | | | | | | | | | | o x x - | | | | | | | | | | | | | | | | | x x . The error in solving: 2.292987e-16 The error in solving: 2.989367e-16 The error in solving: 1.040834e-17 The error in solving: 4.611384e-16 The error in solving: 2.254901e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.250000 [ 2.115713 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.132717 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.234437 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.884175 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0.000000 0.000000 0.000000 0.000000 0.351418 -0.001024]; Dimension: 20 x 20 Off-diagonal entries: 4 (max 380) Diagonal entries: 2.115713 -0.132717 -0.234437 0.331718 2.119038 -0.833220 -0.117465 -1.345897 0.938985 0.557390 2.125975 0.130863 -0.736892 -0.958907 0.172100 -0.209564 -1.317524 1.104293 1.636798 -0.001024 Row indices: 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3 4 Column indices: 2 7 12 18 Off-diagonal values: 0.884175 0.331014 -0.680645 0.351418 x - - - - - - - - - - - - - - - - - - - | o - - - - - - - - - - - - - - - - - - | | o - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | o - - - - - - - - - - - - - - | | | | | | o - - - - - - - - - - - - - | | | | | | | o - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | | o - - - - - - - | | | | | | | | | | | | o o - - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | o - - - - | | | | | | | | | | | | | | | | o - - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | x o The error in solving: 1.249001e-16 The error in solving: 3.684807e-16 The error in solving: 1.118897e-16 The error in solving: 2.001483e-16 The error in solving: 5.551115e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.500000 [ 0.695017 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.068215 -0.614257 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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- - - - - | | | | | | o - - - - - - - - - - - - - | | | | | | | o - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | | o - - - - - - - - - | | | | | | | | | | | o - - - - - - - - | | | | | | | | | | | o o - - - - - - - | | | | | | | | | | | | x o - - - - - - | | | | | | | | | | | | | o x - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | | | o - - | | | | | | | | | | | | | | | | | | o - | | | | | | | | | | | | | | | | | | | o The error in solving: 2.288783e-16 The error in solving: 2.271892e-16 The error in solving: 2.483504e-16 The error in solving: 2.225049e-16 The error in solving: 2.803176e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.750000 [ -1.068366 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.146357 0.325647 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.583947 0.460582 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.307348 -0.376596 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.263791 0.490743 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.372601 -0.661609 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.392260 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.631264 -0.990500 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.503696 0.445501 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.728596 0.008833 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.236064 -0.759518 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.279250 0.818879 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.296968 -0.481102 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.087275 -0.215468 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.945715 1.206833]; Dimension: 20 x 20 Off-diagonal entries: 17 (max 380) Diagonal entries: -1.068366 0.325647 0.460582 -0.376596 0.490743 -0.661609 -0.008406 0.180925 -1.191883 0.705931 1.895928 0.392260 -0.990500 0.445501 0.008833 -0.759518 0.818879 -0.481102 -0.215468 1.206833 Row indices: 0 0 1 2 3 4 5 6 7 8 9 9 9 10 11 12 13 14 15 16 17 Column indices: 0 1 2 3 4 5 6 7 8 11 12 13 14 15 16 17 18 Off-diagonal values: -0.146357 0.583947 -0.307348 -1.263791 -0.372601 0.697256 0.450554 0.221727 -1.646394 -0.631264 -0.503696 0.728596 -0.236064 -0.279250 2.296968 -1.087275 -0.945715 o - - - - - - - - - - - - - - - - - - - o x - - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - | | o o - - - - - - - - - - - - - - - - | | | o x - - - - - - - - - - - - - - - | | | | o o - - - - - - - - - - - - - - | | | | | x o - - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | x o - - - - - - - - - - - | | | | | | | | o x - - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | o o - - - - - - - | | | | | | | | | | | | o x - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | o o - - - - | | | | | | | | | | | | | | | o x - - - | | | | | | | | | | | | | | | | x o - - | | | | | | | | | | | | | | | | | o o - | | | | | | | | | | | | | | | | | | o x The error in solving: 1.112389e-16 The error in solving: 1.570092e-16 The error in solving: 1.112389e-16 The error in solving: 2.220446e-16 The error in solving: 2.222613e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.250000 [ 1.428432 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.378393 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.090550 0.000000 -1.901300 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.191759 0.000000 1.184452 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.103705 0.251960 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.782398 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.042298 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.003357 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.120514 -0.625993 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.884509 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.638170 -0.323898 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.458759 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.355944 0.269996 0.885643 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.433516 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.314170 -1.307483 1.130574 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.719550 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.502315 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.082062 -0.625845 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.500934 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.885924 0.153638]; Dimension: 20 x 20 Off-diagonal entries: 11 (max 380) Diagonal entries: 1.428432 0.378393 -1.901300 1.184452 0.251960 -0.782398 -1.042298 1.003357 -0.625993 0.884509 -0.323898 -0.458759 0.885643 1.433516 1.130574 -0.719550 -1.502315 -0.625845 -2.500934 0.153638 Row indices: 0 0 0 1 2 3 3 3 3 4 4 5 5 7 7 9 9 9 10 10 11 Column indices: 0 1 3 7 9 10 11 12 13 16 18 Off-diagonal values: 0.090550 -1.191759 -0.103705 -0.120514 -0.638170 -0.355944 0.269996 -0.314170 -1.307483 -1.082062 -0.885924 x - - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - x | o - - - - - - - - - - - - - - - - - | o | x - - - - - - - - - - - - - - - - | | | o x - - - - - - - - - - - - - - - | | | | | o - - - - - - - - - - - - - - | | | | | | o - - - - - - - - - - - - - | | | | | | | x - - - - - - - - - - - - | | | | | | | o o - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | o o - - - - - - - - - | | | | | | | | | | | o - - - - - - - - | | | | | | | | | | o x x - - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | o o x - - - - - | | | | | | | | | | | | | | | o - - - - | | | | | | | | | | | | | | | | o - - - | | | | | | | | | | | | | | | | o o - - | | | | | | | | | | | | | | | | | | o - | | | | | | | | | | | | | | | | | | o x The error in solving: 1.146493e-16 The error in solving: 3.143250e-16 The error in solving: 1.665335e-16 The error in solving: 1.178080e-16 The error in solving: 1.359740e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.500000 [ 1.314551 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.536636 1.220130 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.221305 -0.976075 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.700053 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.048212 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.263754 0.000000 -0.006559 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.645908 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.519600 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.703143 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.117979 -1.351740 2.094490 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.065018 1.359045 -0.766557 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.252274 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.408234 -1.111474 0.210440 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.645767 -0.212159 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.761736 -1.048518 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.756380 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.923124 0.475179 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.400132 1.839773 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.980069 0.000000 -0.100602 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.804070 0.885414]; Dimension: 20 x 20 Off-diagonal entries: 15 (max 380) Diagonal entries: 1.314551 1.220130 -0.976075 -0.700053 -1.048212 -0.006559 1.645908 0.519600 0.703143 2.094490 -0.766557 -0.252274 0.210440 -0.212159 -1.048518 0.756380 0.475179 1.839773 -0.100602 0.885414 Row indices: 0 0 1 2 2 2 3 3 3 3 5 7 7 9 10 11 11 12 13 14 15 Column indices: 0 1 3 7 8 8 9 10 11 12 13 15 16 16 18 Off-diagonal values: -1.536636 1.221305 -0.263754 1.117979 -1.351740 -0.065018 1.359045 -1.408234 -1.111474 -0.645767 0.761736 0.923124 -1.400132 0.980069 0.804070 x - - - - - - - - - - - - - - - - - - - o x - - - - - - - - - - - - - - - - - - | x o - - - - - - - - - - - - - - - - - | | | o - - - - - - - - - - - - - - - - | | | | o - - - - - - - - - - - - - - - | | | o | o - - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | | x - - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | x o x - - - - - - - - - - | | | | | | | | o x o - - - - - - - - - | | | | | | | | | | | o - - - - - - - - | | | | | | | | | | o o x - - - - - - - | | | | | | | | | | | | o o - - - - - - | | | | | | | | | | | | | x o - - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | | o x - - | | | | | | | | | | | | | | | | x | o - | | | | | | | | | | | | | | | | | | x x The error in solving: 2.220785e-16 The error in solving: 1.711057e-16 The error in solving: 1.594436e-16 The error in solving: 2.775558e-17 The error in solving: 1.144392e-16 - BAND DIAGONAL MATRIX 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.164567 -0.827445 -1.178357 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.171192 1.417114 0.872909 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.526650 -1.072273 -1.183760 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.796088 0.579661 -0.315583 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.249189 1.516372 0.034696]; Dimension: 20 x 20 Off-diagonal entries: 34 (max 380) Diagonal entries: -1.391990 -0.438596 0.437761 -0.757443 0.977510 -1.040104 0.932039 -0.417876 -1.701245 -0.486086 -0.316020 0.001068 -0.359168 -0.021181 1.228038 -1.178357 0.872909 -1.183760 -0.315583 0.034696 Row indices: 0 0 0 2 4 5 7 9 11 13 15 17 19 21 22 24 26 28 30 32 34 Column indices: 0 1 1 2 2 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 13 13 14 14 15 15 16 16 17 17 18 Off-diagonal values: -0.434511 -0.848439 -0.260176 -0.777316 -1.679154 -0.679502 -0.666820 0.960455 1.195239 2.383211 1.037027 1.668021 -0.090863 2.096664 -0.682732 -1.487582 -0.374420 -0.517069 -0.645730 -0.144727 0.269722 0.724655 1.410849 0.820467 0.164567 -0.827445 0.171192 1.417114 0.526650 -1.072273 -0.796088 0.579661 -0.249189 1.516372 o - - - - - - - - - - - - - - - - - - - | o - - - - - - - - - - - - - - - - - - o o x - - - - - - - - - - - - - - - - - | o o o - - - - - - - - - - - - - - - - | | o | x - - - - - - - - - - - - - - - | | | o o o - - - - - - - - - - - - - - | | | | x x x - - - - - - - - - - - - - | | | | | x x o - - - - - - - - - - - - | | | | | | x o o - - - - - - - - - - - | | | | | | | x o o - - - - - - - - - - | | | | | | | | o o o - - - - - - - - - | | | | | | | | | o o x - - - - - - - - | | | | | | | | | | o x o - - - - - - - | | | | | | | | | | | x | o - - - - - - | | | | | | | | | | | | x x x - - - - - | | | | | | | | | | | | | x o o - - - - | | | | | | | | | | | | | | x x x - - - | | | | | | | | | | | | | | | x o o - - | | | | | | | | | | | | | | | | o x o - | | | | | | | | | | | | | | | | | o x x The error in solving: 1.595946e-16 The error in solving: 4.605356e-16 The error in solving: 3.189628e-16 The error in solving: 2.424645e-16 The error in solving: 8.326673e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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- - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | o . - - - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | | o . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | o . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | o . - - - | | | | | | | | | | | | | | | | x . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.305551e-16 The error in solving: 1.241267e-16 The error in solving: 1.110223e-16 The error in solving: 1.241267e-16 The error in solving: 2.221530e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.565854 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.931286 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.369877 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.062824 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.392551 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.798775 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.847695 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.898876 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.234435 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.710960 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 10 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 1 1 2 3 4 5 5 6 6 7 8 8 9 10 10 10 10 Column indices: 2 4 5 6 7 9 11 12 14 15 Off-diagonal values: 0.565854 0.931286 -0.369877 -2.062824 -1.392551 0.798775 1.847695 0.898876 0.234435 -0.710960 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | | o . - - - - - - - - - - - - - | | | | | | o . - - - - - - - - - - - - | | | | | | | o . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | x . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | x . - - - - - - - | | | | | | | | | | | | x . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | o . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.482534e-16 The error in solving: 7.850462e-17 The error in solving: 3.002225e-16 The error in solving: 0.000000e+00 The error in solving: 3.510833e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 1-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.182747 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.822102 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.653168 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.375104 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.845201 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.586666 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.575450 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.368910 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.825122 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.062947 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.481403 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.951342 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.174998 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.804563 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.403415 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.153040 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 16 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 2 3 4 5 6 7 8 9 9 10 10 11 12 13 14 15 16 16 Column indices: 0 1 2 3 4 5 6 7 8 10 12 13 14 15 16 17 Off-diagonal values: -0.182747 -0.822102 0.653168 0.375104 0.845201 1.586666 1.575450 -1.368910 0.825122 0.062947 -0.481403 -0.951342 0.174998 -0.804563 -0.403415 -0.153040 . - - - - - - - - - - - - - - - - - - - o . - - - - - - - - - - - - - - - - - - | o . - - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | | x . - - - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | | o . - - - - - - - - - - - | | | | | | | | x . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | o . - - - - - - | | | | | | | | | | | | | o . - - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | o . - - - | | | | | | | | | | | | | | | | o . - - | | | | | | | | | | | | | | | | | o . - | | | | | | | | | | | | | | | | | | | . The error in solving: 7.850462e-17 The error in solving: 2.543900e-16 The error in solving: 3.388710e-16 The error in solving: 2.792851e-16 The error in solving: 1.271920e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.580792 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.263253 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.210123 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.271188 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.069504 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.080702 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 6 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 0 0 0 1 2 2 2 2 2 2 2 2 3 4 5 5 6 Column indices: 4 5 13 15 16 17 Off-diagonal values: 0.580792 -0.263253 -1.210123 0.271188 -1.069504 0.080702 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | x | . - - - - - - - - - - - - - | | | | | o | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | o | . - - - - | | | | | | | | | | | | | | | x . - - - | | | | | | | | | | | | | | | | o . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | x | . The error in solving: 2.095500e-16 The error in solving: 2.884444e-16 The error in solving: 2.220446e-16 The error in solving: 1.359740e-16 The error in solving: 2.220446e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.887698 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.060825 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.650135 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.262663 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.975279 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.199419 -0.246456 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.258223 0.595859 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.380907 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.121154 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.193076 0.209399 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.527482 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.427692 0.500026 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.127830 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.869716 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.669957 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.720049 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 20 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 2 3 3 4 5 5 5 7 9 10 11 13 14 16 17 18 19 20 Column indices: 0 1 2 3 5 7 8 8 9 9 11 11 12 13 13 14 14 16 16 17 Off-diagonal values: 0.887698 -0.060825 0.650135 -0.262663 -0.975279 -1.199419 -0.246456 -0.258223 0.595859 -0.380907 1.121154 -1.193076 0.209399 -0.527482 1.427692 0.500026 -0.127830 -0.869716 -0.669957 -1.720049 . - - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | o . - - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | o | . - - - - - - - - - - - - - - | | | | | o . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | o o . - - - - - - - - - - | | | | | | | | o x . - - - - - - - - - | | | | | | | | | o | . - - - - - - - - | | | | | | | | | | | x . - - - - - - - | | | | | | | | | | | o x . - - - - - - | | | | | | | | | | | | | o . - - - - - | | | | | | | | | | | | | x x . - - - - | | | | | | | | | | | | | | o | . - - - | | | | | | | | | | | | | | | | o . - - | | | | | | | | | | | | | | | | o | . - | | | | | | | | | | | | | | | | | o | . The error in solving: 5.933870e-16 The error in solving: 2.574881e-16 The error in solving: 2.543841e-16 The error in solving: 2.543841e-16 The error in solving: 2.619389e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A lower-triangular 2-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.709779 -0.452058 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.412062 1.004489 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.102818 2.024300 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.609896 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.650350 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.713603 0.283714 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.398833 -1.231531 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.338825 -0.028081 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.146369 -1.076440 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.359388 -0.595114 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.599582 1.220264 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.086350 1.585891 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.422895 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.499753 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.718202 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.213012 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.125360 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.496404 -0.087056 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 29 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 2 4 6 7 8 10 12 14 16 18 20 22 23 24 25 26 27 29 Column indices: 0 1 1 2 2 3 4 4 5 6 6 7 7 8 8 9 9 10 10 11 11 12 13 13 15 16 16 17 18 Off-diagonal values: -0.709779 -0.452058 1.412062 1.004489 -1.102818 2.024300 -0.609896 0.650350 -0.713603 0.283714 -1.398833 -1.231531 -0.338825 -0.028081 0.146369 -1.076440 2.359388 -0.595114 1.599582 1.220264 -0.086350 1.585891 -1.422895 -0.499753 0.718202 0.213012 -0.125360 -0.496404 -0.087056 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - o o . - - - - - - - - - - - - - - - - - | x x . - - - - - - - - - - - - - - - - | | o x . - - - - - - - - - - - - - - - | | | | o . - - - - - - - - - - - - - - | | | | x | . - - - - - - - - - - - - - | | | | | o x . - - - - - - - - - - - - | | | | | | o o . - - - - - - - - - - - | | | | | | | o o . - - - - - - - - - - | | | | | | | | x o . - - - - - - - - - | | | | | | | | | x o . - - - - - - - - | | | | | | | | | | x x . - - - - - - - | | | | | | | | | | | o x . - - - - - - | | | | | | | | | | | | | o . - - - - - | | | | | | | | | | | | | o | . - - - - | | | | | | | | | | | | | | | x . - - - | | | | | | | | | | | | | | | | x . - - | | | | | | | | | | | | | | | | o | . - | | | | | | | | | | | | | | | | | o o . The error in solving: 2.884444e-16 The error in solving: 3.489512e-16 The error in solving: 1.179612e-16 The error in solving: 1.688306e-16 The error in solving: 1.359740e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.487547 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.487547 0.000000 0.717042 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.717042 0.000000 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0.000000 0.000000 0.324567]; Dimension: 20 x 20 Off-diagonal entries: 14 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.062397 0.398470 0.000000 0.000000 0.000000 0.346250 0.000000 0.000000 0.569445 0.000000 0.000000 0.324567 Row indices: 0 0 1 3 4 4 5 6 6 6 6 6 7 9 11 12 12 13 14 14 14 Column indices: 2 1 3 2 6 5 12 11 13 12 14 13 17 16 Off-diagonal values: 0.487547 0.487547 0.717042 0.717042 0.057506 0.057506 0.756398 0.756398 0.118474 0.118474 0.787739 0.787739 0.213491 0.213491 . - - - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | x . x - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | x . x - - - - - - | | | | | | | | | | | | x x x - - - - - | | | | | | | | | | | | | x . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | x . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | x The error in solving: 1.570092e-16 The error in solving: 3.241474e-16 The error in solving: 5.236912e-16 The error in solving: 3.330669e-16 The error in solving: 3.565943e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.665271 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.665271 0.927660 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.482497 0.988689 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.988689 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.795726 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.845966 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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- - | | x . - - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | | x . - - - - - - - - - - | | | | | | | | | | . x - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | | | . x - - - - - - | | | | | | | | | | | | x . - - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | | | x - - | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | x x The error in solving: 3.421937e-16 The error in solving: 4.079220e-16 The error in solving: 0.000000e+00 The error in solving: 3.200976e-16 The error in solving: 4.458206e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.750000 [ 0.178190 0.755436 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.755436 0.500921 0.978477 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.978477 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.983645 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.983645 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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15 17 19 21 23 24 24 25 26 26 26 Column indices: 1 0 2 1 4 3 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 17 16 Off-diagonal values: 0.755436 0.755436 0.978477 0.978477 0.983645 0.983645 0.775393 0.775393 0.284765 0.284765 0.403831 0.403831 0.412371 0.412371 0.308299 0.308299 0.960837 0.960837 0.422385 0.422385 0.197144 0.197144 0.883654 0.883654 0.625529 0.625529 x x - - - - - - - - - - - - - - - - - - x x x - - - - - - - - - - - - - - - - - | x . - - - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | | x . - - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | x x x - - - - - - - - - - - - | | | | | | x x x - - - - - - - - - - - | | | | | | | x x x - - - - - - - - - - | | | | | | | | x x x - - - - - - - - - | | | | | | | | | x x x - - - - - - - - | | | | | | | | | | x x x - - - - - - - | | | | | | | | | | | x x x - - - - - - | | | | | | | | | | | | x x x - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | x The error in solving: 5.148360e-16 The error in solving: 4.013777e-16 The error in solving: 5.338892e-16 The error in solving: 3.252410e-16 The error in solving: 4.996004e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.505233 0.000000 0.000000 0.000000 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| | x - - - - - - - - - - - - - | | | | | x | . - - - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | | x . x - - - - - - - - - | | | | | | | | | x . - x - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | x | . - x - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | x x . x - - - - | | | | | | | | | | | | | | x x x - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | x . The error in solving: 3.421937e-16 The error in solving: 1.756788e-16 The error in solving: 3.342214e-16 The error in solving: 1.389512e-16 The error in solving: 7.224785e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.567035 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.567035 0.000000 0.000000 0.573194 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.056836 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.573194 0.056836 0.000000 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0.284669 0.000000 0.418545]; Dimension: 20 x 20 Off-diagonal entries: 32 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.079038 0.000000 0.726385 0.000000 0.000000 0.560649 0.095748 0.000000 0.406602 0.000000 0.000000 0.000000 0.000000 0.341661 0.418545 Row indices: 0 1 3 4 7 9 11 11 13 15 17 19 21 22 23 25 26 28 30 31 32 Column indices: 1 0 3 3 1 2 4 3 5 4 7 5 8 7 10 10 11 8 9 9 13 14 11 12 15 14 17 18 16 19 16 17 Off-diagonal values: 0.567035 0.567035 0.573194 0.056836 0.573194 0.056836 0.683783 0.683783 0.707708 0.707708 0.708145 0.708145 0.155818 0.155818 0.023454 0.847213 0.850447 0.023454 0.847213 0.850447 0.446066 0.081872 0.446066 0.081872 0.434041 0.434041 0.867084 0.101222 0.867084 0.284669 0.101222 0.284669 . x - - - - - - - - - - - - - - - - - - x . - x - - - - - - - - - - - - - - - - | | . x - - - - - - - - - - - - - - - - | x x . x - - - - - - - - - - - - - - - | | | x . x - - - - - - - - - - - - - - | | | | x x - x - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | x | x x - - - - - - - - - - - | | | | | | | x . - x - - - - - - - - - | | | | | | | | | . x x - - - - - - - - | | | | | | | | x x x - - - - - - - - - | | | | | | | | | x | x - x - - - - - - | | | | | | | | | | | | . - x - - - - - | | | | | | | | | | | x | x - - - - - - | | | | | | | | | | | | x | . x - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | | . x x - | | | | | | | | | | | | | | | | x . - x | | | | | | | | | | | | | | | | x | x - | | | | | | | | | | | | | | | | | x | x The error in solving: 4.346651e-16 The error in solving: 3.249448e-16 The error in solving: 4.449557e-16 The error in solving: 4.753239e-16 The error in solving: 4.308824e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.750000 [ 0.649608 0.866323 0.006554 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.866323 0.000000 0.000000 0.895538 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.006554 0.000000 0.988909 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.895538 0.000000 0.747336 0.897253 0.494838 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.897253 0.893042 0.000000 0.061833 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.494838 0.000000 0.000000 0.550657 0.789925 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.061833 0.550657 0.000000 0.933084 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.789925 0.933084 0.428330 0.000000 0.972846 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.047750 0.972762 0.323467 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.972846 0.972762 0.904356 0.940530 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.323467 0.940530 0.688115 0.262834 0.715724 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.891501 0.404204 0.315077 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.174196 0.404204 0.000000 0.325650 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.315077 0.325650 0.810117 0.314956 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.314956 0.936811]; Dimension: 20 x 20 Off-diagonal entries: 54 (max 380) Diagonal entries: 0.649608 0.000000 0.988909 0.747336 0.893042 0.000000 0.000000 0.428330 0.047750 0.904356 0.688115 0.032460 0.875965 0.000000 0.350505 0.000000 0.891501 0.000000 0.810117 0.936811 Row indices: 0 2 4 5 8 10 13 16 19 21 24 28 31 35 39 42 44 47 50 53 54 Column indices: 1 2 0 3 0 1 4 5 3 6 3 6 7 4 5 7 5 6 9 9 10 7 8 10 8 9 11 12 10 12 13 10 11 13 14 11 12 14 15 12 13 16 13 17 14 17 18 15 16 18 16 17 19 18 Off-diagonal values: 0.866323 0.006554 0.866323 0.895538 0.006554 0.895538 0.897253 0.494838 0.897253 0.061833 0.494838 0.550657 0.789925 0.061833 0.550657 0.933084 0.789925 0.933084 0.972846 0.972762 0.323467 0.972846 0.972762 0.940530 0.323467 0.940530 0.262834 0.715724 0.262834 0.378308 0.977439 0.715724 0.378308 0.796152 0.846398 0.977439 0.796152 0.909114 0.349154 0.846398 0.909114 0.446527 0.349154 0.174196 0.446527 0.404204 0.315077 0.174196 0.404204 0.325650 0.315077 0.325650 0.314956 0.314956 x x x - - - - - - - - - - - - - - - - - x . - x - - - - - - - - - - - - - - - - x | x - - - - - - - - - - - - - - - - - | x | x x x - - - - - - - - - - - - - - | | | x x - x - - - - - - - - - - - - - | | | x | . x x - - - - - - - - - - - - | | | | x x . x - - - - - - - - - - - - | | | | | x x x - x - - - - - - - - - - | | | | | | | | x x x - - - - - - - - - | | | | | | | x x x x - - - - - - - - - | | | | | | | | x x x x x - - - - - - - | | | | | | | | | | x x x x - - - - - - | | | | | | | | | | x x x x x - - - - - | | | | | | | | | | | x x . x x - - - - | | | | | | | | | | | | x x x - x - - - | | | | | | | | | | | | | x | . - x - - | | | | | | | | | | | | | | x | x x x - | | | | | | | | | | | | | | | x x . x - | | | | | | | | | | | | | | | | x x x x | | | | | | | | | | | | | | | | | | x x The error in solving: 3.436154e-16 The error in solving: 2.960233e-16 The error in solving: 3.925883e-16 The error in solving: 4.871084e-16 The error in solving: 3.825842e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.685287 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.636186 0.000000 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- - - - | | | | | x x - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | | x The error in solving: 2.294037e-16 The error in solving: 5.551115e-17 The error in solving: 3.855928e-16 The error in solving: 2.723903e-16 The error in solving: 5.236912e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.034785 0.821245 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.821245 0.207840 0.332467 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.332467 0.111872 0.704662 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.704662 0.036328 0.136693 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.136693 0.665174 0.267646 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.267646 0.592888 0.335547 0.000000 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8 14 13 16 15 17 16 Off-diagonal values: 0.821245 0.821245 0.332467 0.332467 0.704662 0.704662 0.136693 0.136693 0.267646 0.267646 0.335547 0.335547 0.280525 0.280525 0.650353 0.650353 0.737457 0.737457 0.072361 0.072361 0.268931 0.268931 x x - - - - - - - - - - - - - - - - - - x x x - - - - - - - - - - - - - - - - - | x x x - - - - - - - - - - - - - - - - | | x x x - - - - - - - - - - - - - - - | | | x x x - - - - - - - - - - - - - - | | | | x x x - - - - - - - - - - - - - | | | | | x x x - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | | x - - - - - - - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | x x x - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | x The error in solving: 2.938194e-16 The error in solving: 4.053169e-16 The error in solving: 5.266395e-16 The error in solving: 4.449557e-16 The error in solving: 6.449813e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.275874 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.926325 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.907755 0.209915 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.335262 0.211775]; Dimension: 20 x 20 Off-diagonal entries: 32 (max 380) Diagonal entries: 0.275874 0.926325 0.907755 0.512261 0.369102 0.038042 0.187196 0.740625 0.119725 0.055907 0.458988 0.232802 0.582996 0.509939 0.827807 0.714812 0.714063 0.346109 0.051758 0.211775 Row indices: 0 0 0 1 3 5 7 9 11 13 15 17 19 21 23 25 26 27 29 31 32 Column indices: 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 17 16 18 17 19 18 Off-diagonal values: 0.209915 0.209915 0.590104 0.590104 0.736679 0.736679 0.753286 0.753286 0.097529 0.097529 0.675310 0.675310 0.099301 0.099301 0.962865 0.962865 0.030664 0.030664 0.092624 0.092624 0.150608 0.150608 0.511322 0.511322 0.087476 0.087476 0.264702 0.264702 0.368690 0.368690 0.335262 0.335262 x - - - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | x x x - - - - - - - - - - - - - - - | | | x x x - - - - - - - - - - - - - - | | | | x x x - - - - - - - - - - - - - | | | | | x x x - - - - - - - - - - - - | | | | | | x x x - - - - - - - - - - - | | | | | | | x x x - - - - - - - - - - | | | | | | | | x x x - - - - - - - - - | | | | | | | | | x x x - - - - - - - - | | | | | | | | | | x x x - - - - - - - | | | | | | | | | | | x x x - - - - - - | | | | | | | | | | | | x x x - - - - - | | | | | | | | | | | | | x x x - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | x x x - | | | | | | | | | | | | | | | | | x x x | | | | | | | | | | | | | | | | | | x x The error in solving: 5.026900e-16 The error in solving: 3.521788e-16 The error in solving: 4.878985e-16 The error in solving: 5.339342e-16 The error in solving: 6.522653e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.516695 0.000000 0.372170 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.945311 0.000000 0.927474 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.372170 0.000000 0.716171 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.927474 0.000000 0.140662 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.470152 0.076174 0.987339 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.076174 0.107721 0.419389 0.000000 0.000000 0.000000 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Off-diagonal values: 0.372170 0.927474 0.372170 0.927474 0.076174 0.987339 0.076174 0.419389 0.987339 0.419389 0.492249 0.492249 0.286284 0.036563 0.286284 0.036563 0.804770 0.804770 0.877195 0.877195 x - x - - - - - - - - - - - - - - - - - | x - x - - - - - - - - - - - - - - - - x | x - - - - - - - - - - - - - - - - - | x | x - - - - - - - - - - - - - - - - | | | | x x x - - - - - - - - - - - - - | | | | x x x - - - - - - - - - - - - - | | | | x x x - - - - - - - - - - - - - | | | | | | | x - - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | x x x x - - - - - - - - | | | | | | | | | x x - - - - - - - - - | | | | | | | | | x | x - - - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | x - x - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | x | x - - - | | | | | | | | | | | | | | | | | x - x | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | x | x The error in solving: 2.220446e-16 The error in solving: 1.841097e-16 The error in solving: 2.355203e-16 The error in solving: 1.468789e-16 The error in solving: 5.162836e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.659604 0.415000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.415000 0.976047 0.302425 0.891110 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.302425 0.665581 0.552534 0.033094 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.891110 0.552534 0.736141 0.859458 0.047052 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.033094 0.859458 0.452343 0.285406 0.322140 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.047052 0.285406 0.089377 0.230547 0.443669 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.322140 0.230547 0.502392 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.443669 0.000000 0.256354 0.000000 0.524936 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.263959 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.027891 0.221609 0.663652 0.000000 0.430453 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.832234 0.000000 0.249405 0.000000 0.399926 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.430453 0.000000 0.815141 0.495813 0.051417 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.399926 0.495813 0.945027 0.999160 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.051417 0.999160 0.215005 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.848738]; Dimension: 20 x 20 Off-diagonal entries: 48 (max 380) Diagonal entries: 0.659604 0.976047 0.665581 0.736141 0.452343 0.089377 0.502392 0.256354 0.263959 0.937874 0.099565 0.395244 0.102727 0.124140 0.663652 0.249405 0.815141 0.945027 0.215005 0.848738 Row indices: 0 1 4 7 11 15 19 21 23 23 25 28 30 32 35 38 40 43 46 48 48 Column indices: 1 0 2 3 1 3 4 1 2 4 5 2 3 5 6 3 4 6 7 4 5 5 9 7 10 9 11 12 10 13 10 14 11 14 15 12 13 16 13 17 14 17 18 15 16 18 16 17 Off-diagonal values: 0.415000 0.415000 0.302425 0.891110 0.302425 0.552534 0.033094 0.891110 0.552534 0.859458 0.047052 0.033094 0.859458 0.285406 0.322140 0.047052 0.285406 0.230547 0.443669 0.322140 0.230547 0.443669 0.524936 0.524936 0.102792 0.102792 0.462197 0.593260 0.462197 0.922412 0.593260 0.027891 0.922412 0.221609 0.832234 0.027891 0.221609 0.430453 0.832234 0.399926 0.430453 0.495813 0.051417 0.399926 0.495813 0.999160 0.051417 0.999160 x x - - - - - - - - - - - - - - - - - - x x x x - - - - - - - - - - - - - - - - | x x x x - - - - - - - - - - - - - - - | x x x x x - - - - - - - - - - - - - - | | x x x x x - - - - - - - - - - - - - | | | x x x x x - - - - - - - - - - - - | | | | x x x - - - - - - - - - - - - - | | | | | x | x - x - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | x | x x - - - - - - - - - | | | | | | | | | x x x x - - - - - - - | | | | | | | | | | x x - x - - - - - - | | | | | | | | | | x | x - x - - - - - | | | | | | | | | | | x | x x x - - - - | | | | | | | | | | | | x x x - x - - - | | | | | | | | | | | | | x | x - x - - | | | | | | | | | | | | | | x | x x x - | | | | | | | | | | | | | | | x x x x - | | | | | | | | | | | | | | | | x x x - | | | | | | | | | | | | | | | | | | | x The error in solving: 4.863170e-16 The error in solving: 3.237572e-16 The error in solving: 3.964289e-16 The error in solving: 3.527423e-16 The error in solving: 4.475452e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.963181 0.842280 0.922258 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.842280 0.006976 0.254723 0.948084 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.922258 0.254723 0.706067 0.000000 0.423641 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.948084 0.000000 0.367124 0.657334 0.933393 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.423641 0.657334 0.948977 0.496529 0.204263 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.933393 0.496529 0.955595 0.000000 0.484443 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.204263 0.000000 0.848397 0.047628 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.484443 0.047628 0.124259 0.000000 0.279040 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.076715 0.000000 0.581904 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.279040 0.000000 0.321646 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.553171 0.133993 0.199129 0.582512 0.737538 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.196179 0.582512 0.905065 0.571080 0.064387 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.737538 0.571080 0.555038 0.508207 0.433571 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.064387 0.508207 0.361796 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.433571 0.000000 0.261915]; Dimension: 20 x 20 Off-diagonal entries: 54 (max 380) Diagonal entries: 0.963181 0.006976 0.706067 0.367124 0.948977 0.955595 0.848397 0.124259 0.076715 0.321646 0.528567 0.260233 0.926661 0.747650 0.060324 0.199129 0.905065 0.555038 0.361796 0.261915 Row indices: 0 2 5 8 11 15 18 20 23 24 25 27 29 32 35 39 43 47 51 53 54 Column indices: 1 2 0 2 3 0 1 4 1 4 5 2 3 5 6 3 4 7 4 7 5 6 9 10 7 8 12 12 13 10 11 14 11 14 15 12 13 15 16 13 14 16 17 14 15 17 18 15 16 18 19 16 17 17 Off-diagonal values: 0.842280 0.922258 0.842280 0.254723 0.948084 0.922258 0.254723 0.423641 0.948084 0.657334 0.933393 0.423641 0.657334 0.496529 0.204263 0.933393 0.496529 0.484443 0.204263 0.047628 0.484443 0.047628 0.279040 0.581904 0.279040 0.581904 0.853677 0.118206 0.976318 0.853677 0.118206 0.083511 0.976318 0.996878 0.553171 0.083511 0.996878 0.133993 0.196179 0.553171 0.133993 0.582512 0.737538 0.196179 0.582512 0.571080 0.064387 0.737538 0.571080 0.508207 0.433571 0.064387 0.508207 0.433571 x x x - - - - - - - - - - - - - - - - - x x x x - - - - - - - - - - - - - - - - x x x - x - - - - - - - - - - - - - - - | x | x x x - - - - - - - - - - - - - - | | x x x x x - - - - - - - - - - - - - | | | x x x - x - - - - - - - - - - - - | | | | x | x x - - - - - - - - - - - - | | | | | x x x - x - - - - - - - - - - | | | | | | | | x - x - - - - - - - - - | | | | | | | x | x - - - - - - - - - - | | | | | | | | x | x - x - - - - - - - | | | | | | | | | | | x x x - - - - - - | | | | | | | | | | x x x - x - - - - - | | | | | | | | | | | x | x x x - - - - | | | | | | | | | | | | x x x x x - - - | | | | | | | | | | | | | x x x x x - - | | | | | | | | | | | | | | x x x x x - | | | | | | | | | | | | | | | x x x x x | | | | | | | | | | | | | | | | x x x - | | | | | | | | | | | | | | | | | x | x The error in solving: 2.259140e-16 The error in solving: 6.533255e-16 The error in solving: 2.691919e-16 The error in solving: 6.684788e-16 The error in solving: 3.515117e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.044184 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.044184 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.558168 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.558168 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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Off-diagonal values: 0.044184 0.044184 0.558168 0.558168 0.789239 0.789239 0.306421 0.306421 0.886457 0.886457 . - - - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | x . - - - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | | x . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | | x . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | x . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.676859e-16 The error in solving: 1.359740e-16 The error in solving: 3.510833e-16 The error in solving: 5.551115e-17 The error in solving: 2.775774e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.511451 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.511451 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.277174 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.277174 0.000000 0.386990 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.386990 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.626178 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.626178 0.000000 0.056652 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.056652 0.000000 0.676095 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.676095 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.285448 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.285448 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.769388 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.769388 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.400444 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.400444 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 18 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 1 2 3 5 6 6 7 9 11 12 12 12 13 14 15 16 17 18 Column indices: 3 2 5 4 6 5 9 8 10 9 11 10 15 14 17 16 19 18 Off-diagonal values: 0.511451 0.511451 0.277174 0.277174 0.386990 0.386990 0.626178 0.626178 0.056652 0.056652 0.676095 0.676095 0.285448 0.285448 0.769388 0.769388 0.400444 0.400444 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . x - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | | x . x - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | | x . x - - - - - - - - - | | | | | | | | | x . x - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | x . - - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | x . The error in solving: 2.044326e-16 The error in solving: 4.588073e-16 The error in solving: 3.885781e-16 The error in solving: 3.330669e-16 The error in solving: 5.258931e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.591382 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.591382 0.000000 0.613830 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.613830 0.000000 0.404740 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.404740 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.029778 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.029778 0.000000 0.444619 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.444619 0.000000 0.575123 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.575123 0.000000 0.009754 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.009754 0.000000 0.878238 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.878238 0.000000 0.675783 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.675783 0.000000 0.306035 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.306035 0.000000 0.043449 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.043449 0.000000 0.201034 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.201034 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.066925 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.066925 0.000000 0.435770 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.435770 0.000000 0.065716 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.065716 0.000000 0.022832 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.022832 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 32 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 5 6 7 9 11 13 15 17 19 21 23 24 25 27 29 31 32 32 Column indices: 1 0 2 1 3 2 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 15 14 16 15 17 16 18 17 Off-diagonal values: 0.591382 0.591382 0.613830 0.613830 0.404740 0.404740 0.029778 0.029778 0.444619 0.444619 0.575123 0.575123 0.009754 0.009754 0.878238 0.878238 0.675783 0.675783 0.306035 0.306035 0.043449 0.043449 0.201034 0.201034 0.066925 0.066925 0.435770 0.435770 0.065716 0.065716 0.022832 0.022832 . x - - - - - - - - - - - - - - - - - - x . x - - - - - - - - - - - - - - - - - | x . x - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | | x . x - - - - - - - - - - - - - | | | | | x . x - - - - - - - - - - - - | | | | | | x . x - - - - - - - - - - - | | | | | | | x . x - - - - - - - - - - | | | | | | | | x . x - - - - - - - - - | | | | | | | | | x . x - - - - - - - - | | | | | | | | | | x . x - - - - - - - | | | | | | | | | | | x . x - - - - - - | | | | | | | | | | | | x . - - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | x . x - - - | | | | | | | | | | | | | | | x . x - - | | | | | | | | | | | | | | | | x . x - | | | | | | | | | | | | | | | | | x . - | | | | | | | | | | | | | | | | | | | . The error in solving: 3.764950e-16 The error in solving: 3.402182e-16 The error in solving: 3.726386e-16 The error in solving: 4.586584e-16 The error in solving: 5.887847e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.848052 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.848052 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.511435 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.645650 0.249800 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.511435 0.645650 0.000000 0.789418 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.249800 0.789418 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.632276 0.387501 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.632276 0.000000 0.000000 0.908726 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.387501 0.000000 0.000000 0.900929 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.908726 0.900929 0.000000 0.618732 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.618732 0.000000 0.029474 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.029474 0.000000 0.986120 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.986120 0.000000 0.000000 0.403384 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.403384 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 26 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 1 2 3 5 8 10 10 10 10 12 14 16 19 21 23 25 25 26 Column indices: 3 2 6 6 7 4 5 7 5 6 12 13 11 14 11 14 12 13 15 14 16 15 17 16 19 17 Off-diagonal values: 0.848052 0.848052 0.511435 0.645650 0.249800 0.511435 0.645650 0.789418 0.249800 0.789418 0.632276 0.387501 0.632276 0.908726 0.387501 0.900929 0.908726 0.900929 0.618732 0.618732 0.029474 0.029474 0.986120 0.986120 0.403384 0.403384 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . x - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | | | . - x - - - - - - - - - - - - - | | | | | . x x - - - - - - - - - - - - | | | | x x . x - - - - - - - - - - - - | | | | | x x . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . x x - - - - - - | | | | | | | | | | | x . - x - - - - - | | | | | | | | | | | x | . x - - - - - | | | | | | | | | | | | x x . x - - - - | | | | | | | | | | | | | | x . x - - - | | | | | | | | | | | | | | | x . x - - | | | | | | | | | | | | | | | | x . - x | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | x | . The error in solving: 1.755417e-16 The error in solving: 1.249754e-16 The error in solving: 6.407872e-16 The error in solving: 1.243205e-16 The error in solving: 3.538156e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.016354 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.608327 0.965212 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.016354 0.608327 0.000000 0.404812 0.358601 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.965212 0.404812 0.000000 0.567567 0.601899 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.358601 0.567567 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.601899 0.000000 0.000000 0.144681 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.144681 0.000000 0.363935 0.435622 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.363935 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.435622 0.000000 0.000000 0.386422 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.386422 0.000000 0.950337 0.763876 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.950337 0.000000 0.000000 0.907500 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.763876 0.000000 0.000000 0.811555 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.907500 0.811555 0.000000 0.000000 0.512749 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.867580 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.512749 0.000000 0.000000 0.521398 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.867580 0.521398 0.000000 0.786944 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.786944 0.000000 0.000000 0.402385 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.042491 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.402385 0.042491 0.000000 0.535232 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.535232 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 44 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 7 11 13 15 18 19 21 24 26 28 31 32 34 37 39 40 43 44 Column indices: 2 2 3 0 1 3 4 1 2 4 5 2 3 3 6 5 7 8 6 6 9 8 10 11 9 12 9 12 10 11 14 15 12 15 13 14 16 15 18 18 16 17 19 18 Off-diagonal values: 0.016354 0.608327 0.965212 0.016354 0.608327 0.404812 0.358601 0.965212 0.404812 0.567567 0.601899 0.358601 0.567567 0.601899 0.144681 0.144681 0.363935 0.435622 0.363935 0.435622 0.386422 0.386422 0.950337 0.763876 0.950337 0.907500 0.763876 0.811555 0.907500 0.811555 0.512749 0.867580 0.512749 0.521398 0.867580 0.521398 0.786944 0.786944 0.402385 0.042491 0.402385 0.042491 0.535232 0.535232 . - x - - - - - - - - - - - - - - - - - | . x x - - - - - - - - - - - - - - - - x x . x x - - - - - - - - - - - - - - - | x x . x x - - - - - - - - - - - - - - | | x x . - - - - - - - - - - - - - - - | | | x | . x - - - - - - - - - - - - - | | | | | x . x x - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | x | . x - - - - - - - - - - | | | | | | | | x . x x - - - - - - - - | | | | | | | | | x . - x - - - - - - - | | | | | | | | | x | . x - - - - - - - | | | | | | | | | | x x . - x - - - - - | | | | | | | | | | | | | . - x - - - - | | | | | | | | | | | | x | . x - - - - | | | | | | | | | | | | | x x . x - - - | | | | | | | | | | | | | | | x . - x - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | x x . x | | | | | | | | | | | | | | | | | | x . The error in solving: 3.191891e-16 The error in solving: 3.945419e-16 The error in solving: 5.185169e-16 The error in solving: 5.502328e-16 The error in solving: 5.324443e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 0.515213 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.488570 0.994681 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.515213 0.488570 0.000000 0.701237 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.994681 0.701237 0.000000 0.209220 0.830099 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.209220 0.000000 0.000000 0.559036 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.830099 0.000000 0.000000 0.000000 0.838429 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.559036 0.000000 0.000000 0.068385 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.838429 0.068385 0.000000 0.199111 0.032419 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.199111 0.000000 0.703139 0.357149 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.032419 0.703139 0.000000 0.211694 0.932281 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.357149 0.211694 0.000000 0.000000 0.200313 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.932281 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.200313 0.000000 0.000000 0.770431 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.770431 0.000000 0.000000 0.714293 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.577807 0.867707 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.714293 0.577807 0.000000 0.000000 0.936779 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.867707 0.000000 0.000000 0.951918 0.701881 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.936779 0.951918 0.000000 0.992374 0.823678 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.701881 0.992374 0.000000 0.718114 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.823678 0.718114 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 52 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 6 10 12 14 16 20 23 27 30 31 33 35 37 40 43 47 50 52 Column indices: 2 2 3 0 1 3 1 2 4 5 3 6 3 7 4 7 5 6 8 9 7 9 10 7 8 10 11 8 9 12 9 10 13 12 15 15 16 13 14 17 14 17 18 15 16 18 19 16 17 19 17 18 Off-diagonal values: 0.515213 0.488570 0.994681 0.515213 0.488570 0.701237 0.994681 0.701237 0.209220 0.830099 0.209220 0.559036 0.830099 0.838429 0.559036 0.068385 0.838429 0.068385 0.199111 0.032419 0.199111 0.703139 0.357149 0.032419 0.703139 0.211694 0.932281 0.357149 0.211694 0.200313 0.932281 0.200313 0.770431 0.770431 0.714293 0.577807 0.867707 0.714293 0.577807 0.936779 0.867707 0.951918 0.701881 0.936779 0.951918 0.992374 0.823678 0.701881 0.992374 0.718114 0.823678 0.718114 . - x - - - - - - - - - - - - - - - - - | . x x - - - - - - - - - - - - - - - - x x . x - - - - - - - - - - - - - - - - | x x . x x - - - - - - - - - - - - - - | | | x . - x - - - - - - - - - - - - - | | | x | . - x - - - - - - - - - - - - | | | | x | . x - - - - - - - - - - - - | | | | | x x . x x - - - - - - - - - - | | | | | | | x . x x - - - - - - - - - | | | | | | | x x . x x - - - - - - - - | | | | | | | | x x . - x - - - - - - - | | | | | | | | | x | . - - - - - - - - | | | | | | | | | | x | . x - - - - - - | | | | | | | | | | | | x . - x - - - - | | | | | | | | | | | | | | . x x - - - | | | | | | | | | | | | | x x . - x - - | | | | | | | | | | | | | | x | . x x - | | | | | | | | | | | | | | | x x . x x | | | | | | | | | | | | | | | | x x . x | | | | | | | | | | | | | | | | | x x . The error in solving: 3.028770e-16 The error in solving: 7.171272e-16 The error in solving: 1.025455e-15 The error in solving: 5.036318e-16 The error in solving: 3.682193e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.436898 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.739452 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.739452 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.921592 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.921592 0.105569 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.474920 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.509508 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.906809 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.906809 0.000000 0.623653 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.623653 -0.506263 0.191564 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.191564 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 10 (max 380) Diagonal entries: 0.000000 -0.436898 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.105569 -0.474920 -0.509508 0.000000 0.000000 0.000000 0.000000 -0.506263 0.000000 Row indices: 0 0 0 0 0 0 1 2 2 2 2 3 4 4 4 4 4 5 7 9 10 Column indices: 6 5 11 10 17 16 18 17 19 18 Off-diagonal values: 0.739452 0.739452 0.921592 0.921592 -0.906809 -0.906809 0.623653 0.623653 0.191564 0.191564 . - - - - - - - - - - - - - - - - - - - | o - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . x - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | | | o - - - - - - - | | | | | | | | | | | | | o - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . o - - | | | | | | | | | | | | | | | | o . x - | | | | | | | | | | | | | | | | | x o x | | | | | | | | | | | | | | | | | | x . The error in solving: 2.288783e-16 The error in solving: 2.938193e-16 The error in solving: 1.241267e-16 The error in solving: 5.561947e-17 The error in solving: 2.992587e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.094210 -0.209253 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.209253 0.000000 -0.137293 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.137293 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-0.935805 -0.935805 0.700264 0.700264 -0.030495 -0.030495 -0.979441 -0.979441 0.901307 0.901307 0.058545 0.058545 -0.905885 -0.905885 -0.582393 -0.582393 0.342391 0.342391 . - - - - - - - - - - - - - - - - - - - | o x - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | o o - - - - - - - - - - - - - - | | | | o x - - - - - - - - - - - - - - | | | | | | . o - - - - - - - - - - - - | | | | | | o . o - - - - - - - - - - - | | | | | | | o . - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | x x o - - - - - - - | | | | | | | | | | | o x - - - - - - - | | | | | | | | | | | | | o o - - - - - | | | | | | | | | | | | | o . x - - - - | | | | | | | | | | | | | | x o x - - - | | | | | | | | | | | | | | | x x o - - | | | | | | | | | | | | | | | | o o o - | | | | | | | | | | | | | | | | | o . x | | | | | | | | | | | | | | | | | | x x The error in solving: 3.805653e-16 The error in solving: 2.513614e-16 The error in solving: 5.689047e-16 The error in solving: 6.503709e-16 The error in solving: 2.733607e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.445469 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.131670 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.445469 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.131670 0.000000 0.576337 0.000000 0.689519 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| | | | | | | o o . - - - - - - - - - | | | | | | | | | o | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | x - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | o o - - - | | | | | | | | | | | | | | | o . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 3.394566e-16 The error in solving: 2.372452e-16 The error in solving: 1.250927e-16 The error in solving: 3.040669e-16 The error in solving: 4.200217e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.500000 [ -0.676362 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.961694 -0.908882 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.908882 -0.247770 0.000000 0.239597 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.967955 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.239597 0.000000 -0.605185 0.000000 0.331484 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.967955 0.000000 0.034799 0.530700 -0.976123 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.331484 0.530700 0.000000 0.238220 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.976123 0.238220 0.000000 -0.875782 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.875782 0.000000 0.250314 -0.014453 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.250314 0.707268 0.004069 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.014453 0.004069 0.593738 -0.903236 -0.314039 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.903236 0.000000 0.000000 -0.615093 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.314039 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.615093 0.000000 0.000000 -0.754508 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.754508 0.000000 0.410155 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.410155 0.000000 0.000000 0.296938 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.728139 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.296938 0.000000 -0.357759 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 34 (max 380) Diagonal entries: -0.676362 0.961694 -0.247770 0.000000 -0.605185 0.034799 0.000000 0.000000 0.000000 0.707268 0.593738 0.000000 0.000000 0.000000 0.000000 0.000000 0.728139 -0.357759 0.000000 0.000000 Row indices: 0 0 1 3 4 6 9 12 15 18 20 24 26 27 29 31 33 33 34 34 34 Column indices: 2 1 4 5 2 6 3 6 7 4 5 7 5 6 8 7 9 10 8 10 8 9 11 12 10 13 10 11 14 13 15 14 17 15 Off-diagonal values: -0.908882 -0.908882 0.239597 0.967955 0.239597 0.331484 0.967955 0.530700 -0.976123 0.331484 0.530700 0.238220 -0.976123 0.238220 -0.875782 -0.875782 0.250314 -0.014453 0.250314 0.004069 -0.014453 0.004069 -0.903236 -0.314039 -0.903236 -0.615093 -0.314039 -0.615093 -0.754508 -0.754508 0.410155 0.410155 0.296938 0.296938 o - - - - - - - - - - - - - - - - - - - | x o - - - - - - - - - - - - - - - - - | o o - x - - - - - - - - - - - - - - - | | | . - x - - - - - - - - - - - - - - | | x | o - x - - - - - - - - - - - - - | | | x | x x o - - - - - - - - - - - - | | | | x x . x - - - - - - - - - - - - | | | | | o x . o - - - - - - - - - - - | | | | | | | o . x o - - - - - - - - - | | | | | | | | x x x - - - - - - - - - | | | | | | | | o x x o o - - - - - - - | | | | | | | | | | o . - o - - - - - - | | | | | | | | | | o | . - - - - - - - | | | | | | | | | | | o | . o - - - - - | | | | | | | | | | | | | o . x - - - - | | | | | | | | | | | | | | x . - x - - | | | | | | | | | | | | | | | | x - - - | | | | | | | | | | | | | | | x | o - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 3.250374e-16 The error in solving: 3.435979e-16 The error in solving: 3.944808e-16 The error in solving: 3.736709e-16 The error in solving: 4.871084e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.750000 [ -0.446844 -0.090009 -0.718949 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.090009 0.696827 -0.207835 0.270616 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.718949 -0.207835 0.000000 0.898912 -0.941190 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.270616 0.898912 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.184332 -0.282633 0.531231 0.361104 0.921366 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.494642 0.361104 0.661736 0.997202 0.676109 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.921366 0.997202 0.076264 0.730117 0.924923 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.676109 0.730117 0.000000 -0.541019 0.837892 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.924923 -0.541019 -0.983100 0.109598 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.837892 0.109598 -0.290037]; Dimension: 20 x 20 Off-diagonal entries: 68 (max 380) Diagonal entries: -0.446844 0.696827 0.000000 -0.248210 -0.771126 -0.073255 0.000000 -0.419449 0.459594 0.000000 -0.451380 -0.953287 -0.118683 -0.088532 0.531231 0.661736 0.076264 0.000000 -0.983100 -0.290037 Row indices: 0 2 5 9 13 17 20 24 26 29 33 37 40 44 47 51 55 59 63 66 68 Column indices: 1 2 0 2 3 0 1 3 4 1 2 4 5 2 3 5 6 3 4 6 4 5 7 8 6 9 6 9 10 7 8 10 11 8 9 11 12 9 10 12 10 11 13 14 12 14 15 12 13 15 16 13 14 16 17 14 15 17 18 15 16 18 19 16 17 19 17 18 Off-diagonal values: -0.090009 -0.718949 -0.090009 -0.207835 0.270616 -0.718949 -0.207835 0.898912 -0.941190 0.270616 0.898912 -0.302427 0.593908 -0.941190 -0.302427 -0.583276 0.242986 0.593908 -0.583276 0.765976 0.242986 0.765976 -0.520265 0.335699 -0.520265 -0.694375 0.335699 0.615931 -0.422955 -0.694375 0.615931 0.562893 0.133668 -0.422955 0.562893 0.001643 -0.067601 0.133668 0.001643 0.117273 -0.067601 0.117273 0.222885 -0.184332 0.222885 -0.282633 0.494642 -0.184332 -0.282633 0.361104 0.921366 0.494642 0.361104 0.997202 0.676109 0.921366 0.997202 0.730117 0.924923 0.676109 0.730117 -0.541019 0.837892 0.924923 -0.541019 0.109598 0.837892 0.109598 o o o - - - - - - - - - - - - - - - - - o x o x - - - - - - - - - - - - - - - - o o . x o - - - - - - - - - - - - - - - | x x o o x - - - - - - - - - - - - - - | | o o o o x - - - - - - - - - - - - - | | | x o o x - - - - - - - - - - - - - | | | | x x . o x - - - - - - - - - - - | | | | | | o o - o - - - - - - - - - - | | | | | | x | x x o - - - - - - - - - | | | | | | | o x . x x - - - - - - - - | | | | | | | | o x o x o - - - - - - - | | | | | | | | | x x o x - - - - - - - | | | | | | | | | | o x o x o - - - - - | | | | | | | | | | | | x o o x - - - - | | | | | | | | | | | | o o x x x - - - | | | | | | | | | | | | | x x x x x - - | | | | | | | | | | | | | | x x x x x - | | | | | | | | | | | | | | | x x . o x | | | | | | | | | | | | | | | | x o o x | | | | | | | | | | | | | | | | | x x o The error in solving: 6.641431e-16 The error in solving: 3.915406e-16 The error in solving: 2.956979e-16 The error in solving: 6.634133e-16 The error in solving: 7.656716e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.250000 [ -0.862686 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.336342 0.981981 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.981981 0.453558 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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- - - - | | | | | | | | | | | x - - - - - - - - | | | | | | | | | | | | o - - - - - - - | | | | | | | | | | | | | o - - - - - - | | | | | | | | | | | | | | o - - - - - | | | | | | | | | | | | | | | x - - - - | | | | | | | | | | | | | | | | o - - - | | | | | | | | | | | | | | | | | o x - | | | | | | | | | | | | | | | | | x o x | | | | | | | | | | | | | | | | | | x o The error in solving: 7.979728e-17 The error in solving: 2.025396e-16 The error in solving: 5.721958e-17 The error in solving: 2.482534e-16 The error in solving: 3.858424e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.500000 [ -0.968309 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.730582 0.631505 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0.000000 0.000000 0.000000 -0.289686 -0.336747 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.837887 0.412780 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.412780 -0.008839]; Dimension: 20 x 20 Off-diagonal entries: 20 (max 380) Diagonal entries: -0.968309 -0.730582 0.600388 -0.808478 0.244339 0.231202 -0.136310 -0.425623 -0.330340 0.135245 -0.395903 0.100033 -0.666184 -0.311046 -0.852483 0.467318 0.885129 -0.336747 -0.837887 -0.008839 Row indices: 0 0 1 3 4 4 4 4 4 5 7 9 11 13 14 14 15 17 18 19 20 Column indices: 2 1 3 2 9 8 10 9 11 10 12 11 13 12 16 15 17 16 19 18 Off-diagonal values: 0.631505 0.631505 -0.247861 -0.247861 0.737452 0.737452 0.564335 0.564335 -0.604892 -0.604892 0.023980 0.023980 0.716312 0.716312 0.136257 0.136257 -0.289686 -0.289686 0.412780 0.412780 o - - - - - - - - - - - - - - - - - - - | o x - - - - - - - - - - - - - - - - - | x x o - - - - - - - - - - - - - - - - | | o o - - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | o - - - - - - - - - - - - - | | | | | | | o - - - - - - - - - - - - | | | | | | | | o x - - - - - - - - - - | | | | | | | | x x x - - - - - - - - - | | | | | | | | | x o o - - - - - - - - | | | | | | | | | | o x x - - - - - - - | | | | | | | | | | | x o x - - - - - - | | | | | | | | | | | | x o - - - - - - | | | | | | | | | | | | | | o - - - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | x x o - - | | | | | | | | | | | | | | | | o o - - | | | | | | | | | | | | | | | | | | o x | | | | | | | | | | | | | | | | | | x o The error in solving: 4.713435e-16 The error in solving: 3.424750e-16 The error in solving: 3.734775e-16 The error in solving: 2.806609e-16 The error in solving: 4.041273e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.752766 0.763714 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.763714 -0.071220 -0.304572 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.304572 -0.604427 -0.852166 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.852166 -0.187145 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.096342 0.010605 0.132983 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.132983 -0.649150 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.877309 -0.120865 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.120865 -0.744749 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.192885]; Dimension: 20 x 20 Off-diagonal entries: 24 (max 380) Diagonal entries: 0.752766 -0.071220 -0.604427 -0.187145 -0.972084 -0.037433 -0.422335 0.899472 0.708795 -0.236196 0.934825 -0.408332 0.468992 -0.774561 -0.159733 0.010605 -0.649150 -0.877309 -0.744749 0.192885 Row indices: 0 1 3 5 6 6 6 7 9 11 13 14 15 17 18 19 21 22 23 24 24 Column indices: 1 0 2 1 3 2 7 6 8 7 9 8 10 9 12 11 13 12 15 14 16 15 18 17 Off-diagonal values: 0.763714 0.763714 -0.304572 -0.304572 -0.852166 -0.852166 -0.268520 -0.268520 -0.504796 -0.504796 0.383259 0.383259 -0.121522 -0.121522 -0.581652 -0.581652 -0.309320 -0.309320 0.096342 0.096342 0.132983 0.132983 -0.120865 -0.120865 x x - - - - - - - - - - - - - - - - - - x o o - - - - - - - - - - - - - - - - - | o o o - - - - - - - - - - - - - - - - | | o o - - - - - - - - - - - - - - - - | | | | o - - - - - - - - - - - - - - - | | | | | o - - - - - - - - - - - - - - | | | | | | o o - - - - - - - - - - - - | | | | | | o x o - - - - - - - - - - - | | | | | | | o x x - - - - - - - - - - | | | | | | | | x o o - - - - - - - - - | | | | | | | | | o x - - - - - - - - - | | | | | | | | | | | o o - - - - - - - | | | | | | | | | | | o x o - - - - - - | | | | | | | | | | | | o o - - - - - - | | | | | | | | | | | | | | o x - - - - | | | | | | | | | | | | | | x x x - - - | | | | | | | | | | | | | | | x o - - - | | | | | | | | | | | | | | | | | o o - | | | | | | | | | | | | | | | | | o o - | | | | | | | | | | | | | | | | | | | x The error in solving: 2.114940e-16 The error in solving: 2.705279e-16 The error in solving: 6.691717e-16 The error in solving: 4.646469e-16 The error in solving: 5.159104e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.250000 [ -0.366641 0.644461 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.644461 -0.101329 0.000000 -0.292306 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.316150 0.000000 0.135423 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.292306 0.000000 0.404248 0.074236 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.135423 0.074236 -0.824881 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.113341 -0.142525 -0.934272 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.142525 0.891245 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.934272 0.000000 0.114394 0.392919 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.392919 -0.639694 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.223381 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.123830 0.460949 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.460949 0.076511 0.000000 -0.654991 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.064088 0.629619 -0.294832 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.654991 0.629619 0.344101 0.367195 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.294832 0.367195 0.915138 0.974147 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.974147 -0.672117 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.177819 -0.504941 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.504941 0.573825 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.874414 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.579638]; Dimension: 20 x 20 Off-diagonal entries: 28 (max 380) Diagonal entries: -0.366641 -0.101329 -0.316150 0.404248 -0.824881 -0.113341 0.891245 0.114394 -0.639694 -0.223381 -0.123830 0.076511 0.064088 0.344101 0.915138 -0.672117 0.177819 0.573825 -0.874414 0.579638 Row indices: 0 1 3 4 6 8 10 11 13 14 14 15 17 19 22 25 26 27 28 28 28 Column indices: 1 0 3 4 1 4 2 3 6 7 5 5 8 7 11 10 13 13 14 11 12 14 12 13 15 14 17 16 Off-diagonal values: 0.644461 0.644461 -0.292306 0.135423 -0.292306 0.074236 0.135423 0.074236 -0.142525 -0.934272 -0.142525 -0.934272 0.392919 0.392919 0.460949 0.460949 -0.654991 0.629619 -0.294832 -0.654991 0.629619 0.367195 -0.294832 0.367195 0.974147 0.974147 -0.504941 -0.504941 o x - - - - - - - - - - - - - - - - - - x o - o - - - - - - - - - - - - - - - - | | o - x - - - - - - - - - - - - - - - | o | x x - - - - - - - - - - - - - - - | | x x o - - - - - - - - - - - - - - - | | | | | o o o - - - - - - - - - - - - | | | | | o x - - - - - - - - - - - - - | | | | | o | x x - - - - - - - - - - - | | | | | | | x o - - - - - - - - - - - | | | | | | | | | o - - - - - - - - - - | | | | | | | | | | o x - - - - - - - - | | | | | | | | | | x x - o - - - - - - | | | | | | | | | | | | x x o - - - - - | | | | | | | | | | | o x x x - - - - - | | | | | | | | | | | | o x x x - - - - | | | | | | | | | | | | | | x o - - - - | | | | | | | | | | | | | | | | x o - - | | | | | | | | | | | | | | | | o x - - | | | | | | | | | | | | | | | | | | o - | | | | | | | | | | | | | | | | | | | x The error in solving: 5.979137e-16 The error in solving: 5.244262e-16 The error in solving: 8.326673e-17 The error in solving: 5.382006e-16 The error in solving: 1.624353e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.500000 [ -0.719522 0.000000 0.958393 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.018146 0.000000 -0.412743 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.958393 0.000000 -0.093359 -0.286973 0.328661 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.412743 -0.286973 0.147306 0.000000 -0.250429 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.328661 0.000000 0.662192 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.250429 0.000000 -0.138634 0.000000 0.983893 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.987964 -0.098472 -0.370177 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.983893 -0.098472 -0.731792 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.370177 0.000000 -0.491056 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.295628 0.397581 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.397581 0.907469 -0.142021 -0.169486 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.142021 0.002842 -0.215927 -0.393175 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.169486 -0.215927 -0.489718 -0.873972 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.393175 -0.873972 -0.877726 0.481555 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.481555 -0.759512 0.512947 0.830071 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.512947 0.067298 -0.396054 0.750930 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.830071 -0.396054 0.805019 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.750930 0.000000 -0.347696 -0.816251 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.816251 -0.634120 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.890605]; Dimension: 20 x 20 Off-diagonal entries: 40 (max 380) Diagonal entries: -0.719522 -0.018146 -0.093359 0.147306 0.662192 -0.138634 0.987964 -0.731792 -0.491056 0.295628 0.907469 0.002842 -0.489718 -0.877726 -0.759512 0.067298 0.805019 -0.347696 -0.634120 -0.890605 Row indices: 0 1 2 5 8 9 11 13 15 16 17 20 23 26 29 32 35 37 39 40 40 Column indices: 2 3 0 3 4 1 2 5 2 3 7 7 8 5 6 6 10 9 11 12 10 12 13 10 11 13 11 12 14 13 15 16 14 16 17 14 15 15 18 17 Off-diagonal values: 0.958393 -0.412743 0.958393 -0.286973 0.328661 -0.412743 -0.286973 -0.250429 0.328661 -0.250429 0.983893 -0.098472 -0.370177 0.983893 -0.098472 -0.370177 0.397581 0.397581 -0.142021 -0.169486 -0.142021 -0.215927 -0.393175 -0.169486 -0.215927 -0.873972 -0.393175 -0.873972 0.481555 0.481555 0.512947 0.830071 0.512947 -0.396054 0.750930 0.830071 -0.396054 0.750930 -0.816251 -0.816251 o - x - - - - - - - - - - - - - - - - - | o - o - - - - - - - - - - - - - - - - x | o o x - - - - - - - - - - - - - - - | o o x - o - - - - - - - - - - - - - - | | x | x - - - - - - - - - - - - - - - | | | o | o - x - - - - - - - - - - - - | | | | | | x o o - - - - - - - - - - - | | | | | x o o - - - - - - - - - - - - | | | | | | o | o - - - - - - - - - - - | | | | | | | | | x x - - - - - - - - - | | | | | | | | | x x o o - - - - - - - | | | | | | | | | | o x o o - - - - - - | | | | | | | | | | o o o o - - - - - - | | | | | | | | | | | o o o x - - - - - | | | | | | | | | | | | | x o x x - - - | | | | | | | | | | | | | | x x o x - - | | | | | | | | | | | | | | x o x - - - | | | | | | | | | | | | | | | x | o o - | | | | | | | | | | | | | | | | | o o - | | | | | | | | | | | | | | | | | | | o The error in solving: 3.533389e-16 The error in solving: 2.775558e-16 The error in solving: 1.782634e-16 The error in solving: 4.879478e-16 The error in solving: 4.357852e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a 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6 8 11 13 16 18 22 24 26 30 31 34 37 40 43 46 48 Column indices: 2 3 1 4 1 5 2 6 3 6 7 4 5 5 8 9 7 9 7 8 10 11 9 12 9 12 10 11 13 14 12 12 15 16 14 16 17 14 15 18 15 18 19 16 17 19 17 18 Off-diagonal values: 0.367219 0.939640 0.367219 -0.877421 0.939640 0.437212 -0.877421 -0.486962 0.437212 -0.459401 0.633344 -0.486962 -0.459401 0.633344 -0.466724 -0.983158 -0.466724 0.730635 -0.983158 0.730635 -0.505260 0.703331 -0.505260 0.763114 0.703331 -0.202416 0.763114 -0.202416 -0.086907 -0.374829 -0.086907 -0.374829 -0.581944 -0.323185 -0.581944 0.955909 0.049410 -0.323185 0.955909 -0.942042 0.049410 -0.054061 0.072021 -0.942042 -0.054061 0.143403 0.072021 0.143403 o - - - - - - - - - - - - - - - - - - - | o x x - - - - - - - - - - - - - - - - | x o - o - - - - - - - - - - - - - - - | x | o - x - - - - - - - - - - - - - - | | o | x - o - - - - - - - - - - - - - | | | x | x o x - - - - - - - - - - - - | | | | o o x - - - - - - - - - - - - - | | | | | x | x o o - - - - - - - - - - | | | | | | | o o x - - - - - - - - - - | | | | | | | o x o o x - - - - - - - - | | | | | | | | | o x - x - - - - - - - | | | | | | | | | x | x o - - - - - - - | | | | | | | | | | x o x o o - - - - - | | | | | | | | | | | | o o - - - - - - | | | | | | | | | | | | o | o o o - - - | | | | | | | | | | | | | | o x x x - - | | | | | | | | | | | | | | o x x - o - | | | | | | | | | | | | | | | x | o o x | | | | | | | | | | | | | | | | o o x x | | | | | | | | | | | | | | | | | x x x The error in solving: 6.088855e-16 The error in solving: 6.843896e-16 The error in solving: 3.727073e-16 The error in solving: 7.301352e-16 The error in solving: 6.544668e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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The error in solving: 6.245005e-17 The error in solving: 1.468687e-16 The error in solving: 1.154862e-16 The error in solving: 2.486410e-16 The error in solving: 1.671107e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.857270 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.857270 0.000000 -0.010180 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.010180 0.000000 0.462590 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.462590 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.800378 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.800378 0.000000 -0.145392 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.145392 0.000000 0.791733 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.791733 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.478160 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.478160 0.000000 -0.872047 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.872047 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.944683 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.944683 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 18 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 5 6 7 9 11 12 12 12 13 15 16 17 18 18 18 18 18 18 Column indices: 1 0 2 1 3 2 5 4 6 5 7 6 11 10 12 11 14 13 Off-diagonal values: 0.857270 0.857270 -0.010180 -0.010180 0.462590 0.462590 0.800378 0.800378 -0.145392 -0.145392 0.791733 0.791733 0.478160 0.478160 -0.872047 -0.872047 0.944683 0.944683 . x - - - - - - - - - - - - - - - - - - x . o - - - - - - - - - - - - - - - - - | o . x - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | | x . o - - - - - - - - - - - - - | | | | | o . x - - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . x - - - - - - - - | | | | | | | | | | x . o - - - - - - - | | | | | | | | | | | o . - - - - - - - | | | | | | | | | | | | | . x - - - - - | | | | | | | | | | | | | x . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.558938e-16 The error in solving: 2.305551e-16 The error in solving: 3.191891e-16 The error in solving: 5.237371e-16 The error in solving: 5.715223e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.248465 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.248465 0.000000 -0.881569 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.881569 0.000000 0.411056 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.411056 0.000000 -0.064245 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.064245 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.936142 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.936142 0.000000 0.828675 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.828675 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.869338 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.869338 0.000000 0.682147 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.682147 0.000000 0.711200 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.711200 0.000000 -0.031930 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.031930 0.000000 0.415603 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.415603 0.000000 0.006617 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.006617 0.000000 0.152024 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.152024 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.208040 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.208040 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.277492 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.277492 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 30 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 5 7 8 9 11 12 13 15 17 19 21 23 25 26 27 28 29 30 Column indices: 1 0 2 1 3 2 4 3 6 5 7 6 9 8 10 9 11 10 12 11 13 12 14 13 15 14 17 16 19 18 Off-diagonal values: 0.248465 0.248465 -0.881569 -0.881569 0.411056 0.411056 -0.064245 -0.064245 0.936142 0.936142 0.828675 0.828675 0.869338 0.869338 0.682147 0.682147 0.711200 0.711200 -0.031930 -0.031930 0.415603 0.415603 0.006617 0.006617 0.152024 0.152024 -0.208040 -0.208040 -0.277492 -0.277492 . x - - - - - - - - - - - - - - - - - - x . o - - - - - - - - - - - - - - - - - | o . x - - - - - - - - - - - - - - - - | | x . o - - - - - - - - - - - - - - - | | | o . - - - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | | x . x - - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | | x . x - - - - - - - - - | | | | | | | | | x . x - - - - - - - - | | | | | | | | | | x . o - - - - - - - | | | | | | | | | | | o . x - - - - - - | | | | | | | | | | | | x . x - - - - - | | | | | | | | | | | | | x . x - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | | . o - - | | | | | | | | | | | | | | | | o . - - | | | | | | | | | | | | | | | | | | . o | | | | | | | | | | | | | | | | | | o . The error in solving: 4.785322e-16 The error in solving: 3.856591e-16 The error in solving: 5.011400e-16 The error in solving: 4.081589e-16 The error in solving: 3.343114e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 -0.048791 0.207494 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.048791 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.207494 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.262881 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.262881 0.000000 0.000000 -0.471508 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.471508 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.747076 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.022682 -0.769203 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.747076 0.022682 0.000000 0.000000 0.414624 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.769203 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.414624 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.373806 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.373806 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 18 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 3 4 4 4 4 5 7 7 8 8 8 9 11 14 15 16 17 17 18 Column indices: 1 2 0 0 7 6 9 7 14 14 15 12 13 16 13 14 19 17 Off-diagonal values: -0.048791 0.207494 -0.048791 0.207494 0.262881 0.262881 -0.471508 -0.471508 0.747076 0.022682 -0.769203 0.747076 0.022682 0.414624 -0.769203 0.414624 0.373806 0.373806 . o x - - - - - - - - - - - - - - - - - o . - - - - - - - - - - - - - - - - - - x | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . x - - - - - - - - - - - - | | | | | | x . - o - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | o | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - x - - - - - | | | | | | | | | | | | | . x o - - - - | | | | | | | | | | | | x x . - x - - - | | | | | | | | | | | | | o | . - - - - | | | | | | | | | | | | | | x | . - - - | | | | | | | | | | | | | | | | | . - x | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | x | . The error in solving: 3.640110e-16 The error in solving: 1.618414e-16 The error in solving: 3.200929e-16 The error in solving: 2.486652e-16 The error in solving: 3.167664e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.239628 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.258686 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.239628 0.258686 0.000000 -0.079182 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.079182 0.000000 0.000000 0.178492 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.616188 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.178492 0.616188 0.000000 0.907469 -0.921075 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.907469 0.000000 0.000000 -0.107083 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.921075 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.107083 0.000000 0.000000 0.000000 -0.770056 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.666834 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.770056 0.666834 0.000000 0.000000 -0.449857 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.449857 0.000000 0.000000 0.000000 -0.711409 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.189127 0.657490 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.711409 0.189127 0.000000 0.000000 0.389398 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.657490 0.000000 0.000000 0.000000 0.116544 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.389398 0.000000 0.000000 -0.132924 0.750063 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.116544 -0.132924 0.000000 -0.617570 -0.257746 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.750063 -0.617570 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.257746 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 40 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 5 7 8 12 14 15 17 18 21 21 23 25 28 30 33 37 39 40 Column indices: 2 2 0 1 3 2 5 5 3 4 6 7 5 8 5 6 10 10 8 9 12 10 14 14 15 12 13 16 13 17 14 17 18 15 16 18 19 16 17 17 Off-diagonal values: 0.239628 0.258686 0.239628 0.258686 -0.079182 -0.079182 0.178492 0.616188 0.178492 0.616188 0.907469 -0.921075 0.907469 -0.107083 -0.921075 -0.107083 -0.770056 0.666834 -0.770056 0.666834 -0.449857 -0.449857 -0.711409 0.189127 0.657490 -0.711409 0.189127 0.389398 0.657490 0.116544 0.389398 -0.132924 0.750063 0.116544 -0.132924 -0.617570 -0.257746 0.750063 -0.617570 -0.257746 . - x - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - x x . o - - - - - - - - - - - - - - - - | | o . - x - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | x x . x o - - - - - - - - - - - - | | | | | x . - o - - - - - - - - - - - | | | | | o | . - - - - - - - - - - - - | | | | | | o | . - o - - - - - - - - - | | | | | | | | | . x - - - - - - - - - | | | | | | | | o x . - o - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | o | . - o - - - - - | | | | | | | | | | | | | . x x - - - - | | | | | | | | | | | | o x . - x - - - | | | | | | | | | | | | | x | . - x - - | | | | | | | | | | | | | | x | . o x - | | | | | | | | | | | | | | | x o . o o | | | | | | | | | | | | | | | | x o . - | | | | | | | | | | | | | | | | | o | . The error in solving: 3.284084e-16 The error in solving: 6.690188e-16 The error in solving: 3.103168e-16 The error in solving: 5.440730e-16 The error in solving: 9.108735e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 -0.590895 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.700783 0.359495 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.590895 -0.700783 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.359495 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.897488 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.897488 0.000000 -0.889784 -0.475749 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.889784 0.000000 0.000000 -0.466183 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.475749 0.000000 0.000000 -0.923158 -0.615112 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.466183 -0.923158 0.000000 -0.171931 0.077068 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.615112 -0.171931 0.000000 -0.858812 0.207436 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.077068 -0.858812 0.000000 0.000000 -0.124934 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.207436 0.000000 0.000000 -0.088110 -0.353391 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.124934 -0.088110 0.000000 -0.328312 0.785650 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.353391 -0.328312 0.000000 0.000000 0.120157 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.785650 0.000000 0.000000 -0.868763 -0.057068 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.120157 -0.868763 0.000000 0.000000 0.906429 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.057068 0.000000 0.000000 0.089777 -0.692983 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.906429 0.089777 0.000000 0.980223 0.345140 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.692983 0.980223 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.345140 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 52 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 5 6 7 10 12 15 19 23 26 29 33 36 39 42 45 49 51 52 Column indices: 2 2 3 0 1 1 5 4 6 7 5 8 5 8 9 6 7 9 10 7 8 10 11 8 9 12 9 12 13 10 11 13 14 11 12 15 12 15 16 13 14 17 14 17 18 15 16 18 19 16 17 17 Off-diagonal values: -0.590895 -0.700783 0.359495 -0.590895 -0.700783 0.359495 0.897488 0.897488 -0.889784 -0.475749 -0.889784 -0.466183 -0.475749 -0.923158 -0.615112 -0.466183 -0.923158 -0.171931 0.077068 -0.615112 -0.171931 -0.858812 0.207436 0.077068 -0.858812 -0.124934 0.207436 -0.088110 -0.353391 -0.124934 -0.088110 -0.328312 0.785650 -0.353391 -0.328312 0.120157 0.785650 -0.868763 -0.057068 0.120157 -0.868763 0.906429 -0.057068 0.089777 -0.692983 0.906429 0.089777 0.980223 0.345140 -0.692983 0.980223 0.345140 . - o - - - - - - - - - - - - - - - - - | . o x - - - - - - - - - - - - - - - - o o . - - - - - - - - - - - - - - - - - | x | . - - - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | | x . o o - - - - - - - - - - - - | | | | | o . - o - - - - - - - - - - - | | | | | o | . o o - - - - - - - - - - | | | | | | o o . o x - - - - - - - - - | | | | | | | o o . o x - - - - - - - - | | | | | | | | x o . - o - - - - - - - | | | | | | | | | x | . o o - - - - - - | | | | | | | | | | o o . o x - - - - - | | | | | | | | | | | o o . - x - - - - | | | | | | | | | | | | x | . o o - - - | | | | | | | | | | | | | x o . - x - - | | | | | | | | | | | | | | o | . x o - | | | | | | | | | | | | | | | x x . x x | | | | | | | | | | | | | | | | o x . - | | | | | | | | | | | | | | | | | x | . The error in solving: 4.791355e-16 The error in solving: 6.025362e-16 The error in solving: 6.544691e-16 The error in solving: 4.967492e-16 The error in solving: 4.202482e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.250000 [ -0.190830 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.693586]; Dimension: 20 x 20 Off-diagonal entries: 8 (max 380) Diagonal entries: -0.190830 0.000000 0.000000 0.000000 0.000000 0.696406 1.294515 0.000000 -0.653762 -0.580927 0.000000 0.000000 -1.117739 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.693586 Row indices: 0 0 0 0 1 2 2 2 3 4 4 5 6 6 6 6 7 8 8 8 8 Column indices: 4 3 8 7 11 10 16 15 Off-diagonal values: -0.771565 -0.771565 0.775961 0.775961 -1.799906 -1.799906 1.127385 1.127385 o - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . o - - - - - - - - - - - - - - - | | | o . - - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | | . x - - - - - - - - - - - | | | | | | | x o - - - - - - - - - - - | | | | | | | | | o - - - - - - - - - - | | | | | | | | | | . o - - - - - - - - | | | | | | | | | | o . - - - - - - - - | | | | | | | | | | | | o - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | x . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | x The error in solving: 1.359740e-16 The error in solving: 2.145734e-17 The error in solving: 2.547623e-16 The error in solving: 8.355535e-17 The error in solving: 3.510833e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.500000 [ 0.171021 -0.770139 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.770139 -1.261369 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.777245 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.124572 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.124572 -0.530144 0.087144 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.087144 0.000000 -0.124583 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.124583 0.000000 0.359707 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.359707 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.202742 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.202742 0.000000 -0.518623 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.518623 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.554374 0.345585 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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- - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | | x o x - - - - - - - - - - - - - - | | | | x . o - - - - - - - - - - - - - | | | | | o . x - - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | | | . o - - - - - - - - - - | | | | | | | | o . o - - - - - - - - - | | | | | | | | | o . - - - - - - - - - | | | | | | | | | | | o x - - - - - - - | | | | | | | | | | | x . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | x . The error in solving: 4.051396e-16 The error in solving: 3.122502e-17 The error in solving: 1.570188e-16 The error in solving: 2.220717e-16 The error in solving: 5.367785e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.750000 [ -1.628346 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.487507 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.017369 0.789288 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.789288 -1.272677 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0.000000 0.000000 0.000000 0.000000 1.120275 0.061213]; Dimension: 20 x 20 Off-diagonal entries: 24 (max 380) Diagonal entries: -1.628346 -0.487507 0.017369 -1.272677 -2.737150 1.219726 -1.530494 0.000000 -0.631110 1.571821 0.000000 -1.370497 0.000000 -0.109596 0.000000 0.754358 -0.868471 0.000000 0.533348 0.061213 Row indices: 0 0 0 1 3 5 6 6 7 9 11 13 14 15 16 17 19 21 22 23 24 Column indices: 3 2 4 3 5 4 8 7 9 8 10 9 11 10 13 12 15 14 16 15 17 16 19 18 Off-diagonal values: 0.789288 0.789288 0.471730 0.471730 0.001508 0.001508 1.092736 1.092736 -0.235543 -0.235543 0.978808 0.978808 0.214610 0.214610 -0.468181 -0.468181 0.708201 0.708201 -2.322700 -2.322700 2.414628 2.414628 1.120275 1.120275 o - - - - - - - - - - - - - - - - - - - | o - - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | x o x - - - - - - - - - - - - - - - | | | x o x - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | | | | | | o - - - - - - - - - - - - - | | | | | | | . x - - - - - - - - - - - | | | | | | | x o o - - - - - - - - - - | | | | | | | | o x x - - - - - - - - - | | | | | | | | | x . x - - - - - - - - | | | | | | | | | | x o - - - - - - - - | | | | | | | | | | | | . o - - - - - - | | | | | | | | | | | | o o - - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | x x o - - - | | | | | | | | | | | | | | | o o x - - | | | | | | | | | | | | | | | | x . - - | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | x x The error in solving: 2.237726e-16 The error in solving: 6.503339e-16 The error in solving: 3.201117e-16 The error in solving: 1.359740e-16 The error in solving: 3.560974e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.250000 [ 0.000000 -1.444499 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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1.258666 -1.381721 -1.167538 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.316950 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.466069 -1.297259 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.466069 0.000000 0.000000 0.743503 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.297259 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.743503 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.734618 0.000000 1.021741 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.568676 0.985143 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.021741 0.985143 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 22 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.024379 0.000000 0.000000 0.000000 0.990843 1.140641 -1.309057 -0.077204 -1.167538 -0.316950 0.000000 0.000000 0.000000 0.000000 -0.734618 -1.568676 0.000000 Row indices: 0 1 2 2 2 2 2 2 3 5 8 10 12 12 14 16 17 18 19 20 22 Column indices: 1 0 8 7 9 8 10 11 9 11 9 10 14 15 13 16 13 14 19 19 17 18 Off-diagonal values: -1.444499 -1.444499 1.288223 1.288223 -0.991976 -0.991976 -1.446645 1.258666 -1.446645 -1.381721 1.258666 -1.381721 -0.466069 -1.297259 -0.466069 0.743503 -1.297259 0.743503 1.021741 0.985143 1.021741 0.985143 . o - - - - - - - - - - - - - - - - - - o . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | x - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | x x o - - - - - - - - - - | | | | | | | | o o o x - - - - - - - - | | | | | | | | | o o o - - - - - - - - | | | | | | | | | x o o - - - - - - - - | | | | | | | | | | | | o - - - - - - - | | | | | | | | | | | | | . o o - - - - | | | | | | | | | | | | | o . - x - - - | | | | | | | | | | | | | o | . - - - - | | | | | | | | | | | | | | x | . - - - | | | | | | | | | | | | | | | | | o - x | | | | | | | | | | | | | | | | | | o x | | | | | | | | | | | | | | | | | x x . The error in solving: 4.227951e-16 The error in solving: 4.055545e-16 The error in solving: 3.724448e-16 The error in solving: 2.558938e-16 The error in solving: 3.402182e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 -0.423518 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.423518 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.383411 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.548112 0.225795 -0.873210 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.225795 -0.988188 1.410631 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.873210 1.410631 -1.375637 -0.308330 0.122398 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.308330 0.000000 0.079839 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.122398 0.079839 0.000000 0.000000 0.659168 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.967764]; Dimension: 20 x 20 Off-diagonal entries: 30 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.383411 0.548112 -0.988188 -1.375637 0.000000 0.000000 0.000000 0.245780 0.223664 0.000000 -0.170801 0.000000 -2.832632 0.000000 0.456116 0.000000 0.967764 Row indices: 0 1 1 2 2 4 6 10 12 15 15 17 18 20 22 25 27 29 30 30 30 Column indices: 2 0 5 6 4 6 4 5 7 8 6 8 6 7 10 8 11 10 13 14 12 14 12 13 16 16 17 14 15 15 Off-diagonal values: -0.423518 -0.423518 0.225795 -0.873210 0.225795 1.410631 -0.873210 1.410631 -0.308330 0.122398 -0.308330 0.079839 0.122398 0.079839 0.659168 0.659168 -0.913139 -0.913139 0.168959 0.047399 0.168959 -0.620207 0.047399 -0.620207 0.570997 -0.268157 -0.626055 0.570997 -0.268157 -0.626055 . - o - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - o | . - - - - - - - - - - - - - - - - - | | | x - - - - - - - - - - - - - - - - | | | | x x o - - - - - - - - - - - - - | | | | x o x - - - - - - - - - - - - - | | | | o x o o x - - - - - - - - - - - | | | | | | o . x - - - - - - - - - - - | | | | | | x x . - x - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | x | x o - - - - - - - - | | | | | | | | | | o x - - - - - - - - | | | | | | | | | | | | . x x - - - - - | | | | | | | | | | | | x o o - - - - - | | | | | | | | | | | | x o . - x - - - | | | | | | | | | | | | | | | o o o - - | | | | | | | | | | | | | | x o . - - - | | | | | | | | | | | | | | | o | x - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | x The error in solving: 6.597516e-16 The error in solving: 2.363557e-16 The error in solving: 3.005430e-16 The error in solving: 3.885781e-16 The error in solving: 2.963485e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.750000 [ 0.502178 0.334061 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.334061 0.000000 -0.206398 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.206398 0.187936 0.000000 -0.991372 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.404970 -0.604023 -0.078447 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.991372 -0.604023 -0.019876 0.000000 0.125219 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.078447 0.000000 0.246663 0.281723 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.125219 0.281723 -0.965920 -0.731775 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.731775 0.000000 0.476372 -0.522490 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.476372 -0.470485 -1.193464 1.297628 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.522490 -1.193464 0.000000 0.191436 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.297628 0.191436 1.634287 -0.452806 -1.562201 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.452806 1.545080 0.856216 -0.385387 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.562201 0.856216 -0.284557 0.070545 -0.737885 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.385387 0.070545 -1.078896 -1.515133 1.250431 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.737885 -1.515133 -0.209189 0.000000 -1.211078 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.250431 0.000000 0.000000 -0.203345 0.408895 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.211078 -0.203345 0.000000 0.007125 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.408895 0.007125 0.000000 0.000000 0.088210 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.934098 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.088210 -1.934098 -1.046944]; Dimension: 20 x 20 Off-diagonal entries: 54 (max 380) Diagonal entries: 0.502178 0.000000 0.187936 -1.404970 -0.019876 0.246663 -0.965920 0.000000 -0.470485 0.000000 1.634287 1.545080 -0.284557 -1.078896 -0.209189 0.000000 0.000000 0.000000 0.000000 -1.046944 Row indices: 0 1 3 5 7 10 12 15 18 21 24 28 31 35 39 42 45 48 51 52 54 Column indices: 1 0 2 1 4 4 5 2 3 6 3 6 4 5 7 6 8 9 7 9 10 7 8 10 8 9 11 12 10 12 13 10 11 13 14 11 12 14 15 12 13 16 13 16 17 14 15 17 15 16 19 19 17 18 Off-diagonal values: 0.334061 0.334061 -0.206398 -0.206398 -0.991372 -0.604023 -0.078447 -0.991372 -0.604023 0.125219 -0.078447 0.281723 0.125219 0.281723 -0.731775 -0.731775 0.476372 -0.522490 0.476372 -1.193464 1.297628 -0.522490 -1.193464 0.191436 1.297628 0.191436 -0.452806 -1.562201 -0.452806 0.856216 -0.385387 -1.562201 0.856216 0.070545 -0.737885 -0.385387 0.070545 -1.515133 1.250431 -0.737885 -1.515133 -1.211078 1.250431 -0.203345 0.408895 -1.211078 -0.203345 0.007125 0.408895 0.007125 0.088210 -1.934098 0.088210 -1.934098 x x - - - - - - - - - - - - - - - - - - x . o - - - - - - - - - - - - - - - - - | o x - o - - - - - - - - - - - - - - - | | | o o o - - - - - - - - - - - - - - | | o o o - x - - - - - - - - - - - - - | | | o | x x - - - - - - - - - - - - - | | | | x x o o - - - - - - - - - - - - | | | | | | o . x o - - - - - - - - - - | | | | | | | x o o x - - - - - - - - - | | | | | | | o o . x - - - - - - - - - | | | | | | | | x x x o o - - - - - - - | | | | | | | | | | o x x o - - - - - - | | | | | | | | | | o x o x o - - - - - | | | | | | | | | | | o x o o x - - - - | | | | | | | | | | | | o o o - o - - - | | | | | | | | | | | | | x | . o x - - | | | | | | | | | | | | | | o o . x - - | | | | | | | | | | | | | | | x x . - x | | | | | | | | | | | | | | | | | | . o | | | | | | | | | | | | | | | | | x o o The error in solving: 3.805653e-16 The error in solving: 2.990373e-16 The error in solving: 7.248405e-16 The error in solving: 4.886873e-16 The error in solving: 5.568928e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.250000 [ -1.255862 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.015828 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.544850 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.296739 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.292934 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.134618 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.954774 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.566247 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.666398 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.613697 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.252610 2.568729 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.568729 -1.074581 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.459246 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.234203 -1.770849 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.770849 0.075676 0.568241 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.568241 -2.350354 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.045185 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.398554 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.582331 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.096177]; Dimension: 20 x 20 Off-diagonal entries: 6 (max 380) Diagonal entries: -1.255862 -1.015828 0.544850 -0.296739 1.292934 -0.134618 -0.954774 0.566247 0.666398 0.613697 -0.252610 -1.074581 -1.459246 0.234203 0.075676 -2.350354 -0.045185 -0.398554 0.582331 1.096177 Row indices: 0 0 0 0 0 0 0 0 0 0 0 1 2 2 3 5 6 6 6 6 6 Column indices: 11 10 14 13 15 14 Off-diagonal values: 2.568729 2.568729 -1.770849 -1.770849 0.568241 0.568241 o - - - - - - - - - - - - - - - - - - - | o - - - - - - - - - - - - - - - - - - | | x - - - - - - - - - - - - - - - - - | | | o - - - - - - - - - - - - - - - - | | | | x - - - - - - - - - - - - - - - | | | | | o - - - - - - - - - - - - - - | | | | | | o - - - - - - - - - - - - - | | | | | | | x - - - - - - - - - - - - | | | | | | | | x - - - - - - - - - - - | | | | | | | | | x - - - - - - - - - - | | | | | | | | | | o x - - - - - - - - | | | | | | | | | | x o - - - - - - - - | | | | | | | | | | | | o - - - - - - - | | | | | | | | | | | | | x o - - - - - | | | | | | | | | | | | | o x x - - - - | | | | | | | | | | | | | | x o - - - - | | | | | | | | | | | | | | | | o - - - | | | | | | | | | | | | | | | | | o - - | | | | | | | | | | | | | | | | | | x - | | | | | | | | | | | | | | | | | | | x The error in solving: 2.551400e-16 The error in solving: 2.288783e-16 The error in solving: 1.570092e-16 The error in solving: 2.254890e-16 The error in solving: 2.326341e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.500000 [ -1.728971 -0.061736 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.061736 1.626841 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.003343 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.166071 1.580629 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.580629 2.470684 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.574982 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.717917 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.414964 1.065480 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.065480 -0.930191 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.010532 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.105795 1.585334 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.585334 -0.396855 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.414047 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.115189 -0.744820 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.744820 0.430290 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.570897 1.539976 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.539976 -0.636878 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.944168 1.708154 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.708154 -0.044600 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.619395]; Dimension: 20 x 20 Off-diagonal entries: 14 (max 380) Diagonal entries: -1.728971 1.626841 -1.003343 0.166071 2.470684 0.574982 0.717917 -0.414964 -0.930191 -0.010532 -0.105795 -0.396855 0.414047 0.115189 0.430290 0.570897 -0.636878 -0.944168 -0.044600 -0.619395 Row indices: 0 1 2 2 3 4 4 4 5 6 6 7 8 8 9 10 11 12 13 14 14 Column indices: 1 0 4 3 8 7 11 10 14 13 16 15 18 17 Off-diagonal values: -0.061736 -0.061736 1.580629 1.580629 1.065480 1.065480 1.585334 1.585334 -0.744820 -0.744820 1.539976 1.539976 1.708154 1.708154 o o - - - - - - - - - - - - - - - - - - o x - - - - - - - - - - - - - - - - - - | | o - - - - - - - - - - - - - - - - - | | | x x - - - - - - - - - - - - - - - | | | x x - - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | x - - - - - - - - - - - - - | | | | | | | o x - - - - - - - - - - - | | | | | | | x o - - - - - - - - - - - | | | | | | | | | o - - - - - - - - - - | | | | | | | | | | o x - - - - - - - - | | | | | | | | | | x o - - - - - - - - | | | | | | | | | | | | x - - - - - - - | | | | | | | | | | | | | x o - - - - - | | | | | | | | | | | | | o x - - - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | x o - - - | | | | | | | | | | | | | | | | | o x - | | | | | | | | | | | | | | | | | x o - | | | | | | | | | | | | | | | | | | | o The error in solving: 3.734775e-16 The error in solving: 1.422050e-16 The error in solving: 1.271920e-16 The error in solving: 6.293007e-17 The error in solving: 5.149763e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.750000 [ -0.626275 -0.299080 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.299080 2.035982 -0.451132 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.451132 -0.160376 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0.000000 0.000000 0.000000 0.000000 1.506655 -0.147123 0.058201 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.058201 0.801236]; Dimension: 20 x 20 Off-diagonal entries: 30 (max 380) Diagonal entries: -0.626275 2.035982 -0.160376 0.290253 -0.355762 0.174886 -0.020763 0.179999 -0.968981 -0.528230 0.496214 0.170275 -0.783886 1.271067 -1.685831 0.191647 -0.296843 0.551065 -0.147123 0.801236 Row indices: 0 1 3 5 7 9 10 11 13 15 17 19 20 21 22 23 25 26 27 29 30 Column indices: 1 0 2 1 3 2 4 3 5 4 7 6 8 7 9 8 10 9 11 10 13 12 15 14 16 15 18 17 19 18 Off-diagonal values: -0.299080 -0.299080 -0.451132 -0.451132 0.034925 0.034925 0.089662 0.089662 -0.263314 -0.263314 0.372038 0.372038 -2.790895 -2.790895 1.633516 1.633516 0.110006 0.110006 -1.034960 -1.034960 -0.560305 -0.560305 -0.734679 -0.734679 1.114782 1.114782 1.506655 1.506655 0.058201 0.058201 o o - - - - - - - - - - - - - - - - - - o x o - - - - - - - - - - - - - - - - - | o o x - - - - - - - - - - - - - - - - | | x x x - - - - - - - - - - - - - - - | | | x o o - - - - - - - - - - - - - - | | | | o x - - - - - - - - - - - - - - | | | | | | o x - - - - - - - - - - - - | | | | | | x x o - - - - - - - - - - - | | | | | | | o o x - - - - - - - - - - | | | | | | | | x o x - - - - - - - - - | | | | | | | | | x x o - - - - - - - - | | | | | | | | | | o x - - - - - - - - | | | | | | | | | | | | o o - - - - - - | | | | | | | | | | | | o x - - - - - - | | | | | | | | | | | | | | o o - - - - | | | | | | | | | | | | | | o x x - - - | | | | | | | | | | | | | | | x o - - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | x o x | | | | | | | | | | | | | | | | | | x x The error in solving: 5.004189e-16 The error in solving: 3.399350e-16 The error in solving: 2.498002e-16 The error in solving: 3.200929e-16 The error in solving: 6.781682e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.250000 [ -0.219797 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.269927 0.000000 0.037489 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.412819 0.000000 -1.141764 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.037489 0.000000 0.766453 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.141764 0.000000 1.556047 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.227937 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.165373 0.000000 1.010679 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.461856 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.010679 0.000000 -0.623678 0.420418 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.420418 -1.212511 0.000000 1.187444 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.865623 0.012678 0.332608 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.187444 0.012678 2.242489 0.000000 0.053006 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.332608 0.000000 -0.255016 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.053006 0.000000 -1.252939 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.497073 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.844693 0.031627 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.031627 -0.218076 0.000000 -0.176350 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.091195 0.000000 1.161311 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.176350 0.000000 0.036295 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.161311 0.000000 -0.078726]; Dimension: 20 x 20 Off-diagonal entries: 22 (max 380) Diagonal entries: -0.219797 -0.269927 -0.412819 0.766453 1.556047 1.227937 0.165373 -0.461856 -0.623678 -1.212511 -1.865623 2.242489 -0.255016 -1.252939 0.497073 -0.844693 -0.218076 -1.091195 0.036295 -0.078726 Row indices: 0 0 1 2 3 4 4 5 5 7 9 11 14 15 16 16 17 19 20 21 22 Column indices: 3 4 1 2 8 6 9 8 11 11 12 9 10 13 10 11 16 15 18 19 16 17 Off-diagonal values: 0.037489 -1.141764 0.037489 -1.141764 1.010679 1.010679 0.420418 0.420418 1.187444 0.012678 0.332608 1.187444 0.012678 0.053006 0.332608 0.053006 0.031627 0.031627 -0.176350 1.161311 -0.176350 1.161311 o - - - - - - - - - - - - - - - - - - - | o - x - - - - - - - - - - - - - - - - | | o - o - - - - - - - - - - - - - - - | x | x - - - - - - - - - - - - - - - - | | o | x - - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | x - x - - - - - - - - - - - | | | | | | | o - - - - - - - - - - - - | | | | | | x | o x - - - - - - - - - - | | | | | | | | x o - x - - - - - - - - | | | | | | | | | | o x x - - - - - - - | | | | | | | | | x x x - x - - - - - - | | | | | | | | | | x | o - - - - - - - | | | | | | | | | | | x | o - - - - - - | | | | | | | | | | | | | | x - - - - - | | | | | | | | | | | | | | | o x - - - | | | | | | | | | | | | | | | x o - o - | | | | | | | | | | | | | | | | | o - x | | | | | | | | | | | | | | | | o | x - | | | | | | | | | | | | | | | | | x | o The error in solving: 2.577685e-16 The error in solving: 3.388000e-16 The error in solving: 2.603762e-16 The error in solving: 3.521788e-16 The error in solving: 2.618456e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.500000 [ -0.212037 0.000000 -0.454891 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.700604 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.454891 0.000000 0.535073 0.000000 0.861153 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.129082 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.861153 0.000000 -1.420768 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.318360 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.410270 -1.218781 0.875099 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.218781 -0.279937 1.294205 0.104102 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.875099 1.294205 1.003129 0.000000 2.270541 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.104102 0.000000 -1.951184 -0.887173 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.270541 -0.887173 0.269709 -0.626855 0.001528 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.626855 0.100436 -0.378515 -1.815933 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.001528 -0.378515 0.609576 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.815933 0.000000 1.769291 0.499307 1.140692 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.499307 -1.033842 -1.091424 -2.203990 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.140692 -1.091424 -0.774936 -0.927633 0.576609 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.203990 -0.927633 -1.739167 0.953060 0.096327 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.576609 0.953060 -0.371845 0.104373 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.096327 0.104373 0.017593 1.027207 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.027207 0.256132]; Dimension: 20 x 20 Off-diagonal entries: 44 (max 380) Diagonal entries: -0.212037 1.700604 0.535073 -1.129082 -1.420768 1.318360 -1.410270 -0.279937 1.003129 -1.951184 0.269709 0.100436 0.609576 1.769291 -1.033842 -0.774936 -1.739167 -0.371845 0.017593 0.256132 Row indices: 0 1 1 3 3 4 4 6 9 12 14 18 21 23 26 29 33 37 40 43 44 Column indices: 2 0 4 2 7 8 6 8 9 6 7 10 7 10 8 9 11 12 10 12 13 10 11 11 14 15 13 15 16 13 14 16 17 14 15 17 18 15 16 18 16 17 19 18 Off-diagonal values: -0.454891 -0.454891 0.861153 0.861153 -1.218781 0.875099 -1.218781 1.294205 0.104102 0.875099 1.294205 2.270541 0.104102 -0.887173 2.270541 -0.887173 -0.626855 0.001528 -0.626855 -0.378515 -1.815933 0.001528 -0.378515 -1.815933 0.499307 1.140692 0.499307 -1.091424 -2.203990 1.140692 -1.091424 -0.927633 0.576609 -2.203990 -0.927633 0.953060 0.096327 0.576609 0.953060 0.104373 0.096327 0.104373 1.027207 1.027207 o - o - - - - - - - - - - - - - - - - - | x - - - - - - - - - - - - - - - - - - o | x - x - - - - - - - - - - - - - - - | | | o - - - - - - - - - - - - - - - - | | x | o - - - - - - - - - - - - - - - | | | | | x - - - - - - - - - - - - - - | | | | | | o o x - - - - - - - - - - - | | | | | | o o x x - - - - - - - - - - | | | | | | x x x - x - - - - - - - - - | | | | | | | x | o o - - - - - - - - - | | | | | | | | x o x o x - - - - - - - | | | | | | | | | | o x o o - - - - - - | | | | | | | | | | x o x - - - - - - - | | | | | | | | | | | o | x x x - - - - | | | | | | | | | | | | | x o o o - - - | | | | | | | | | | | | | x o o o x - - | | | | | | | | | | | | | | o o o x x - | | | | | | | | | | | | | | | x x o x - | | | | | | | | | | | | | | | | x x x x | | | | | | | | | | | | | | | | | | x x The error in solving: 6.776000e-16 The error in solving: 2.747662e-16 The error in solving: 3.800589e-16 The error in solving: 4.876795e-16 The error in solving: 7.077672e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.750000 [ -0.683172 0.000000 -0.480893 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.527778 0.000000 1.177265 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.480893 0.000000 -0.212197 0.000000 -2.438719 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.177265 0.000000 0.195438 0.000000 -0.372251 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.438719 0.000000 0.850350 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.372251 0.000000 -1.769109 0.009960 0.957229 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.009960 -1.714281 0.042135 0.291266 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.957229 0.042135 -2.314579 0.000000 0.097700 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.291266 0.000000 1.444867 0.000000 0.919894 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.097700 0.000000 0.909302 0.000000 0.576833 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.919894 0.000000 0.288165 -0.207441 1.012272 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.576833 -0.207441 1.147211 1.878480 0.264320 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.012272 1.878480 -1.127137 -1.069577 2.170215 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.264320 -1.069577 -1.128720 -1.355721 0.431070 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.170215 -1.355721 0.645216 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.431070 0.000000 0.070237 -0.267054 -0.664778 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.267054 0.797673 -1.150696 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.664778 -1.150696 1.907963 0.383921 0.309627 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.383921 1.224940 0.191742 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.309627 0.191742 -1.099146]; Dimension: 20 x 20 Off-diagonal entries: 50 (max 380) Diagonal entries: -0.683172 0.527778 -0.212197 0.195438 0.850350 -1.769109 -1.714281 -2.314579 1.444867 0.909302 0.288165 1.147211 -1.127137 -1.128720 0.645216 0.070237 0.797673 1.907963 1.224940 -1.099146 Row indices: 0 1 2 4 6 7 10 13 16 18 20 23 27 31 35 37 40 42 46 48 50 Column indices: 2 3 0 4 1 5 2 3 6 7 5 7 8 5 6 9 6 10 7 11 8 11 12 9 10 12 13 10 11 13 14 11 12 14 15 12 13 13 16 17 15 17 15 16 18 19 17 19 17 18 Off-diagonal values: -0.480893 1.177265 -0.480893 -2.438719 1.177265 -0.372251 -2.438719 -0.372251 0.009960 0.957229 0.009960 0.042135 0.291266 0.957229 0.042135 0.097700 0.291266 0.919894 0.097700 0.576833 0.919894 -0.207441 1.012272 0.576833 -0.207441 1.878480 0.264320 1.012272 1.878480 -1.069577 2.170215 0.264320 -1.069577 -1.355721 0.431070 2.170215 -1.355721 0.431070 -0.267054 -0.664778 -0.267054 -1.150696 -0.664778 -1.150696 0.383921 0.309627 0.383921 0.191742 0.309627 0.191742 o - o - - - - - - - - - - - - - - - - - | x - x - - - - - - - - - - - - - - - - o | o - o - - - - - - - - - - - - - - - | x | x - o - - - - - - - - - - - - - - | | o | x - - - - - - - - - - - - - - - | | | o | o x x - - - - - - - - - - - - | | | | | x o x x - - - - - - - - - - - | | | | | x x o - x - - - - - - - - - - | | | | | | x | x - x - - - - - - - - - | | | | | | | x | x - x - - - - - - - - | | | | | | | | x | x o x - - - - - - - | | | | | | | | | x o x x x - - - - - - | | | | | | | | | | x x o o x - - - - - | | | | | | | | | | | x o o o x - - - - | | | | | | | | | | | | x o x - - - - - | | | | | | | | | | | | | x | x o o - - | | | | | | | | | | | | | | | o x o - - | | | | | | | | | | | | | | | o o x x x | | | | | | | | | | | | | | | | | x x x | | | | | | | | | | | | | | | | | x x o The error in solving: 4.839350e-16 The error in solving: 5.966238e-16 The error in solving: 6.156484e-16 The error in solving: 5.585702e-16 The error in solving: 7.217784e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 0 0 0 1 2 2 2 2 2 3 4 4 5 7 8 8 8 Column indices: 7 6 13 12 16 15 17 16 Off-diagonal values: 1.247424 1.247424 0.137401 0.137401 -0.918227 -0.918227 2.099054 2.099054 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . x - - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . x - - - - - - | | | | | | | | | | | | x . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . o - - - | | | | | | | | | | | | | | | o . x - - | | | | | | | | | | | | | | | | x . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 3.191891e-16 The error in solving: 2.490280e-16 The error in solving: 2.498002e-16 The error in solving: 2.603704e-16 The error in solving: 7.858125e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.500000 [ 0.000000 -3.656326 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -3.656326 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.102728 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.102728 0.000000 -1.111576 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.111576 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.806831 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.806831 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.371321 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.371321 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.552985 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.552985 0.000000 -0.686371 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.686371 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 14 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 3 5 6 7 8 8 8 8 8 9 10 11 13 14 14 14 14 14 Column indices: 1 0 3 2 4 3 6 5 12 11 14 13 15 14 Off-diagonal values: -3.656326 -3.656326 -1.102728 -1.102728 -1.111576 -1.111576 -0.806831 -0.806831 1.371321 1.371321 -0.552985 -0.552985 -0.686371 -0.686371 . o - - - - - - - - - - - - - - - - - - o . - - - - - - - - - - - - - - - - - - | | . o - - - - - - - - - - - - - - - - | | o . o - - - - - - - - - - - - - - - | | | o . - - - - - - - - - - - - - - - | | | | | . o - - - - - - - - - - - - - | | | | | o . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | x . - - - - - - - | | | | | | | | | | | | | . o - - - - - | | | | | | | | | | | | | o . o - - - - | | | | | | | | | | | | | | o . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 3.236840e-16 The error in solving: 2.833924e-16 The error in solving: 4.041273e-16 The error in solving: 3.236829e-16 The error in solving: 3.524521e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 1-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.750000 [ 0.000000 -1.932277 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.932277 0.000000 -0.237315 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.237315 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.371113 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.371113 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.212536 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.212536 0.000000 0.004425 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.004425 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.960992 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.960992 0.000000 -0.023434 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.023434 0.000000 0.946052 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.946052 0.000000 -0.094301 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.094301 0.000000 0.396386 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.396386 0.000000 0.131083 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.131083 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.787022 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.787022 0.000000 -0.110236 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.110236 0.000000 0.522418 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.522418 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 28 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 4 5 6 7 9 10 11 13 15 17 19 21 22 22 23 25 27 28 Column indices: 1 0 2 1 4 3 6 5 7 6 9 8 10 9 11 10 12 11 13 12 14 13 17 16 18 17 19 18 Off-diagonal values: -1.932277 -1.932277 -0.237315 -0.237315 -0.371113 -0.371113 1.212536 1.212536 0.004425 0.004425 -0.960992 -0.960992 -0.023434 -0.023434 0.946052 0.946052 -0.094301 -0.094301 0.396386 0.396386 0.131083 0.131083 -0.787022 -0.787022 -0.110236 -0.110236 0.522418 0.522418 . o - - - - - - - - - - - - - - - - - - o . o - - - - - - - - - - - - - - - - - | o . - - - - - - - - - - - - - - - - - | | | . o - - - - - - - - - - - - - - - | | | o . - - - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | | x . x - - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | | | . o - - - - - - - - - - | | | | | | | | o . o - - - - - - - - - | | | | | | | | | o . x - - - - - - - - | | | | | | | | | | x . o - - - - - - - | | | | | | | | | | | o . x - - - - - - | | | | | | | | | | | | x . x - - - - - | | | | | | | | | | | | | x . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . o - - | | | | | | | | | | | | | | | | o . o - | | | | | | | | | | | | | | | | | o . x | | | | | | | | | | | | | | | | | | x . The error in solving: 2.167780e-16 The error in solving: 4.062662e-16 The error in solving: 3.725256e-16 The error in solving: 3.576056e-16 The error in solving: 3.345094e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.710942 -0.612578 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.710942 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.612578 0.000000 0.000000 0.841277 -0.155303 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.841277 0.000000 -0.109394 -0.657649 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.155303 -0.109394 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.657649 0.000000 0.000000 0.000000 0.402407 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.125605 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.402407 -1.125605 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.258273 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.258273 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 18 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 2 3 6 9 11 13 14 16 16 16 17 18 18 18 18 18 18 Column indices: 4 5 3 3 6 7 5 7 8 5 6 6 10 10 8 9 14 13 Off-diagonal values: 0.710942 -0.612578 0.710942 -0.612578 0.841277 -0.155303 0.841277 -0.109394 -0.657649 -0.155303 -0.109394 -0.657649 0.402407 -1.125605 0.402407 -1.125605 1.258273 1.258273 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . x o - - - - - - - - - - - - - - | | | x . - - - - - - - - - - - - - - - | | | o | . x o - - - - - - - - - - - - | | | | | x . o o - - - - - - - - - - - | | | | | o o . - - - - - - - - - - - - | | | | | | o | . - x - - - - - - - - - | | | | | | | | | . o - - - - - - - - - | | | | | | | | x o . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . x - - - - - | | | | | | | | | | | | | x . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.733607e-16 The error in solving: 2.734281e-16 The error in solving: 3.848428e-16 The error in solving: 3.333559e-16 The error in solving: 2.237726e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.540739 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.540739 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.312929 -0.731026 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.312929 0.000000 -0.837079 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.731026 -0.837079 0.000000 0.535653 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.535653 0.000000 -1.827554 1.339596 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.827554 0.000000 1.070846 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.339596 1.070846 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.785919 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.785919 0.000000 0.000000 -0.005014 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.121969 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.005014 1.121969 0.000000 0.000000 0.359204 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.359204 0.000000 0.000000 -0.671341 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.671341 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.177492 -1.801485 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.177492 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.801485 0.000000 0.000000 0.000000 -0.689227 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.795069 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.689227 -0.795069 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 34 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 4 6 9 12 14 16 17 19 20 23 23 25 26 28 29 31 32 34 Column indices: 1 0 3 4 2 4 2 3 5 4 6 7 5 7 5 6 9 8 11 11 9 10 13 11 14 13 16 17 15 15 19 19 17 18 Off-diagonal values: 0.540739 0.540739 0.312929 -0.731026 0.312929 -0.837079 -0.731026 -0.837079 0.535653 0.535653 -1.827554 1.339596 -1.827554 1.070846 1.339596 1.070846 1.785919 1.785919 -0.005014 1.121969 -0.005014 1.121969 0.359204 0.359204 -0.671341 -0.671341 -0.177492 -1.801485 -0.177492 -1.801485 -0.689227 -0.795069 -0.689227 -0.795069 . x - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | | . x o - - - - - - - - - - - - - - - | | x . o - - - - - - - - - - - - - - - | | o o . x - - - - - - - - - - - - - - | | | | x . o x - - - - - - - - - - - - | | | | | o . x - - - - - - - - - - - - | | | | | x x . - - - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | | x . - o - - - - - - - - | | | | | | | | | | . x - - - - - - - - | | | | | | | | | o x . - x - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | x | . o - - - - - | | | | | | | | | | | | | o . - - - - - | | | | | | | | | | | | | | | . o o - - | | | | | | | | | | | | | | | o . - - - | | | | | | | | | | | | | | | o | . - o | | | | | | | | | | | | | | | | | | . o | | | | | | | | | | | | | | | | | o o . The error in solving: 9.438490e-16 The error in solving: 4.744905e-16 The error in solving: 6.568174e-16 The error in solving: 6.527357e-16 The error in solving: 5.985173e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A symmetric 2-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.435669 -0.811833 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.435669 0.000000 -0.364691 -1.171088 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.811833 -0.364691 0.000000 1.262771 0.273468 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.171088 1.262771 0.000000 0.565215 0.168099 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.273468 0.565215 0.000000 -0.177835 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.168099 -0.177835 0.000000 0.329964 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.329964 0.000000 0.000000 0.911025 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.913244 0.434363 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.911025 -0.913244 0.000000 0.336288 -0.227039 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.434363 0.336288 0.000000 -0.683066 -0.874742 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.227039 -0.683066 0.000000 -0.800767 -1.259810 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.874742 -0.800767 0.000000 -0.307573 1.327796 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.259810 -0.307573 0.000000 1.642937 0.397213 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.327796 1.642937 0.000000 -0.314206 -0.519489 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.397213 -0.314206 0.000000 0.806312 -1.272505 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.519489 0.806312 0.000000 0.948749 1.222025 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.272505 0.948749 0.000000 -0.308603 0.626773 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.222025 -0.308603 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.626773 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 62 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 2 5 9 13 16 19 21 23 27 31 35 39 43 47 51 55 59 61 62 Column indices: 2 3 1 3 4 1 2 4 5 2 3 5 6 3 4 6 4 5 7 6 9 9 10 7 8 10 11 8 9 11 12 9 10 12 13 10 11 13 14 11 12 14 15 12 13 15 16 13 14 16 17 14 15 17 18 15 16 18 19 16 17 17 Off-diagonal values: -0.435669 -0.811833 -0.435669 -0.364691 -1.171088 -0.811833 -0.364691 1.262771 0.273468 -1.171088 1.262771 0.565215 0.168099 0.273468 0.565215 -0.177835 0.168099 -0.177835 0.329964 0.329964 0.911025 -0.913244 0.434363 0.911025 -0.913244 0.336288 -0.227039 0.434363 0.336288 -0.683066 -0.874742 -0.227039 -0.683066 -0.800767 -1.259810 -0.874742 -0.800767 -0.307573 1.327796 -1.259810 -0.307573 1.642937 0.397213 1.327796 1.642937 -0.314206 -0.519489 0.397213 -0.314206 0.806312 -1.272505 -0.519489 0.806312 0.948749 1.222025 -1.272505 0.948749 -0.308603 0.626773 1.222025 -0.308603 0.626773 . - - - - - - - - - - - - - - - - - - - | . o o - - - - - - - - - - - - - - - - | o . o o - - - - - - - - - - - - - - - | o o . x x - - - - - - - - - - - - - - | | o x . x x - - - - - - - - - - - - - | | | x x . o - - - - - - - - - - - - - | | | | x o . x - - - - - - - - - - - - | | | | | | x . - x - - - - - - - - - - | | | | | | | | . o x - - - - - - - - - | | | | | | | x o . x o - - - - - - - - | | | | | | | | x x . o o - - - - - - - | | | | | | | | | o o . o o - - - - - - | | | | | | | | | | o o . o x - - - - - | | | | | | | | | | | o o . x x - - - - | | | | | | | | | | | | x x . o o - - - | | | | | | | | | | | | | x o . x o - - | | | | | | | | | | | | | | o x . x x - | | | | | | | | | | | | | | | o x . o x | | | | | | | | | | | | | | | | x o . - | | | | | | | | | | | | | | | | | x | . The error in solving: 3.764949e-16 The error in solving: 6.010460e-16 The error in solving: 3.608892e-16 The error in solving: 4.783309e-16 The error in solving: 6.708873e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.224145 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.224145 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.645258 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.645258 0.000000 0.969488 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.969488 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.438482 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.438482 0.000000 0.529413 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.529413 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.959970 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.959970 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 12 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 2 3 5 6 6 6 7 9 10 10 10 10 10 10 10 10 11 12 Column indices: 2 1 4 3 5 4 9 8 10 9 19 18 Off-diagonal values: 0.224145 -0.224145 -0.645258 0.645258 0.969488 -0.969488 -0.438482 0.438482 0.529413 -0.529413 -0.959970 0.959970 . - - - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | o . - - - - - - - - - - - - - - - - - | | | . o - - - - - - - - - - - - - - - | | | x . x - - - - - - - - - - - - - - | | | | o . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . o - - - - - - - - - - | | | | | | | | x . x - - - - - - - - - | | | | | | | | | o . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . o | | | | | | | | | | | | | | | | | | x . The error in solving: 2.547623e-16 The error in solving: 1.665335e-16 The error in solving: 1.144392e-16 The error in solving: 1.576478e-16 The error in solving: 4.053169e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.640706 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.640706 0.000000 0.754830 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.754830 0.000000 0.477850 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.477850 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.697770 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.697770 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.686306 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.686306 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.654910 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.654910 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.363456 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.363456 0.000000 0.589940 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.589940 0.000000 -0.807851 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.807851 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 18 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 3 5 6 6 6 7 8 9 10 11 12 12 12 13 15 17 18 18 Column indices: 2 1 3 2 4 3 8 7 10 9 12 11 16 15 17 16 18 17 Off-diagonal values: 0.640706 -0.640706 0.754830 -0.754830 0.477850 -0.477850 0.697770 -0.697770 0.686306 -0.686306 -0.654910 0.654910 -0.363456 0.363456 0.589940 -0.589940 -0.807851 0.807851 . - - - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | o . x - - - - - - - - - - - - - - - - | | o . x - - - - - - - - - - - - - - - | | | o . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . x - - - - - - - - - - - | | | | | | | o . - - - - - - - - - - - | | | | | | | | | . x - - - - - - - - - | | | | | | | | | o . - - - - - - - - - | | | | | | | | | | | . o - - - - - - - | | | | | | | | | | | x . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . o - - - | | | | | | | | | | | | | | | x . x - - | | | | | | | | | | | | | | | | o . o - | | | | | | | | | | | | | | | | | x . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.366804e-16 The error in solving: 2.719701e-16 The error in solving: 1.782634e-16 The error in solving: 1.144392e-16 The error in solving: 3.734131e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.750000 [ 0.000000 -0.591983 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.591983 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.892696 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.892696 0.000000 -0.274201 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.274201 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.566160 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.566160 0.000000 0.587876 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.587876 0.000000 -0.795573 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.795573 0.000000 0.439457 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.439457 0.000000 0.563127 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.563127 0.000000 0.845887 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.845887 0.000000 0.168015 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.168015 0.000000 -0.541124 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.541124 0.000000 0.851771 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.851771 0.000000 0.698823 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.698823 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.877598 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.877598 0.000000 -0.076996 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.076996 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 30 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 3 5 6 7 9 11 13 15 17 19 21 23 25 26 26 27 29 30 Column indices: 1 0 3 2 4 3 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 18 17 19 18 Off-diagonal values: -0.591983 0.591983 0.892696 -0.892696 -0.274201 0.274201 -0.566160 0.566160 0.587876 -0.587876 -0.795573 0.795573 0.439457 -0.439457 0.563127 -0.563127 0.845887 -0.845887 0.168015 -0.168015 -0.541124 0.541124 0.851771 -0.851771 0.698823 -0.698823 -0.877598 0.877598 -0.076996 0.076996 . o - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | | . x - - - - - - - - - - - - - - - - | | o . o - - - - - - - - - - - - - - - | | | x . - - - - - - - - - - - - - - - | | | | | . o - - - - - - - - - - - - - | | | | | x . x - - - - - - - - - - - - | | | | | | o . o - - - - - - - - - - - | | | | | | | x . x - - - - - - - - - - | | | | | | | | o . x - - - - - - - - - | | | | | | | | | o . x - - - - - - - - | | | | | | | | | | o . x - - - - - - - | | | | | | | | | | | o . o - - - - - - | | | | | | | | | | | | x . x - - - - - | | | | | | | | | | | | | o . x - - - - | | | | | | | | | | | | | | o . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . o - | | | | | | | | | | | | | | | | | x . o | | | | | | | | | | | | | | | | | | x . The error in solving: 4.744905e-16 The error in solving: 4.118133e-16 The error in solving: 6.855121e-16 The error in solving: 3.557156e-16 The error in solving: 3.706438e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 -0.370946 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.370946 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.967767 0.107123 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.967767 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.107123 0.000000 0.000000 0.000000 0.204682 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.204682 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.182817 0.672279 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.182817 0.000000 -0.673524 0.064465 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.672279 0.673524 0.000000 0.000000 0.009983 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.064465 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.009983 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.996528 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.996528 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 20 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 4 5 7 7 8 8 8 8 8 8 8 10 13 16 17 18 19 20 Column indices: 1 0 3 4 2 2 6 4 14 15 13 15 16 13 14 17 14 15 19 18 Off-diagonal values: -0.370946 0.370946 0.967767 0.107123 -0.967767 -0.107123 0.204682 -0.204682 0.182817 0.672279 -0.182817 -0.673524 0.064465 -0.672279 0.673524 0.009983 -0.064465 -0.009983 0.996528 -0.996528 . o - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | | . x x - - - - - - - - - - - - - - - | | o . - - - - - - - - - - - - - - - - | | o | . - x - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | o | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . x x - - - - | | | | | | | | | | | | | o . o x - - - | | | | | | | | | | | | | o x . - x - - | | | | | | | | | | | | | | o | . - - - | | | | | | | | | | | | | | | o | . - - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | o . The error in solving: 4.579670e-16 The error in solving: 4.761113e-16 The error in solving: 5.495324e-16 The error in solving: 4.543784e-16 The error in solving: 5.209256e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.699251 -0.866975 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.699251 0.000000 -0.836541 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.866975 0.836541 0.000000 0.000000 0.413729 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.413729 0.000000 0.000000 0.000000 -0.048780 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.588439 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.048780 0.588439 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.201216 -0.709012 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.201216 0.000000 0.132090 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.709012 -0.132090 0.000000 -0.189957 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.189957 0.000000 -0.326574 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.326574 0.000000 0.827219 -0.358325 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.827219 0.000000 0.000000 -0.361906 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.358325 0.000000 0.000000 -0.655786 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.361906 0.655786 0.000000 0.000000 0.209776 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.722651 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.209776 -0.722651 0.000000 0.916947 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.916947 0.000000 -0.325025 -0.089347 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.325025 0.000000 -0.930894 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.089347 0.930894 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 42 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 4 7 7 9 10 12 14 16 19 21 24 26 28 31 32 35 38 40 42 Column indices: 1 2 0 2 0 1 4 2 6 6 4 5 8 9 7 9 7 8 10 9 11 10 12 13 11 14 11 14 12 13 16 16 14 15 17 16 18 19 17 19 17 18 Off-diagonal values: 0.699251 -0.866975 -0.699251 -0.836541 0.866975 0.836541 0.413729 -0.413729 -0.048780 -0.588439 0.048780 0.588439 -0.201216 -0.709012 0.201216 0.132090 0.709012 -0.132090 -0.189957 0.189957 -0.326574 0.326574 0.827219 -0.358325 -0.827219 -0.361906 0.358325 -0.655786 0.361906 0.655786 0.209776 0.722651 -0.209776 -0.722651 0.916947 -0.916947 -0.325025 -0.089347 0.325025 -0.930894 0.089347 0.930894 . x o - - - - - - - - - - - - - - - - - o . o - - - - - - - - - - - - - - - - - x x . - x - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | o | . - o - - - - - - - - - - - - - | | | | | . o - - - - - - - - - - - - - | | | | x x . - - - - - - - - - - - - - | | | | | | | . o o - - - - - - - - - - | | | | | | | x . x - - - - - - - - - - | | | | | | | x o . o - - - - - - - - - | | | | | | | | | x . o - - - - - - - - | | | | | | | | | | x . x o - - - - - - | | | | | | | | | | | o . - o - - - - - | | | | | | | | | | | x | . o - - - - - | | | | | | | | | | | | x x . - x - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | o o . x - - | | | | | | | | | | | | | | | | o . o o | | | | | | | | | | | | | | | | | x . o | | | | | | | | | | | | | | | | | x x . The error in solving: 4.275170e-16 The error in solving: 4.767177e-16 The error in solving: 4.022324e-16 The error in solving: 6.218736e-16 The error in solving: 5.266707e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a random diagonal and a density of 0.750000 [ 0.000000 0.335981 0.883453 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.335981 0.000000 0.000000 -0.111555 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.883453 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.111555 0.000000 0.000000 -0.662231 -0.039988 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.662231 0.000000 -0.374485 -0.592684 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.039988 0.374485 0.000000 -0.952549 0.970987 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.592684 0.952549 0.000000 -0.115160 0.227341 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.970987 0.115160 0.000000 -0.380887 -0.008686 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.227341 0.380887 0.000000 -0.065969 -0.906857 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.008686 0.065969 0.000000 -0.752870 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.906857 0.752870 0.000000 0.730905 0.691381 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.730905 0.000000 0.651066 -0.709791 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.691381 -0.651066 0.000000 -0.425919 -0.543251 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.709791 0.425919 0.000000 -0.597183 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.543251 0.597183 0.000000 -0.448004 0.647069 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.448004 0.000000 0.000000 0.439791 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.647069 0.000000 0.000000 -0.875898 0.562382 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.439791 0.875898 0.000000 -0.795588 -0.184323 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.562382 0.795588 0.000000 -0.782782 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.184323 0.782782 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 62 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 4 5 8 11 15 19 23 27 30 34 37 41 44 48 50 53 57 60 62 Column indices: 1 2 0 3 0 1 4 5 3 5 6 3 4 6 7 4 5 7 8 5 6 8 9 6 7 9 10 7 8 10 8 9 11 12 10 12 13 10 11 13 14 11 12 14 12 13 15 16 14 17 14 17 18 15 16 18 19 16 17 19 17 18 Off-diagonal values: 0.335981 0.883453 -0.335981 -0.111555 -0.883453 0.111555 -0.662231 -0.039988 0.662231 -0.374485 -0.592684 0.039988 0.374485 -0.952549 0.970987 0.592684 0.952549 -0.115160 0.227341 -0.970987 0.115160 -0.380887 -0.008686 -0.227341 0.380887 -0.065969 -0.906857 0.008686 0.065969 -0.752870 0.906857 0.752870 0.730905 0.691381 -0.730905 0.651066 -0.709791 -0.691381 -0.651066 -0.425919 -0.543251 0.709791 0.425919 -0.597183 0.543251 0.597183 -0.448004 0.647069 0.448004 0.439791 -0.647069 -0.875898 0.562382 -0.439791 0.875898 -0.795588 -0.184323 -0.562382 0.795588 -0.782782 0.184323 0.782782 . x x - - - - - - - - - - - - - - - - - o . - o - - - - - - - - - - - - - - - - o | . - - - - - - - - - - - - - - - - - | x | . o o - - - - - - - - - - - - - - | | | x . o o - - - - - - - - - - - - - | | | x x . o x - - - - - - - - - - - - | | | | x x . o x - - - - - - - - - - - | | | | | o x . o o - - - - - - - - - - | | | | | | o x . o o - - - - - - - - - | | | | | | | x x . o - - - - - - - - - | | | | | | | | x x . x x - - - - - - - | | | | | | | | | | o . x o - - - - - - | | | | | | | | | | o o . o o - - - - - | | | | | | | | | | | x x . o - - - - - | | | | | | | | | | | | x x . o x - - - | | | | | | | | | | | | | | x . - x - - | | | | | | | | | | | | | | o | . o x - | | | | | | | | | | | | | | | o x . o o | | | | | | | | | | | | | | | | o x . o | | | | | | | | | | | | | | | | | x x . The error in solving: 5.026868e-16 The error in solving: 6.383782e-16 The error in solving: 7.133237e-16 The error in solving: 7.839415e-16 The error in solving: 6.433369e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.869545 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.869545 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.320606 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.320606 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.494518 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.494518 0.000000 -0.371051 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.371051 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.903104 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.903104 0.000000 -0.329038 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.329038 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 12 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 0 1 2 2 2 2 2 3 4 4 5 7 8 8 9 11 12 Column indices: 5 4 11 10 14 13 15 14 18 17 19 18 Off-diagonal values: -0.869545 0.869545 -0.320606 0.320606 -0.494518 0.494518 -0.371051 0.371051 -0.903104 0.903104 -0.329038 0.329038 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . o - - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . o - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . o - - - - - | | | | | | | | | | | | | x . o - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . o - | | | | | | | | | | | | | | | | | x . o | | | | | | | | | | | | | | | | | | x . The error in solving: 2.989367e-16 The error in solving: 3.557325e-16 The error in solving: 3.103168e-17 The error in solving: 2.543841e-16 The error in solving: 3.143250e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.455118 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.455118 0.000000 0.212530 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.212530 0.000000 -0.833867 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.833867 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.199314 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.199314 0.000000 -0.094195 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.094195 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.492511 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.492511 0.000000 0.808930 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.808930 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.629148 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.629148 0.000000 0.212456 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.212456 0.000000 0.914896 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.914896 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.028619 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.028619 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 22 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 1 3 5 6 6 7 9 10 11 13 14 15 17 19 20 20 21 22 Column indices: 3 2 4 3 5 4 8 7 9 8 11 10 12 11 14 13 15 14 16 15 19 18 Off-diagonal values: -0.455118 0.455118 0.212530 -0.212530 -0.833867 0.833867 0.199314 -0.199314 -0.094195 0.094195 -0.492511 0.492511 0.808930 -0.808930 -0.629148 0.629148 0.212456 -0.212456 0.914896 -0.914896 0.028619 -0.028619 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . o - - - - - - - - - - - - - - - - | | x . x - - - - - - - - - - - - - - - | | | o . o - - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . x - - - - - - - - - - - | | | | | | | o . o - - - - - - - - - - | | | | | | | | x . - - - - - - - - - - | | | | | | | | | | . o - - - - - - - - | | | | | | | | | | x . x - - - - - - - | | | | | | | | | | | o . - - - - - - - | | | | | | | | | | | | | . o - - - - - | | | | | | | | | | | | | x . x - - - - | | | | | | | | | | | | | | o . x - - - | | | | | | | | | | | | | | | o . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | o . The error in solving: 2.733662e-16 The error in solving: 2.020636e-16 The error in solving: 2.782488e-16 The error in solving: 5.769305e-16 The error in solving: 5.694968e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.000000 -0.144833 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.144833 0.000000 -0.839908 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.839908 0.000000 -0.403266 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.403266 0.000000 0.478406 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.478406 0.000000 0.391923 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.391923 0.000000 0.719604 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.719604 0.000000 -0.071984 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.071984 0.000000 0.721977 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.721977 0.000000 0.120434 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.120434 0.000000 -0.869394 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.869394 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.699070 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.699070 0.000000 -0.087595 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.087595 0.000000 0.811608 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.811608 0.000000 0.140842 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.140842 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.727854 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.727854 0.000000 -0.049521 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.049521 0.000000 -0.250381 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.250381 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 34 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 5 7 9 11 13 15 17 19 20 21 23 25 27 28 29 31 33 34 Column indices: 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 12 11 13 12 14 13 15 14 17 16 18 17 19 18 Off-diagonal values: -0.144833 0.144833 -0.839908 0.839908 -0.403266 0.403266 0.478406 -0.478406 0.391923 -0.391923 0.719604 -0.719604 -0.071984 0.071984 0.721977 -0.721977 0.120434 -0.120434 -0.869394 0.869394 0.699070 -0.699070 -0.087595 0.087595 0.811608 -0.811608 0.140842 -0.140842 -0.727854 0.727854 -0.049521 0.049521 -0.250381 0.250381 . o - - - - - - - - - - - - - - - - - - x . o - - - - - - - - - - - - - - - - - | x . o - - - - - - - - - - - - - - - - | | x . x - - - - - - - - - - - - - - - | | | o . x - - - - - - - - - - - - - - | | | | o . x - - - - - - - - - - - - - | | | | | o . o - - - - - - - - - - - - | | | | | | x . x - - - - - - - - - - - | | | | | | | o . x - - - - - - - - - - | | | | | | | | o . o - - - - - - - - - | | | | | | | | | x . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | o . o - - - - - - | | | | | | | | | | | | x . x - - - - - | | | | | | | | | | | | | o . x - - - - | | | | | | | | | | | | | | o . - - - - | | | | | | | | | | | | | | | | . o - - | | | | | | | | | | | | | | | | x . o - | | | | | | | | | | | | | | | | | x . o | | | | | | | | | | | | | | | | | | x . The error in solving: 6.212950e-16 The error in solving: 3.510965e-16 The error in solving: 4.552253e-16 The error in solving: 5.699834e-16 The error in solving: 4.941740e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.000000 -0.948241 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.948241 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.510829 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.510829 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.674686 0.923827 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.674686 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.923827 0.000000 0.000000 0.000000 -0.657439 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.657439 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.097551 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.097551 0.000000 -0.710961 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.710961 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.344058 0.738952 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.344058 0.000000 -0.548456 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.738952 0.548456 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 20 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 3 3 4 6 7 9 9 10 10 10 10 11 13 14 14 16 18 20 Column indices: 1 0 4 2 6 7 5 5 9 7 14 13 15 14 18 19 17 19 17 18 Off-diagonal values: -0.948241 0.948241 -0.510829 0.510829 0.674686 0.923827 -0.674686 -0.923827 -0.657439 0.657439 -0.097551 0.097551 -0.710961 0.710961 -0.344058 0.738952 0.344058 -0.548456 -0.738952 0.548456 . o - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | | . - o - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | x | . - - - - - - - - - - - - - - - | | | | | . x x - - - - - - - - - - - - | | | | | o . - - - - - - - - - - - - - | | | | | o | . - o - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | x | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . o - - - - - | | | | | | | | | | | | | x . o - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . o x | | | | | | | | | | | | | | | | | x . o | | | | | | | | | | | | | | | | | o x . The error in solving: 1.387779e-16 The error in solving: 3.600210e-16 The error in solving: 4.594496e-16 The error in solving: 1.678295e-16 The error in solving: 2.789401e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.157477 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.591742 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.157477 -0.591742 0.000000 0.000000 0.117919 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.722057 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.117919 -0.722057 0.000000 -0.955257 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.955257 0.000000 0.000000 0.713676 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.713676 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.521900 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.934561 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.521900 0.934561 0.000000 -0.199687 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.199687 0.000000 0.000000 -0.727175 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.909001 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.727175 0.000000 0.000000 0.000000 0.057460 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.909001 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.057460 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.694953 0.268749 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.694953 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.268749 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 28 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 2 5 6 9 11 11 12 13 14 17 19 20 22 23 24 26 27 28 Column indices: 3 3 1 2 5 5 3 4 6 5 8 6 11 11 9 10 12 11 14 15 12 16 13 14 18 19 17 17 Off-diagonal values: -0.157477 0.591742 0.157477 -0.591742 0.117919 0.722057 -0.117919 -0.722057 -0.955257 0.955257 0.713676 -0.713676 -0.521900 -0.934561 0.521900 0.934561 -0.199687 0.199687 -0.727175 -0.909001 0.727175 0.057460 0.909001 -0.057460 0.694953 0.268749 -0.694953 -0.268749 . - - - - - - - - - - - - - - - - - - - | . - o - - - - - - - - - - - - - - - - | | . x - - - - - - - - - - - - - - - - | x o . - x - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | o o . o - - - - - - - - - - - - - | | | | | x . - x - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | o | . - - - - - - - - - - - | | | | | | | | | . - o - - - - - - - - | | | | | | | | | | . o - - - - - - - - | | | | | | | | | x x . o - - - - - - - | | | | | | | | | | | x . - o - - - - - | | | | | | | | | | | | | . - o - - - - | | | | | | | | | | | | x | . - x - - - | | | | | | | | | | | | | x | . - - - - | | | | | | | | | | | | | | o | . - - - | | | | | | | | | | | | | | | | | . x x | | | | | | | | | | | | | | | | | o . - | | | | | | | | | | | | | | | | | o | . The error in solving: 3.661212e-16 The error in solving: 2.521025e-16 The error in solving: 5.236912e-16 The error in solving: 1.387779e-16 The error in solving: 2.820300e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.000000 0.570569 0.788539 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.570569 0.000000 0.897119 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.788539 -0.897119 0.000000 0.181990 0.202307 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.181990 0.000000 -0.486281 -0.050990 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.202307 0.486281 0.000000 0.304718 0.587132 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.050990 -0.304718 0.000000 0.000000 0.536110 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.587132 0.000000 0.000000 -0.082940 0.717454 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.536110 0.082940 0.000000 -0.710227 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.717454 0.710227 0.000000 0.000000 -0.113726 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.827088 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.113726 0.000000 0.000000 0.977658 -0.683865 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.827088 -0.977658 0.000000 0.000000 0.535372 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.683865 0.000000 0.000000 0.067516 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.535372 -0.067516 0.000000 -0.955228 0.278166 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.955228 0.000000 -0.682805 0.442718 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.278166 0.682805 0.000000 0.000000 0.639783 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.442718 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.639783 0.000000 0.000000 -0.894766 0.496837 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.894766 0.000000 -0.207016 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.496837 0.207016 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 54 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 4 8 11 15 18 21 24 27 28 31 34 36 40 43 46 47 50 52 54 Column indices: 1 2 0 2 0 1 3 4 2 4 5 2 3 5 6 3 4 7 4 7 8 5 6 8 6 7 10 11 8 11 12 9 10 13 10 13 11 12 14 15 13 15 16 13 14 17 14 15 18 19 17 19 17 18 Off-diagonal values: 0.570569 0.788539 -0.570569 0.897119 -0.788539 -0.897119 0.181990 0.202307 -0.181990 -0.486281 -0.050990 -0.202307 0.486281 0.304718 0.587132 0.050990 -0.304718 0.536110 -0.587132 -0.082940 0.717454 -0.536110 0.082940 -0.710227 -0.717454 0.710227 -0.113726 0.827088 0.113726 0.977658 -0.683865 -0.827088 -0.977658 0.535372 0.683865 0.067516 -0.535372 -0.067516 -0.955228 0.278166 0.955228 -0.682805 0.442718 -0.278166 0.682805 0.639783 -0.442718 -0.639783 -0.894766 0.496837 0.894766 -0.207016 -0.496837 0.207016 . x x - - - - - - - - - - - - - - - - - o . x - - - - - - - - - - - - - - - - - o o . x x - - - - - - - - - - - - - - - | | o . o o - - - - - - - - - - - - - - | | o x . x x - - - - - - - - - - - - - | | | x o . - x - - - - - - - - - - - - | | | | o | . o x - - - - - - - - - - - | | | | | o x . o - - - - - - - - - - - | | | | | | o x . - o - - - - - - - - - | | | | | | | | | . - x - - - - - - - - | | | | | | | | x | . x o - - - - - - - | | | | | | | | | o o . - x - - - - - - | | | | | | | | | | x | . x - - - - - - | | | | | | | | | | | o o . o x - - - - | | | | | | | | | | | | | x . o x - - - | | | | | | | | | | | | | o x . - x - - | | | | | | | | | | | | | | o | . - - - | | | | | | | | | | | | | | | o | . o x | | | | | | | | | | | | | | | | | x . o | | | | | | | | | | | | | | | | | o x . The error in solving: 3.928613e-16 The error in solving: 4.494775e-16 The error in solving: 6.212635e-16 The error in solving: 3.425453e-16 The error in solving: 6.431895e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.863191 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.863191 0.000000 -0.587191 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.587191 0.000000 0.036211 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.036211 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.606134 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.606134 0.000000 0.142110 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.142110 0.000000 -0.870893 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.870893 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.490097 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.490097 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.475895 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.475895 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.550604 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.550604 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.348124 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.348124 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 20 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 3 5 6 6 6 7 9 11 12 13 14 15 16 17 18 19 20 20 Column indices: 2 1 3 2 4 3 8 7 9 8 10 9 12 11 14 13 16 15 18 17 Off-diagonal values: 0.863191 -0.863191 -0.587191 0.587191 0.036211 -0.036211 0.606134 -0.606134 0.142110 -0.142110 -0.870893 0.870893 0.490097 -0.490097 0.475895 -0.475895 0.550604 -0.550604 -0.348124 0.348124 . - - - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | o . o - - - - - - - - - - - - - - - - | | x . x - - - - - - - - - - - - - - - | | | o . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . x - - - - - - - - - - - | | | | | | | o . x - - - - - - - - - - | | | | | | | | o . o - - - - - - - - - | | | | | | | | | x . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | o . - - - - - - - | | | | | | | | | | | | | . x - - - - - | | | | | | | | | | | | | o . - - - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | o . - - - | | | | | | | | | | | | | | | | | . o - | | | | | | | | | | | | | | | | | x . - | | | | | | | | | | | | | | | | | | | . The error in solving: 4.492766e-16 The error in solving: 4.007774e-16 The error in solving: 5.269906e-16 The error in solving: 1.250927e-16 The error in solving: 2.940702e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.659751 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.659751 0.000000 -0.162868 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.162868 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.843155 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.843155 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.546897 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.546897 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.650771 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.650771 0.000000 -0.085311 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.085311 0.000000 0.883926 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.883926 0.000000 -0.986364 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.986364 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.884899 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.884899 0.000000 -0.865640 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.865640 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 20 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 1 3 4 5 6 7 8 8 9 11 13 15 16 16 17 19 20 Column indices: 4 3 5 4 7 6 9 8 12 11 13 12 14 13 15 14 18 17 19 18 Off-diagonal values: 0.659751 -0.659751 -0.162868 0.162868 0.843155 -0.843155 -0.546897 0.546897 0.650771 -0.650771 -0.085311 0.085311 0.883926 -0.883926 -0.986364 0.986364 -0.884899 0.884899 -0.865640 0.865640 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | | o . o - - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | | | . x - - - - - - - - - - - - | | | | | | o . - - - - - - - - - - - - | | | | | | | | . o - - - - - - - - - - | | | | | | | | x . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | o . o - - - - - - | | | | | | | | | | | | x . x - - - - - | | | | | | | | | | | | | o . o - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . o - | | | | | | | | | | | | | | | | | x . o | | | | | | | | | | | | | | | | | | x . The error in solving: 3.858580e-16 The error in solving: 3.019216e-16 The error in solving: 3.260542e-16 The error in solving: 5.125513e-16 The error in solving: 2.371437e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.491390 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.491390 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.568836 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.568836 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.188139 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.188139 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.669200 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.669200 0.000000 -0.211823 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.211823 0.000000 0.146808 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.146808 0.000000 0.275523 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.275523 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.328723 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.328723 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.469694 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.469694 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.781347 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.781347 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.484515 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.484515 0.000000 0.484137 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.484137 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 24 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 3 4 5 6 7 9 11 13 14 15 16 17 18 19 20 21 23 24 Column indices: 1 0 3 2 5 4 7 6 8 7 9 8 10 9 12 11 14 13 16 15 18 17 19 18 Off-diagonal values: 0.491390 -0.491390 -0.568836 0.568836 -0.188139 0.188139 -0.669200 0.669200 -0.211823 0.211823 0.146808 -0.146808 0.275523 -0.275523 -0.328723 0.328723 -0.469694 0.469694 -0.781347 0.781347 -0.484515 0.484515 0.484137 -0.484137 . x - - - - - - - - - - - - - - - - - - o . - - - - - - - - - - - - - - - - - - | | . o - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | | | . o - - - - - - - - - - - - - - | | | | x . - - - - - - - - - - - - - - | | | | | | . o - - - - - - - - - - - - | | | | | | x . o - - - - - - - - - - - | | | | | | | x . x - - - - - - - - - - | | | | | | | | o . x - - - - - - - - - | | | | | | | | | o . - - - - - - - - - | | | | | | | | | | | . o - - - - - - - | | | | | | | | | | | x . - - - - - - - | | | | | | | | | | | | | . o - - - - - | | | | | | | | | | | | | x . - - - - - | | | | | | | | | | | | | | | . o - - - | | | | | | | | | | | | | | | x . - - - | | | | | | | | | | | | | | | | | . o - | | | | | | | | | | | | | | | | | x . x | | | | | | | | | | | | | | | | | | o . The error in solving: 3.555125e-16 The error in solving: 1.551584e-16 The error in solving: 3.002225e-16 The error in solving: 5.034405e-16 The error in solving: 2.720365e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.060458 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.060458 0.000000 0.000000 0.864598 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.864598 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.368712 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.368712 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.002978 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.002978 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 8 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 1 3 4 4 4 5 6 6 6 6 6 6 6 6 7 7 8 8 Column indices: 3 1 4 3 8 7 18 16 Off-diagonal values: 0.060458 -0.060458 0.864598 -0.864598 0.368712 -0.368712 0.002978 -0.002978 . - - - - - - - - - - - - - - - - - - - | . - x - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | o | . x - - - - - - - - - - - - - - - | | | o . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . x - - - - - - - - - - - | | | | | | | o . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - x - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | o | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.571649e-16 The error in solving: 2.221530e-16 The error in solving: 3.152427e-16 The error in solving: 1.570092e-16 The error in solving: 2.006289e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.870690 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.870690 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.750775 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.750775 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.383288 -0.262083 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.383288 0.000000 -0.417322 0.220760 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.262083 0.417322 0.000000 0.000000 -0.289790 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.220760 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.289790 0.000000 0.000000 0.000000 0.940009 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.638424 -0.903168 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.940009 0.638424 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.903168 0.000000 0.000000 -0.439827 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.439827 0.000000 -0.593276 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.593276 0.000000 0.000000 -0.857106 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.165782 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.857106 -0.165782 0.000000 0.634371 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.634371 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 30 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 1 2 2 2 3 4 6 9 12 13 15 17 19 21 23 25 26 29 30 Column indices: 2 0 6 5 8 9 7 9 10 7 8 11 8 9 13 13 14 11 12 12 15 14 16 15 18 18 16 17 19 18 Off-diagonal values: 0.870690 -0.870690 -0.750775 0.750775 -0.383288 -0.262083 0.383288 -0.417322 0.220760 0.262083 0.417322 -0.289790 -0.220760 0.289790 0.940009 -0.638424 -0.903168 -0.940009 0.638424 0.903168 -0.439827 0.439827 -0.593276 0.593276 -0.857106 0.165782 0.857106 -0.165782 0.634371 -0.634371 . - x - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - o | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . o - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | | | . o o - - - - - - - - - - | | | | | | | x . o x - - - - - - - - - | | | | | | | x x . - o - - - - - - - - | | | | | | | | o | . - - - - - - - - - | | | | | | | | | x | . - x - - - - - - | | | | | | | | | | | | . o o - - - - - | | | | | | | | | | | o x . - - - - - - | | | | | | | | | | | | x | . o - - - - | | | | | | | | | | | | | | x . o - - - | | | | | | | | | | | | | | | x . - o - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | x o . x | | | | | | | | | | | | | | | | | | o . The error in solving: 7.196406e-16 The error in solving: 2.558938e-16 The error in solving: 4.243092e-16 The error in solving: 3.382310e-16 The error in solving: 5.003738e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (0, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.000000 -0.062345 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.281180 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.062345 0.281180 0.000000 0.271831 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.271831 0.000000 -0.367888 -0.876553 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.367888 0.000000 0.000000 -0.268427 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.876553 0.000000 0.000000 0.373164 -0.955197 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.268427 -0.373164 0.000000 0.558021 -0.911141 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.955197 -0.558021 0.000000 0.000000 0.124742 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.911141 0.000000 0.000000 -0.214134 -0.257267 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.124742 0.214134 0.000000 0.096527 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.257267 -0.096527 0.000000 0.528469 0.964453 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.528469 0.000000 0.666711 0.811911 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.964453 -0.666711 0.000000 0.000000 -0.523844 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.811911 0.000000 0.000000 -0.196581 0.401932 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.523844 0.196581 0.000000 0.002547 -0.710621 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.401932 -0.002547 0.000000 -0.849282 -0.324048 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.710621 0.849282 0.000000 0.510478 0.874977 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.324048 -0.510478 0.000000 -0.794007 -0.092567 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.874977 0.794007 0.000000 -0.638627 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.092567 0.638627 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 60 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 5 8 10 13 17 20 23 26 30 33 36 39 43 47 51 55 58 60 Column indices: 2 2 0 1 3 2 4 5 3 6 3 6 7 4 5 7 8 5 6 9 6 9 10 7 8 10 8 9 11 12 10 12 13 10 11 14 11 14 15 12 13 15 16 13 14 16 17 14 15 17 18 15 16 18 19 16 17 19 17 18 Off-diagonal values: -0.062345 -0.281180 0.062345 0.281180 0.271831 -0.271831 -0.367888 -0.876553 0.367888 -0.268427 0.876553 0.373164 -0.955197 0.268427 -0.373164 0.558021 -0.911141 0.955197 -0.558021 0.124742 0.911141 -0.214134 -0.257267 -0.124742 0.214134 0.096527 0.257267 -0.096527 0.528469 0.964453 -0.528469 0.666711 0.811911 -0.964453 -0.666711 -0.523844 -0.811911 -0.196581 0.401932 0.523844 0.196581 0.002547 -0.710621 -0.401932 -0.002547 -0.849282 -0.324048 0.710621 0.849282 0.510478 0.874977 0.324048 -0.510478 -0.794007 -0.092567 -0.874977 0.794007 -0.638627 0.092567 0.638627 . - o - - - - - - - - - - - - - - - - - | . o - - - - - - - - - - - - - - - - - x x . x - - - - - - - - - - - - - - - - | | o . o o - - - - - - - - - - - - - - | | | x . - o - - - - - - - - - - - - - | | | x | . x o - - - - - - - - - - - - | | | | x o . x o - - - - - - - - - - - | | | | | x o . - x - - - - - - - - - - | | | | | | x | . o o - - - - - - - - - | | | | | | | o x . x - - - - - - - - - | | | | | | | | x o . x x - - - - - - - | | | | | | | | | | o . x x - - - - - - | | | | | | | | | | o o . - o - - - - - | | | | | | | | | | | o | . o x - - - - | | | | | | | | | | | | x x . x o - - - | | | | | | | | | | | | | o o . o o - - | | | | | | | | | | | | | | x x . x x - | | | | | | | | | | | | | | | x o . o o | | | | | | | | | | | | | | | | o x . o | | | | | | | | | | | | | | | | | x x . The error in solving: 6.031651e-16 The error in solving: 4.335560e-16 The error in solving: 4.720998e-16 The error in solving: 6.683797e-16 The error in solving: 7.776516e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.476989 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.476989 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.864093 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.864093 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.140042 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.140042 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.477553 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.477553 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 8 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 0 0 0 0 0 1 2 2 3 4 5 6 6 6 7 8 8 Column indices: 9 8 12 11 14 13 18 17 Off-diagonal values: -0.476989 0.476989 -0.864093 0.864093 0.140042 -0.140042 0.477553 -0.477553 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . o - - - - - - - - - - | | | | | | | | x . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . o - - - - - - - | | | | | | | | | | | x . - - - - - - - | | | | | | | | | | | | | . x - - - - - | | | | | | | | | | | | | o . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | | o . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.242025e-16 The error in solving: 2.993118e-16 The error in solving: 2.775558e-16 The error in solving: 2.305551e-16 The error in solving: 2.607400e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.282307 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.282307 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.507104 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.507104 0.000000 0.917013 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.917013 0.000000 -0.964162 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.964162 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.975638 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.975638 0.000000 0.064274 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.064274 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.150107 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.150107 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.990116 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.990116 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 16 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 2 3 5 7 8 8 8 9 11 12 12 13 14 14 15 16 16 16 Column indices: 2 1 4 3 5 4 6 5 10 9 11 10 14 13 17 16 Off-diagonal values: 0.282307 -0.282307 0.507104 -0.507104 0.917013 -0.917013 -0.964162 0.964162 0.975638 -0.975638 0.064274 -0.064274 -0.150107 0.150107 -0.990116 0.990116 . - - - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | o . - - - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | | o . x - - - - - - - - - - - - - - | | | | o . o - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . x - - - - - - - - - | | | | | | | | | o . x - - - - - - - - | | | | | | | | | | o . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . o - - - - - | | | | | | | | | | | | | x . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . o - - | | | | | | | | | | | | | | | | x . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 4.015126e-16 The error in solving: 2.371437e-16 The error in solving: 2.288783e-16 The error in solving: 2.355394e-16 The error in solving: 3.682193e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.750000 [ 0.000000 -0.975852 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.975852 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.574310 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.574310 0.000000 0.578224 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.578224 0.000000 -0.337029 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.337029 0.000000 -0.917912 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.917912 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.765410 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.765410 0.000000 -0.757267 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.757267 0.000000 0.223950 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.223950 0.000000 0.517551 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.517551 0.000000 0.058215 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.058215 0.000000 -0.204193 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.204193 0.000000 -0.600304 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.600304 0.000000 0.056782 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.056782 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.402420 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.402420 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 28 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 3 5 7 9 10 10 11 13 15 17 19 21 23 25 26 26 27 28 Column indices: 1 0 3 2 4 3 5 4 6 5 9 8 10 9 11 10 12 11 13 12 14 13 15 14 16 15 19 18 Off-diagonal values: -0.975852 0.975852 0.574310 -0.574310 0.578224 -0.578224 -0.337029 0.337029 -0.917912 0.917912 -0.765410 0.765410 -0.757267 0.757267 0.223950 -0.223950 0.517551 -0.517551 0.058215 -0.058215 -0.204193 0.204193 -0.600304 0.600304 0.056782 -0.056782 0.402420 -0.402420 . o - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | | . x - - - - - - - - - - - - - - - - | | o . x - - - - - - - - - - - - - - - | | | o . o - - - - - - - - - - - - - - | | | | x . o - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . o - - - - - - - - - - | | | | | | | | x . o - - - - - - - - - | | | | | | | | | x . x - - - - - - - - | | | | | | | | | | o . x - - - - - - - | | | | | | | | | | | o . x - - - - - - | | | | | | | | | | | | o . o - - - - - | | | | | | | | | | | | | x . o - - - - | | | | | | | | | | | | | | x . x - - - | | | | | | | | | | | | | | | o . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | o . The error in solving: 3.935032e-16 The error in solving: 5.915916e-16 The error in solving: 2.990172e-16 The error in solving: 4.167960e-16 The error in solving: 3.764949e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.710267 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.710267 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.453214 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.453214 0.000000 0.000000 -0.055492 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.055492 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.272829 -0.529504 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.272829 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.529504 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.544257 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.544257 0.000000 0.000000 0.468495 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.973033 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.468495 -0.973033 0.000000 0.839779 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.839779 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 18 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 1 1 2 3 5 5 6 8 9 10 10 10 11 13 14 17 18 Column indices: 5 3 7 6 9 7 11 12 10 10 16 15 18 18 16 17 19 18 Off-diagonal values: -0.710267 0.710267 -0.453214 0.453214 -0.055492 0.055492 0.272829 -0.529504 -0.272829 0.529504 -0.544257 0.544257 0.468495 0.973033 -0.468495 -0.973033 0.839779 -0.839779 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - o - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | x | . - - - - - - - - - - - - - - | | | | | | . o - - - - - - - - - - - - | | | | | | x . - o - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | x | . - - - - - - - - - - | | | | | | | | | | . x o - - - - - - - | | | | | | | | | | o . - - - - - - - - | | | | | | | | | | x | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . o - - - | | | | | | | | | | | | | | | x . - x - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | o o . x | | | | | | | | | | | | | | | | | | o . The error in solving: 2.543841e-16 The error in solving: 3.140185e-16 The error in solving: 2.558938e-16 The error in solving: 3.684971e-16 The error in solving: 3.376612e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 0.577367 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.577367 0.000000 0.000000 -0.740043 0.601951 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.740043 0.000000 0.140780 0.707722 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.601951 -0.140780 0.000000 0.000000 -0.045415 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.707722 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.045415 0.000000 0.000000 0.000000 -0.836122 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.534275 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.836122 0.000000 0.000000 0.000000 0.904168 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.534275 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.904168 0.000000 0.000000 0.038637 -0.001519 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.038637 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.001519 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.640252 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.710856 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.640252 0.710856 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.929035 0.876144 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.929035 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.876144 0.000000 0.000000]; 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The error in solving: 1.948149e-16 The error in solving: 5.044199e-16 The error in solving: 3.859048e-16 The error in solving: 3.845925e-16 The error in solving: 1.338325e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a random diagonal and a density of 0.750000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.946214 0.093056 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.946214 0.000000 -0.509907 0.781287 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.093056 0.509907 0.000000 0.238631 -0.765077 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.781287 -0.238631 0.000000 0.741899 0.555254 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.765077 -0.741899 0.000000 0.707297 0.285294 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.555254 -0.707297 0.000000 -0.881218 0.720594 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.285294 0.881218 0.000000 0.000000 0.475214 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.720594 0.000000 0.000000 0.907519 0.186360 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.475214 -0.907519 0.000000 0.787710 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.186360 -0.787710 0.000000 0.836586 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.836586 0.000000 0.999702 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.999702 0.000000 -0.969606 0.154076 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.969606 0.000000 0.771450 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.154076 -0.771450 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.300996 -0.816050 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.300996 0.000000 0.484569 -0.743266 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.816050 -0.484569 0.000000 0.000000 -0.423029 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.743266 0.000000 0.000000 -0.747940 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.423029 0.747940 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 54 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 2 5 9 13 17 21 24 27 30 33 35 38 40 42 44 47 50 52 54 Column indices: 2 3 1 3 4 1 2 4 5 2 3 5 6 3 4 6 7 4 5 7 8 5 6 9 6 9 10 7 8 10 8 9 11 10 12 11 13 14 12 14 12 13 16 17 15 17 18 15 16 19 16 19 17 18 Off-diagonal values: 0.946214 0.093056 -0.946214 -0.509907 0.781287 -0.093056 0.509907 0.238631 -0.765077 -0.781287 -0.238631 0.741899 0.555254 0.765077 -0.741899 0.707297 0.285294 -0.555254 -0.707297 -0.881218 0.720594 -0.285294 0.881218 0.475214 -0.720594 0.907519 0.186360 -0.475214 -0.907519 0.787710 -0.186360 -0.787710 0.836586 -0.836586 0.999702 -0.999702 -0.969606 0.154076 0.969606 0.771450 -0.154076 -0.771450 -0.300996 -0.816050 0.300996 0.484569 -0.743266 0.816050 -0.484569 -0.423029 0.743266 -0.747940 0.423029 0.747940 . - - - - - - - - - - - - - - - - - - - | . x x - - - - - - - - - - - - - - - - | o . o x - - - - - - - - - - - - - - - | o x . x o - - - - - - - - - - - - - - | | o o . x x - - - - - - - - - - - - - | | | x o . x x - - - - - - - - - - - - | | | | o o . o x - - - - - - - - - - - | | | | | o x . - x - - - - - - - - - - | | | | | | o | . x x - - - - - - - - - | | | | | | | o o . x - - - - - - - - - | | | | | | | | o o . x - - - - - - - - | | | | | | | | | | o . x - - - - - - - | | | | | | | | | | | o . o x - - - - - | | | | | | | | | | | | x . x - - - - - | | | | | | | | | | | | o o . - - - - - | | | | | | | | | | | | | | | . o o - - | | | | | | | | | | | | | | | x . x o - | | | | | | | | | | | | | | | x o . - o | | | | | | | | | | | | | | | | x | . o | | | | | | | | | | | | | | | | | x x . The error in solving: 5.274016e-16 The error in solving: 2.423651e-16 The error in solving: 5.742185e-16 The error in solving: 3.608225e-16 The error in solving: 4.712449e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.000000 -0.470132 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.470132 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.812691 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.812691 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.862304 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.862304 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.468686 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.468686 0.000000 0.936372 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.936372 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.311367 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.311367 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.178502 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.178502 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.924703 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.924703 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.859027 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.859027 0.000000 0.087608 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.087608 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 20 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 3 4 5 6 7 9 10 10 11 12 13 14 14 15 16 17 19 20 Column indices: 1 0 3 2 5 4 7 6 8 7 11 10 13 12 16 15 18 17 19 18 Off-diagonal values: -0.470132 0.470132 0.812691 -0.812691 0.862304 -0.862304 0.468686 -0.468686 0.936372 -0.936372 0.311367 -0.311367 0.178502 -0.178502 -0.924703 0.924703 0.859027 -0.859027 0.087608 -0.087608 . o - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | | . x - - - - - - - - - - - - - - - - | | o . - - - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | | o . - - - - - - - - - - - - - - | | | | | | . x - - - - - - - - - - - - | | | | | | o . x - - - - - - - - - - - | | | | | | | o . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . x - - - - - - - - | | | | | | | | | | o . - - - - - - - - | | | | | | | | | | | | . x - - - - - - | | | | | | | | | | | | o . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . o - - - | | | | | | | | | | | | | | | x . - - - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | | o . x | | | | | | | | | | | | | | | | | | o . The error in solving: 3.191891e-16 The error in solving: 2.513374e-16 The error in solving: 1.494683e-16 The error in solving: 2.719480e-16 The error in solving: 5.440773e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.945663 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.945663 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.235072 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.235072 0.000000 0.784190 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.784190 0.000000 0.395063 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.395063 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000711 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.000711 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.560259 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.560259 0.000000 0.363802 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.363802 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.064391 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.064391 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 16 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 2 2 3 5 7 8 8 9 10 10 10 11 13 14 14 15 16 16 Column indices: 2 1 5 4 6 5 7 6 10 9 14 13 15 14 18 17 Off-diagonal values: -0.945663 0.945663 0.235072 -0.235072 0.784190 -0.784190 0.395063 -0.395063 0.000711 -0.000711 0.560259 -0.560259 0.363802 -0.363802 -0.064391 0.064391 . - - - - - - - - - - - - - - - - - - - | . o - - - - - - - - - - - - - - - - - | x . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | | o . x - - - - - - - - - - - - - | | | | | o . x - - - - - - - - - - - - | | | | | | o . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . x - - - - - - - - - | | | | | | | | | o . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . x - - - - - | | | | | | | | | | | | | o . x - - - - | | | | | | | | | | | | | | o . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . o - | | | | | | | | | | | | | | | | | x . - | | | | | | | | | | | | | | | | | | | . The error in solving: 4.745032e-16 The error in solving: 5.253091e-16 The error in solving: 2.309724e-16 The error in solving: 6.938894e-17 The error in solving: 2.155529e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.000000 0.373090 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.373090 0.000000 -0.108005 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.108005 0.000000 -0.611979 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.611979 0.000000 -0.023444 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.023444 0.000000 0.632110 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.632110 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.521514 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.521514 0.000000 -0.476388 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.476388 0.000000 0.827246 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.827246 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.485128 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.485128 0.000000 0.506773 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.506773 0.000000 -0.625507 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.625507 0.000000 -0.572011 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.572011 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.068186 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.068186 0.000000 -0.815423 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.815423 0.000000 -0.381261 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.381261 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 30 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 5 7 9 10 11 13 15 16 16 17 19 21 23 24 25 27 29 30 Column indices: 1 0 2 1 3 2 4 3 5 4 7 6 8 7 9 8 12 11 13 12 14 13 15 14 17 16 18 17 19 18 Off-diagonal values: 0.373090 -0.373090 -0.108005 0.108005 -0.611979 0.611979 -0.023444 0.023444 0.632110 -0.632110 -0.521514 0.521514 -0.476388 0.476388 0.827246 -0.827246 0.485128 -0.485128 0.506773 -0.506773 -0.625507 0.625507 -0.572011 0.572011 -0.068186 0.068186 -0.815423 0.815423 -0.381261 0.381261 . x - - - - - - - - - - - - - - - - - - o . o - - - - - - - - - - - - - - - - - | x . o - - - - - - - - - - - - - - - - | | x . o - - - - - - - - - - - - - - - | | | x . x - - - - - - - - - - - - - - | | | | o . - - - - - - - - - - - - - - | | | | | | . o - - - - - - - - - - - - | | | | | | x . o - - - - - - - - - - - | | | | | | | x . x - - - - - - - - - - | | | | | | | | o . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | o . x - - - - - - | | | | | | | | | | | | o . o - - - - - | | | | | | | | | | | | | x . o - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | | . o - - | | | | | | | | | | | | | | | | x . o - | | | | | | | | | | | | | | | | | x . o | | | | | | | | | | | | | | | | | | x . The error in solving: 3.886400e-16 The error in solving: 6.109380e-16 The error in solving: 2.618456e-16 The error in solving: 1.415262e-16 The error in solving: 5.606781e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.527223 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.527223 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.978804 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.978804 0.000000 0.000000 0.955412 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.955412 0.000000 -0.956501 0.475834 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.956501 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.475834 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.191736 0.760276 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.191736 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.760276 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.247590 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.247590 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 16 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 1 2 2 3 3 5 8 9 10 12 13 14 14 14 15 16 16 16 Column indices: 3 2 7 5 8 7 9 10 8 8 12 13 11 11 17 16 Off-diagonal values: 0.527223 -0.527223 -0.978804 0.978804 0.955412 -0.955412 -0.956501 0.475834 0.956501 -0.475834 -0.191736 0.760276 0.191736 -0.760276 0.247590 -0.247590 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . x - - - - - - - - - - - - - - - - | | o . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - o - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | x | . x - - - - - - - - - - - | | | | | | | o . o x - - - - - - - - - | | | | | | | | x . - - - - - - - - - - | | | | | | | | o | . - - - - - - - - - | | | | | | | | | | | . o x - - - - - - | | | | | | | | | | | x . - - - - - - - | | | | | | | | | | | o | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | o . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.273812e-16 The error in solving: 4.611103e-16 The error in solving: 1.576595e-16 The error in solving: 3.613569e-16 The error in solving: 1.271920e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.500000 [ 0.000000 -0.052381 0.481429 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.052381 0.000000 0.857388 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.481429 -0.857388 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.565005 -0.436042 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.565005 0.000000 0.555081 -0.762155 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.436042 -0.555081 0.000000 0.035170 -0.166444 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.762155 -0.035170 0.000000 0.956642 0.053859 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.166444 -0.956642 0.000000 0.000000 -0.667501 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.053859 0.000000 0.000000 0.303743 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.667501 -0.303743 0.000000 -0.309489 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.309489 0.000000 0.940531 -0.381418 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.940531 0.000000 -0.146934 -0.155336 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.381418 0.146934 0.000000 -0.060725 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.155336 0.060725 0.000000 0.000000 0.254154 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.254154 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.137130 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.406743 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.137130 0.406743 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 44 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 4 6 6 8 11 15 19 22 24 27 30 33 36 39 39 40 41 42 44 Column indices: 1 2 0 2 0 1 5 6 4 6 7 4 5 7 8 5 6 8 9 6 7 10 7 10 8 9 11 10 12 13 11 13 14 11 12 14 12 13 16 14 19 19 17 18 Off-diagonal values: -0.052381 0.481429 0.052381 0.857388 -0.481429 -0.857388 -0.565005 -0.436042 0.565005 0.555081 -0.762155 0.436042 -0.555081 0.035170 -0.166444 0.762155 -0.035170 0.956642 0.053859 0.166444 -0.956642 -0.667501 -0.053859 0.303743 0.667501 -0.303743 -0.309489 0.309489 0.940531 -0.381418 -0.940531 -0.146934 -0.155336 0.381418 0.146934 -0.060725 0.155336 0.060725 0.254154 -0.254154 0.137130 -0.406743 -0.137130 0.406743 . o x - - - - - - - - - - - - - - - - - x . x - - - - - - - - - - - - - - - - - o o . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . o o - - - - - - - - - - - - - | | | | x . x o - - - - - - - - - - - - | | | | x o . x o - - - - - - - - - - - | | | | | x o . x x - - - - - - - - - - | | | | | | x o . - o - - - - - - - - - | | | | | | | o | . x - - - - - - - - - | | | | | | | | x o . o - - - - - - - - | | | | | | | | | | x . x o - - - - - - | | | | | | | | | | | o . o o - - - - - | | | | | | | | | | | x x . o - - - - - | | | | | | | | | | | | x x . - x - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | o | . - - - | | | | | | | | | | | | | | | | | . - x | | | | | | | | | | | | | | | | | | . o | | | | | | | | | | | | | | | | | o x . The error in solving: 2.761645e-16 The error in solving: 1.694000e-16 The error in solving: 5.353864e-16 The error in solving: 4.972941e-16 The error in solving: 3.787899e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a dense diagonal and a density of 0.750000 [ 0.000000 0.000000 0.281937 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.973234 -0.513438 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.281937 -0.973234 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.513438 0.000000 0.000000 -0.702880 -0.522680 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.702880 0.000000 -0.977380 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.522680 0.977380 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.607635 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.607635 0.000000 0.766317 0.658544 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.766317 0.000000 0.000000 0.676896 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.658544 0.000000 0.000000 0.000000 0.202885 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.676896 0.000000 0.000000 0.162032 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.202885 -0.162032 0.000000 0.278566 0.975785 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.278566 0.000000 -0.133734 -0.470311 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.975785 0.133734 0.000000 0.306679 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.470311 -0.306679 0.000000 0.434770 -0.914807 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.434770 0.000000 0.000000 -0.119241 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.914807 0.000000 0.000000 0.000000 0.112302 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.119241 0.000000 0.000000 -0.778526 0.382502 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.112302 0.778526 0.000000 -0.919560 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.382502 0.919560 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 48 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 5 8 10 12 13 16 18 20 22 26 29 32 36 38 40 43 46 48 Column indices: 2 2 3 0 1 1 4 5 3 5 3 4 7 6 8 9 7 10 7 11 8 11 9 10 12 13 11 13 14 11 12 14 12 13 15 16 14 17 14 18 15 18 19 16 17 19 17 18 Off-diagonal values: 0.281937 0.973234 -0.513438 -0.281937 -0.973234 0.513438 -0.702880 -0.522680 0.702880 -0.977380 0.522680 0.977380 -0.607635 0.607635 0.766317 0.658544 -0.766317 0.676896 -0.658544 0.202885 -0.676896 0.162032 -0.202885 -0.162032 0.278566 0.975785 -0.278566 -0.133734 -0.470311 -0.975785 0.133734 0.306679 0.470311 -0.306679 0.434770 -0.914807 -0.434770 -0.119241 0.914807 0.112302 0.119241 -0.778526 0.382502 -0.112302 0.778526 -0.919560 -0.382502 0.919560 . - x - - - - - - - - - - - - - - - - - | . x o - - - - - - - - - - - - - - - - o o . - - - - - - - - - - - - - - - - - | x | . o o - - - - - - - - - - - - - - | | | x . o - - - - - - - - - - - - - - | | | x x . - - - - - - - - - - - - - - | | | | | | . o - - - - - - - - - - - - | | | | | | x . x x - - - - - - - - - - | | | | | | | o . - x - - - - - - - - - | | | | | | | o | . - x - - - - - - - - | | | | | | | | o | . x - - - - - - - - | | | | | | | | | o o . x x - - - - - - | | | | | | | | | | | o . o o - - - - - | | | | | | | | | | | o x . x - - - - - | | | | | | | | | | | | x o . x o - - - | | | | | | | | | | | | | | o . - o - - | | | | | | | | | | | | | | x | . - x - | | | | | | | | | | | | | | | x | . o x | | | | | | | | | | | | | | | | o x . o | | | | | | | | | | | | | | | | | o x . The error in solving: 2.775774e-16 The error in solving: 2.740643e-16 The error in solving: 5.775665e-16 The error in solving: 6.621465e-16 The error in solving: 3.895681e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.173494 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.173494 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.969079 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.969079 0.000000 0.649936 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.649936 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 6 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 1 2 2 2 2 2 2 2 2 2 2 3 5 6 6 6 6 Column indices: 4 3 15 14 16 15 Off-diagonal values: -0.173494 0.173494 0.969079 -0.969079 0.649936 -0.649936 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . o - - - - - - - - - - - - - - - | | | x . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | | o . x - - - | | | | | | | | | | | | | | | o . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 0.000000e+00 The error in solving: 2.305551e-16 The error in solving: 2.220446e-16 The error in solving: 5.353302e-16 The error in solving: 8.327124e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.611375 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.611375 0.000000 -0.011581 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.011581 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.084118 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.084118 0.000000 -0.095658 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.095658 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.532510 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.532510 0.000000 0.780598 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.780598 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.674158 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.674158 0.000000 0.376570 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.376570 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.705897 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.705897 0.000000 0.956519 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.956519 0.000000 -0.671020 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.671020 0.000000 0.548110 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.548110 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 24 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 3 4 4 5 7 8 9 11 12 13 15 16 16 17 19 21 23 24 Column indices: 2 1 3 2 6 5 7 6 9 8 10 9 12 11 13 12 16 15 17 16 18 17 19 18 Off-diagonal values: 0.611375 -0.611375 -0.011581 0.011581 0.084118 -0.084118 -0.095658 0.095658 0.532510 -0.532510 0.780598 -0.780598 -0.674158 0.674158 0.376570 -0.376570 0.705897 -0.705897 0.956519 -0.956519 -0.671020 0.671020 0.548110 -0.548110 . - - - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | o . o - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | | o . o - - - - - - - - - - - - | | | | | | x . - - - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | | o . x - - - - - - - - - | | | | | | | | | o . - - - - - - - - - | | | | | | | | | | | . o - - - - - - - | | | | | | | | | | | x . x - - - - - - | | | | | | | | | | | | o . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | o . x - - | | | | | | | | | | | | | | | | o . o - | | | | | | | | | | | | | | | | | x . x | | | | | | | | | | | | | | | | | | o . The error in solving: 3.002225e-16 The error in solving: 5.396301e-16 The error in solving: 3.042054e-16 The error in solving: 2.237726e-16 The error in solving: 1.694000e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 -0.077341 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.077341 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.063704 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.063704 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.190394 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.190394 0.000000 -0.176338 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.176338 0.000000 -0.958269 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.958269 0.000000 0.409484 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.409484 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.511963 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.511963 0.000000 0.515355 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.515355 0.000000 0.261620 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.261620 0.000000 0.984753 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.984753 0.000000 0.034425 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.034425 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.564480 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.564480 0.000000 -0.572274 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.572274 0.000000 0.964659 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.964659 0.000000 0.976543 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.976543 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 30 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 3 4 5 7 9 11 12 13 15 17 19 21 22 23 25 27 29 30 Column indices: 1 0 3 2 5 4 6 5 7 6 8 7 10 9 11 10 12 11 13 12 14 13 16 15 17 16 18 17 19 18 Off-diagonal values: -0.077341 0.077341 -0.063704 0.063704 0.190394 -0.190394 -0.176338 0.176338 -0.958269 0.958269 0.409484 -0.409484 0.511963 -0.511963 0.515355 -0.515355 0.261620 -0.261620 0.984753 -0.984753 0.034425 -0.034425 0.564480 -0.564480 -0.572274 0.572274 0.964659 -0.964659 0.976543 -0.976543 . o - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | | . o - - - - - - - - - - - - - - - - | | x . - - - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | | o . o - - - - - - - - - - - - - | | | | | x . o - - - - - - - - - - - - | | | | | | x . x - - - - - - - - - - - | | | | | | | o . - - - - - - - - - - - | | | | | | | | | . x - - - - - - - - - | | | | | | | | | o . x - - - - - - - - | | | | | | | | | | o . x - - - - - - - | | | | | | | | | | | o . x - - - - - - | | | | | | | | | | | | o . x - - - - - | | | | | | | | | | | | | o . - - - - - | | | | | | | | | | | | | | | . x - - - | | | | | | | | | | | | | | | o . o - - | | | | | | | | | | | | | | | | x . x - | | | | | | | | | | | | | | | | | o . x | | | | | | | | | | | | | | | | | | o . The error in solving: 3.331392e-16 The error in solving: 5.662882e-16 The error in solving: 3.245741e-16 The error in solving: 3.682193e-16 The error in solving: 5.580528e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.757220 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.233365 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.757220 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.233365 0.000000 0.000000 0.000000 0.878661 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.384003 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.878661 -0.384003 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.262358 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.262358 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.365242 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.365242 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.332787 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.332787 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.262559 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.262559 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 16 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 2 3 5 6 8 8 9 9 10 11 12 13 14 15 15 16 16 16 Column indices: 3 4 1 2 6 6 4 5 10 8 12 11 14 13 17 15 Off-diagonal values: -0.757220 0.233365 0.757220 -0.233365 0.878661 0.384003 -0.878661 -0.384003 -0.262358 0.262358 0.365242 -0.365242 -0.332787 0.332787 0.262559 -0.262559 . - - - - - - - - - - - - - - - - - - - | . - o - - - - - - - - - - - - - - - - | | . - x - - - - - - - - - - - - - - - | x | . - - - - - - - - - - - - - - - - | | o | . - x - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | o o . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - o - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | x | . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | o . - - - - - - - | | | | | | | | | | | | | . o - - - - - | | | | | | | | | | | | | x . - - - - - | | | | | | | | | | | | | | | . - x - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | o | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.665335e-16 The error in solving: 4.024558e-16 The error in solving: 5.360492e-16 The error in solving: 3.330669e-16 The error in solving: 2.897767e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.933776 -0.282655 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.933776 0.000000 -0.556044 0.370972 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.282655 0.556044 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.370972 0.000000 0.000000 0.000000 -0.268658 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.189726 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.268658 -0.189726 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.770723 0.417635 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.770723 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.417635 0.000000 0.000000 -0.522721 0.398654 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.522721 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.398654 0.000000 0.000000 0.000000 0.713437 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.716853 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.713437 0.716853 0.000000 0.000000 -0.178158 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.645468 0.682799 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.178158 0.645468 0.000000 0.000000 0.524278 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.682799 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.524278 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 32 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 2 5 7 9 10 12 14 15 18 19 21 22 25 27 30 31 32 Column indices: 4 5 3 5 6 3 4 4 8 8 6 7 10 11 9 9 12 13 11 11 15 15 13 14 17 17 18 15 16 19 16 17 Off-diagonal values: -0.933776 -0.282655 0.933776 -0.556044 0.370972 0.282655 0.556044 -0.370972 -0.268658 0.189726 0.268658 -0.189726 -0.770723 0.417635 0.770723 -0.417635 -0.522721 0.398654 0.522721 -0.398654 0.713437 -0.716853 -0.713437 0.716853 -0.178158 -0.645468 0.682799 0.178158 0.645468 0.524278 -0.682799 -0.524278 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . o o - - - - - - - - - - - - - - | | | x . o x - - - - - - - - - - - - - | | | x x . - - - - - - - - - - - - - - | | | | o | . - o - - - - - - - - - - - | | | | | | | . x - - - - - - - - - - - | | | | | | x o . - - - - - - - - - - - | | | | | | | | | . o x - - - - - - - - | | | | | | | | | x . - - - - - - - - - | | | | | | | | | o | . o x - - - - - - | | | | | | | | | | | x . - - - - - - - | | | | | | | | | | | o | . - x - - - - | | | | | | | | | | | | | | . o - - - - | | | | | | | | | | | | | o x . - o - - | | | | | | | | | | | | | | | | . o x - | | | | | | | | | | | | | | | x x . - x | | | | | | | | | | | | | | | | o | . - | | | | | | | | | | | | | | | | | o | . The error in solving: 5.309954e-16 The error in solving: 2.747662e-16 The error in solving: 5.640599e-16 The error in solving: 3.392804e-16 The error in solving: 1.401588e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a uniform (-1, 1) distribution with a zero diagonal and a density of 0.750000 [ 0.000000 -0.686961 0.316371 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.686961 0.000000 -0.520379 0.921131 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.316371 0.520379 0.000000 -0.433178 -0.612676 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.921131 0.433178 0.000000 0.479908 0.595638 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.612676 -0.479908 0.000000 0.129406 0.891332 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.595638 -0.129406 0.000000 0.000000 0.737137 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.891332 0.000000 0.000000 -0.003250 -0.665109 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.737137 0.003250 0.000000 -0.742855 -0.884486 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.665109 0.742855 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.884486 0.000000 0.000000 0.557907 0.321486 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.557907 0.000000 0.010434 0.036763 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.321486 -0.010434 0.000000 0.364051 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.036763 -0.364051 0.000000 -0.231343 -0.061763 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.231343 0.000000 -0.690202 -0.935330 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.061763 0.690202 0.000000 0.404558 -0.732331 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.935330 -0.404558 0.000000 -0.253275 -0.399491 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.732331 0.253275 0.000000 0.528775 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.399491 -0.528775 0.000000 0.803919 -0.152365 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.803919 0.000000 0.461848 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.152365 -0.461848 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 64 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 5 9 13 17 20 23 27 29 32 35 38 42 45 49 53 56 60 62 64 Column indices: 1 2 0 2 3 0 1 3 4 1 2 4 5 2 3 5 6 3 4 7 4 7 8 5 6 8 9 6 7 7 10 11 9 11 12 9 10 12 10 11 13 14 12 14 15 12 13 15 16 13 14 16 17 14 15 17 15 16 18 19 17 19 17 18 Off-diagonal values: -0.686961 0.316371 0.686961 -0.520379 0.921131 -0.316371 0.520379 -0.433178 -0.612676 -0.921131 0.433178 0.479908 0.595638 0.612676 -0.479908 0.129406 0.891332 -0.595638 -0.129406 0.737137 -0.891332 -0.003250 -0.665109 -0.737137 0.003250 -0.742855 -0.884486 0.665109 0.742855 0.884486 0.557907 0.321486 -0.557907 0.010434 0.036763 -0.321486 -0.010434 0.364051 -0.036763 -0.364051 -0.231343 -0.061763 0.231343 -0.690202 -0.935330 0.061763 0.690202 0.404558 -0.732331 0.935330 -0.404558 -0.253275 -0.399491 0.732331 0.253275 0.528775 0.399491 -0.528775 0.803919 -0.152365 -0.803919 0.461848 0.152365 -0.461848 . o x - - - - - - - - - - - - - - - - - x . o x - - - - - - - - - - - - - - - - o x . o o - - - - - - - - - - - - - - - | o x . x x - - - - - - - - - - - - - - | | x o . x x - - - - - - - - - - - - - | | | o o . - x - - - - - - - - - - - - | | | | o | . o o - - - - - - - - - - - | | | | | o x . o o - - - - - - - - - - | | | | | | x x . - - - - - - - - - - - | | | | | | | x | . x x - - - - - - - - | | | | | | | | | o . x x - - - - - - - | | | | | | | | | o o . x - - - - - - - | | | | | | | | | | o o . o o - - - - - | | | | | | | | | | | | x . o o - - - - | | | | | | | | | | | | x x . x o - - - | | | | | | | | | | | | | x o . o o - - | | | | | | | | | | | | | | x x . x - - | | | | | | | | | | | | | | | x o . x o | | | | | | | | | | | | | | | | | o . x | | | | | | | | | | | | | | | | | x o . The error in solving: 4.744905e-16 The error in solving: 4.815412e-16 The error in solving: 6.544668e-16 The error in solving: 4.755548e-16 The error in solving: 4.878985e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.244954 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.244954 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.204349 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.204349 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.581982 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.581982 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.545267 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.545267 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.823050 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.823050 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 10 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 0 0 1 2 2 3 4 4 5 6 7 8 8 8 8 9 10 Column indices: 6 5 9 8 12 11 14 13 19 18 Off-diagonal values: 1.244954 -1.244954 -1.204349 1.204349 0.581982 -0.581982 0.545267 -0.545267 0.823050 -0.823050 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | | o . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . o - - - - - - - - - - | | | | | | | | x . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | o . - - - - - - - | | | | | | | | | | | | | . x - - - - - | | | | | | | | | | | | | o . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | o . The error in solving: 5.585702e-16 The error in solving: 4.603297e-16 The error in solving: 4.002966e-16 The error in solving: 4.710277e-16 The error in solving: 8.783938e-17 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.479034 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.479034 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.471333 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.471333 0.000000 0.407161 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.407161 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.213962 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.213962 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.053805 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.053805 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.159611 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.159611 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.042154 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.042154 0.000000 -0.582749 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.582749 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 16 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 2 2 2 2 3 5 6 7 8 9 10 10 11 12 13 15 16 16 Column indices: 2 1 7 6 8 7 10 9 12 11 15 14 17 16 18 17 Off-diagonal values: 1.479034 -1.479034 -1.471333 1.471333 0.407161 -0.407161 -0.213962 0.213962 0.053805 -0.053805 -1.159611 1.159611 0.042154 -0.042154 -0.582749 0.582749 . - - - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | o . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . o - - - - - - - - - - - - | | | | | | x . x - - - - - - - - - - - | | | | | | | o . - - - - - - - - - - - | | | | | | | | | . o - - - - - - - - - | | | | | | | | | x . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | o . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . o - - - - | | | | | | | | | | | | | | x . - - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | o . o - | | | | | | | | | | | | | | | | | x . - | | | | | | | | | | | | | | | | | | | . The error in solving: 4.041422e-16 The error in solving: 1.755417e-16 The error in solving: 4.965068e-16 The error in solving: 2.326341e-16 The error in solving: 6.083125e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.750000 [ 0.000000 -0.712963 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.712963 0.000000 -0.357147 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.357147 0.000000 2.130384 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.130384 0.000000 0.764863 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.764863 0.000000 0.614734 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.614734 0.000000 -0.597501 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.597501 0.000000 1.246996 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.246996 0.000000 0.576413 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.576413 0.000000 -0.548373 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.548373 0.000000 -0.832865 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.832865 0.000000 0.729899 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.729899 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.379562 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.379562 0.000000 -0.344983 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.344983 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.314771 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.314771 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 28 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 5 7 9 11 13 15 17 19 21 22 22 22 22 23 25 26 27 28 Column indices: 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 16 15 17 16 19 18 Off-diagonal values: -0.712963 0.712963 -0.357147 0.357147 2.130384 -2.130384 0.764863 -0.764863 0.614734 -0.614734 -0.597501 0.597501 1.246996 -1.246996 0.576413 -0.576413 -0.548373 0.548373 -0.832865 0.832865 0.729899 -0.729899 -0.379562 0.379562 -0.344983 0.344983 -2.314771 2.314771 . o - - - - - - - - - - - - - - - - - - x . o - - - - - - - - - - - - - - - - - | x . x - - - - - - - - - - - - - - - - | | o . x - - - - - - - - - - - - - - - | | | o . x - - - - - - - - - - - - - - | | | | o . o - - - - - - - - - - - - - | | | | | x . x - - - - - - - - - - - - | | | | | | o . x - - - - - - - - - - - | | | | | | | o . o - - - - - - - - - - | | | | | | | | x . o - - - - - - - - - | | | | | | | | | x . x - - - - - - - - | | | | | | | | | | o . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . o - - - | | | | | | | | | | | | | | | x . o - - | | | | | | | | | | | | | | | | x . - - | | | | | | | | | | | | | | | | | | . o | | | | | | | | | | | | | | | | | | x . The error in solving: 6.131407e-16 The error in solving: 5.181918e-16 The error in solving: 2.939422e-16 The error in solving: 6.407896e-16 The error in solving: 6.161273e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.480905 0.542734 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.480905 0.000000 0.605657 -0.062136 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.542734 -0.605657 0.000000 0.524955 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.062136 -0.524955 0.000000 1.515205 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.515205 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.872050 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.872050 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.723118 1.450994 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.723118 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.450994 0.000000 0.000000 0.452680 1.026367 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.452680 0.000000 0.811627 1.385906 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.026367 -0.811627 0.000000 0.000000 -1.051082 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.385906 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.051082 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.079813 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.079813 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 30 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 2 5 8 11 12 13 14 16 17 20 23 26 27 28 28 29 30 Column indices: 4 5 3 5 6 3 4 6 4 5 7 6 9 8 11 12 10 10 13 14 12 14 15 12 13 16 13 14 19 18 Off-diagonal values: 0.480905 0.542734 -0.480905 0.605657 -0.062136 -0.542734 -0.605657 0.524955 0.062136 -0.524955 1.515205 -1.515205 -0.872050 0.872050 -0.723118 1.450994 0.723118 -1.450994 0.452680 1.026367 -0.452680 0.811627 1.385906 -1.026367 -0.811627 -1.051082 -1.385906 1.051082 0.079813 -0.079813 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . x x - - - - - - - - - - - - - - | | | o . x o - - - - - - - - - - - - - | | | o o . x - - - - - - - - - - - - - | | | | x o . x - - - - - - - - - - - - | | | | | | o . - - - - - - - - - - - - | | | | | | | | . o - - - - - - - - - - | | | | | | | | x . - - - - - - - - - - | | | | | | | | | | . o x - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | o | . x x - - - - - | | | | | | | | | | | | o . x x - - - - | | | | | | | | | | | | o o . - o - - - | | | | | | | | | | | | | o | . - - - - | | | | | | | | | | | | | | x | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | o . The error in solving: 6.977644e-16 The error in solving: 3.925231e-16 The error in solving: 5.282682e-16 The error in solving: 3.376612e-16 The error in solving: 6.568168e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.500000 [ 0.000000 -0.780135 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.780135 0.000000 0.512228 0.096496 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.512228 0.000000 0.000000 -0.536085 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.096496 0.000000 0.000000 -1.259293 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.536085 1.259293 0.000000 0.000000 0.088763 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.092001 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.088763 -0.092001 0.000000 1.483015 0.618981 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.483015 0.000000 0.000000 -0.495103 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.618981 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.495103 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.277974 0.072052 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.277974 0.000000 -0.290084 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.072052 0.290084 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.216034 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.216034 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.884773 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.884773 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 30 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 4 6 8 11 12 16 18 19 20 20 22 24 26 27 27 28 28 29 30 Column indices: 1 0 2 3 1 4 1 4 2 3 6 6 4 5 7 8 6 9 6 7 12 13 11 13 11 12 16 14 19 18 Off-diagonal values: -0.780135 0.780135 0.512228 0.096496 -0.512228 -0.536085 -0.096496 -1.259293 0.536085 1.259293 0.088763 0.092001 -0.088763 -0.092001 1.483015 0.618981 -1.483015 -0.495103 -0.618981 0.495103 -0.277974 0.072052 0.277974 -0.290084 -0.072052 0.290084 1.216034 -1.216034 1.884773 -1.884773 . o - - - - - - - - - - - - - - - - - - x . x x - - - - - - - - - - - - - - - - | o . - o - - - - - - - - - - - - - - - | o | . o - - - - - - - - - - - - - - - | | x x . - x - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | o o . x x - - - - - - - - - - - | | | | | | o . - o - - - - - - - - - - | | | | | | o | . - - - - - - - - - - - | | | | | | | x | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . o x - - - - - - | | | | | | | | | | | x . o - - - - - - | | | | | | | | | | | o x . - - - - - - | | | | | | | | | | | | | | . - x - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | o | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | o . The error in solving: 3.725256e-16 The error in solving: 2.419675e-16 The error in solving: 5.125396e-16 The error in solving: 3.424750e-16 The error in solving: 3.886749e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a standard normal distribution with a random diagonal and a density of 0.750000 [ 0.000000 -0.076647 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.076647 0.000000 -1.358224 -0.646384 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.358224 0.000000 0.000000 -2.057488 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.646384 0.000000 0.000000 0.139188 -1.032786 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.057488 -0.139188 0.000000 0.000000 0.050885 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.032786 0.000000 0.000000 -0.659556 -0.745356 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.050885 0.659556 0.000000 1.545528 0.302745 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.745356 -1.545528 0.000000 0.000000 -2.023549 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.302745 0.000000 0.000000 0.000000 -0.481785 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.023549 0.000000 0.000000 0.480142 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.481785 -0.480142 0.000000 -1.299737 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.299737 0.000000 0.082047 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.082047 0.000000 0.726611 -1.052383 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.726611 0.000000 0.893699 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.052383 -0.893699 0.000000 1.555548 0.115268 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.555548 0.000000 -1.084927 -1.622981 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.115268 1.084927 0.000000 0.107605 -0.212681 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.622981 -0.107605 0.000000 -1.916343 0.708877 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.212681 1.916343 0.000000 0.297051 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.708877 -0.297051 0.000000]; 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The error in solving: 2.095859e-16 The error in solving: 7.557026e-16 The error in solving: 5.297876e-16 The error in solving: 7.551608e-16 The error in solving: 5.633767e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.250000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.331449 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.331449 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.092670 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.092670 0.000000 -2.135207 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.135207 0.000000 0.496519 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.496519 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 8 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 0 0 0 1 2 3 5 7 8 8 8 8 8 8 8 8 8 8 8 Column indices: 5 4 7 6 8 7 9 8 Off-diagonal values: 0.331449 -0.331449 -0.092670 0.092670 -2.135207 2.135207 0.496519 -0.496519 . - - - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . x - - - - - - - - - - - - - - | | | | o . - - - - - - - - - - - - - - | | | | | | . o - - - - - - - - - - - - | | | | | | x . o - - - - - - - - - - - | | | | | | | x . x - - - - - - - - - - | | | | | | | | o . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | | | . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.797158e-17 The error in solving: 5.438960e-16 The error in solving: 3.376612e-16 The error in solving: 2.937374e-16 The error in solving: 1.922963e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.500000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.841296 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.841296 0.000000 -1.743728 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.743728 0.000000 -0.440914 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.440914 0.000000 -0.761021 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.761021 0.000000 -0.757129 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.757129 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.697331 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.697331 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.135867 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.135867 0.000000 -0.704666 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.704666 0.000000 -2.134214 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.134214 0.000000 -0.889138 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.889138 0.000000 1.093980 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.093980 0.000000 -0.487788 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.487788 0.000000 0.526330 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.526330 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 26 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 3 5 7 9 10 11 12 12 12 12 13 15 17 19 21 23 25 26 Column indices: 2 1 3 2 4 3 5 4 6 5 8 7 13 12 14 13 15 14 16 15 17 16 18 17 19 18 Off-diagonal values: 0.841296 -0.841296 -1.743728 1.743728 -0.440914 0.440914 -0.761021 0.761021 -0.757129 0.757129 -0.697331 0.697331 -1.135867 1.135867 -0.704666 0.704666 -2.134214 2.134214 -0.889138 0.889138 1.093980 -1.093980 -0.487788 0.487788 0.526330 -0.526330 . - - - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | o . o - - - - - - - - - - - - - - - - | | x . o - - - - - - - - - - - - - - - | | | x . o - - - - - - - - - - - - - - | | | | x . o - - - - - - - - - - - - - | | | | | x . - - - - - - - - - - - - - | | | | | | | . o - - - - - - - - - - - | | | | | | | x . - - - - - - - - - - - | | | | | | | | | . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . - - - - - - - - | | | | | | | | | | | | . o - - - - - - | | | | | | | | | | | | x . o - - - - - | | | | | | | | | | | | | x . o - - - - | | | | | | | | | | | | | | x . o - - - | | | | | | | | | | | | | | | x . x - - | | | | | | | | | | | | | | | | o . o - | | | | | | | | | | | | | | | | | x . x | | | | | | | | | | | | | | | | | | o . The error in solving: 3.201681e-16 The error in solving: 1.618414e-16 The error in solving: 2.790264e-16 The error in solving: 3.399350e-16 The error in solving: 5.324895e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.750000 [ 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.129888 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.129888 0.000000 0.579590 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.579590 0.000000 -0.959971 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.959971 0.000000 1.049476 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.049476 0.000000 2.248629 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.248629 0.000000 0.916519 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.916519 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.640094 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.640094 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.679945 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.679945 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.359729 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.359729 0.000000 -0.231428 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.231428 0.000000 -0.819132 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.819132 0.000000 -0.516508 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.516508 0.000000 0.322239 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.322239 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 26 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 0 1 3 5 7 9 11 12 13 14 15 16 16 17 19 21 23 25 26 26 Column indices: 2 1 3 2 4 3 5 4 6 5 7 6 9 8 11 10 14 13 15 14 16 15 17 16 18 17 Off-diagonal values: 0.129888 -0.129888 0.579590 -0.579590 -0.959971 0.959971 1.049476 -1.049476 2.248629 -2.248629 0.916519 -0.916519 -1.640094 1.640094 -0.679945 0.679945 -0.359729 0.359729 -0.231428 0.231428 -0.819132 0.819132 -0.516508 0.516508 0.322239 -0.322239 . - - - - - - - - - - - - - - - - - - - | . x - - - - - - - - - - - - - - - - - | o . x - - - - - - - - - - - - - - - - | | o . o - - - - - - - - - - - - - - - | | | x . x - - - - - - - - - - - - - - | | | | o . x - - - - - - - - - - - - - | | | | | o . x - - - - - - - - - - - - | | | | | | o . - - - - - - - - - - - - | | | | | | | | . o - - - - - - - - - - | | | | | | | | x . - - - - - - - - - - | | | | | | | | | | . o - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . o - - - - - | | | | | | | | | | | | | x . o - - - - | | | | | | | | | | | | | | x . o - - - | | | | | | | | | | | | | | | x . o - - | | | | | | | | | | | | | | | | x . x - | | | | | | | | | | | | | | | | | o . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.831853e-16 The error in solving: 3.066489e-16 The error in solving: 3.692639e-16 The error in solving: 6.013363e-16 The error in solving: 2.859506e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.250000 [ 0.000000 0.244463 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.244463 0.000000 0.181825 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.181825 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.270701 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.270701 0.000000 1.570982 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.570982 0.000000 -0.141549 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.141549 0.000000 -1.912053 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.912053 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.660814 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.660814 0.000000 1.006641 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.006641 0.000000 0.000000 0.181083 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.181083 0.000000 0.000000 0.000000 0.794553 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.033262 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.794553 -2.033262 0.000000 0.000000 -1.099123 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.099123 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 24 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 4 4 4 5 7 9 11 12 12 13 15 17 17 19 20 23 23 24 Column indices: 1 0 2 1 6 5 7 6 8 7 9 8 12 11 13 12 15 13 17 17 15 16 19 17 Off-diagonal values: 0.244463 -0.244463 0.181825 -0.181825 0.270701 -0.270701 1.570982 -1.570982 -0.141549 0.141549 -1.912053 1.912053 0.660814 -0.660814 1.006641 -1.006641 0.181083 -0.181083 0.794553 2.033262 -0.794553 -2.033262 -1.099123 1.099123 . x - - - - - - - - - - - - - - - - - - o . x - - - - - - - - - - - - - - - - - | o . - - - - - - - - - - - - - - - - - | | | . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | | o . x - - - - - - - - - - - - | | | | | | o . o - - - - - - - - - - - | | | | | | | x . o - - - - - - - - - - | | | | | | | | x . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | o . x - - - - - - | | | | | | | | | | | | o . - x - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | o | . - x - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | o o . - o | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | x | . The error in solving: 3.376790e-16 The error in solving: 6.449813e-16 The error in solving: 4.775250e-16 The error in solving: 3.516999e-16 The error in solving: 5.661155e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.500000 [ 0.000000 0.000000 -1.913930 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.913930 0.000000 0.000000 -0.288892 -0.290195 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.288892 0.000000 0.000000 1.484999 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.290195 0.000000 0.000000 0.091759 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.484999 -0.091759 0.000000 0.734728 0.462463 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.734728 0.000000 -0.349621 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.462463 0.349621 0.000000 0.747567 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.747567 0.000000 -0.660769 1.137184 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.660769 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.137184 0.000000 0.000000 0.992155 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.992155 0.000000 -1.724245 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.724245 0.000000 0.442022 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.442022 0.000000 0.000000 0.751892 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.063093 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.751892 -1.063093 0.000000 0.000000 -0.693687 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.593356 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.693687 0.000000 0.000000 0.000000 0.812151 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.593356 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.812151 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 38 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 1 4 6 8 12 14 17 20 21 23 25 27 29 30 33 34 36 37 38 Column indices: 2 0 3 4 2 5 2 5 3 4 6 7 5 7 5 6 8 7 9 10 8 8 11 10 12 11 13 12 15 15 13 14 17 18 15 19 16 17 Off-diagonal values: -1.913930 1.913930 -0.288892 -0.290195 0.288892 1.484999 0.290195 0.091759 -1.484999 -0.091759 0.734728 0.462463 -0.734728 -0.349621 -0.462463 0.349621 0.747567 -0.747567 -0.660769 1.137184 0.660769 -1.137184 0.992155 -0.992155 -1.724245 1.724245 0.442022 -0.442022 0.751892 1.063093 -0.751892 -1.063093 -0.693687 0.593356 0.693687 0.812151 -0.593356 -0.812151 . - o - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - x | . o o - - - - - - - - - - - - - - - | | x . - x - - - - - - - - - - - - - - | | x | . x - - - - - - - - - - - - - - | | | o o . x x - - - - - - - - - - - - | | | | | o . o - - - - - - - - - - - - | | | | | o x . x - - - - - - - - - - - | | | | | | | o . o x - - - - - - - - - | | | | | | | | x . - - - - - - - - - - | | | | | | | | o | . x - - - - - - - - | | | | | | | | | | o . o - - - - - - - | | | | | | | | | | | x . x - - - - - - | | | | | | | | | | | | o . - x - - - - | | | | | | | | | | | | | | . x - - - - | | | | | | | | | | | | | o o . - o - - | | | | | | | | | | | | | | | | . - x - | | | | | | | | | | | | | | | x | . - x | | | | | | | | | | | | | | | | o | . - | | | | | | | | | | | | | | | | | o | . The error in solving: 3.651335e-16 The error in solving: 4.537421e-16 The error in solving: 6.033248e-16 The error in solving: 3.106269e-16 The error in solving: 3.646882e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a standard normal distribution with a dense diagonal and a density of 0.750000 [ 0.000000 0.499304 -2.351050 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.499304 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.351050 0.000000 0.000000 0.000000 1.116670 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 3.156832 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.116670 -3.156832 0.000000 0.696625 -0.850001 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.696625 0.000000 -0.436875 -0.773345 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.850001 0.436875 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.773345 0.000000 0.000000 0.000000 -2.064866 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.465684 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.064866 -0.465684 0.000000 0.779530 -0.343910 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.779530 0.000000 -1.866702 -0.578378 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.343910 1.866702 0.000000 0.000000 0.578731 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.578378 0.000000 0.000000 -1.318178 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.578731 1.318178 0.000000 0.533927 -1.553576 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.533927 0.000000 1.620171 -0.898988 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.553576 -1.620171 0.000000 -1.674254 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.898988 1.674254 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.420075 0.476376 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.420075 0.000000 1.396264 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.476376 -1.396264 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 48 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 3 5 6 10 13 15 17 18 22 25 28 30 34 37 40 42 44 46 48 Column indices: 1 2 0 0 4 4 2 3 5 6 4 6 7 4 5 5 9 9 7 8 10 11 9 11 12 9 10 13 10 13 11 12 14 15 13 15 16 13 14 16 14 15 18 19 17 19 17 18 Off-diagonal values: 0.499304 -2.351050 -0.499304 2.351050 1.116670 3.156832 -1.116670 -3.156832 0.696625 -0.850001 -0.696625 -0.436875 -0.773345 0.850001 0.436875 0.773345 -2.064866 0.465684 2.064866 -0.465684 0.779530 -0.343910 -0.779530 -1.866702 -0.578378 0.343910 1.866702 0.578731 0.578378 -1.318178 -0.578731 1.318178 0.533927 -1.553576 -0.533927 1.620171 -0.898988 1.553576 -1.620171 -1.674254 0.898988 1.674254 -1.420075 0.476376 1.420075 1.396264 -0.476376 -1.396264 . x o - - - - - - - - - - - - - - - - - o . - - - - - - - - - - - - - - - - - - x | . - x - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | o o . x o - - - - - - - - - - - - - | | | | o . o o - - - - - - - - - - - - | | | | x x . - - - - - - - - - - - - - | | | | | x | . - o - - - - - - - - - - | | | | | | | | . x - - - - - - - - - - | | | | | | | x o . x o - - - - - - - - | | | | | | | | | o . o o - - - - - - - | | | | | | | | | x x . - x - - - - - - | | | | | | | | | | x | . o - - - - - - | | | | | | | | | | | o x . x o - - - - | | | | | | | | | | | | | o . x o - - - | | | | | | | | | | | | | x o . o - - - | | | | | | | | | | | | | | x x . - - - | | | | | | | | | | | | | | | | | . o x | | | | | | | | | | | | | | | | | x . x | | | | | | | | | | | | | | | | | o o . The error in solving: 2.375748e-16 The error in solving: 4.248054e-16 The error in solving: 5.119584e-16 The error in solving: 4.170847e-16 The error in solving: 3.043636e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.250000 [ 0.000000 -0.150200 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.150200 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.768264 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.768264 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.001691 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.001691 0.000000 0.624140 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.624140 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.976931 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.976931 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 10 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 2 3 4 4 4 4 4 5 7 8 8 8 8 8 9 10 10 10 Column indices: 1 0 4 3 10 9 11 10 17 16 Off-diagonal values: -0.150200 0.150200 0.768264 -0.768264 0.001691 -0.001691 0.624140 -0.624140 0.976931 -0.976931 . o - - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | | o . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . - - - - - - - - - - - - | | | | | | | | . - - - - - - - - - - - | | | | | | | | | . x - - - - - - - - - | | | | | | | | | o . x - - - - - - - - | | | | | | | | | | o . - - - - - - - - | | | | | | | | | | | | . - - - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - - - - | | | | | | | | | | | | | | | | . x - - | | | | | | | | | | | | | | | | o . - - | | | | | | | | | | | | | | | | | | . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.144392e-16 The error in solving: 3.236829e-16 The error in solving: 3.421937e-16 The error in solving: 2.662447e-16 The error in solving: 3.376612e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.500000 [ 0.000000 1.278467 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.278467 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.382326 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.382326 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.714448 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.714448 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.592827 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.592827 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.613346 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.613346 0.000000 -0.451547 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.451547 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.544302 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.544302 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.262627 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.262627 0.000000 -0.560209 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.560209 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.336876 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.336876 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 20 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 2 2 3 4 5 6 7 8 9 11 12 13 14 15 17 18 19 20 20 Column indices: 1 0 4 3 6 5 8 7 10 9 11 10 13 12 15 14 16 15 18 17 Off-diagonal values: 1.278467 -1.278467 -0.382326 0.382326 0.714448 -0.714448 -1.592827 1.592827 1.613346 -1.613346 -0.451547 0.451547 1.544302 -1.544302 -0.262627 0.262627 -0.560209 0.560209 1.336876 -1.336876 . x - - - - - - - - - - - - - - - - - - o . - - - - - - - - - - - - - - - - - - | | . - - - - - - - - - - - - - - - - - | | | . o - - - - - - - - - - - - - - - | | | x . - - - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | | o . - - - - - - - - - - - - - | | | | | | | . o - - - - - - - - - - - | | | | | | | x . - - - - - - - - - - - | | | | | | | | | . x - - - - - - - - - | | | | | | | | | o . o - - - - - - - - | | | | | | | | | | x . - - - - - - - - | | | | | | | | | | | | . x - - - - - - | | | | | | | | | | | | o . - - - - - - | | | | | | | | | | | | | | . o - - - - | | | | | | | | | | | | | | x . o - - - | | | | | | | | | | | | | | | x . - - - | | | | | | | | | | | | | | | | | . x - | | | | | | | | | | | | | | | | | o . - | | | | | | | | | | | | | | | | | | | . The error in solving: 4.302114e-16 The error in solving: 3.188873e-16 The error in solving: 0.000000e+00 The error in solving: 3.388544e-16 The error in solving: 1.666780e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 1-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.750000 [ 0.000000 0.211526 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.211526 0.000000 -0.928061 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.928061 0.000000 0.712202 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.712202 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.626496 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.626496 0.000000 -0.882937 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.882937 0.000000 -0.244056 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.244056 0.000000 2.590484 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.590484 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.260365 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.260365 0.000000 0.177212 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.177212 0.000000 -0.788049 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.788049 0.000000 -0.310040 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.310040 0.000000 1.410622 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.410622 0.000000 1.203107 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.203107 0.000000 -0.783569 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.783569 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 28 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 5 6 6 7 9 11 13 14 14 15 17 19 21 23 25 27 28 28 Column indices: 1 0 2 1 3 2 6 5 7 6 8 7 9 8 12 11 13 12 14 13 15 14 16 15 17 16 18 17 Off-diagonal values: 0.211526 -0.211526 -0.928061 0.928061 0.712202 -0.712202 -0.626496 0.626496 -0.882937 0.882937 -0.244056 0.244056 2.590484 -2.590484 0.260365 -0.260365 0.177212 -0.177212 -0.788049 0.788049 -0.310040 0.310040 1.410622 -1.410622 1.203107 -1.203107 -0.783569 0.783569 . x - - - - - - - - - - - - - - - - - - o . o - - - - - - - - - - - - - - - - - | x . x - - - - - - - - - - - - - - - - | | o . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . o - - - - - - - - - - - - - | | | | | x . o - - - - - - - - - - - - | | | | | | x . o - - - - - - - - - - - | | | | | | | x . x - - - - - - - - - - | | | | | | | | o . - - - - - - - - - - | | | | | | | | | | . - - - - - - - - - | | | | | | | | | | | . x - - - - - - - | | | | | | | | | | | o . x - - - - - - | | | | | | | | | | | | o . o - - - - - | | | | | | | | | | | | | x . o - - - - | | | | | | | | | | | | | | x . x - - - | | | | | | | | | | | | | | | o . x - - | | | | | | | | | | | | | | | | o . o - | | | | | | | | | | | | | | | | | x . - | | | | | | | | | | | | | | | | | | | . The error in solving: 1.710969e-16 The error in solving: 3.203936e-16 The error in solving: 1.783394e-16 The error in solving: 3.935053e-16 The error in solving: 5.633767e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.250000 [ 0.000000 0.000000 -1.193806 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.193806 0.000000 0.000000 0.634135 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.634135 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.536114 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.536114 0.000000 2.526802 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.526802 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.467422 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.896596 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.467422 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.896596 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.831663 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.831663 0.000000 0.000000 -0.031773 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.031773 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 16 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 1 3 4 4 4 4 5 7 8 9 10 11 12 12 13 13 15 16 16 Column indices: 2 0 3 2 8 7 9 8 12 13 10 11 17 15 18 17 Off-diagonal values: -1.193806 1.193806 0.634135 -0.634135 -0.536114 0.536114 2.526802 -2.526802 2.467422 -0.896596 -2.467422 0.896596 -0.831663 0.831663 -0.031773 0.031773 . - o - - - - - - - - - - - - - - - - - | . - - - - - - - - - - - - - - - - - - x | . x - - - - - - - - - - - - - - - - | | o . - - - - - - - - - - - - - - - - | | | | . - - - - - - - - - - - - - - - | | | | | . - - - - - - - - - - - - - - | | | | | | . - - - - - - - - - - - - - | | | | | | | . o - - - - - - - - - - - | | | | | | | x . x - - - - - - - - - - | | | | | | | | o . - - - - - - - - - - | | | | | | | | | | . - x - - - - - - - | | | | | | | | | | | . - o - - - - - - | | | | | | | | | | o | . - - - - - - - | | | | | | | | | | | x | . - - - - - - | | | | | | | | | | | | | | . - - - - - | | | | | | | | | | | | | | | . - o - - | | | | | | | | | | | | | | | | . - - - | | | | | | | | | | | | | | | x | . o - | | | | | | | | | | | | | | | | | x . - | | | | | | | | | | | | | | | | | | | . The error in solving: 2.723019e-16 The error in solving: 1.671107e-16 The error in solving: 1.570092e-16 The error in solving: 3.005430e-16 The error in solving: 2.775558e-16 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.500000 [ 0.000000 -0.426320 -0.020238 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.426320 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.020238 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.731069 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.731069 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.921729 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.921729 0.000000 0.416880 1.109779 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.416880 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.109779 0.000000 0.000000 0.776012 -0.116419 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.776012 0.000000 0.000000 -0.603341 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.116419 0.000000 0.000000 0.000000 0.558735 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.603341 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.558735 0.000000 0.000000 0.000000 0.013377 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.013377 0.000000 0.000000 0.000000 -0.346522 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.759546 -0.139744 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.346522 -0.759546 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.139744 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.249329 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.249329 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 30 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 3 4 5 6 7 10 11 14 16 18 19 21 21 23 25 27 28 29 30 Column indices: 1 2 0 0 4 3 6 5 7 8 6 6 9 10 8 11 8 12 9 10 14 12 16 16 17 14 15 15 19 18 Off-diagonal values: -0.426320 -0.020238 0.426320 0.020238 0.731069 -0.731069 0.921729 -0.921729 0.416880 1.109779 -0.416880 -1.109779 0.776012 -0.116419 -0.776012 -0.603341 0.116419 0.558735 0.603341 -0.558735 0.013377 -0.013377 -0.346522 0.759546 -0.139744 0.346522 -0.759546 0.139744 0.249329 -0.249329 . o o - - - - - - - - - - - - - - - - - x . - - - - - - - - - - - - - - - - - - x | . - - - - - - - - - - - - - - - - - | | | . x - - - - - - - - - - - - - - - | | | o . - - - - - - - - - - - - - - - | | | | | . x - - - - - - - - - - - - - | | | | | o . x x - - - - - - - - - - - | | | | | | o . - - - - - - - - - - - - | | | | | | o | . x o - - - - - - - - - | | | | | | | | o . - o - - - - - - - - | | | | | | | | x | . - x - - - - - - - | | | | | | | | | x | . - - - - - - - - | | | | | | | | | | o | . - x - - - - - | | | | | | | | | | | | | . - - - - - - | | | | | | | | | | | | o | . - o - - - | | | | | | | | | | | | | | | . x o - - | | | | | | | | | | | | | | x o . - - - | | | | | | | | | | | | | | | x | . - - | | | | | | | | | | | | | | | | | | . x | | | | | | | | | | | | | | | | | | o . The error in solving: 3.287015e-16 The error in solving: 6.550551e-16 The error in solving: 3.104913e-16 The error in solving: 3.858424e-16 The error in solving: 1.082290e-15 - BAND DIAGONAL MATRIX ---------------------------------------------------------------------------------------------------- A skew-symmetric 2-band-diagonal matrix using a standard normal distribution with a zero diagonal and a density of 0.750000 [ 0.000000 -0.785282 0.292285 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.785282 0.000000 0.000000 -0.635460 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.292285 0.000000 0.000000 0.518559 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.635460 -0.518559 0.000000 0.000000 -0.823612 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.023912 0.907155 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.823612 0.023912 0.000000 0.702364 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.907155 -0.702364 0.000000 0.565500 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.565500 0.000000 0.399795 1.398199 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.399795 0.000000 0.005819 0.576896 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.398199 -0.005819 0.000000 -0.760663 -1.563939 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.576896 0.760663 0.000000 2.514375 1.183971 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.563939 -2.514375 0.000000 -0.615183 0.642827 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.183971 0.615183 0.000000 -1.888367 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.642827 1.888367 0.000000 -0.029929 1.478615 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.029929 0.000000 -1.514252 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.478615 1.514252 0.000000 -0.324939 -0.531144 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.324939 0.000000 -0.631324 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.531144 0.631324 0.000000 -1.039510 -0.985800 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.039510 0.000000 -1.483044 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.985800 1.483044 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 58 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 2 4 6 9 11 14 17 20 23 27 31 35 38 42 44 48 50 54 56 58 Column indices: 1 2 0 3 0 3 1 2 5 5 6 3 4 6 4 5 7 6 8 9 7 9 10 7 8 10 11 8 9 11 12 9 10 12 13 10 11 13 11 12 14 15 13 15 13 14 16 17 15 17 15 16 18 19 17 19 17 18 Off-diagonal values: -0.785282 0.292285 0.785282 -0.635460 -0.292285 0.518559 0.635460 -0.518559 -0.823612 -0.023912 0.907155 0.823612 0.023912 0.702364 -0.907155 -0.702364 0.565500 -0.565500 0.399795 1.398199 -0.399795 0.005819 0.576896 -1.398199 -0.005819 -0.760663 -1.563939 -0.576896 0.760663 2.514375 1.183971 1.563939 -2.514375 -0.615183 0.642827 -1.183971 0.615183 -1.888367 -0.642827 1.888367 -0.029929 1.478615 0.029929 -1.514252 -1.478615 1.514252 -0.324939 -0.531144 0.324939 -0.631324 0.531144 0.631324 -1.039510 -0.985800 1.039510 -1.483044 0.985800 1.483044 . o x - - - - - - - - - - - - - - - - - x . - o - - - - - - - - - - - - - - - - o | . x - - - - - - - - - - - - - - - - | x o . - o - - - - - - - - - - - - - - | | | | . o x - - - - - - - - - - - - - | | | x x . x - - - - - - - - - - - - - | | | | o o . x - - - - - - - - - - - - | | | | | | o . x x - - - - - - - - - - | | | | | | | o . x x - - - - - - - - - | | | | | | | o o . o o - - - - - - - - | | | | | | | | o x . x x - - - - - - - | | | | | | | | | x o . o x - - - - - - | | | | | | | | | | o x . o - - - - - - | | | | | | | | | | | o x . o x - - - - | | | | | | | | | | | | | x . o - - - - | | | | | | | | | | | | | o x . o o - - | | | | | | | | | | | | | | | x . o - - | | | | | | | | | | | | | | | x x . o o | | | | | | | | | | | | | | | | | x . o | | | | | | | | | | | | | | | | | x x . The error in solving: 4.458206e-16 The error in solving: 6.510739e-16 The error in solving: 2.346947e-16 The error in solving: 2.154412e-16 The error in solving: 4.088652e-16 - TRIDIAGONAL MATRIX ------------------------------------------------------------------------------------------------------ A tridiagonal matrix using a uniform (0, 1) distribution [ 0.244856 0.419968 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.875915 0.230022 0.329010 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.076342 0.333145 0.098065 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.642302 0.315533 0.178976 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.342263 0.570823 0.981206 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.686218 0.337614 0.166602 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.435444 0.035018 0.036089 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.666851 0.234184 0.770291 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.022874 0.910250 0.252492 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.082112 0.240491 0.881712 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.332575 0.229238 0.151849 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.175993 0.741090 0.861082 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.510144 0.815093 0.501923 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.964071 0.634526 0.503812 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.681315 0.653624 0.484545 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.433854 0.999481 0.620412 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.228355 0.225029 0.423241 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.114598 0.019890 0.550397 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.244326 0.388029 0.464606 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.662344 0.295671]; Dimension: 20 x 20 Off-diagonal entries: 38 (max 380) Diagonal entries: 0.244856 0.230022 0.333145 0.315533 0.570823 0.337614 0.035018 0.234184 0.910250 0.240491 0.229238 0.741090 0.815093 0.634526 0.653624 0.999481 0.225029 0.019890 0.388029 0.295671 Row indices: 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 38 Column indices: 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 16 15 17 16 18 17 19 18 Off-diagonal values: 0.419968 0.875915 0.329010 0.076342 0.098065 0.642302 0.178976 0.342263 0.981206 0.686218 0.166602 0.435444 0.036089 0.666851 0.770291 0.022874 0.252492 0.082112 0.881712 0.332575 0.151849 0.175993 0.861082 0.510144 0.501923 0.964071 0.503812 0.681315 0.484545 0.433854 0.620412 0.228355 0.423241 0.114598 0.550397 0.244326 0.464606 0.662344 x x - - - - - - - - - - - - - - - - - - x x x - - - - - - - - - - - - - - - - - | x x x - - - - - - - - - - - - - - - - | | x x x - - - - - - - - - - - - - - - | | | x x x - - - - - - - - - - - - - - | | | | x x x - - - - - - - - - - - - - | | | | | x x x - - - - - - - - - - - - | | | | | | x x x - - - - - - - - - - - | | | | | | | x x x - - - - - - - - - - | | | | | | | | x x x - - - - - - - - - | | | | | | | | | x x x - - - - - - - - | | | | | | | | | | x x x - - - - - - - | | | | | | | | | | | x x x - - - - - - | | | | | | | | | | | | x x x - - - - - | | | | | | | | | | | | | x x x - - - - | | | | | | | | | | | | | | x x x - - - | | | | | | | | | | | | | | | x x x - - | | | | | | | | | | | | | | | | x x x - | | | | | | | | | | | | | | | | | x x x | | | | | | | | | | | | | | | | | | x x The error in solving: 3.609726e-16 The error in solving: 6.451306e-16 The error in solving: 6.145917e-16 The error in solving: 4.918301e-16 The error in solving: 5.026749e-16 - TRIDIAGONAL MATRIX ------------------------------------------------------------------------------------------------------ A tridiagonal matrix using a uniform (-1, 1) distribution [ -0.526376 0.440451 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.699739 -0.369631 -0.732813 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.696142 0.713211 -0.469075 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.087994 -0.535412 -0.045167 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.777296 -0.407512 -0.732913 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.916380 -0.807083 0.371106 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.475904 0.879961 0.616183 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.070990 0.870190 -0.872673 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.107816 -0.401632 0.273349 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.149238 0.236364 0.408683 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.423452 -0.900363 0.745118 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.922398 -0.611839 0.787132 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.744900 -0.954517 0.592642 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.341517 0.298080 -0.786255 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.783391 -0.938279 -0.899405 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.827394 0.418773 -0.951612 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.574755 0.640480 -0.665862 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.841897 0.822936 -0.763046 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.985373 0.163542 -0.311851 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.808918 -0.100047]; Dimension: 20 x 20 Off-diagonal entries: 38 (max 380) Diagonal entries: -0.526376 -0.369631 0.713211 -0.535412 -0.407512 -0.807083 0.879961 0.870190 -0.401632 0.236364 -0.900363 -0.611839 -0.954517 0.298080 -0.938279 0.418773 0.640480 0.822936 0.163542 -0.100047 Row indices: 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 38 Column indices: 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 16 15 17 16 18 17 19 18 Off-diagonal values: 0.440451 -0.699739 -0.732813 -0.696142 -0.469075 0.087994 -0.045167 0.777296 -0.732913 -0.916380 0.371106 -0.475904 0.616183 0.070990 -0.872673 -0.107816 0.273349 0.149238 0.408683 0.423452 0.745118 -0.922398 0.787132 0.744900 0.592642 -0.341517 -0.786255 -0.783391 -0.899405 -0.827394 -0.951612 0.574755 -0.665862 -0.841897 -0.763046 -0.985373 -0.311851 -0.808918 o x - - - - - - - - - - - - - - - - - - o o o - - - - - - - - - - - - - - - - - | o x o - - - - - - - - - - - - - - - - | | x o o - - - - - - - - - - - - - - - | | | x o o - - - - - - - - - - - - - - | | | | o o x - - - - - - - - - - - - - | | | | | o x x - - - - - - - - - - - - | | | | | | x x o - - - - - - - - - - - | | | | | | | o o x - - - - - - - - - - | | | | | | | | x x x - - - - - - - - - | | | | | | | | | x o x - - - - - - - - | | | | | | | | | | o o x - - - - - - - | | | | | | | | | | | x o x - - - - - - | | | | | | | | | | | | o x o - - - - - | | | | | | | | | | | | | o o o - - - - | | | | | | | | | | | | | | o x o - - - | | | | | | | | | | | | | | | x x o - - | | | | | | | | | | | | | | | | o x o - | | | | | | | | | | | | | | | | | o x o | | | | | | | | | | | | | | | | | | o o The error in solving: 2.677666e-16 The error in solving: 5.236912e-16 The error in solving: 6.012462e-16 The error in solving: 4.374256e-16 The error in solving: 5.324443e-16 - TRIDIAGONAL MATRIX ------------------------------------------------------------------------------------------------------ A tridiagonal matrix using a standard normal distribution [ -0.476731 -0.133952 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.577425 0.813268 0.727702 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.092766 0.714001 -1.269446 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.911480 -1.287463 -0.671292 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.478880 0.782238 0.766118 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.540275 0.678556 0.186628 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.498047 -0.357530 -1.632138 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.622074 1.302220 -1.239000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.698377 1.764464 0.265646 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.241587 -1.897499 1.681207 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.666533 -0.191789 0.117153 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.987223 0.088077 0.386101 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.087645 -1.219840 -0.150962 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.730667 -0.819352 0.731049 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.788492 0.396452 0.459904 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.632805 0.534484 -0.515740 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.374012 1.602081 -0.862140 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.005036 -1.650830 -0.330548 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.621981 1.674901 -1.270718 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.524310 0.430438]; Dimension: 20 x 20 Off-diagonal entries: 38 (max 380) Diagonal entries: -0.476731 0.813268 0.714001 -1.287463 0.782238 0.678556 -0.357530 1.302220 1.764464 -1.897499 -0.191789 0.088077 -1.219840 -0.819352 0.396452 0.534484 1.602081 -1.650830 1.674901 0.430438 Row indices: 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 38 Column indices: 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 16 15 17 16 18 17 19 18 Off-diagonal values: -0.133952 2.577425 0.727702 -1.092766 -1.269446 1.911480 -0.671292 -0.478880 0.766118 -0.540275 0.186628 0.498047 -1.632138 0.622074 -1.239000 -0.698377 0.265646 -1.241587 1.681207 0.666533 0.117153 -0.987223 0.386101 -1.087645 -0.150962 0.730667 0.731049 -0.788492 0.459904 0.632805 -0.515740 0.374012 -0.862140 2.005036 -0.330548 -1.621981 -1.270718 0.524310 o o - - - - - - - - - - - - - - - - - - x x x - - - - - - - - - - - - - - - - - | o x o - - - - - - - - - - - - - - - - | | x o o - - - - - - - - - - - - - - - | | | o x x - - - - - - - - - - - - - - | | | | o x x - - - - - - - - - - - - - | | | | | x o o - - - - - - - - - - - - | | | | | | x x o - - - - - - - - - - - | | | | | | | o x x - - - - - - - - - - | | | | | | | | o o x - - - - - - - - - | | | | | | | | | x o x - - - - - - - - | | | | | | | | | | o x x - - - - - - - | | | | | | | | | | | o o o - - - - - - | | | | | | | | | | | | x o x - - - - - | | | | | | | | | | | | | o x x - - - - | | | | | | | | | | | | | | x x o - - - | | | | | | | | | | | | | | | x x o - - | | | | | | | | | | | | | | | | x o o - | | | | | | | | | | | | | | | | | o x o | | | | | | | | | | | | | | | | | | x x The error in solving: 4.227603e-16 The error in solving: 3.554448e-16 The error in solving: 4.091337e-16 The error in solving: 8.688939e-16 The error in solving: 3.693070e-16 - TRIDIAGONAL MATRIX ------------------------------------------------------------------------------------------------------ A upper-triangular tridiagonal matrix using a uniform (0, 1) distribution [ 0.576223 0.483199 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.056773 2.577425 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.892626 0.888678 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.608823 -1.092766 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.978080 0.232606 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.068439 1.911480 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.885891 0.039171 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.337617 -0.478880 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.195577 0.886589 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.436235 -0.540275 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.879600 0.912956 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.495792 0.498047 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.828486 0.160537 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.311874 0.622074 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.088742 0.359164 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.009403 -0.698377 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.896799 0.117360 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.037818 -1.241587 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.685668 0.767478 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.957265]; Dimension: 20 x 20 Off-diagonal entries: 19 (max 380) Diagonal entries: 0.576223 0.056773 0.892626 0.608823 0.978080 0.068439 0.885891 0.337617 0.195577 0.436235 0.879600 0.495792 0.828486 0.311874 0.088742 0.009403 0.896799 0.037818 0.685668 0.957265 Row indices: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 