Malicious Data Attacks on Smart Grid State Estimation: Attack Strategies and Countermeasures

Contents

Problem formulation

The modern smart grid depends heavily on communication, with the purpose of making the power system more efficient and flexible. However, this integration with the cyber infrastrucutre makes the network more vulnerable to cyber attacks. The authors of this paper investigate the problem of constructing malicious data attack of smart grid state estimation with countermeasures that detect the presence of such attacks. The attacks are constructed such that to minimize the residue energy of attack while guaranteeing a certain level of increase of mean square error. For attacks detection, the Generalized Likelihood Ratio Test (GLRT) is used, and regularized by an $L_1$ norm penalty of the strength of the attack.

Proposed solution

The first step is to represent the power system, achieved by adopting a graph theoretic model. The power system is composed of Buses, transmission lines, and power flow meters. The goal of state estimation is to recover the full state of system, i.e in case of power system the voltage and phase and of every bus in the network. Adopting a DC power flow model, which is a linearized version of the AC power flow model:

where $z \in \mathbf{R}^m$ is the vector power flow measurements, $\mathbf{x} \in \mathbf{R}^n$ the system state (voltage phase angles), $\mathbf{e}$ the Gaussian measurement noise with zero mean and covariance matrix $\Sigma_e$, and vector $\mathbf{a}$ is malicious data injected by adversary.

The authors consider a Bayesian framework, with random state variables with Gaussian distribution $\mathcal{N} (\mu_x,\Sigma_x)$, with $\mu_x=0$. In the case there is no attack i.e $\mathbf{a=0}$, The minimum mean square error (MMSE) estimator of the sate vector $\mathbf{x}$ is a linear estimator given by:

where

The minimum mean square error, in the absence of attack is given by:

In the case of presence of an attack, then the estimator $\mathbf{\hat{x} = Kz}$ is a naive estimator that ignores the possibility of attack. The mean square error (MSE) in this case is given by:

where the impact on the estimator from a particular attack $\mathbf{a}$ is the term $\Vert \mathbf{Ka} \Vert_2^2$.

For the detection problem at the control center, the authors assume a Bayesian model of starte variables with a multivariable Gaussian distribution $\mathbf{e \sim \mathcal{N} (0,\Sigma_e)}$.

The following composite binary hypothesis are considered under the observation model of the DC power flow:

The goal is to design a detector $\delta$: $\mathbf{R} \Longrightarrow \lbrace 0,1 \rbrace$, with $\delta(\mathbf{z})=1$ indicating a detection of attack $\mathcal({H}_1)$ and $\delta(\mathbf{(z)}=0$ the null hypothesis $\mathcal({H}_0)$

There exits no uniformly most powerful test for the given composite binary hypotheses, therefore the authors propose a generalized likelihood ratio test (GLRT). The distribution of the measurement $\mathbf{z}$ under the two hypotheses differ only in their means:

where $\mathbf{\Sigma_z} \equiv \mathbf{H \Sigma_x H^T + \Sigma_e}$. From that the GLRT can be written as:

Thus the GLRT reduces to solving

The $L_0$ in the above optimization problem makes it non-convex, but for a small k it can be solved exactly by exhaustively searching through all sparsity patterns. For larger k, this is not feasible, however it is a well known that the above optimization problem can be approximated by the following convex optimization

where the $L_1$ norm constraint is a heuristic replacement for the sparsity of $\mathbf{a}$. By solving the above optimization problem multiple times, the solution will involve an $\mathbf{a}$ with a sparsity $k$ with adjustment of the constant $\nu$.

Data sources

The DC power flow model data used by the authors is obtained by using a DC State Estimation Model, using the Weighted Least Squares Method (WLS). The DC model is a linearized version of the AC model. The assumptions in this model are that Buses voltages are known and equal to 1.0 pu, also all shunt elements are branch resistances are neglected. Power flow is approximated by:

$$P_{ik}=\frac{\theta_i - \theta_k}{x_{ik}}+ e$$

where $x_{ik}$ is the reactance of branch $i-k$, $\theta_i$ is the phase angle at bus i, and $e$ is the measurement error. Also, power injection measurement at bus $i$ is given by:

$$P_i=\sum_{j \in N_j} P_{ij} +e$$

where $N_j$ is the set of buses connected to bus j. Hence, the DC model for the real power measurements can be expressed in matrix form as follows:

$$z = H \theta + e$$

where $z$ includes flow and injection measurements, $H$ is a function of the branch reactances only, and $e$ is the vector of random errors. The code used to generate the power flow measurements is obtained by following the algorithm described in [1].

Solution

clear;clc;
load Power_DC

%GLRT
%1- Sparsity =2, SNR=10db
k=2; SNR=10;
[a_1,Co_z1,Co_x1,Co_e1] = GLRT(k,z,SNR,H,x);

%2- Sparsity =3, SNR=10db
k=3; SNR=10;
[a_2,Co_z2,Co_x2,Co_e2] = GLRT(k,z,SNR,H,x);

%3- Sparsity =3, SNR=6db
k=3; SNR=6;
[a_3,Co_z3,Co_x3,Co_e3] = GLRT(k,z,SNR,H,x);

%4- Sparsity =6, SNR=10db
k=6;SNR=10;
[a_4,Co_z4,Co_x4,Co_e4] = GLRT(k,z,SNR,H,x);

 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|1.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.808|1.000|6.6e+00|2.3e-02|4.6e+02| 1.711849e+01 -1.086196e+01| 0:0:00| chol  1  1 
 2|0.971|1.000|1.9e-01|2.3e-03|1.6e+01| 2.947725e-01 -2.833353e+00| 0:0:00| chol  1  1 
 3|0.986|0.987|2.8e-03|2.6e-04|2.2e-01| 5.820107e-03 -3.828632e-02| 0:0:00| chol  1  1 
 4|0.988|0.989|3.3e-05|1.5e-04|2.9e-03| 6.856033e-05 -3.808082e-04| 0:0:00| chol  1  1 
 5|0.988|0.989|3.9e-07|5.5e-06|3.7e-05| 7.526611e-07  6.497825e-07| 0:0:00| chol  1  1 
 6|0.755|0.949|1.5e-07|3.6e-07|1.0e-05| 2.056559e-07 -1.623756e-08| 0:0:00| chol  1  1 
 7|0.631|0.968|7.0e-08|4.1e-08|4.7e-06| 8.247837e-08 -1.960432e-08| 0:0:00| chol  1  1 
 8|0.606|1.000|3.5e-08|1.4e-08|2.3e-06| 3.547904e-08 -9.521141e-09| 0:0:00| chol  1  1 
 9|0.594|1.000|1.8e-08|7.1e-09|1.2e-06| 1.583248e-08 -4.775136e-09| 0:0:00| chol  1  1 
10|0.473|1.000|9.5e-09|3.6e-09|7.4e-07| 1.031259e-08 -2.440108e-09| 0:0:00| chol  1  1 
11|0.473|1.000|5.0e-09|1.9e-09|4.6e-07| 6.511586e-09 -1.528680e-09| 0:0:00| chol  1  1 
12|0.474|1.000|2.6e-09|1.0e-09|2.8e-07| 4.032795e-09 -9.483603e-10| 0:0:00| chol  1  1 
13|0.474|1.000|1.4e-09|5.3e-10|1.8e-07| 2.469781e-09 -5.880465e-10| 0:0:00| chol  1  1 
14|0.474|1.000|7.3e-10|2.8e-10|1.1e-07| 1.503115e-09 -3.646026e-10| 0:0:00| chol  1  1 
15|0.473|1.000|3.8e-10|1.5e-10|6.7e-08| 9.119591e-10 -2.261049e-10| 0:0:00| chol  1  1 
16|0.473|1.000|2.0e-10|7.7e-11|4.2e-08| 5.527109e-10 -1.402612e-10| 0:0:00| chol  1  1 
17|0.473|1.000|1.1e-10|4.0e-11|2.6e-08| 3.350754e-10 -8.704314e-11| 0:0:00| chol  1  1 
18|0.473|1.000|5.6e-11|2.1e-11|1.6e-08| 2.033664e-10 -5.403926e-11| 0:0:00| chol  1  1 
19|0.473|1.000|3.0e-11|1.1e-11|1.0e-08| 1.236325e-10 -3.356367e-11| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 19
 primal objective value =  1.23632498e-10
 dual   objective value = -3.35636746e-11
 gap := trace(XZ)       = 9.99e-09
 relative gap           = 9.99e-09
 actual relative gap    = 1.57e-10
 rel. primal infeas (scaled problem)   = 2.96e-11
 rel. dual     "        "       "      = 1.12e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 7.1e-01, 1.7e+02, 1.1e+03
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 2.8e+01
 Total CPU time (secs)  = 0.13  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 3.0e-11  0.0e+00  1.6e-11  0.0e+00  1.6e-10  1.0e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +1.23633e-10
 
sparsity =
     0
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|1.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.809|1.000|6.5e+00|2.3e-02|4.6e+02| 1.704690e+01 -1.403167e+01| 0:0:00| chol  1  1 
 2|0.977|1.000|1.5e-01|2.3e-03|1.6e+01| 1.551542e-01 -5.955735e+00| 0:0:00| chol  1  1 
 3|0.992|0.988|1.2e-03|2.6e-04|1.8e+00|-7.137319e-02 -1.855420e+00| 0:0:00| chol  1  1 
 4|1.000|0.613|3.3e-08|3.5e-04|8.3e-01|-1.931522e-01 -1.017523e+00| 0:0:00| chol  1  1 
 5|0.717|0.422|1.0e-08|2.0e-04|3.8e-01|-6.511320e-01 -1.027977e+00| 0:0:00| chol  1  1 
 6|0.882|0.724|6.3e-09|5.6e-05|1.3e-01|-7.886687e-01 -9.162468e-01| 0:0:00| chol  1  1 
 7|1.000|0.952|3.0e-09|2.7e-06|2.7e-02|-8.420246e-01 -8.686195e-01| 0:0:00| chol  1  1 
 8|0.969|0.977|4.1e-10|6.4e-08|8.3e-04|-8.636492e-01 -8.644776e-01| 0:0:00| chol  1  1 
 9|0.969|0.986|2.6e-10|1.2e-09|2.4e-05|-8.643490e-01 -8.643732e-01| 0:0:00| chol  1  1 
10|0.944|0.986|2.6e-11|6.9e-11|2.4e-06|-8.643692e-01 -8.643716e-01| 0:0:00| chol  2  2 
11|0.559|1.000|1.2e-11|5.3e-12|1.3e-06|-8.643702e-01 -8.643715e-01| 0:0:00| chol  2  1 
12|0.563|1.000|1.3e-11|2.3e-12|6.7e-07|-8.643708e-01 -8.643715e-01| 0:0:00| chol  1  1 
13|0.564|1.000|3.9e-12|2.6e-12|3.6e-07|-8.643711e-01 -8.643715e-01| 0:0:00| chol  1  1 
14|0.566|1.000|1.6e-12|1.0e-12|1.9e-07|-8.643713e-01 -8.643715e-01| 0:0:00| chol  1  1 
15|0.567|1.000|7.0e-13|1.0e-12|1.0e-07|-8.643714e-01 -8.643715e-01| 0:0:00| chol  1  1 
16|0.567|1.000|3.7e-13|1.0e-12|5.4e-08|-8.643714e-01 -8.643715e-01| 0:0:00| chol  1  1 
17|0.568|1.000|1.8e-13|1.0e-12|2.9e-08|-8.643715e-01 -8.643715e-01| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 17
 primal objective value = -8.64371461e-01
 dual   objective value = -8.64371490e-01
 gap := trace(XZ)       = 2.89e-08
 relative gap           = 1.06e-08
 actual relative gap    = 1.06e-08
 rel. primal infeas (scaled problem)   = 1.79e-13
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 7.3e-01, 7.7e+00, 5.0e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 2.8e+01
 Total CPU time (secs)  = 0.12  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 1.8e-13  0.0e+00  1.4e-12  0.0e+00  1.1e-08  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -0.864371
 
sparsity =
     1
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|1.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.810|1.000|6.4e+00|2.3e-02|4.5e+02| 1.697514e+01 -1.718384e+01| 0:0:00| chol  1  1 
 2|0.981|1.000|1.2e-01|2.3e-03|1.7e+01| 5.130885e-02 -8.965352e+00| 0:0:00| chol  1  1 
 3|0.994|0.989|6.9e-04|2.5e-04|1.9e+00|-1.528395e-01 -2.060520e+00| 0:0:00| chol  1  1 
 4|0.431|0.155|3.9e-04|3.6e-04|1.4e+00|-6.781424e-01 -2.035882e+00| 0:0:00| chol  1  1 
 5|0.796|0.414|8.0e-05|2.9e-04|7.5e-01|-1.077034e+00 -1.824545e+00| 0:0:00| chol  1  1 
 6|1.000|0.434|7.9e-09|1.8e-04|4.0e-01|-1.256594e+00 -1.652032e+00| 0:0:00| chol  1  1 
 7|0.741|0.863|3.4e-09|2.5e-05|1.2e-01|-1.370899e+00 -1.489000e+00| 0:0:00| chol  1  1 
 8|1.000|0.716|2.1e-10|7.0e-06|3.4e-02|-1.429610e+00 -1.463120e+00| 0:0:00| chol  1  1 
 9|0.977|0.972|5.9e-11|2.0e-07|9.9e-04|-1.451596e+00 -1.452581e+00| 0:0:00| chol  1  1 
10|0.985|0.984|8.6e-13|3.2e-09|1.5e-05|-1.452251e+00 -1.452266e+00| 0:0:00| chol  1  1 
11|0.983|0.988|5.2e-13|4.0e-11|3.5e-07|-1.452261e+00 -1.452261e+00| 0:0:00| chol  2  2 
12|0.557|0.956|5.3e-13|2.7e-12|1.6e-07|-1.452261e+00 -1.452261e+00| 0:0:00| chol  1  2 
13|0.560|1.000|2.6e-13|1.0e-12|8.2e-08|-1.452261e+00 -1.452261e+00| 0:0:00| chol  2  2 
14|0.561|1.000|2.3e-13|1.0e-12|4.4e-08|-1.452261e+00 -1.452261e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 14
 primal objective value = -1.45226095e+00
 dual   objective value = -1.45226100e+00
 gap := trace(XZ)       = 4.39e-08
 relative gap           = 1.12e-08
 actual relative gap    = 1.12e-08
 rel. primal infeas (scaled problem)   = 2.30e-13
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 7.9e-01, 6.6e+00, 3.7e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 2.8e+01
 Total CPU time (secs)  = 0.18  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 2.3e-13  0.0e+00  1.4e-12  0.0e+00  1.1e-08  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -1.45226
 