19 Column indices: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Off-diagonal values: 0.483199 2.577425 0.888678 -1.092766 0.232606 1.911480 0.039171 -0.478880 0.886589 -0.540275 0.912956 0.498047 0.160537 0.622074 0.359164 -0.698377 0.117360 -1.241587 0.767478 x x - - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | | x o - - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | x o - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | x o - - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | | x x - - - - - - - | | | | | | | | | | | | x x - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | x o - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | x o - | | | | | | | | | | | | | | | | | | x x | | | | | | | | | | | | | | | | | | | x The error in solving: 3.188873e-16 The error in solving: 1.144392e-16 The error in solving: 2.559173e-16 The error in solving: 1.309228e-16 The error in solving: 9.639819e-17 - TRIDIAGONAL MATRIX ------------------------------------------------------------------------------------------------------ A upper-triangular tridiagonal matrix using a uniform (-1, 1) distribution [ 0.574481 -0.482066 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.037632 2.577425 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.999435 0.950719 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.208379 -1.092766 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.624197 -0.981407 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.392632 1.911480 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.407517 -0.789115 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.976172 -0.478880 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.219366 -0.519000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.298813 -0.540275 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.381971 -0.580569 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.660495 0.498047 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.916869 -0.106099 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.546809 0.622074 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.796265 -0.135456 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.407216 -0.698377 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.249168 0.771547 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.803562 -1.241587 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.264369 0.436670 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.439296]; Dimension: 20 x 20 Off-diagonal entries: 19 (max 380) Diagonal entries: 0.574481 0.037632 -0.999435 0.208379 0.624197 0.392632 0.407517 -0.976172 0.219366 -0.298813 0.381971 -0.660495 -0.916869 0.546809 -0.796265 -0.407216 -0.249168 0.803562 -0.264369 0.439296 Row indices: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 19 Column indices: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Off-diagonal values: -0.482066 2.577425 0.950719 -1.092766 -0.981407 1.911480 -0.789115 -0.478880 -0.519000 -0.540275 -0.580569 0.498047 -0.106099 0.622074 -0.135456 -0.698377 0.771547 -1.241587 0.436670 x o - - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - | | o x - - - - - - - - - - - - - - - - | | | x o - - - - - - - - - - - - - - - | | | | x o - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | x o - - - - - - - - - - - - | | | | | | | o o - - - - - - - - - - - | | | | | | | | x o - - - - - - - - - - | | | | | | | | | o o - - - - - - - - - | | | | | | | | | | x o - - - - - - - - | | | | | | | | | | | o x - - - - - - - | | | | | | | | | | | | o o - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | o o - - - - | | | | | | | | | | | | | | | o o - - - | | | | | | | | | | | | | | | | o x - - | | | | | | | | | | | | | | | | | x o - | | | | | | | | | | | | | | | | | | o x | | | | | | | | | | | | | | | | | | | x The error in solving: 2.573946e-16 The error in solving: 2.224779e-16 The error in solving: 0.000000e+00 The error in solving: 3.140185e-16 The error in solving: 2.498002e-16 - TRIDIAGONAL MATRIX ------------------------------------------------------------------------------------------------------ A upper-triangular tridiagonal matrix using a standard normal distribution [ 0.712430 1.055963 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.691374 2.577425 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.360591 1.811924 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.317979 -1.092766 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.186378 0.082704 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.145994 1.911480 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.803084 -0.433249 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.428196 -0.478880 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.643070 -0.567752 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.235999 -0.540275 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.350579 -1.611066 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.036637 0.498047 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.605464 -0.794004 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.213131 0.622074 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.164770 0.880967 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.036996 -0.698377 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.710807 0.420798 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.096981 -1.241587 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.301308 1.343063 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.494054]; Dimension: 20 x 20 Off-diagonal entries: 19 (max 380) Diagonal entries: 0.712430 -0.691374 -1.360591 0.317979 0.186378 2.145994 0.803084 -0.428196 -0.643070 -0.235999 0.350579 0.036637 -0.605464 -0.213131 0.164770 -1.036996 1.710807 -0.096981 -1.301308 2.494054 Row indices: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 19 Column indices: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Off-diagonal values: 1.055963 2.577425 1.811924 -1.092766 0.082704 1.911480 -0.433249 -0.478880 -0.567752 -0.540275 -1.611066 0.498047 -0.794004 0.622074 0.880967 -0.698377 0.420798 -1.241587 1.343063 x x - - - - - - - - - - - - - - - - - - | o x - - - - - - - - - - - - - - - - - | | o x - - - - - - - - - - - - - - - - | | | x o - - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | x o - - - - - - - - - - - - | | | | | | | o o - - - - - - - - - - - | | | | | | | | o o - - - - - - - - - - | | | | | | | | | o o - - - - - - - - - | | | | | | | | | | x o - - - - - - - - | | | | | | | | | | | x x - - - - - - - | | | | | | | | | | | | o o - - - - - - | | | | | | | | | | | | | o x - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | o o - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | o o - | | | | | | | | | | | | | | | | | | o x | | | | | | | | | | | | | | | | | | | x The error in solving: 9.714451e-17 The error in solving: 3.600210e-16 The error in solving: 1.118863e-16 The error in solving: 2.775558e-16 The error in solving: 3.103168e-17 - TRIDIAGONAL MATRIX ------------------------------------------------------------------------------------------------------ A lower-triangular tridiagonal matrix using a uniform (0, 1) distribution [ 0.114257 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.054282 0.935526 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.415419 0.504660 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.316497 0.430893 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.585359 0.872007 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.832629 0.244643 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.641437 0.126286 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.104462 0.763954 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.381014 0.581228 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.400212 0.485354 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.390103 0.015539 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.983443 0.350696 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.757983 0.585132 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.717146 0.195667 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.463972 0.251480]; Dimension: 20 x 20 Off-diagonal entries: 19 (max 380) Diagonal entries: 0.114257 0.935526 0.504660 0.430893 0.815902 0.045347 0.012729 0.787468 0.693062 0.872007 0.244643 0.126286 0.763954 0.581228 0.485354 0.015539 0.350696 0.585132 0.195667 0.251480 Row indices: 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Column indices: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Off-diagonal values: 0.054282 0.415419 0.316497 0.000874 0.919708 0.672235 0.908679 0.814220 0.585359 0.832629 0.641437 0.104462 0.381014 0.400212 0.390103 0.983443 0.757983 0.717146 0.463972 x - - - - - - - - - - - - - - - - - - - x x - - - - - - - - - - - - - - - - - - | x x - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | | x x - - - - - - - - - - - - - - - | | | | x x - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | x x - - - - - - - - - - | | | | | | | | | x x - - - - - - - - - | | | | | | | | | | x x - - - - - - - - | | | | | | | | | | | x x - - - - - - - | | | | | | | | | | | | x x - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | x x - - - - | | | | | | | | | | | | | | | x x - - - | | | | | | | | | | | | | | | | x x - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | x x The error in solving: 2.830524e-16 The error in solving: 1.279469e-16 The error in solving: 5.551115e-17 The error in solving: 1.570092e-16 The error in solving: 2.543841e-16 - TRIDIAGONAL MATRIX ------------------------------------------------------------------------------------------------------ A lower-triangular tridiagonal matrix using a uniform (-1, 1) distribution [ -0.445678 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.840836 -0.836701 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.909472 0.455750 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.810180 -0.798353 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.993441 -0.698288 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.964105 0.339598 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.714330 -0.104859 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.439556 -0.819081 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.320964 -0.511663 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.916678 -0.492165 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.389875 0.680631 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.368503 -0.746668 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.766830 -0.976899 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.840258 0.973023 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.338689 0.652577 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.089603 -0.486580 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.793896 -0.979719 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.005661 -0.874006 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.245713 0.349987 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.924907 -0.097647]; Dimension: 20 x 20 Off-diagonal entries: 19 (max 380) Diagonal entries: -0.445678 -0.836701 0.455750 -0.798353 -0.698288 0.339598 -0.104859 -0.819081 -0.511663 -0.492165 0.680631 -0.746668 -0.976899 0.973023 0.652577 -0.486580 -0.979719 -0.874006 0.349987 -0.097647 Row indices: 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Column indices: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Off-diagonal values: 0.840836 -0.909472 -0.810180 0.993441 -0.964105 0.714330 -0.439556 0.320964 -0.916678 0.389875 0.368503 0.766830 0.840258 0.338689 0.089603 0.793896 0.005661 0.245713 -0.924907 o - - - - - - - - - - - - - - - - - - - x o - - - - - - - - - - - - - - - - - - | o x - - - - - - - - - - - - - - - - - | | o o - - - - - - - - - - - - - - - - | | | x o - - - - - - - - - - - - - - - | | | | o x - - - - - - - - - - - - - - | | | | | x o - - - - - - - - - - - - - | | | | | | o o - - - - - - - - - - - - | | | | | | | x o - - - - - - - - - - - | | | | | | | | o o - - - - - - - - - - | | | | | | | | | x x - - - - - - - - - | | | | | | | | | | x o - - - - - - - - | | | | | | | | | | | x o - - - - - - - | | | | | | | | | | | | x x - - - - - - | | | | | | | | | | | | | x x - - - - - | | | | | | | | | | | | | | x o - - - - | | | | | | | | | | | | | | | x o - - - | | | | | | | | | | | | | | | | x o - - | | | | | | | | | | | | | | | | | x x - | | | | | | | | | | | | | | | | | | o o The error in solving: 5.745576e-17 The error in solving: 2.288783e-16 The error in solving: 2.500891e-16 The error in solving: 2.577685e-16 The error in solving: 2.543841e-16 - TRIDIAGONAL MATRIX ------------------------------------------------------------------------------------------------------ A lower-triangular tridiagonal matrix using a standard normal distribution [ 0.874209 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.808176 -2.158102 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.968853 -0.505577 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.074790 0.374521 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.098568 0.528051 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.857879 -0.310786 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.078314 1.142994 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.425455 0.126128 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.017097 0.613463 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.318646 -0.447270 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.137730 -0.436813 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.478685 -0.137741 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.292950 0.779116 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.277958 0.168097 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.561393 0.836357 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.119822 -0.128026 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.844097 0.051201 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.026418 1.178866 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.349066 0.115793 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.151406 -1.334271]; Dimension: 20 x 20 Off-diagonal entries: 19 (max 380) Diagonal entries: 0.874209 -2.158102 -0.505577 0.374521 0.528051 -0.310786 1.142994 0.126128 0.613463 -0.447270 -0.436813 -0.137741 0.779116 0.168097 0.836357 -0.128026 0.051201 1.178866 0.115793 -1.334271 Row indices: 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Column indices: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Off-diagonal values: -0.808176 1.968853 1.074790 -1.098568 -0.857879 1.078314 0.425455 0.017097 -1.318646 1.137730 -1.478685 -1.292950 -0.277958 -1.561393 -0.119822 -0.844097 -1.026418 -0.349066 -1.151406 x - - - - - - - - - - - - - - - - - - - o o - - - - - - - - - - - - - - - - - - | x o - - - - - - - - - - - - - - - - - | | x x - - - - - - - - - - - - - - - - | | | o x - - - - - - - - - - - - - - - | | | | o o - - - - - - - - - - - - - - | | | | | x x - - - - - - - - - - - - - | | | | | | x x - - - - - - - - - - - - | | | | | | | x x - - - - - - - - - - - | | | | | | | | o o - - - - - - - - - - | | | | | | | | | x o - - - - - - - - - | | | | | | | | | | o o - - - - - - - - | | | | | | | | | | | o x - - - - - - - | | | | | | | | | | | | o x - - - - - - | | | | | | | | | | | | | o x - - - - - | | | | | | | | | | | | | | o o - - - - | | | | | | | | | | | | | | | o x - - - | | | | | | | | | | | | | | | | o x - - | | | | | | | | | | | | | | | | | o x - | | | | | | | | | | | | | | | | | | o o The error in solving: 0.000000e+00 The error in solving: 2.576809e-16 The error in solving: 4.807407e-17 The error in solving: 5.034405e-16 The error in solving: 5.605063e-17 - TRIDIAGONAL MATRIX ------------------------------------------------------------------------------------------------------ A symmetric tridiagonal matrix using a uniform (0, 1) distribution [ 0.350138 0.338629 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.338629 0.227990 0.270626 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.270626 0.143222 0.643875 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.643875 0.214428 0.101053 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.101053 0.879014 0.733030 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.733030 0.015047 0.315566 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.315566 0.889319 0.019405 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.019405 0.934099 0.807919 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.807919 0.751848 0.064428 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.064428 0.951881 0.446118 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.446118 0.468237 0.989569 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.989569 0.847579 0.270576 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.270576 0.448961 0.485347 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.485347 0.415317 0.273623 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.273623 0.391493 0.207666 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.207666 0.403076 0.248824 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.248824 0.552121 0.809455 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.809455 0.250178 0.067592 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.067592 0.672359 0.800200 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.800200 0.558505]; Dimension: 20 x 20 Off-diagonal entries: 38 (max 380) Diagonal entries: 0.350138 0.227990 0.143222 0.214428 0.879014 0.015047 0.889319 0.934099 0.751848 0.951881 0.468237 0.847579 0.448961 0.415317 0.391493 0.403076 0.552121 0.250178 0.672359 0.558505 Row indices: 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 38 Column indices: 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 16 15 17 16 18 17 19 18 Off-diagonal values: 0.338629 0.338629 0.270626 0.270626 0.643875 0.643875 0.101053 0.101053 0.733030 0.733030 0.315566 0.315566 0.019405 0.019405 0.807919 0.807919 0.064428 0.064428 0.446118 0.446118 0.989569 0.989569 0.270576 0.270576 0.485347 0.485347 0.273623 0.273623 0.207666 0.207666 0.248824 0.248824 0.809455 0.809455 0.067592 0.067592 0.800200 0.800200 x x - - - - - - - - - - - - - - - - - - x x x - - - - - - - - - - - - - - - - - | x x x - - - - - - - - - - - - - - - - | | x x x - - - - - - - - - - - - - - - | | | x x x - - - - - - - - - - - - - - | | | | x x x - - - - - - - - - - - - - | | | | | x x x - - - - - - - - - - - - | | | | | | x x x - - - - - - - - - - - | | | | | | | x x x - - - - - - - - - - | | | | | | | | x x x - - - - - - - - - | | | | | | | | | x x x - - - - - - - - | | | | | | | | | | x x x - - - - - - - | | | | | | | | | | | x x x - - - - - - | | | | | | | | | | | | x x x - - - - - | | | | | | | | | | | | | x x x - - - - | | | | | | | | | | | | | | x x x - - - | | | | | | | | | | | | | | | x x x - - | | | | | | | | | | | | | | | | x x x - | | | | | | | | | | | | | | | | | x x x | | | | | | | | | | | | | | | | | | x x The error in solving: 6.106227e-16 The error in solving: 3.598203e-16 The error in solving: 4.041868e-16 The error in solving: 3.206940e-16 The error in solving: 3.983675e-16 - TRIDIAGONAL MATRIX ------------------------------------------------------------------------------------------------------ A symmetric tridiagonal matrix using a uniform (-1, 1) distribution [ 0.607142 0.513039 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.513039 0.726986 -0.126374 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.126374 -0.573781 0.231637 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.231637 -0.397784 0.538166 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.538166 0.403085 -0.099419 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.099419 0.323126 -0.272379 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.272379 -0.607564 0.454442 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.454442 -0.779215 0.701246 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.701246 0.732885 -0.428662 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.428662 -0.153253 0.344772 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.344772 -0.166811 -0.569048 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.569048 0.482560 0.996742 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.996742 -0.074287 0.945155 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.945155 -0.516459 0.220282 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.220282 0.838912 0.536348 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.536348 0.543126 -0.331969 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.331969 0.779360 -0.896099 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.896099 0.544970 -0.328269 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.328269 0.156893 -0.846471 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.846471 -0.472658]; Dimension: 20 x 20 Off-diagonal entries: 38 (max 380) Diagonal entries: 0.607142 0.726986 -0.573781 -0.397784 0.403085 0.323126 -0.607564 -0.779215 0.732885 -0.153253 -0.166811 0.482560 -0.074287 -0.516459 0.838912 0.543126 0.779360 0.544970 0.156893 -0.472658 Row indices: 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 38 Column indices: 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 16 15 17 16 18 17 19 18 Off-diagonal values: 0.513039 0.513039 -0.126374 -0.126374 0.231637 0.231637 0.538166 0.538166 -0.099419 -0.099419 -0.272379 -0.272379 0.454442 0.454442 0.701246 0.701246 -0.428662 -0.428662 0.344772 0.344772 -0.569048 -0.569048 0.996742 0.996742 0.945155 0.945155 0.220282 0.220282 0.536348 0.536348 -0.331969 -0.331969 -0.896099 -0.896099 -0.328269 -0.328269 -0.846471 -0.846471 x x - - - - - - - - - - - - - - - - - - x x o - - - - - - - - - - - - - - - - - | o o x - - - - - - - - - - - - - - - - | | x o x - - - - - - - - - - - - - - - | | | x x o - - - - - - - - - - - - - - | | | | o x o - - - - - - - - - - - - - | | | | | o o x - - - - - - - - - - - - | | | | | | x o x - - - - - - - - - - - | | | | | | | x x o - - - - - - - - - - | | | | | | | | o o x - - - - - - - - - | | | | | | | | | x o o - - - - - - - - | | | | | | | | | | o x x - - - - - - - | | | | | | | | | | | x o x - - - - - - | | | | | | | | | | | | x o x - - - - - | | | | | | | | | | | | | x x x - - - - | | | | | | | | | | | | | | x x o - - - | | | | | | | | | | | | | | | o x o - - | | | | | | | | | | | | | | | | o x o - | | | | | | | | | | | | | | | | | o x o | | | | | | | | | | | | | | | | | | o o The error in solving: 4.492632e-16 The error in solving: 4.356056e-16 The error in solving: 5.211105e-16 The error in solving: 5.509324e-16 The error in solving: 6.069847e-16 - TRIDIAGONAL MATRIX ------------------------------------------------------------------------------------------------------ A symmetric tridiagonal matrix using a standard normal distribution [ -0.447784 -0.594675 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.594675 -1.814021 0.429194 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.429194 0.151097 2.265769 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.265769 -0.731121 -0.513805 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.513805 -0.816092 1.027877 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.027877 0.829984 -0.870461 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.870461 -1.045306 -1.051317 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.051317 -0.628506 0.261479 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.261479 -0.322290 2.333577 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.333577 0.774616 -1.740722 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.740722 -0.298044 0.158008 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.158008 -0.687058 0.328059 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.328059 -1.051732 -0.980735 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.980735 0.084089 2.328084 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.328084 -0.702592 0.199607 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.199607 1.795589 -0.237354 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.237354 1.404513 1.536746 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.536746 -0.252966 -0.859954 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.859954 -1.295480 2.544208 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.544208 -0.522775]; Dimension: 20 x 20 Off-diagonal entries: 38 (max 380) Diagonal entries: -0.447784 -1.814021 0.151097 -0.731121 -0.816092 0.829984 -1.045306 -0.628506 -0.322290 0.774616 -0.298044 -0.687058 -1.051732 0.084089 -0.702592 1.795589 1.404513 -0.252966 -1.295480 -0.522775 Row indices: 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 38 Column indices: 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 16 15 17 16 18 17 19 18 Off-diagonal values: -0.594675 -0.594675 0.429194 0.429194 2.265769 2.265769 -0.513805 -0.513805 1.027877 1.027877 -0.870461 -0.870461 -1.051317 -1.051317 0.261479 0.261479 2.333577 2.333577 -1.740722 -1.740722 0.158008 0.158008 0.328059 0.328059 -0.980735 -0.980735 2.328084 2.328084 0.199607 0.199607 -0.237354 -0.237354 1.536746 1.536746 -0.859954 -0.859954 2.544208 2.544208 o o - - - - - - - - - - - - - - - - - - o o x - - - - - - - - - - - - - - - - - | x x x - - - - - - - - - - - - - - - - | | x o o - - - - - - - - - - - - - - - | | | o o x - - - - - - - - - - - - - - | | | | x x o - - - - - - - - - - - - - | | | | | o o o - - - - - - - - - - - - | | | | | | o o x - - - - - - - - - - - | | | | | | | x o x - - - - - - - - - - | | | | | | | | x x o - - - - - - - - - | | | | | | | | | o o x - - - - - - - - | | | | | | | | | | x o x - - - - - - - | | | | | | | | | | | x o o - - - - - - | | | | | | | | | | | | o x x - - - - - | | | | | | | | | | | | | x o x - - - - | | | | | | | | | | | | | | x x o - - - | | | | | | | | | | | | | | | o x x - - | | | | | | | | | | | | | | | | x o o - | | | | | | | | | | | | | | | | | o o x | | | | | | | | | | | | | | | | | | x o The error in solving: 3.070412e-16 The error in solving: 4.002966e-16 The error in solving: 3.640110e-16 The error in solving: 2.604628e-16 The error in solving: 6.011086e-16 - TRIDIAGONAL MATRIX ------------------------------------------------------------------------------------------------------ A skew-symmetric tridiagonal matrix using a uniform (0, 1) distribution [ 0.000000 -0.852681 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.852681 0.000000 0.830903 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.830903 0.000000 -0.098841 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.927355 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 38 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 38 Column indices: 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 16 15 17 16 18 17 19 18 Off-diagonal values: -0.852681 0.852681 0.830903 -0.830903 -0.098841 0.098841 0.920184 -0.920184 -0.040236 0.040236 -0.934840 0.934840 0.506570 -0.506570 0.673661 -0.673661 0.157580 -0.157580 -0.145784 0.145784 0.565674 -0.565674 0.182470 -0.182470 -0.768393 0.768393 0.592001 -0.592001 -0.457240 0.457240 -0.185278 0.185278 -0.310483 0.310483 -0.987310 0.987310 0.927355 -0.927355 . o - - - - - - - - - - - - - - - - - - x . x - - - - - - - - - - - - - - - - - | o . o - - - - - - - - - - - - - - - - | | x . x - - - - - - - - - - - - - - - | | | o . o - - - - - - - - - - - - - - | | | | x . o - - - - - - - - - - - - - | | | | | x . x - - - - - - - - - - - - | | | | | | o . x - - - - - - - - - - - | | | | | | | o . x - - - - - - - - - - | | | | | | | | o . o - - - - - - - - - | | | | | | | | | x . x - - - - - - - - | | | | | | | | | | o . x - - - - - - - | | | | | | | | | | | o . o - - - - - - | | | | | | | | | | | | x . x - - - - - | | | | | | | | | | | | | o . o - - - - | | | | | | | | | | | | | | x . o - - - | | | | | | | | | | | | | | | x . o - - | | | | | | | | | | | | | | | | x . o - | | | | | | | | | | | | | | | | | x . x | | | | | | | | | | | | | | | | | | o . The error in solving: 4.055545e-16 The error in solving: 6.877561e-16 The error in solving: 1.251408e-16 The error in solving: 4.016175e-16 The error in solving: 4.518280e-16 - TRIDIAGONAL MATRIX ------------------------------------------------------------------------------------------------------ A skew-symmetric tridiagonal matrix using a uniform (-1, 1) distribution [ 0.000000 0.746874 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.746874 0.000000 0.067475 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.067475 0.000000 -0.112876 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.112876 0.000000 -0.451041 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.451041 0.000000 0.570998 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.570998 0.000000 -0.661861 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.661861 0.000000 0.208541 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.208541 0.000000 -0.968045 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.968045 0.000000 0.515419 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.515419 0.000000 0.905360 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.905360 0.000000 -0.203757 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.203757 0.000000 -0.678869 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.678869 0.000000 -0.620326 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.620326 0.000000 -0.308112 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.308112 0.000000 0.342944 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.342944 0.000000 0.999918 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.999918 0.000000 0.472101 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.472101 0.000000 -0.462451 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.462451 0.000000 -0.363954 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.363954 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 38 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 38 Column indices: 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 16 15 17 16 18 17 19 18 Off-diagonal values: 0.746874 -0.746874 0.067475 -0.067475 -0.112876 0.112876 -0.451041 0.451041 0.570998 -0.570998 -0.661861 0.661861 0.208541 -0.208541 -0.968045 0.968045 0.515419 -0.515419 0.905360 -0.905360 -0.203757 0.203757 -0.678869 0.678869 -0.620326 0.620326 -0.308112 0.308112 0.342944 -0.342944 0.999918 -0.999918 0.472101 -0.472101 -0.462451 0.462451 -0.363954 0.363954 . x - - - - - - - - - - - - - - - - - - o . x - - - - - - - - - - - - - - - - - | o . o - - - - - - - - - - - - - - - - | | x . o - - - - - - - - - - - - - - - | | | x . x - - - - - - - - - - - - - - | | | | o . o - - - - - - - - - - - - - | | | | | x . x - - - - - - - - - - - - | | | | | | o . o - - - - - - - - - - - | | | | | | | x . x - - - - - - - - - - | | | | | | | | o . x - - - - - - - - - | | | | | | | | | o . o - - - - - - - - | | | | | | | | | | x . o - - - - - - - | | | | | | | | | | | x . o - - - - - - | | | | | | | | | | | | x . o - - - - - | | | | | | | | | | | | | x . x - - - - | | | | | | | | | | | | | | o . x - - - | | | | | | | | | | | | | | | o . x - - | | | | | | | | | | | | | | | | o . o - | | | | | | | | | | | | | | | | | x . o | | | | | | | | | | | | | | | | | | x . The error in solving: 3.299442e-16 The error in solving: 6.055552e-16 The error in solving: 4.041273e-16 The error in solving: 4.135488e-16 The error in solving: 6.329245e-16 - TRIDIAGONAL MATRIX ------------------------------------------------------------------------------------------------------ A skew-symmetric tridiagonal matrix using a standard normal distribution [ 0.000000 0.885782 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.885782 0.000000 -2.011765 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.011765 0.000000 -2.003126 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.003126 0.000000 -0.573084 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.573084 0.000000 -0.064676 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.064676 0.000000 0.186040 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.186040 0.000000 -1.588570 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.588570 0.000000 -0.324063 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.324063 0.000000 0.197845 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.197845 0.000000 0.104946 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.104946 0.000000 1.103823 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.103823 0.000000 1.561121 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.561121 0.000000 0.837855 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.837855 0.000000 1.124894 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.124894 0.000000 0.111728 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.111728 0.000000 -0.975662 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.975662 0.000000 1.534494 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.534494 0.000000 1.536738 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -1.536738 0.000000 -0.818963 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.818963 0.000000]; Dimension: 20 x 20 Off-diagonal entries: 38 (max 380) Diagonal entries: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Row indices: 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 38 Column indices: 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 16 15 17 16 18 17 19 18 Off-diagonal values: 0.885782 -0.885782 -2.011765 2.011765 -2.003126 2.003126 -0.573084 0.573084 -0.064676 0.064676 0.186040 -0.186040 -1.588570 1.588570 -0.324063 0.324063 0.197845 -0.197845 0.104946 -0.104946 1.103823 -1.103823 1.561121 -1.561121 0.837855 -0.837855 1.124894 -1.124894 0.111728 -0.111728 -0.975662 0.975662 1.534494 -1.534494 1.536738 -1.536738 -0.818963 0.818963 . x - - - - - - - - - - - - - - - - - - o . o - - - - - - - - - - - - - - - - - | x . o - - - - - - - - - - - - - - - - | | x . o - - - - - - - - - - - - - - - | | | x . o - - - - - - - - - - - - - - | | | | x . x - - - - - - - - - - - - - | | | | | o . o - - - - - - - - - - - - | | | | | | x . o - - - - - - - - - - - | | | | | | | x . x - - - - - - - - - - | | | | | | | | o . x - - - - - - - - - | | | | | | | | | o . x - - - - - - - - | | | | | | | | | | o . x - - - - - - - | | | | | | | | | | | o . x - - - - - - | | | | | | | | | | | | o . x - - - - - | | | | | | | | | | | | | o . x - - - - | | | | | | | | | | | | | | o . o - - - | | | | | | | | | | | | | | | x . x - - | | | | | | | | | | | | | | | | o . x - | | | | | | | | | | | | | | | | | o . o | | | | | | | | | | | | | | | | | | x . The error in solving: 3.584125e-16 The error in solving: 4.379756e-16 The error in solving: 4.615277e-16 The error in solving: 4.520411e-16 The error in solving: 6.231111e-16 - TESTING WITH A GENERIC POSITIVE DEFINITE MATRIX ------------------------------------------------------------------------- The Jacobi method converged after 8 iterations with an error 6.861616e-10 The Gauss-Seidel method converged after 6 iterations with an error 1.039134e-11 The minimal-residual method converged after 263 iterations with an error 1.733069e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 1.846421e-08 The Jacobi method converged after 8 iterations with an error 1.580732e-09 The Gauss-Seidel method converged after 6 iterations with an error 2.469513e-11 The minimal-residual method converged after 267 iterations with an error 1.718983e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 1.433908e-08 The Jacobi method converged after 8 iterations with an error 1.901344e-09 The Gauss-Seidel method converged after 6 iterations with an error 3.609991e-11 The minimal-residual method converged after 265 iterations with an error 1.779358e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 1.574492e-08 The Jacobi method converged after 8 iterations with an error 8.619286e-10 The Gauss-Seidel method converged after 6 iterations with an error 1.882034e-11 The minimal-residual method converged after 266 iterations with an error 1.809847e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 1.494944e-08 The Jacobi method converged after 8 iterations with an error 1.438127e-09 The Gauss-Seidel method converged after 6 iterations with an error 2.327920e-11 The minimal-residual method converged after 263 iterations with an error 1.756368e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 2.626838e-08 The Jacobi method converged after 8 iterations with an error 3.078414e-09 The Gauss-Seidel method converged after 7 iterations with an error 1.007129e-11 The minimal-residual method converged after 269 iterations with an error 1.668030e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 3.395030e-08 The Jacobi method converged after 8 iterations with an error 5.986153e-09 The Gauss-Seidel method converged after 7 iterations with an error 1.482220e-11 The minimal-residual method converged after 280 iterations with an error 1.820794e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 4.473189e-08 The Jacobi method converged after 9 iterations with an error 9.025973e-10 The Gauss-Seidel method converged after 7 iterations with an error 1.885721e-11 The minimal-residual method converged after 276 iterations with an error 1.740911e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 2.101427e-08 The Jacobi method converged after 8 iterations with an error 8.372215e-09 The Gauss-Seidel method converged after 7 iterations with an error 2.293082e-11 The minimal-residual method converged after 271 iterations with an error 1.741882e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 1.963316e-08 The Jacobi method converged after 8 iterations with an error 5.497285e-09 The Gauss-Seidel method converged after 7 iterations with an error 1.879988e-11 The minimal-residual method converged after 274 iterations with an error 1.773474e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 3.150546e-08 The Jacobi method converged after 10 iterations with an error 1.781716e-09 The Gauss-Seidel method converged after 8 iterations with an error 1.611116e-11 The minimal-residual method converged after 279 iterations with an error 1.742268e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 2.876160e-08 The Jacobi method converged after 10 iterations with an error 1.257879e-09 The Gauss-Seidel method converged after 8 iterations with an error 1.188208e-11 The minimal-residual method converged after 277 iterations with an error 1.748581e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 3.545779e-08 The Jacobi method converged after 10 iterations with an error 1.733006e-09 The Gauss-Seidel method converged after 8 iterations with an error 1.361693e-11 The minimal-residual method converged after 282 iterations with an error 1.670144e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 2.888914e-08 The Jacobi method converged after 10 iterations with an error 3.949997e-09 The Gauss-Seidel method converged after 8 iterations with an error 1.833702e-11 The minimal-residual method converged after 290 iterations with an error 1.719064e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 1.673004e-08 The Jacobi method converged after 10 iterations with an error 2.819159e-09 The Gauss-Seidel method converged after 7 iterations with an error 2.166301e-10 The minimal-residual method converged after 284 iterations with an error 1.731152e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 2.505169e-08 The Jacobi method converged after 8 iterations with an error 2.362079e-09 The Gauss-Seidel method converged after 6 iterations with an error 7.831354e-11 The minimal-residual method converged after 276 iterations with an error 1.757182e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 1.131531e-08 The Jacobi method converged after 8 iterations with an error 2.717123e-09 The Gauss-Seidel method converged after 6 iterations with an error 3.519294e-11 The minimal-residual method converged after 268 iterations with an error 1.760495e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 1.377316e-08 The Jacobi method converged after 8 iterations with an error 3.986165e-09 The Gauss-Seidel method converged after 6 iterations with an error 7.863433e-11 The minimal-residual method converged after 280 iterations with an error 1.735981e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 1.053442e-08 The Jacobi method converged after 8 iterations with an error 2.174825e-09 The Gauss-Seidel method converged after 6 iterations with an error 4.169430e-11 The minimal-residual method converged after 260 iterations with an error 1.711379e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 1.883762e-08 The Jacobi method converged after 8 iterations with an error 1.340561e-09 The Gauss-Seidel method converged after 6 iterations with an error 2.930112e-11 The minimal-residual method converged after 261 iterations with an error 1.680672e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 1.386408e-08 The Jacobi method converged after 8 iterations with an error 6.762159e-09 The Gauss-Seidel method converged after 7 iterations with an error 1.604278e-11 The minimal-residual method converged after 264 iterations with an error 1.677937e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 4.315746e-08 The Jacobi method converged after 9 iterations with an error 2.817371e-09 The Gauss-Seidel method converged after 7 iterations with an error 4.149167e-11 The minimal-residual method converged after 291 iterations with an error 1.763645e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 1.836907e-08 The Jacobi method converged after 8 iterations with an error 9.275809e-09 The Gauss-Seidel method converged after 7 iterations with an error 8.784250e-12 The minimal-residual method converged after 267 iterations with an error 1.682127e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 1.587122e-08 The Jacobi method converged after 9 iterations with an error 1.411489e-09 The Gauss-Seidel method converged after 6 iterations with an error 4.286252e-10 The minimal-residual method converged after 276 iterations with an error 1.734103e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 3.117204e-08 The Jacobi method converged after 9 iterations with an error 9.188296e-10 The Gauss-Seidel method converged after 7 iterations with an error 3.479421e-11 The minimal-residual method converged after 270 iterations with an error 1.690886e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 4.618929e-08 The Jacobi method converged after 10 iterations with an error 2.914846e-09 The Gauss-Seidel method converged after 8 iterations with an error 7.500746e-11 The minimal-residual method converged after 305 iterations with an error 1.696915e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 1.939616e-08 The Jacobi method converged after 10 iterations with an error 2.731344e-09 The Gauss-Seidel method converged after 8 iterations with an error 3.265657e-11 The minimal-residual method converged after 279 iterations with an error 1.645190e-07 The residual-norm steepest-descent method converged after 13 iterations with an error 4.250715e-08 The Jacobi method converged after 10 iterations with an error 2.383988e-09 The Gauss-Seidel method converged after 8 iterations with an error 4.873920e-11 The minimal-residual method converged after 278 iterations with an error 1.697819e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 5.613038e-08 The Jacobi method converged after 10 iterations with an error 5.207216e-09 The Gauss-Seidel method converged after 8 iterations with an error 6.725514e-11 The minimal-residual method converged after 285 iterations with an error 1.688841e-07 The residual-norm steepest-descent method converged after 13 iterations with an error 4.101053e-08 The Jacobi method converged after 10 iterations with an error 4.115522e-09 The Gauss-Seidel method converged after 8 iterations with an error 9.015019e-11 The minimal-residual method converged after 301 iterations with an error 1.623462e-07 The residual-norm steepest-descent method converged after 13 iterations with an error 1.902393e-08 The Jacobi method converged after 7 iterations with an error 8.292206e-09 The Gauss-Seidel method converged after 6 iterations with an error 2.242810e-11 The minimal-residual method converged after 268 iterations with an error 1.828822e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 6.757073e-09 The Jacobi method converged after 8 iterations with an error 2.078809e-09 The Gauss-Seidel method converged after 6 iterations with an error 4.804526e-11 The minimal-residual method converged after 273 iterations with an error 1.752897e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 9.613100e-09 The Jacobi method converged after 8 iterations with an error 8.853434e-10 The Gauss-Seidel method converged after 7 iterations with an error 9.069213e-13 The minimal-residual method converged after 274 iterations with an error 1.754871e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 1.713666e-08 The Jacobi method converged after 8 iterations with an error 6.604133e-10 The Gauss-Seidel method converged after 6 iterations with an error 3.412747e-11 The minimal-residual method converged after 283 iterations with an error 1.775060e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 1.255025e-08 The Jacobi method converged after 8 iterations with an error 1.080263e-09 The Gauss-Seidel method converged after 7 iterations with an error 1.051138e-12 The minimal-residual method converged after 276 iterations with an error 1.765757e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 3.237820e-08 The Jacobi method converged after 8 iterations with an error 6.265096e-09 The Gauss-Seidel method converged after 7 iterations with an error 1.437692e-11 The minimal-residual method converged after 267 iterations with an error 1.813552e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 2.669181e-08 The Jacobi method converged after 9 iterations with an error 1.003371e-09 The Gauss-Seidel method converged after 6 iterations with an error 2.139172e-10 The minimal-residual method converged after 290 iterations with an error 1.758367e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 4.695466e-08 The Jacobi method converged after 9 iterations with an error 1.278369e-09 The Gauss-Seidel method converged after 7 iterations with an error 1.404824e-11 The minimal-residual method converged after 282 iterations with an error 1.803748e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 3.154192e-08 The Jacobi method converged after 9 iterations with an error 9.163808e-10 The Gauss-Seidel method converged after 7 iterations with an error 2.062362e-11 The minimal-residual method converged after 280 iterations with an error 1.759586e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 2.892844e-08 The Jacobi method converged after 9 iterations with an error 1.186734e-09 The Gauss-Seidel method converged after 7 iterations with an error 1.023728e-11 The minimal-residual method converged after 277 iterations with an error 1.749770e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 2.279541e-08 The Jacobi method converged after 9 iterations with an error 3.171915e-09 The Gauss-Seidel method converged after 7 iterations with an error 6.234149e-11 The minimal-residual method converged after 271 iterations with an error 1.708902e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 4.582278e-08 The Jacobi method converged after 9 iterations with an error 2.513679e-09 The Gauss-Seidel method converged after 7 iterations with an error 5.986357e-11 The minimal-residual method converged after 291 iterations with an error 1.676893e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 3.454103e-08 The Jacobi method converged after 9 iterations with an error 3.809987e-09 The Gauss-Seidel method converged after 7 iterations with an error 7.234671e-11 The minimal-residual