sparsity =
     2
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|6.1e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.606|1.000|1.3e+01|7.1e-03|3.4e+03| 3.915008e+01 -3.487488e+01| 0:0:00| chol  1  1 
 2|0.976|1.000|3.2e-01|7.1e-04|9.4e+01| 4.994455e-01 -1.643170e+01| 0:0:00| chol  1  1 
 3|0.986|0.988|4.5e-03|7.8e-05|1.3e+00| 6.187787e-03 -2.271013e-01| 0:0:00| chol  1  1 
 4|0.989|0.989|5.1e-05|2.2e-04|1.6e-02| 7.121988e-05 -2.453377e-03| 0:0:00| chol  1  1 
 5|0.989|0.989|5.6e-07|5.6e-06|2.0e-04| 7.837882e-07 -2.202465e-05| 0:0:00| chol  1  1 
 6|0.945|0.949|1.2e-07|4.7e-07|3.3e-05| 2.725446e-07 -9.150707e-07| 0:0:00| chol  1  1 
 7|0.589|0.958|6.0e-08|4.3e-08|1.5e-05| 1.421503e-07 -9.471225e-08| 0:0:00| chol  1  1 
 8|0.588|1.000|3.1e-08|1.2e-08|7.7e-06| 7.441055e-08 -3.078851e-08| 0:0:00| chol  1  1 
 9|0.584|1.000|1.6e-08|6.2e-09|4.0e-06| 3.904170e-08 -1.587169e-08| 0:0:00| chol  1  1 
10|0.476|1.000|8.4e-09|3.2e-09|2.5e-06| 2.492690e-08 -8.238875e-09| 0:0:00| chol  1  1 
11|0.475|1.000|4.4e-09|1.7e-09|1.5e-06| 1.576254e-08 -5.126145e-09| 0:0:00| chol  1  1 
12|0.475|1.000|2.3e-09|8.8e-10|9.4e-07| 9.893512e-09 -3.168841e-09| 0:0:00| chol  1  1 
13|0.474|1.000|1.2e-09|4.6e-10|5.8e-07| 6.180255e-09 -1.960923e-09| 0:0:00| chol  1  1 
14|0.474|1.000|6.4e-10|2.4e-10|3.6e-07| 3.849114e-09 -1.214589e-09| 0:0:00| chol  1  1 
15|0.473|1.000|3.4e-10|1.3e-10|2.2e-07| 2.392893e-09 -7.529357e-10| 0:0:00| chol  1  1 
16|0.473|1.000|1.8e-10|6.8e-11|1.4e-07| 1.486052e-09 -4.670906e-10| 0:0:00| chol  1  1 
17|0.473|1.000|9.4e-11|3.6e-11|8.6e-08| 9.223984e-10 -2.899464e-10| 0:0:00| chol  1  1 
18|0.473|1.000|5.0e-11|1.9e-11|5.4e-08| 5.724339e-10 -1.800830e-10| 0:0:00| chol  1  1 
19|0.472|1.000|2.6e-11|9.9e-12|3.3e-08| 3.552622e-10 -1.118986e-10| 0:0:00| chol  1  1 
20|0.472|1.000|1.4e-11|5.2e-12|2.1e-08| 2.205199e-10 -6.956035e-11| 0:0:00| chol  1  1 
21|0.472|1.000|7.3e-12|2.8e-12|1.3e-08| 1.369166e-10 -4.325493e-11| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 21
 primal objective value =  1.36916557e-10
 dual   objective value = -4.32549270e-11
 gap := trace(XZ)       = 1.29e-08
 relative gap           = 1.29e-08
 actual relative gap    = 1.80e-10
 rel. primal infeas (scaled problem)   = 7.28e-12
 rel. dual     "        "       "      = 2.76e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 7.1e-01, 8.7e+02, 5.6e+03
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 9.2e+01
 Total CPU time (secs)  = 0.24  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 7.3e-12  0.0e+00  2.9e-12  0.0e+00  1.8e-10  1.3e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +1.36916e-10
 
sparsity =
     0
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|6.1e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.607|1.000|1.3e+01|7.1e-03|3.4e+03| 3.910867e+01 -4.693206e+01| 0:0:00| chol  1  1 
 2|0.978|1.000|2.9e-01|7.1e-04|9.9e+01| 4.029629e-01 -2.838157e+01| 0:0:00| chol  1  1 
 3|0.988|0.988|3.4e-03|7.9e-05|9.6e+00|-4.227044e-02 -9.016468e+00| 0:0:00| chol  1  1 
 4|1.000|0.800|3.8e-08|7.1e-04|1.9e+00|-6.975027e-02 -1.947295e+00| 0:0:00| chol  1  1 
 5|0.250|0.097|2.8e-08|6.4e-04|1.6e+00|-3.902318e-01 -1.941647e+00| 0:0:00| chol  1  1 
 6|0.635|0.239|9.1e-09|4.9e-04|7.6e-01|-1.237558e+00 -1.993663e+00| 0:0:00| chol  1  1 
 7|1.000|0.576|1.0e-09|2.1e-04|3.8e-01|-1.286780e+00 -1.665658e+00| 0:0:00| chol  1  1 
 8|0.957|0.967|1.1e-10|6.9e-06|1.6e-02|-1.535833e+00 -1.552116e+00| 0:0:00| chol  1  1 
 9|0.902|0.978|9.2e-11|1.5e-07|1.3e-03|-1.546650e+00 -1.547954e+00| 0:0:00| chol  1  1 
10|0.854|0.964|1.3e-11|5.4e-09|2.7e-04|-1.547475e+00 -1.547740e+00| 0:0:00| chol  1  1 
11|0.959|0.975|4.5e-12|1.4e-10|1.2e-05|-1.547717e+00 -1.547729e+00| 0:0:00| chol  1  1 
12|0.989|0.996|3.5e-11|1.6e-12|2.5e-07|-1.547729e+00 -1.547729e+00| 0:0:00| chol  2  2 
13|0.532|1.000|1.6e-11|1.5e-12|1.4e-07|-1.547729e+00 -1.547729e+00| 0:0:00| chol  1  2 
14|0.535|1.000|1.7e-11|2.3e-12|7.8e-08|-1.547729e+00 -1.547729e+00| 0:0:00| chol  1  1 
15|0.536|1.000|6.4e-12|3.4e-12|4.3e-08|-1.547729e+00 -1.547729e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 15
 primal objective value = -1.54772916e+00
 dual   objective value = -1.54772920e+00
 gap := trace(XZ)       = 4.34e-08
 relative gap           = 1.06e-08
 actual relative gap    = 1.06e-08
 rel. primal infeas (scaled problem)   = 6.40e-12
 rel. dual     "        "       "      = 3.38e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 7.4e-01, 1.6e+01, 9.2e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 9.2e+01
 Total CPU time (secs)  = 0.11  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 6.4e-12  0.0e+00  3.6e-12  0.0e+00  1.1e-08  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -1.54773
 
sparsity =
     1
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|6.1e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.608|1.000|1.3e+01|7.1e-03|3.4e+03| 3.906711e+01 -5.892024e+01| 0:0:00| chol  1  1 
 2|0.979|1.000|2.8e-01|7.1e-04|1.1e+02| 3.649902e-01 -4.008342e+01| 0:0:00| chol  1  1 
 3|0.992|0.988|2.3e-03|7.8e-05|1.4e+01|-8.828040e-02 -1.344776e+01| 0:0:00| chol  1  1 
 4|1.000|0.750|2.9e-08|4.8e-04|3.7e+00|-1.536818e-01 -3.814375e+00| 0:0:00| chol  1  1 
 5|0.169|0.104|2.4e-08|4.3e-04|3.2e+00|-6.092909e-01 -3.821284e+00| 0:0:00| chol  1  1 
 6|0.461|0.465|1.3e-08|2.3e-04|2.2e+00|-1.634744e+00 -3.795257e+00| 0:0:00| chol  1  1 
 7|0.523|0.148|7.1e-09|2.0e-04|3.2e+00| 1.901809e-01 -3.034963e+00| 0:0:00| chol  1  1 
 8|0.457|0.706|3.8e-09|5.8e-05|2.2e+00|-1.546094e+00 -3.721149e+00| 0:0:00| chol  1  1 
 9|0.957|0.870|3.3e-10|7.6e-06|2.6e-01|-2.619090e+00 -2.880306e+00| 0:0:00| chol  1  1 
10|0.962|0.924|1.2e-11|5.7e-07|2.6e-02|-2.749777e+00 -2.776070e+00| 0:0:00| chol  1  1 
11|0.980|0.911|2.5e-13|5.1e-08|1.2e-03|-2.766573e+00 -2.767805e+00| 0:0:00| chol  1  1 
12|0.984|0.879|6.3e-15|6.1e-09|1.1e-04|-2.767131e+00 -2.767240e+00| 0:0:00| chol  1  1 
13|0.986|0.965|5.4e-14|2.2e-10|6.7e-06|-2.767162e+00 -2.767169e+00| 0:0:00| chol  1  1 
14|0.581|0.951|3.0e-12|1.2e-11|2.3e-06|-2.767164e+00 -2.767166e+00| 0:0:00| chol  1  1 
15|0.574|1.000|2.3e-13|1.0e-12|1.1e-06|-2.767165e+00 -2.767166e+00| 0:0:00| chol  1  2 
16|0.572|1.000|2.7e-13|1.0e-12|5.9e-07|-2.767165e+00 -2.767166e+00| 0:0:00| chol  1  2 
17|0.572|1.000|1.6e-13|1.0e-12|3.1e-07|-2.767166e+00 -2.767166e+00| 0:0:00| chol  2  2 
18|0.571|1.000|5.7e-14|1.0e-12|1.6e-07|-2.767166e+00 -2.767166e+00| 0:0:00| chol  1  2 
19|0.571|1.000|1.4e-13|1.0e-12|8.6e-08|-2.767166e+00 -2.767166e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 19
 primal objective value = -2.76716575e+00
 dual   objective value = -2.76716584e+00
 gap := trace(XZ)       = 8.62e-08
 relative gap           = 1.32e-08
 actual relative gap    = 1.32e-08
 rel. primal infeas (scaled problem)   = 1.37e-13
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 7.9e-01, 1.5e+01, 7.8e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 9.2e+01
 Total CPU time (secs)  = 0.13  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 1.4e-13  0.0e+00  1.1e-12  0.0e+00  1.3e-08  1.3e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -2.76717
 
sparsity =
     2
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.3e+01|6.5e+00|6.1e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.610|1.000|1.3e+01|7.1e-03|3.4e+03| 3.902540e+01 -7.083957e+01| 0:0:00| chol  1  1 
 2|0.979|1.000|2.7e-01|7.1e-04|1.2e+02| 3.290787e-01 -5.153961e+01| 0:0:00| chol  1  1 
 3|0.996|0.989|1.2e-03|7.8e-05|1.6e+01|-1.334970e-01 -1.558615e+01| 0:0:00| chol  1  1 
 4|1.000|0.708|2.2e-08|2.7e-04|5.3e+00|-2.604449e-01 -5.560761e+00| 0:0:00| chol  1  1 
 5|0.154|0.105|1.9e-08|2.4e-04|4.7e+00|-9.195761e-01 -5.609240e+00| 0:0:00| chol  1  1 
 6|0.389|0.730|1.2e-08|6.5e-05|3.1e+00|-1.939700e+00 -5.082236e+00| 0:0:00| chol  1  1 
 7|1.000|0.424|3.8e-10|3.7e-05|2.0e+00|-2.040893e+00 -4.086467e+00| 0:0:00| chol  1  1 
 8|0.893|0.969|8.4e-11|1.2e-06|3.6e-01|-3.538997e+00 -3.899167e+00| 0:0:00| chol  1  1 
 9|0.902|0.944|3.9e-11|6.6e-08|3.8e-02|-3.764841e+00 -3.803309e+00| 0:0:00| chol  1  1 
10|0.909|0.960|3.5e-12|2.7e-09|3.9e-03|-3.793336e+00 -3.797260e+00| 0:0:00| chol  1  1 
11|0.945|0.976|2.2e-13|6.6e-11|2.3e-04|-3.796763e+00 -3.796996e+00| 0:0:00| chol  1  1 
12|0.966|0.983|1.3e-13|2.1e-12|8.0e-06|-3.796980e+00 -3.796988e+00| 0:0:00| chol  1  2 
13|0.989|1.000|2.2e-13|1.0e-12|3.1e-07|-3.796988e+00 -3.796988e+00| 0:0:00| chol  1  2 
14|0.552|1.000|2.1e-13|1.0e-12|1.7e-07|-3.796988e+00 -3.796988e+00| 0:0:00| chol  1  2 
15|0.557|1.000|1.1e-13|1.0e-12|9.0e-08|-3.796988e+00 -3.796988e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 15
 primal objective value = -3.79698817e+00
 dual   objective value = -3.79698826e+00
 gap := trace(XZ)       = 9.00e-08
 relative gap           = 1.05e-08
 actual relative gap    = 1.05e-08
 rel. primal infeas (scaled problem)   = 1.12e-13
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 8.5e-01, 1.4e+01, 6.7e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 9.2e+01
 Total CPU time (secs)  = 0.25  
 CPU time per iteration = 0.02  
 termination code       =  0
 DIMACS: 1.1e-13  0.0e+00  1.1e-12  0.0e+00  1.0e-08  1.0e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -3.79699
 
sparsity =
     2
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.3e+01|6.5e+00|6.1e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.611|1.000|1.3e+01|7.1e-03|3.3e+03| 3.898354e+01 -8.269020e+01| 0:0:00| chol  1  1 
 2|0.979|1.000|2.7e-01|7.1e-04|1.3e+02| 3.021478e-01 -6.275370e+01| 0:0:00| chol  1  1 
 3|0.998|0.989|4.5e-04|7.8e-05|1.6e+01|-1.780653e-01 -1.657020e+01| 0:0:00| chol  1  1 
 4|1.000|0.673|1.7e-08|1.2e-04|6.7e+00|-4.064492e-01 -7.149920e+00| 0:0:00| chol  1  1 
 5|0.167|0.115|1.5e-08|1.1e-04|5.9e+00|-1.329641e+00 -7.223743e+00| 0:0:00| chol  1  1 
 6|0.385|1.000|9.8e-09|7.4e-08|3.3e+00|-2.380719e+00 -5.719367e+00| 0:0:00| chol  1  1 
 7|1.000|0.385|5.8e-10|5.0e-08|1.6e+00|-3.608792e+00 -5.216020e+00| 0:0:00| chol  1  1 
 8|0.798|0.880|1.0e-10|6.7e-09|4.5e-01|-4.329568e+00 -4.784163e+00| 0:0:00| chol  1  1 
 9|0.995|0.690|1.8e-11|2.2e-09|1.2e-01|-4.570431e+00 -4.688072e+00| 0:0:00| chol  1  1 
10|0.957|0.955|7.9e-13|1.1e-10|6.4e-03|-4.646788e+00 -4.653163e+00| 0:0:00| chol  1  1 
11|0.939|0.923|4.3e-14|9.9e-12|4.3e-04|-4.651255e+00 -4.651683e+00| 0:0:00| chol  1  1 
12|0.823|0.796|6.8e-13|3.0e-12|1.1e-04|-4.651481e+00 -4.651596e+00| 0:0:00| chol  1  1 
13|0.736|0.802|4.0e-11|1.6e-12|4.4e-05|-4.651534e+00 -4.651578e+00| 0:0:00| chol  2  1 
14|0.751|0.847|6.7e-11|1.7e-12|1.7e-05|-4.651556e+00 -4.651573e+00| 0:0:00| chol  1  1 
15|0.811|0.985|7.2e-12|2.3e-12|5.7e-06|-4.651566e+00 -4.651572e+00| 0:0:00| chol  2  2 
16|0.557|1.000|3.0e-12|1.4e-12|3.0e-06|-4.651569e+00 -4.651572e+00| 0:0:00| chol  2  2 
17|0.568|1.000|1.2e-12|1.0e-12|1.6e-06|-4.651570e+00 -4.651572e+00| 0:0:00| chol  2  2 
18|0.568|1.000|6.4e-13|1.0e-12|8.3e-07|-4.651571e+00 -4.651572e+00| 0:0:00| chol  2  2 
19|0.568|1.000|2.5e-13|1.0e-12|4.4e-07|-4.651572e+00 -4.651572e+00| 0:0:00| chol  2  2 
20|0.568|1.000|8.1e-14|1.0e-12|2.3e-07|-4.651572e+00 -4.651572e+00| 0:0:00| chol  1  1 
21|0.568|1.000|9.9e-12|1.0e-12|1.2e-07|-4.651572e+00 -4.651572e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 21
 primal objective value = -4.65157188e+00
 dual   objective value = -4.65157200e+00
 gap := trace(XZ)       = 1.23e-07
 relative gap           = 1.19e-08
 actual relative gap    = 1.19e-08
 rel. primal infeas (scaled problem)   = 9.86e-12
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 9.2e-01, 1.3e+01, 5.7e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.1e+00, 9.2e+01
 Total CPU time (secs)  = 0.18  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 1.0e-11  0.0e+00  1.1e-12  0.0e+00  1.2e-08  1.2e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -4.65157
 