method converged after 268 iterations with an error 1.601377e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 1.943174e-08 The Jacobi method converged after 9 iterations with an error 3.570724e-09 The Gauss-Seidel method converged after 7 iterations with an error 1.006149e-10 The minimal-residual method converged after 270 iterations with an error 1.624434e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 2.731129e-08 The Jacobi method converged after 9 iterations with an error 1.488055e-09 The Gauss-Seidel method converged after 7 iterations with an error 8.741000e-11 The minimal-residual method converged after 279 iterations with an error 1.626908e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 2.347039e-08 The Jacobi method converged after 7 iterations with an error 6.506778e-09 The Gauss-Seidel method converged after 6 iterations with an error 5.119255e-11 The minimal-residual method converged after 269 iterations with an error 1.834488e-07 The residual-norm steepest-descent method converged after 8 iterations with an error 2.900236e-08 The Jacobi method converged after 7 iterations with an error 7.023143e-09 The Gauss-Seidel method converged after 6 iterations with an error 1.810753e-11 The minimal-residual method converged after 269 iterations with an error 1.757224e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 7.110707e-09 The Jacobi method converged after 8 iterations with an error 6.971926e-10 The Gauss-Seidel method converged after 6 iterations with an error 1.126804e-10 The minimal-residual method converged after 267 iterations with an error 1.803266e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 1.290762e-08 The Jacobi method converged after 8 iterations with an error 7.065181e-10 The Gauss-Seidel method converged after 6 iterations with an error 1.262244e-10 The minimal-residual method converged after 281 iterations with an error 1.743625e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 1.971755e-08 The Jacobi method converged after 7 iterations with an error 9.000378e-09 The Gauss-Seidel method converged after 6 iterations with an error 1.485059e-10 The minimal-residual method converged after 280 iterations with an error 1.821760e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 9.360836e-09 The Jacobi method converged after 9 iterations with an error 1.859068e-09 The Gauss-Seidel method converged after 7 iterations with an error 1.165645e-10 The minimal-residual method converged after 273 iterations with an error 1.653319e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 3.425039e-08 The Jacobi method converged after 9 iterations with an error 8.089447e-10 The Gauss-Seidel method converged after 7 iterations with an error 2.248631e-11 The minimal-residual method converged after 273 iterations with an error 1.730246e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 3.665000e-08 The Jacobi method converged after 9 iterations with an error 9.679938e-10 The Gauss-Seidel method converged after 7 iterations with an error 1.130254e-10 The minimal-residual method converged after 277 iterations with an error 1.750743e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 2.073642e-08 The Jacobi method converged after 9 iterations with an error 1.602893e-09 The Gauss-Seidel method converged after 7 iterations with an error 7.223854e-11 The minimal-residual method converged after 277 iterations with an error 1.685825e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 3.465696e-08 The Jacobi method converged after 9 iterations with an error 1.217928e-09 The Gauss-Seidel method converged after 7 iterations with an error 7.490825e-11 The minimal-residual method converged after 285 iterations with an error 1.762692e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 1.299819e-08 The Jacobi method converged after 9 iterations with an error 2.404381e-09 The Gauss-Seidel method converged after 7 iterations with an error 5.559394e-11 The minimal-residual method converged after 281 iterations with an error 1.746061e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 4.588408e-08 The Jacobi method converged after 9 iterations with an error 1.970648e-09 The Gauss-Seidel method converged after 7 iterations with an error 4.792139e-11 The minimal-residual method converged after 278 iterations with an error 1.726977e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 2.076785e-08 The Jacobi method converged after 9 iterations with an error 3.413493e-09 The Gauss-Seidel method converged after 7 iterations with an error 5.122770e-11 The minimal-residual method converged after 286 iterations with an error 1.773810e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 5.848609e-08 The Jacobi method converged after 9 iterations with an error 1.942085e-09 The Gauss-Seidel method converged after 7 iterations with an error 6.615516e-11 The minimal-residual method converged after 277 iterations with an error 1.685827e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 5.198419e-08 The Jacobi method converged after 9 iterations with an error 3.171078e-09 The Gauss-Seidel method converged after 7 iterations with an error 2.106960e-11 The minimal-residual method converged after 276 iterations with an error 1.686156e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 2.002691e-08 The Jacobi method converged after 8 iterations with an error 2.505714e-09 The Gauss-Seidel method converged after 6 iterations with an error 1.339536e-11 The minimal-residual method converged after 271 iterations with an error 1.733684e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 1.179921e-08 The Jacobi method converged after 8 iterations with an error 1.271590e-09 The Gauss-Seidel method converged after 6 iterations with an error 1.513377e-11 The minimal-residual method converged after 280 iterations with an error 1.689560e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 2.789480e-08 The Jacobi method converged after 8 iterations with an error 2.342112e-09 The Gauss-Seidel method converged after 6 iterations with an error 1.239723e-11 The minimal-residual method converged after 271 iterations with an error 1.820386e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 2.781941e-08 The Jacobi method converged after 8 iterations with an error 1.822047e-09 The Gauss-Seidel method converged after 6 iterations with an error 3.681565e-11 The minimal-residual method converged after 268 iterations with an error 1.790406e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 3.243002e-08 The Jacobi method converged after 8 iterations with an error 1.848797e-09 The Gauss-Seidel method converged after 6 iterations with an error 3.195771e-11 The minimal-residual method converged after 270 iterations with an error 1.787621e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 1.502619e-08 The Jacobi method converged after 9 iterations with an error 1.218417e-09 The Gauss-Seidel method converged after 7 iterations with an error 2.968607e-11 The minimal-residual method converged after 275 iterations with an error 1.659925e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 3.763742e-08 The Jacobi method converged after 8 iterations with an error 4.219969e-09 The Gauss-Seidel method converged after 7 iterations with an error 3.010879e-11 The minimal-residual method converged after 272 iterations with an error 1.719752e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 3.501178e-08 The Jacobi method converged after 8 iterations with an error 5.310577e-09 The Gauss-Seidel method converged after 7 iterations with an error 2.464565e-11 The minimal-residual method converged after 275 iterations with an error 1.687147e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 1.715981e-08 The Jacobi method converged after 9 iterations with an error 8.243078e-10 The Gauss-Seidel method converged after 7 iterations with an error 1.586308e-11 The minimal-residual method converged after 275 iterations with an error 1.709320e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 3.549285e-08 The Jacobi method converged after 8 iterations with an error 8.567129e-09 The Gauss-Seidel method converged after 7 iterations with an error 1.732526e-11 The minimal-residual method converged after 283 iterations with an error 1.703563e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 3.646811e-08 The Jacobi method converged after 10 iterations with an error 3.676595e-09 The Gauss-Seidel method converged after 8 iterations with an error 2.418326e-11 The minimal-residual method converged after 280 iterations with an error 1.691766e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 2.326439e-08 The Jacobi method converged after 9 iterations with an error 7.752234e-09 The Gauss-Seidel method converged after 7 iterations with an error 1.475107e-10 The minimal-residual method converged after 282 iterations with an error 1.730964e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 4.770907e-08 The Jacobi method converged after 9 iterations with an error 7.662362e-09 The Gauss-Seidel method converged after 7 iterations with an error 2.055240e-10 The minimal-residual method converged after 288 iterations with an error 1.714699e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 3.229694e-08 The Jacobi method converged after 9 iterations with an error 8.895456e-09 The Gauss-Seidel method converged after 8 iterations with an error 2.108974e-11 The minimal-residual method converged after 282 iterations with an error 1.648450e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 3.758263e-08 The Jacobi method converged after 9 iterations with an error 9.376995e-09 The Gauss-Seidel method converged after 7 iterations with an error 1.884156e-10 The minimal-residual method converged after 264 iterations with an error 1.647636e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 1.641803e-08 - TESTING WITH A SYMMETRIC POSITIVE DEFINITE MATRIX ----------------------------------------------------------------------- The Jacobi method converged after 8 iterations with an error 6.025228e-09 The gauss-Seidel method converged after 6 iterations with an error 2.394702e-11 The steepest-descent method converged after 9 iterations with an error 1.644617e-10 The minimal-residual method converged after 271 iterations with an error 1.710610e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 1.207590e-08 The Jacobi method converged after 8 iterations with an error 2.267474e-09 The gauss-Seidel method converged after 6 iterations with an error 1.237156e-11 The steepest-descent method converged after 9 iterations with an error 1.585905e-10 The minimal-residual method converged after 260 iterations with an error 1.684315e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 1.646912e-08 The Jacobi method converged after 8 iterations with an error 2.935399e-09 The gauss-Seidel method converged after 6 iterations with an error 1.645410e-11 The steepest-descent method converged after 8 iterations with an error 9.119664e-10 The minimal-residual method converged after 271 iterations with an error 1.743185e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 4.372604e-08 The Jacobi method converged after 8 iterations with an error 2.447676e-09 The gauss-Seidel method converged after 6 iterations with an error 6.258024e-12 The steepest-descent method converged after 8 iterations with an error 9.734735e-10 The minimal-residual method converged after 269 iterations with an error 1.725796e-07 The residual-norm steepest-descent method converged after 9 iterations with an error 4.828567e-08 The Jacobi method converged after 9 iterations with an error 1.188021e-09 The gauss-Seidel method converged after 6 iterations with an error 1.419059e-11 The steepest-descent method converged after 9 iterations with an error 4.409483e-10 The minimal-residual method converged after 278 iterations with an error 1.698596e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 3.649718e-08 The Jacobi method converged after 11 iterations with an error 7.362301e-09 The gauss-Seidel method converged after 8 iterations with an error 2.013809e-11 The steepest-descent method converged after 11 iterations with an error 6.274747e-10 The minimal-residual method converged after 274 iterations with an error 1.519926e-07 The residual-norm steepest-descent method converged after 14 iterations with an error 2.696090e-08 The Jacobi method converged after 11 iterations with an error 3.341759e-09 The gauss-Seidel method converged after 7 iterations with an error 1.747851e-10 The steepest-descent method converged after 11 iterations with an error 5.349942e-10 The minimal-residual method converged after 267 iterations with an error 1.516857e-07 The residual-norm steepest-descent method converged after 13 iterations with an error 7.193264e-08 The Jacobi method converged after 11 iterations with an error 2.757342e-09 The gauss-Seidel method converged after 7 iterations with an error 2.780580e-10 The steepest-descent method converged after 11 iterations with an error 9.608795e-10 The minimal-residual method converged after 252 iterations with an error 1.493761e-07 The residual-norm steepest-descent method converged after 14 iterations with an error 3.514447e-08 The Jacobi method converged after 11 iterations with an error 2.317368e-09 The gauss-Seidel method converged after 7 iterations with an error 2.117721e-10 The steepest-descent method converged after 11 iterations with an error 7.805002e-10 The minimal-residual method converged after 257 iterations with an error 1.534921e-07 The residual-norm steepest-descent method converged after 14 iterations with an error 4.762892e-08 The Jacobi method converged after 11 iterations with an error 1.931891e-09 The gauss-Seidel method converged after 7 iterations with an error 2.580917e-10 The steepest-descent method converged after 11 iterations with an error 5.342530e-10 The minimal-residual method converged after 256 iterations with an error 1.534530e-07 The residual-norm steepest-descent method converged after 14 iterations with an error 2.582874e-08 The Jacobi method converged after 12 iterations with an error 3.961853e-09 The gauss-Seidel method converged after 7 iterations with an error 5.401121e-10 The steepest-descent method converged after 12 iterations with an error 6.045185e-10 The minimal-residual method converged after 262 iterations with an error 1.521947e-07 The residual-norm steepest-descent method converged after 15 iterations with an error 3.927886e-08 The Jacobi method converged after 12 iterations with an error 1.963249e-09 The gauss-Seidel method converged after 7 iterations with an error 4.158636e-10 The steepest-descent method converged after 11 iterations with an error 1.606230e-09 The minimal-residual method converged after 266 iterations with an error 1.564452e-07 The residual-norm steepest-descent method converged after 15 iterations with an error 3.638337e-08 The Jacobi method converged after 12 iterations with an error 7.648830e-09 The gauss-Seidel method converged after 8 iterations with an error 1.650863e-10 The steepest-descent method converged after 12 iterations with an error 1.894334e-09 The minimal-residual method converged after 254 iterations with an error 1.467379e-07 The residual-norm steepest-descent method converged after 15 iterations with an error 9.267202e-08 The Jacobi method converged after 12 iterations with an error 2.986866e-09 The gauss-Seidel method converged after 7 iterations with an error 3.368161e-10 The steepest-descent method converged after 12 iterations with an error 5.566556e-10 The minimal-residual method converged after 275 iterations with an error 1.505062e-07 The residual-norm steepest-descent method converged after 15 iterations with an error 6.868114e-08 The Jacobi method converged after 12 iterations with an error 1.872793e-09 The gauss-Seidel method converged after 8 iterations with an error 3.972681e-11 The steepest-descent method converged after 12 iterations with an error 4.853095e-10 The minimal-residual method converged after 253 iterations with an error 1.511124e-07 The residual-norm steepest-descent method converged after 15 iterations with an error 6.591065e-08 The Jacobi method converged after 9 iterations with an error 1.016938e-09 The gauss-Seidel method converged after 6 iterations with an error 1.133846e-10 The steepest-descent method converged after 9 iterations with an error 2.782537e-10 The minimal-residual method converged after 268 iterations with an error 1.680570e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 2.610474e-08 The Jacobi method converged after 9 iterations with an error 5.961838e-09 The gauss-Seidel method converged after 7 iterations with an error 6.936806e-12 The steepest-descent method converged after 9 iterations with an error 9.261268e-10 The minimal-residual method converged after 270 iterations with an error 1.647878e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 1.380214e-08 The Jacobi method converged after 9 iterations with an error 1.691160e-09 The gauss-Seidel method converged after 7 iterations with an error 5.717498e-12 The steepest-descent method converged after 9 iterations with an error 3.349477e-10 The minimal-residual method converged after 269 iterations with an error 1.653214e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 2.771986e-08 The Jacobi method converged after 9 iterations with an error 3.979233e-09 The gauss-Seidel method converged after 7 iterations with an error 6.158682e-12 The steepest-descent method converged after 9 iterations with an error 2.266466e-10 The minimal-residual method converged after 257 iterations with an error 1.669759e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 2.784359e-08 The Jacobi method converged after 9 iterations with an error 9.580720e-10 The gauss-Seidel method converged after 7 iterations with an error 6.180566e-12 The steepest-descent method converged after 9 iterations with an error 1.654095e-10 The minimal-residual method converged after 266 iterations with an error 1.701642e-07 The residual-norm steepest-descent method converged after 10 iterations with an error 1.405976e-08 The Jacobi method converged after 10 iterations with an error 8.259613e-09 The gauss-Seidel method converged after 7 iterations with an error 1.937589e-10 The steepest-descent method converged after 10 iterations with an error 7.173200e-10 The minimal-residual method converged after 276 iterations with an error 1.664576e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 4.017748e-08 The Jacobi method converged after 11 iterations with an error 2.572483e-09 The gauss-Seidel method converged after 7 iterations with an error 4.372714e-10 The steepest-descent method converged after 10 iterations with an error 8.698776e-10 The minimal-residual method converged after 256 iterations with an error 1.576588e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 3.696671e-08 The Jacobi method converged after 11 iterations with an error 1.860412e-09 The gauss-Seidel method converged after 7 iterations with an error 1.820885e-10 The steepest-descent method converged after 10 iterations with an error 8.988279e-10 The minimal-residual method converged after 263 iterations with an error 1.577839e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 4.947397e-08 The Jacobi method converged after 10 iterations with an error 9.034571e-09 The gauss-Seidel method converged after 7 iterations with an error 1.814418e-10 The steepest-descent method converged after 10 iterations with an error 6.167465e-10 The minimal-residual method converged after 273 iterations with an error 1.555825e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 4.064555e-08 The Jacobi method converged after 10 iterations with an error 5.586171e-09 The gauss-Seidel method converged after 7 iterations with an error 3.054742e-10 The steepest-descent method converged after 10 iterations with an error 5.204794e-10 The minimal-residual method converged after 257 iterations with an error 1.569126e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 3.178548e-08 The Jacobi method converged after 12 iterations with an error 1.976366e-09 The gauss-Seidel method converged after 8 iterations with an error 5.223144e-11 The steepest-descent method converged after 11 iterations with an error 8.377054e-10 The minimal-residual method converged after 247 iterations with an error 1.459351e-07 The residual-norm steepest-descent method converged after 14 iterations with an error 8.952186e-08 The Jacobi method converged after 12 iterations with an error 3.688763e-09 The gauss-Seidel method converged after 7 iterations with an error 4.739389e-10 The steepest-descent method converged after 12 iterations with an error 3.459288e-10 The minimal-residual method converged after 261 iterations with an error 1.463017e-07 The residual-norm steepest-descent method converged after 14 iterations with an error 3.320673e-08 The Jacobi method converged after 11 iterations with an error 7.150686e-09 The gauss-Seidel method converged after 8 iterations with an error 4.002191e-11 The steepest-descent method converged after 11 iterations with an error 7.841916e-10 The minimal-residual method converged after 256 iterations with an error 1.554619e-07 The residual-norm steepest-descent method converged after 14 iterations with an error 5.298865e-08 The Jacobi method converged after 12 iterations with an error 4.181963e-09 The gauss-Seidel method converged after 8 iterations with an error 7.018419e-11 The steepest-descent method converged after 11 iterations with an error 1.625715e-09 The minimal-residual method converged after 270 iterations with an error 1.592240e-07 The residual-norm steepest-descent method converged after 14 iterations with an error 6.429853e-08 The Jacobi method converged after 12 iterations with an error 1.754480e-09 The gauss-Seidel method converged after 7 iterations with an error 3.831323e-10 The steepest-descent method converged after 11 iterations with an error 2.945146e-10 The minimal-residual method converged after 253 iterations with an error 1.615380e-07 The residual-norm steepest-descent method converged after 13 iterations with an error 5.801311e-08 The Jacobi method converged after 9 iterations with an error 7.889306e-09 The gauss-Seidel method converged after 7 iterations with an error 7.077938e-12 The steepest-descent method converged after 10 iterations with an error 1.998948e-10 The minimal-residual method converged after 263 iterations with an error 1.545499e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 3.627621e-08 The Jacobi method converged after 9 iterations with an error 1.046154e-08 The gauss-Seidel method converged after 7 iterations with an error 2.175313e-11 The steepest-descent method converged after 9 iterations with an error 1.228369e-09 The minimal-residual method converged after 253 iterations with an error 1.612539e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 4.198884e-08 The Jacobi method converged after 9 iterations with an error 9.412076e-09 The gauss-Seidel method converged after 7 iterations with an error 9.788726e-12 The steepest-descent method converged after 9 iterations with an error 8.788565e-10 The minimal-residual method converged after 262 iterations with an error 1.584864e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 1.661210e-08 The Jacobi method converged after 9 iterations with an error 1.106333e-08 The gauss-Seidel method converged after 6 iterations with an error 2.457467e-10 The steepest-descent method converged after 10 iterations with an error 2.319270e-10 The minimal-residual method converged after 250 iterations with an error 1.578799e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 5.388520e-08 The Jacobi method converged after 10 iterations with an error 1.416543e-09 The gauss-Seidel method converged after 7 iterations with an error 1.949302e-11 The steepest-descent method converged after 10 iterations with an error 1.579127e-10 The minimal-residual method converged after 252 iterations with an error 1.589044e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 4.169618e-08 The Jacobi method converged after 10 iterations with an error 5.528347e-09 The gauss-Seidel method converged after 7 iterations with an error 1.211612e-10 The steepest-descent method converged after 10 iterations with an error 1.007856e-09 The minimal-residual method converged after 257 iterations with an error 1.538719e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 5.671803e-08 The Jacobi method converged after 11 iterations with an error 2.204899e-09 The gauss-Seidel method converged after 7 iterations with an error 1.159757e-10 The steepest-descent method converged after 10 iterations with an error 5.137129e-10 The minimal-residual method converged after 280 iterations with an error 1.642521e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 3.966467e-08 The Jacobi method converged after 11 iterations with an error 1.992213e-09 The gauss-Seidel method converged after 7 iterations with an error 2.760826e-11 The steepest-descent method converged after 10 iterations with an error 5.515125e-10 The minimal-residual method converged after 272 iterations with an error 1.621286e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 2.388599e-08 The Jacobi method converged after 10 iterations with an error 6.096244e-09 The gauss-Seidel method converged after 7 iterations with an error 1.157507e-10 The steepest-descent method converged after 10 iterations with an error 1.489908e-09 The minimal-residual method converged after 259 iterations with an error 1.632166e-07 The residual-norm steepest-descent method converged after 13 iterations with an error 3.206221e-08 The Jacobi method converged after 11 iterations with an error 2.452519e-09 The gauss-Seidel method converged after 7 iterations with an error 3.732102e-11 The steepest-descent method converged after 10 iterations with an error 2.208851e-10 The minimal-residual method converged after 281 iterations with an error 1.692392e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 5.446639e-08 The Jacobi method converged after 11 iterations with an error 3.271049e-09 The gauss-Seidel method converged after 8 iterations with an error 5.088923e-11 The steepest-descent method converged after 10 iterations with an error 1.489508e-09 The minimal-residual method converged after 249 iterations with an error 1.577491e-07 The residual-norm steepest-descent method converged after 13 iterations with an error 4.907071e-08 The Jacobi method converged after 11 iterations with an error 7.977542e-09 The gauss-Seidel method converged after 8 iterations with an error 2.298991e-11 The steepest-descent method converged after 11 iterations with an error 5.125902e-10 The minimal-residual method converged after 285 iterations with an error 1.552660e-07 The residual-norm steepest-descent method converged after 13 iterations with an error 6.191076e-08 The Jacobi method converged after 12 iterations with an error 2.280244e-09 The gauss-Seidel method converged after 7 iterations with an error 2.873727e-10 The steepest-descent method converged after 11 iterations with an error 2.778876e-10 The minimal-residual method converged after 293 iterations with an error 1.655715e-07 The residual-norm steepest-descent method converged after 13 iterations with an error 4.135788e-08 The Jacobi method converged after 12 iterations with an error 2.483138e-09 The gauss-Seidel method converged after 8 iterations with an error 8.841400e-11 The steepest-descent method converged after 12 iterations with an error 3.888173e-10 The minimal-residual method converged after 252 iterations with an error 1.514243e-07 The residual-norm steepest-descent method converged after 14 iterations with an error 6.132540e-08 The Jacobi method converged after 11 iterations with an error 1.030831e-08 The gauss-Seidel method converged after 8 iterations with an error 5.389343e-11 The steepest-descent method converged after 11 iterations with an error 1.667068e-09 The minimal-residual method converged after 249 iterations with an error 1.484498e-07 The residual-norm steepest-descent method converged after 15 iterations with an error 2.575736e-08 The Jacobi method converged after 10 iterations with an error 5.412771e-09 The gauss-Seidel method converged after 7 iterations with an error 2.874662e-11 The steepest-descent method converged after 10 iterations with an error 4.653450e-10 The minimal-residual method converged after 274 iterations with an error 1.585516e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 2.008429e-08 The Jacobi method converged after 10 iterations with an error 2.270139e-09 The gauss-Seidel method converged after 7 iterations with an error 1.148215e-11 The steepest-descent method converged after 10 iterations with an error 4.859035e-10 The minimal-residual method converged after 260 iterations with an error 1.600643e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 2.376536e-08 The Jacobi method converged after 10 iterations with an error 4.078348e-09 The gauss-Seidel method converged after 7 iterations with an error 3.587388e-11 The steepest-descent method converged after 10 iterations with an error 2.214377e-10 The minimal-residual method converged after 279 iterations with an error 1.598856e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 4.349981e-08 The Jacobi method converged after 10 iterations with an error 7.345889e-09 The gauss-Seidel method converged after 7 iterations with an error 4.384031e-11 The steepest-descent method converged after 10 iterations with an error 4.695944e-10 The minimal-residual method converged after 276 iterations with an error 1.576642e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 1.881560e-08 The Jacobi method converged after 10 iterations with an error 2.189585e-09 The gauss-Seidel method converged after 7 iterations with an error 2.291233e-11 The steepest-descent method converged after 10 iterations with an error 3.311586e-10 The minimal-residual method converged after 260 iterations with an error 1.626477e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 5.868245e-08 The Jacobi method converged after 10 iterations with an error 9.597988e-09 The gauss-Seidel method converged after 7 iterations with an error 1.109020e-10 The steepest-descent method converged after 10 iterations with an error 1.117165e-09 The minimal-residual method converged after 264 iterations with an error 1.607813e-07 The residual-norm steepest-descent method converged after 13 iterations with an error 1.639148e-08 The Jacobi method converged after 11 iterations with an error 1.928576e-09 The gauss-Seidel method converged after 7 iterations with an error 4.980806e-11 The steepest-descent method converged after 10 iterations with an error 1.192902e-09 The minimal-residual method converged after 269 iterations with an error 1.588244e-07 The residual-norm steepest-descent method converged after 13 iterations with an error 2.267102e-08 The Jacobi method converged after 10 iterations with an error 5.478351e-09 The gauss-Seidel method converged after 7 iterations with an error 1.034091e-10 The steepest-descent method converged after 10 iterations with an error 6.117785e-10 The minimal-residual method converged after 268 iterations with an error 1.615425e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 3.534709e-08 The Jacobi method converged after 11 iterations with an error 2.276350e-09 The gauss-Seidel method converged after 7 iterations with an error 1.095839e-10 The steepest-descent method converged after 11 iterations with an error 2.693497e-10 The minimal-residual method converged after 265 iterations with an error 1.620146e-07 The residual-norm steepest-descent method converged after 13 iterations with an error 5.710502e-08 The Jacobi method converged after 11 iterations with an error 2.335962e-09 The gauss-Seidel method converged after 7 iterations with an error 8.644590e-11 The steepest-descent method converged after 11 iterations with an error 4.808191e-10 The minimal-residual method converged after 261 iterations with an error 1.599871e-07 The residual-norm steepest-descent method converged after 13 iterations with an error 6.271192e-08 The Jacobi method converged after 12 iterations with an error 3.612443e-09 The gauss-Seidel method converged after 8 iterations with an error 4.610088e-11 The steepest-descent method converged after 11 iterations with an error 1.642898e-09 The minimal-residual method converged after 264 iterations with an error 1.529418e-07 The residual-norm steepest-descent method converged after 14 iterations with an error 3.862612e-08 The Jacobi method converged after 12 iterations with an error 2.840340e-09 The gauss-Seidel method converged after 8 iterations with an error 3.537124e-11 The steepest-descent method converged after 11 iterations with an error 1.478186e-09 The minimal-residual method converged after 266 iterations with an error 1.527455e-07 The residual-norm steepest-descent method converged after 14 iterations with an error 5.283949e-08 The Jacobi method converged after 12 iterations with an error 2.591765e-09 The gauss-Seidel method converged after 8 iterations with an error 7.725906e-11 The steepest-descent method converged after 11 iterations with an error 9.385722e-10 The minimal-residual method converged after 241 iterations with an error 1.461825e-07 The residual-norm steepest-descent method converged after 15 iterations with an error 3.740157e-08 The Jacobi method converged after 12 iterations with an error 4.514659e-09 The gauss-Seidel method converged after 8 iterations with an error 8.194175e-11 The steepest-descent method converged after 12 iterations with an error 7.124647e-10 The minimal-residual method converged after 252 iterations with an error 1.516482e-07 The residual-norm steepest-descent method converged after 15 iterations with an error 3.001382e-08 The Jacobi method converged after 11 iterations with an error 8.197208e-09 The gauss-Seidel method converged after 7 iterations with an error 3.165093e-10 The steepest-descent method converged after 11 iterations with an error 1.183857e-09 The minimal-residual method converged after 263 iterations with an error 1.505478e-07 The residual-norm steepest-descent method converged after 14 iterations with an error 4.477280e-08 The Jacobi method converged after 10 iterations with an error 1.824001e-09 The gauss-Seidel method converged after 6 iterations with an error 2.781393e-11 The steepest-descent method converged after 9 iterations with an error 9.463182e-10 The minimal-residual method converged after 264 iterations with an error 1.688612e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 2.619980e-08 The Jacobi method converged after 10 iterations with an error 2.724514e-09 The gauss-Seidel method converged after 6 iterations with an error 6.795456e-11 The steepest-descent method converged after 9 iterations with an error 1.040339e-09 The minimal-residual method converged after 285 iterations with an error 1.589649e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 3.063952e-08 The Jacobi method converged after 10 iterations with an error 2.862389e-09 The gauss-Seidel method converged after 6 iterations with an error 1.535195e-10 The steepest-descent method converged after 10 iterations with an error 2.810459e-10 The minimal-residual method converged after 265 iterations with an error 1.614111e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 1.390052e-08 The Jacobi method converged after 10 iterations with an error 2.809121e-09 The gauss-Seidel method converged after 6 iterations with an error 3.333764e-10 The steepest-descent method converged after 9 iterations with an error 8.759343e-10 The minimal-residual method converged after 269 iterations with an error 1.707887e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 1.560129e-08 The Jacobi method converged after 10 iterations with an error 2.210453e-09 The gauss-Seidel method converged after 7 iterations with an error 3.279776e-12 The steepest-descent method converged after 9 iterations with an error 1.196241e-09 The minimal-residual method converged after 271 iterations with an error 1.684089e-07 The residual-norm steepest-descent method converged after 11 iterations with an error 1.942815e-08 The Jacobi method converged after 11 iterations with an error 3.410733e-09 The gauss-Seidel method converged after 7 iterations with an error 1.386923e-10 The steepest-descent method converged after 10 iterations with an error 6.332090e-10 The minimal-residual method converged after 284 iterations with an error 1.623417e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 3.320772e-08 The Jacobi method converged after 11 iterations with an error 1.562652e-09 The gauss-Seidel method converged after 7 iterations with an error 8.367780e-11 The steepest-descent method converged after 10 iterations with an error 1.214235e-09 The minimal-residual method converged after 261 iterations with an error 1.554447e-07 The residual-norm steepest-descent method converged after 13 iterations with an error 1.789350e-08 The Jacobi method converged after 10 iterations with an error 5.061083e-09 The gauss-Seidel method converged after 7 iterations with an error 9.239295e-11 The steepest-descent method converged after 10 iterations with an error 5.442739e-10 The minimal-residual method converged after 265 iterations with an error 1.672319e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 2.916877e-08 The Jacobi method converged after 10 iterations with an error 8.472678e-09 The gauss-Seidel method converged after 7 iterations with an error 9.791288e-11 The steepest-descent method converged after 10 iterations with an error 1.108199e-09 The minimal-residual method converged after 264 iterations with an error 1.554998e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 4.455903e-08 The Jacobi method converged after 11 iterations with an error 1.387137e-09 The gauss-Seidel method converged after 7 iterations with an error 7.414139e-11 The steepest-descent method converged after 10 iterations with an error 3.789293e-10 The minimal-residual method converged after 265 iterations with an error 1.622089e-07 The residual-norm steepest-descent method converged after 12 iterations with an error 2.032936e-08 The Jacobi method converged after 11 iterations with an error 8.963980e-09 The gauss-Seidel method converged after 8 iterations with an error 1.129553e-10 The steepest-descent method converged after 11 iterations with an error 1.797230e-09 The minimal-residual method converged after 259 iterations with an error 1.482941e-07 The residual-norm steepest-descent method converged after 15 iterations with an error 3.679042e-08 The Jacobi method converged after 12 iterations with an error 3.215129e-09 The gauss-Seidel method converged after 8 iterations with an error 4.532489e-11 The steepest-descent method converged after 12 iterations with an error 1.144798e-09 The minimal-residual method converged after 253 iterations with an error 1.461599e-07 The residual-norm steepest-descent method converged after 16 iterations with an error 5.561323e-08 The Jacobi method converged after 12 iterations with an error 9.752023e-09 The gauss-Seidel method converged after 8 iterations with an error 8.262459e-11 The steepest-descent method converged after 12 iterations with an error 1.569216e-09 The minimal-residual method converged after 251 iterations with an error 1.431011e-07 The residual-norm steepest-descent method converged after 16 iterations with an error 6.493064e-08 The Jacobi method converged after 12 iterations with an error 6.071384e-09 The gauss-Seidel method converged after 8 iterations with an error 1.395944e-10 The steepest-descent method converged after 12 iterations with an error 6.772579e-10 The minimal-residual method converged after 249 iterations with an error 1.462575e-07 The residual-norm steepest-descent method converged after 15 iterations with an error 5.321854e-08 The Jacobi method converged after 12 iterations with an error 6.696522e-09 The gauss-Seidel method converged after 7 iterations with an error 3.241623e-10 The steepest-descent method converged after 12 iterations with an error 1.336214e-09 The minimal-residual method converged after 250 iterations with an error 1.447235e-07 The residual-norm steepest-descent method converged after 16 iterations with an error 6.243007e-08 - TESTING WITH A GENERIC MATRIX ------------------------------------------------------------------------------------------- ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 17109 iterations with an error 9.040397e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 18095 iterations with an error 9.921043e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 16163 iterations with an error 1.043987e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 15981 iterations with an error 1.097446e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 16811 iterations with an error 9.925629e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 3071 iterations with an error 5.203321e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 3128 iterations with an error 4.463219e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 2823 iterations with an error 5.521704e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 3448 iterations with an error 4.478636e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 3422 iterations with an error 4.576253e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 2197 iterations with an error 4.667232e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 1965 iterations with an error 4.423641e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 1870 iterations with an error 4.650673e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 1943 iterations with an error 4.251464e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 2118 iterations with an error 4.161227e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 76689 iterations with an error 2.251767e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 74911 iterations with an error 2.301537e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 74875 iterations with an error 2.260579e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 76467 iterations with an error 2.263881e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 65475 iterations with an error 2.276596e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 32151 iterations with an error 1.786914e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 30383 iterations with an error 1.981963e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 31618 iterations with an error 1.703111e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 31257 iterations with an error 1.647523e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 26952 iterations with an error 1.691834e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 3856 iterations with an error 5.305594e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 3885 iterations with an error 5.463728e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 3497 iterations with an error 6.595106e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 4052 iterations with an error 5.404130e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 4001 iterations with an error 5.097833e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 64866 iterations with an error 1.765392e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 62864 iterations with an error 1.903479e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 63714 iterations with an error 1.752441e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 59917 iterations with an error 1.871237e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 64464 iterations with an error 1.780476e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 10719 iterations with an error 7.955869e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 7418 iterations with an error 8.632718e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 8535 iterations with an error 8.160954e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 7071 iterations with an error 9.433790e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 10945 iterations with an error 8.472725e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 12975 iterations with an error 1.000143e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 12369 iterations with an error 9.616349e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 11556 iterations with an error 1.171103e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 13207 iterations with an error 1.052154e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 13329 iterations with an error 9.929504e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 8027 iterations with an error 7.190248e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 7513 iterations with an error 7.005506e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 7403 iterations with an error 6.892512e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 7691 iterations with an error 6.552934e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 6737 iterations with an error 8.449811e-07 ERROR: the Gauss-Seidel method did not converge! ERROR: the residual-norm steepest-descent method did not converge! ERROR: the Gauss-Seidel method did not converge! ERROR: the residual-norm steepest-descent method did not converge! ERROR: the Gauss-Seidel method did not converge! ERROR: the residual-norm steepest-descent method did not converge! ERROR: the Gauss-Seidel method did not converge! ERROR: the residual-norm steepest-descent method did not converge! ERROR: the Gauss-Seidel method did not converge! ERROR: the residual-norm steepest-descent method did not converge! ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 7397 iterations with an error 8.933348e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 7707 iterations with an error 1.008488e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 8302 iterations with an error 8.978911e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 6986 iterations with an error 1.060273e-06 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 8751 iterations with an error 8.770398e-07 ERROR: the Gauss-Seidel method did not converge! ERROR: the residual-norm steepest-descent method did not converge! ERROR: the Gauss-Seidel method did not converge! ERROR: the residual-norm steepest-descent method did not converge! ERROR: the Gauss-Seidel method did not converge! ERROR: the residual-norm steepest-descent method did not converge! ERROR: the Gauss-Seidel method did not converge! ERROR: the residual-norm steepest-descent method did not converge! ERROR: the Gauss-Seidel method did not converge! ERROR: the residual-norm steepest-descent method did not converge! ERROR: the Gauss-Seidel method did not converge! ERROR: the residual-norm steepest-descent method did not converge! ERROR: the Gauss-Seidel method did not converge! ERROR: the residual-norm steepest-descent method did not converge! ERROR: the Gauss-Seidel method did not converge! ERROR: the residual-norm steepest-descent method did not converge! ERROR: the Gauss-Seidel method did not converge! ERROR: the residual-norm steepest-descent method did not converge! ERROR: the Gauss-Seidel method did not converge! ERROR: the residual-norm steepest-descent method did not converge! ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 3402 iterations with an error 5.440872e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 3385 iterations with an error 5.727433e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 3355 iterations with an error 6.082866e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 2805 iterations with an error 5.479547e-07 ERROR: the Gauss-Seidel method did not converge! The residual-norm steepest-descent method method converged after 3333 iterations with an error 6.129672e-07