sparsity =
     3
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|1.6e+03| 2.208732e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.830|1.000|5.8e+00|2.8e-02|3.2e+02| 8.044245e+00 -9.228228e+00| 0:0:00| chol  1  1 
 2|0.970|1.000|1.8e-01|2.8e-03|1.1e+01|-1.119452e-01 -2.052043e+00| 0:0:00| chol  1  1 
 3|0.984|0.985|2.9e-03|3.2e-04|1.8e-01| 1.253727e-03 -3.041559e-02| 0:0:00| chol  1  1 
 4|0.988|0.989|3.5e-05|1.5e-04|2.4e-03| 1.210948e-05 -2.986173e-04| 0:0:00| chol  1  1 
 5|0.988|0.989|4.4e-07|6.1e-06|3.2e-05| 7.521483e-08  1.495439e-06| 0:0:00| chol  1  1 
 6|0.674|0.949|1.9e-07|4.0e-07|1.1e-05| 2.074915e-08  3.163489e-08| 0:0:00| chol  1  1 
 7|0.635|0.973|9.3e-08|5.0e-08|4.9e-06| 5.706555e-09 -1.961523e-08| 0:0:00| chol  1  1 
 8|0.609|1.000|4.6e-08|1.9e-08|2.5e-06| 1.329845e-09 -1.003003e-08| 0:0:00| chol  1  1 
 9|0.595|1.000|2.4e-08|9.2e-09|1.3e-06| 9.539145e-11 -5.005620e-09| 0:0:00| chol  1  1 
10|0.473|1.000|1.2e-08|4.7e-09|7.7e-07| 3.288310e-09 -2.555881e-09| 0:0:00| chol  1  1 
11|0.473|1.000|6.5e-09|2.5e-09|4.8e-07| 3.397913e-09 -1.600455e-09| 0:0:00| chol  1  1 
12|0.474|1.000|3.4e-09|1.3e-09|3.0e-07| 2.662536e-09 -9.928526e-10| 0:0:00| chol  1  1 
13|0.474|1.000|1.8e-09|6.9e-10|1.8e-07| 1.872763e-09 -6.157535e-10| 0:0:00| chol  1  1 
14|0.473|1.000|9.5e-10|3.6e-10|1.1e-07| 1.246790e-09 -3.818967e-10| 0:0:00| chol  1  1 
15|0.473|1.000|5.0e-10|1.9e-10|7.1e-08| 8.043772e-10 -2.369083e-10| 0:0:00| chol  1  1 
16|0.473|1.000|2.6e-10|1.0e-10|4.4e-08| 5.092012e-10 -1.470124e-10| 0:0:00| chol  1  1 
17|0.473|1.000|1.4e-10|5.3e-11|2.7e-08| 3.185977e-10 -9.126094e-11| 0:0:00| chol  1  1 
18|0.473|1.000|7.3e-11|2.8e-11|1.7e-08| 1.979169e-10 -5.667405e-11| 0:0:00| chol  1  1 
19|0.473|1.000|3.9e-11|1.5e-11|1.0e-08| 1.224270e-10 -3.520792e-11| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 19
 primal objective value =  1.22427019e-10
 dual   objective value = -3.52079197e-11
 gap := trace(XZ)       = 1.05e-08
 relative gap           = 1.05e-08
 actual relative gap    = 1.58e-10
 rel. primal infeas (scaled problem)   = 3.87e-11
 rel. dual     "        "       "      = 1.47e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 7.1e-01, 1.3e+02, 8.6e+02
 norm(A), norm(b), norm(C) = 1.7e+01, 2.0e+00, 2.4e+01
 Total CPU time (secs)  = 0.13  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 3.9e-11  0.0e+00  3.0e-11  0.0e+00  1.6e-10  1.0e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +1.22427e-10
 
sparsity =
     0
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|1.6e+03| 2.208732e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.831|1.000|5.7e+00|2.8e-02|3.2e+02| 8.003902e+00 -1.179839e+01| 0:0:00| chol  1  1 
 2|0.972|1.000|1.6e-01|2.8e-03|1.3e+01|-1.988546e-01 -4.591171e+00| 0:0:00| chol  1  1 
 3|0.997|0.986|4.9e-04|3.1e-04|1.5e+00|-1.322212e-01 -1.599082e+00| 0:0:00| chol  1  1 
 4|1.000|0.624|7.0e-08|2.3e-04|6.5e-01|-2.786913e-01 -9.241608e-01| 0:0:00| chol  1  1 
 5|0.613|0.423|2.4e-08|1.4e-04|3.2e-01|-6.605009e-01 -9.785647e-01| 0:0:00| chol  1  1 
 6|0.859|0.957|1.5e-08|6.1e-06|4.8e-02|-8.084751e-01 -8.568260e-01| 0:0:00| chol  1  1 
 7|0.980|0.972|8.4e-09|2.0e-07|6.6e-03|-8.415435e-01 -8.481417e-01| 0:0:00| chol  1  1 
 8|0.980|0.975|8.4e-10|9.4e-09|1.7e-04|-8.475014e-01 -8.476720e-01| 0:0:00| chol  1  1 
 9|0.989|0.989|1.4e-11|2.7e-10|1.9e-06|-8.476578e-01 -8.476598e-01| 0:0:00| chol  1  1 
10|0.566|0.974|1.1e-11|9.9e-12|9.6e-07|-8.476587e-01 -8.476596e-01| 0:0:00| chol  1  2 
11|0.570|1.000|4.6e-12|2.1e-12|5.1e-07|-8.476591e-01 -8.476596e-01| 0:0:00| chol  1  1 
12|0.570|1.000|1.3e-12|1.0e-12|2.7e-07|-8.476593e-01 -8.476596e-01| 0:0:00| chol  1  1 
13|0.570|1.000|1.2e-12|1.0e-12|1.4e-07|-8.476595e-01 -8.476596e-01| 0:0:00| chol  1  1 
14|0.570|1.000|7.6e-13|1.0e-12|7.5e-08|-8.476595e-01 -8.476596e-01| 0:0:00| chol  1  1 
15|0.571|1.000|3.2e-13|1.0e-12|4.0e-08|-8.476596e-01 -8.476596e-01| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 15
 primal objective value = -8.47659575e-01
 dual   objective value = -8.47659615e-01
 gap := trace(XZ)       = 3.97e-08
 relative gap           = 1.47e-08
 actual relative gap    = 1.47e-08
 rel. primal infeas (scaled problem)   = 3.21e-13
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 7.3e-01, 8.2e+00, 5.5e+01
 norm(A), norm(b), norm(C) = 1.7e+01, 2.0e+00, 2.4e+01
 Total CPU time (secs)  = 0.11  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 3.2e-13  0.0e+00  2.0e-12  0.0e+00  1.5e-08  1.5e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -0.84766
 
sparsity =
     1
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|1.6e+03| 2.208732e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.833|1.000|5.6e+00|2.8e-02|3.2e+02| 7.963455e+00 -1.435432e+01| 0:0:00| chol  1  1 
 2|0.973|1.000|1.5e-01|2.8e-03|1.5e+01|-2.762340e-01 -7.030042e+00| 0:0:00| chol  1  1 
 3|0.998|0.988|3.0e-04|3.1e-04|1.8e+00|-2.708010e-01 -2.107877e+00| 0:0:00| chol  1  1 
 4|0.381|0.215|1.9e-04|3.1e-04|1.4e+00|-6.418499e-01 -2.017350e+00| 0:0:00| chol  1  1 
 5|0.690|0.957|5.8e-05|5.3e-05|6.5e-01|-1.236030e+00 -1.886140e+00| 0:0:00| chol  1  1 
 6|1.000|0.284|3.3e-09|5.0e-05|7.3e-01|-9.198684e-01 -1.650053e+00| 0:0:00| chol  1  1 
 7|0.911|0.977|3.1e-10|1.2e-06|8.5e-02|-1.516141e+00 -1.601260e+00| 0:0:00| chol  1  1 
 8|0.974|0.986|2.3e-11|1.9e-08|2.1e-03|-1.588624e+00 -1.590730e+00| 0:0:00| chol  1  1 
 9|0.804|0.971|2.1e-10|8.4e-10|3.8e-04|-1.589827e+00 -1.590209e+00| 0:0:00| chol  1  1 
10|0.951|0.970|1.4e-11|3.2e-11|3.3e-05|-1.590073e+00 -1.590106e+00| 0:0:00| chol  1  1 
11|0.989|0.989|1.2e-11|3.2e-12|7.3e-07|-1.590101e+00 -1.590102e+00| 0:0:00| chol  2  2 
12|0.569|0.969|5.1e-12|2.5e-12|3.6e-07|-1.590101e+00 -1.590102e+00| 0:0:00| chol  1  2 
13|0.572|1.000|2.2e-12|1.0e-12|1.9e-07|-1.590101e+00 -1.590102e+00| 0:0:00| chol  1  2 
14|0.572|1.000|8.6e-13|1.0e-12|9.9e-08|-1.590101e+00 -1.590102e+00| 0:0:00| chol  1  1 
15|0.572|1.000|1.7e-12|1.0e-12|5.2e-08|-1.590101e+00 -1.590102e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 15
 primal objective value = -1.59010147e+00
 dual   objective value = -1.59010153e+00
 gap := trace(XZ)       = 5.21e-08
 relative gap           = 1.25e-08
 actual relative gap    = 1.25e-08
 rel. primal infeas (scaled problem)   = 1.74e-12
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 8.0e-01, 7.3e+00, 4.8e+01
 norm(A), norm(b), norm(C) = 1.7e+01, 2.0e+00, 2.4e+01
 Total CPU time (secs)  = 0.12  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 1.8e-12  0.0e+00  2.0e-12  0.0e+00  1.2e-08  1.2e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -1.5901
 
sparsity =
     1
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.3e+01|6.5e+00|1.6e+03| 2.208732e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.834|1.000|5.5e+00|2.8e-02|3.2e+02| 7.922903e+00 -1.689604e+01| 0:0:00| chol  1  1 
 2|0.974|1.000|1.4e-01|2.8e-03|1.6e+01|-3.543186e-01 -9.370568e+00| 0:0:00| chol  1  1 
 3|0.999|0.902|1.6e-04|5.3e-04|2.5e+00|-4.129562e-01 -2.870198e+00| 0:0:00| chol  1  1 
 4|1.000|0.312|6.8e-09|4.0e-04|1.2e+00|-1.353368e+00 -2.595861e+00| 0:0:00| chol  1  1 
 5|0.801|0.802|3.6e-09|8.2e-05|3.5e-01|-2.013039e+00 -2.364200e+00| 0:0:00| chol  1  1 
 6|0.688|0.971|6.4e-09|2.6e-06|1.1e-01|-2.129919e+00 -2.241906e+00| 0:0:00| chol  1  1 
 7|1.000|0.974|3.4e-09|9.8e-08|2.5e-02|-2.204146e+00 -2.228904e+00| 0:0:00| chol  1  1 
 8|0.885|0.988|9.2e-10|4.6e-09|4.0e-03|-2.223555e+00 -2.227578e+00| 0:0:00| chol  1  1 
 9|0.998|0.977|4.9e-10|5.6e-10|1.6e-04|-2.227301e+00 -2.227465e+00| 0:0:00| chol  1  1 
10|0.987|0.986|6.2e-12|1.0e-10|2.1e-06|-2.227455e+00 -2.227457e+00| 0:0:00| chol  1  1 
11|0.567|1.000|1.1e-11|1.2e-12|1.1e-06|-2.227456e+00 -2.227457e+00| 0:0:00| chol  1  1 
12|0.559|1.000|3.2e-12|1.9e-12|5.8e-07|-2.227457e+00 -2.227457e+00| 0:0:00| chol  1  1 
13|0.560|1.000|1.2e-12|1.0e-12|3.1e-07|-2.227457e+00 -2.227457e+00| 0:0:00| chol  1  1 
14|0.562|1.000|1.2e-12|1.0e-12|1.7e-07|-2.227457e+00 -2.227457e+00| 0:0:00| chol  1  1 
15|0.563|1.000|3.0e-13|1.0e-12|8.9e-08|-2.227457e+00 -2.227457e+00| 0:0:00| chol  1  1 
16|0.564|1.000|1.2e-13|1.0e-12|4.7e-08|-2.227457e+00 -2.227457e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 16
 primal objective value = -2.22745714e+00
 dual   objective value = -2.22745719e+00
 gap := trace(XZ)       = 4.73e-08
 relative gap           = 8.67e-09
 actual relative gap    = 8.67e-09
 rel. primal infeas (scaled problem)   = 1.19e-13
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 9.1e-01, 6.6e+00, 4.2e+01
 norm(A), norm(b), norm(C) = 1.7e+01, 2.0e+00, 2.4e+01
 Total CPU time (secs)  = 0.13  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 1.2e-13  0.0e+00  2.0e-12  0.0e+00  8.7e-09  8.7e-09
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -2.22746
 
sparsity =
     2
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.3e+01|6.5e+00|1.6e+03| 2.208732e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.835|1.000|5.4e+00|2.8e-02|3.2e+02| 7.882245e+00 -1.942359e+01| 0:0:00| chol  1  1 
 2|0.974|1.000|1.4e-01|2.8e-03|1.8e+01|-4.295840e-01 -1.161516e+01| 0:0:00| chol  1  1 
 3|0.999|0.822|1.4e-04|7.3e-04|3.3e+00|-5.563516e-01 -3.851716e+00| 0:0:00| chol  1  1 
 4|1.000|0.398|7.4e-09|4.8e-04|1.8e+00|-1.401055e+00 -3.186874e+00| 0:0:00| chol  1  1 
 5|0.730|0.747|2.8e-09|1.2e-04|6.3e-01|-2.441422e+00 -3.074704e+00| 0:0:00| chol  1  1 
 6|0.735|0.910|4.5e-09|1.1e-05|1.9e-01|-2.643965e+00 -2.830663e+00| 0:0:00| chol  1  1 
 7|0.985|0.907|6.9e-10|1.1e-06|3.9e-02|-2.754446e+00 -2.793175e+00| 0:0:00| chol  1  1 
 8|0.973|0.968|1.1e-10|3.7e-08|1.1e-03|-2.786368e+00 -2.787457e+00| 0:0:00| chol  1  1 
 9|0.979|0.985|7.9e-11|8.4e-10|2.2e-05|-2.787242e+00 -2.787264e+00| 0:0:00| chol  1  1 
10|0.913|0.982|1.1e-11|3.1e-11|2.6e-06|-2.787258e+00 -2.787260e+00| 0:0:00| chol  2  2 
11|0.566|0.986|4.5e-12|2.6e-12|1.3e-06|-2.787259e+00 -2.787260e+00| 0:0:00| chol  1  2 
12|0.568|1.000|2.0e-12|1.0e-12|6.9e-07|-2.787259e+00 -2.787260e+00| 0:0:00| chol  1  1 
13|0.568|1.000|3.3e-12|1.0e-12|3.7e-07|-2.787260e+00 -2.787260e+00| 0:0:00| chol  1  1 
14|0.568|1.000|1.5e-12|1.0e-12|1.9e-07|-2.787260e+00 -2.787260e+00| 0:0:00| chol  1  1 
15|0.568|1.000|7.1e-13|1.0e-12|1.0e-07|-2.787260e+00 -2.787260e+00| 0:0:00| chol  1  1 
16|0.568|1.000|3.1e-13|1.0e-12|5.4e-08|-2.787260e+00 -2.787260e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 16
 primal objective value = -2.78725996e+00
 dual   objective value = -2.78726002e+00
 gap := trace(XZ)       = 5.41e-08
 relative gap           = 8.22e-09
 actual relative gap    = 8.22e-09
 rel. primal infeas (scaled problem)   = 3.06e-13
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 9.8e-01, 6.4e+00, 3.9e+01
 norm(A), norm(b), norm(C) = 1.7e+01, 2.1e+00, 2.4e+01
 Total CPU time (secs)  = 0.18  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 3.2e-13  0.0e+00  2.0e-12  0.0e+00  8.2e-09  8.2e-09
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -2.78726
 
sparsity =
     3
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.615|1.000|1.3e+01|8.8e-03|2.6e+03| 3.715084e+01 -2.812188e+01| 0:0:00| chol  1  1 
 2|0.976|1.000|3.1e-01|8.8e-04|7.5e+01| 5.229692e-01 -1.303457e+01| 0:0:00| chol  1  1 
 3|0.986|0.988|4.6e-03|9.8e-05|1.1e+00| 6.376350e-03 -1.783665e-01| 0:0:00| chol  1  1 
 4|0.989|0.989|5.1e-05|2.2e-04|1.3e-02| 7.349197e-05 -1.916682e-03| 0:0:00| chol  1  1 
 5|0.989|0.989|5.6e-07|5.8e-06|1.6e-04| 8.085084e-07 -1.612679e-05| 0:0:00| chol  1  1 
 6|0.945|0.949|1.2e-07|4.9e-07|2.7e-05| 2.224733e-07 -5.608809e-07| 0:0:00| chol  1  1 
 7|0.589|0.958|6.1e-08|4.5e-08|1.2e-05| 1.148759e-07 -6.868319e-08| 0:0:00| chol  1  1 
 8|0.588|1.000|3.1e-08|1.2e-08|6.2e-06| 5.964796e-08 -2.478543e-08| 0:0:00| chol  1  1 
 9|0.584|1.000|1.6e-08|6.3e-09|3.2e-06| 3.109906e-08 -1.278678e-08| 0:0:00| chol  1  1 
10|0.476|1.000|8.5e-09|3.3e-09|2.0e-06| 2.002438e-08 -6.641306e-09| 0:0:00| chol  1  1 
11|0.475|1.000|4.5e-09|1.7e-09|1.2e-06| 1.272938e-08 -4.136969e-09| 0:0:00| chol  1  1 
12|0.474|1.000|2.4e-09|9.0e-10|7.6e-07| 8.015443e-09 -2.559475e-09| 0:0:00| chol  1  1 
13|0.474|1.000|1.2e-09|4.7e-10|4.7e-07| 5.016543e-09 -1.584791e-09| 0:0:00| chol  1  1 
14|0.474|1.000|6.5e-10|2.5e-10|2.9e-07| 3.127565e-09 -9.820450e-10| 0:0:00| chol  1  1 
15|0.473|1.000|3.4e-10|1.3e-10|1.8e-07| 1.945245e-09 -6.089768e-10| 0:0:00| chol  1  1 
16|0.473|1.000|1.8e-10|6.9e-11|1.1e-07| 1.208190e-09 -3.778754e-10| 0:0:00| chol  1  1 
17|0.473|1.000|9.5e-11|3.6e-11|7.0e-08| 7.498492e-10 -2.346075e-10| 0:0:00| chol  1  1 
18|0.473|1.000|5.0e-11|1.9e-11|4.3e-08| 4.652408e-10 -1.457321e-10| 0:0:00| chol  1  1 
19|0.472|1.000|2.7e-11|1.0e-11|2.7e-08| 2.886476e-10 -9.056359e-11| 0:0:00| chol  1  1 
20|0.472|1.000|1.4e-11|5.3e-12|1.7e-08| 1.791104e-10 -5.630091e-11| 0:0:00| chol  1  1 
21|0.472|1.000|7.4e-12|2.8e-12|1.0e-08| 1.111676e-10 -3.501189e-11| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 21
 primal objective value =  1.11167576e-10
 dual   objective value = -3.50118913e-11
 gap := trace(XZ)       = 1.04e-08
 relative gap           = 1.04e-08
 actual relative gap    = 1.46e-10
 rel. primal infeas (scaled problem)   = 7.39e-12
 rel. dual     "        "       "      = 2.79e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 7.1e-01, 6.9e+02, 4.5e+03
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 7.4e+01
 Total CPU time (secs)  = 0.15  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 7.4e-12  0.0e+00  3.0e-12  0.0e+00  1.5e-10  1.0e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +1.11168e-10
 
sparsity =
     0
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.617|1.000|1.3e+01|8.8e-03|2.6e+03| 3.710522e+01 -3.773762e+01| 0:0:00| chol  1  1 
 2|0.979|1.000|2.7e-01|8.8e-04|7.6e+01| 3.856204e-01 -2.256516e+01| 0:0:00| chol  1  1 
 3|0.988|0.988|3.3e-03|9.8e-05|7.5e+00|-4.209956e-02 -7.066708e+00| 0:0:00| chol  1  1 
 4|1.000|0.777|3.6e-08|6.8e-04|1.7e+00|-7.041715e-02 -1.727365e+00| 0:0:00| chol  1  1 
 5|0.210|0.098|2.9e-08|6.1e-04|1.4e+00|-3.480013e-01 -1.740679e+00| 0:0:00| chol  1  1 
 6|0.639|0.245|9.0e-09|4.6e-04|6.8e-01|-1.105946e+00 -1.785494e+00| 0:0:00| chol  1  1 
 7|1.000|0.572|9.7e-10|2.0e-04|3.4e-01|-1.152359e+00 -1.493259e+00| 0:0:00| chol  1  1 
 8|0.960|0.970|1.1e-10|5.9e-06|1.3e-02|-1.375584e+00 -1.388993e+00| 0:0:00| chol  1  1 
 9|0.939|0.983|7.7e-11|1.0e-07|6.6e-04|-1.384729e+00 -1.385393e+00| 0:0:00| chol  1  1 
10|0.862|0.969|1.1e-11|3.1e-09|1.0e-04|-1.385164e+00 -1.385264e+00| 0:0:00| chol  1  1 
11|0.989|0.988|7.6e-12|4.0e-11|6.2e-06|-1.385250e+00 -1.385256e+00| 0:0:00| chol  1  1 
12|0.565|1.000|2.5e-12|1.5e-12|3.2e-06|-1.385253e+00 -1.385256e+00| 0:0:00| chol  1  1 
13|0.558|1.000|4.5e-13|1.0e-12|1.7e-06|-1.385254e+00 -1.385256e+00| 0:0:00| chol  1  1 
14|0.560|1.000|1.3e-13|1.0e-12|9.3e-07|-1.385255e+00 -1.385256e+00| 0:0:00| chol  1  1 
15|0.562|1.000|5.8e-14|1.0e-12|5.0e-07|-1.385256e+00 -1.385256e+00| 0:0:00| chol  1  1 
16|0.563|1.000|1.8e-14|1.0e-12|2.7e-07|-1.385256e+00 -1.385256e+00| 0:0:00| chol  1  1 
17|0.564|1.000|1.4e-14|1.0e-12|1.4e-07|-1.385256e+00 -1.385256e+00| 0:0:00| chol  1  1 
18|0.565|1.000|1.0e-14|1.0e-12|7.6e-08|-1.385256e+00 -1.385256e+00| 0:0:00| chol  1  1 
19|0.566|1.000|8.7e-15|1.0e-12|4.1e-08|-1.385256e+00 -1.385256e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 19
 primal objective value = -1.38525604e+00
 dual   objective value = -1.38525608e+00
 gap := trace(XZ)       = 4.06e-08
 relative gap           = 1.08e-08
 actual relative gap    = 1.08e-08
 rel. primal infeas (scaled problem)   = 8.69e-15
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 7.4e-01, 1.4e+01, 8.3e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 7.4e+01
 Total CPU time (secs)  = 0.15  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 8.7e-15  0.0e+00  1.1e-12  0.0e+00  1.1e-08  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -1.38526
 
sparsity =
     1
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.618|1.000|1.3e+01|8.8e-03|2.6e+03| 3.705945e+01 -4.729866e+01| 0:0:00| chol  1  1 
 2|0.979|1.000|2.6e-01|8.8e-04|8.3e+01| 3.488943e-01 -3.189471e+01| 0:0:00| chol  1  1 
 3|0.991|0.988|2.4e-03|9.8e-05|1.1e+01|-8.771356e-02 -1.040015e+01| 0:0:00| chol  1  1 
 4|1.000|0.724|2.7e-08|5.1e-04|3.2e+00|-1.573150e-01 -3.365236e+00| 0:0:00| chol  1  1 
 5|0.157|0.102|2.3e-08|4.6e-04|2.8e+00|-5.906943e-01 -3.411351e+00| 0:0:00| chol  1  1 
 6|0.461|0.609|1.2e-08|1.8e-04|1.9e+00|-1.456507e+00 -3.330016e+00| 0:0:00| chol  1  1 
 7|1.000|0.248|8.2e-10|1.3e-04|2.7e+00| 8.158339e-02 -2.579418e+00| 0:0:00| chol  1  1 
 8|0.435|0.547|4.0e-10|6.1e-05|1.7e+00|-1.301198e+00 -2.966672e+00| 0:0:00| chol  1  1 
 9|0.955|0.830|1.7e-10|1.0e-05|2.4e-01|-2.300562e+00 -2.535701e+00| 0:0:00| chol  1  1 
10|0.634|0.785|6.1e-11|2.2e-06|9.2e-02|-2.371520e+00 -2.463146e+00| 0:0:00| chol  1  1 
11|0.883|0.933|7.2e-12|1.5e-07|1.6e-02|-2.418083e+00 -2.434172e+00| 0:0:00| chol  1  1 
12|0.978|0.959|1.5e-13|6.1e-09|4.8e-04|-2.430701e+00 -2.431184e+00| 0:0:00| chol  1  1 
13|0.985|0.975|2.3e-15|1.6e-10|8.7e-06|-2.431047e+00 -2.431056e+00| 0:0:00| chol  1  1 
14|0.606|0.876|4.2e-14|2.0e-11|3.3e-06|-2.431050e+00 -2.431053e+00| 0:0:00| chol  1  1 
15|0.587|0.972|3.3e-13|1.6e-12|1.6e-06|-2.431052e+00 -2.431053e+00| 0:0:00| chol  1  1 
16|0.578|1.000|4.9e-12|1.0e-12|8.2e-07|-2.431052e+00 -2.431053e+00| 0:0:00| chol  1  2 
17|0.576|1.000|2.1e-12|1.0e-12|4.3e-07|-2.431053e+00 -2.431053e+00| 0:0:00| chol  1  1 
18|0.575|1.000|1.4e-11|1.0e-12|2.3e-07|-2.431053e+00 -2.431053e+00| 0:0:00| chol  1  2 
19|0.574|1.000|6.2e-12|1.5e-12|1.2e-07|-2.431053e+00 -2.431053e+00| 0:0:00| chol  1  1 
20|0.573|1.000|3.2e-12|1.2e-12|6.3e-08|-2.431053e+00 -2.431053e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 20
 primal objective value = -2.43105307e+00
 dual   objective value = -2.43105314e+00
 gap := trace(XZ)       = 6.26e-08
 relative gap           = 1.07e-08
 actual relative gap    = 1.07e-08
 rel. primal infeas (scaled problem)   = 3.15e-12
 rel. dual     "        "       "      = 1.23e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 8.0e-01, 1.2e+01, 6.5e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 7.4e+01
 Total CPU time (secs)  = 0.16  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 3.2e-12  0.0e+00  1.3e-12  0.0e+00  1.1e-08  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -2.43105
 
sparsity =
     2
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.3e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.620|1.000|1.3e+01|8.8e-03|2.6e+03| 3.701351e+01 -5.680510e+01| 0:0:00| chol  1  1 
 2|0.980|1.000|2.6e-01|8.8e-04|9.1e+01| 3.118696e-01 -4.102492e+01| 0:0:00| chol  1  1 
 3|0.994|0.989|1.5e-03|9.7e-05|1.2e+01|-1.325978e-01 -1.190502e+01| 0:0:00| chol  1  1 
 4|1.000|0.680|2.0e-08|3.5e-04|4.6e+00|-2.745905e-01 -4.876896e+00| 0:0:00| chol  1  1 
 5|0.158|0.108|1.7e-08|3.1e-04|4.0e+00|-9.274815e-01 -4.964263e+00| 0:0:00| chol  1  1 
 6|0.396|0.982|1.1e-08|5.7e-06|2.4e+00|-1.767127e+00 -4.207890e+00| 0:0:00| chol  1  1 
 7|1.000|0.468|2.6e-10|3.0e-06|1.3e+00|-2.197188e+00 -3.510812e+00| 0:0:00| chol  1  1 
 8|0.880|0.785|8.2e-11|6.5e-07|3.0e-01|-3.051626e+00 -3.354118e+00| 0:0:00| chol  1  1 
 9|0.985|0.891|2.4e-11|7.1e-08|3.9e-02|-3.235598e+00 -3.274895e+00| 0:0:00| chol  1  1 
10|0.955|0.938|1.1e-12|4.4e-09|2.1e-03|-3.265750e+00 -3.267828e+00| 0:0:00| chol  1  1 
11|0.937|0.951|1.2e-13|2.2e-10|1.3e-04|-3.267333e+00 -3.267468e+00| 0:0:00| chol  1  1 
12|0.934|0.974|6.2e-13|6.7e-12|8.6e-06|-3.267442e+00 -3.267451e+00| 0:0:00| chol  1  2 
13|0.986|0.992|2.4e-13|1.1e-12|4.8e-07|-3.267450e+00 -3.267450e+00| 0:0:00| chol  2  2 
14|0.533|1.000|3.6e-13|1.0e-12|2.6e-07|-3.267450e+00 -3.267450e+00| 0:0:00| chol  1  2 
15|0.536|1.000|1.3e-13|1.0e-12|1.4e-07|-3.267450e+00 -3.267450e+00| 0:0:00| chol  1  1 
16|0.537|1.000|3.3e-12|1.0e-12|8.0e-08|-3.267450e+00 -3.267450e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 16
 primal objective value = -3.26745029e+00
 dual   objective value = -3.26745037e+00
 gap := trace(XZ)       = 8.03e-08
 relative gap           = 1.07e-08
 actual relative gap    = 1.07e-08
 rel. primal infeas (scaled problem)   = 3.28e-12
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 8.7e-01, 1.2e+01, 5.5e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 7.4e+01
 Total CPU time (secs)  = 0.12  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 3.4e-12  0.0e+00  1.1e-12  0.0e+00  1.1e-08  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -3.26745
 
sparsity =
     2
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.3e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.621|1.000|1.2e+01|8.8e-03|2.6e+03| 3.696741e+01 -6.625707e+01| 0:0:00| chol  1  1 
 2|0.980|1.000|2.5e-01|8.8e-04|9.8e+01| 2.827630e-01 -4.995870e+01| 0:0:00| chol  1  1 
 3|0.996|0.989|9.7e-04|9.7e-05|1.2e+01|-1.767987e-01 -1.251835e+01| 0:0:00| chol  1  1 
 4|1.000|0.627|1.6e-08|2.4e-04|5.7e+00|-4.559533e-01 -6.197793e+00| 0:0:00| chol  1  1 
 5|0.208|0.140|1.3e-08|2.0e-04|4.8e+00|-1.405663e+00 -6.252294e+00| 0:0:00| chol  1  1 
 6|0.425|0.939|8.6e-09|1.3e-05|2.6e+00|-2.259360e+00 -4.846833e+00| 0:0:00| chol  1  1 
 7|0.518|0.747|4.2e-09|3.2e-06|1.6e+00|-3.187921e+00 -4.751887e+00| 0:0:00| chol  1  1 
 8|1.000|0.505|8.6e-11|1.6e-06|8.1e-01|-3.389311e+00 -4.195811e+00| 0:0:00| chol  1  1 
 9|0.960|0.947|7.6e-12|8.3e-08|9.4e-02|-3.888837e+00 -3.982717e+00| 0:0:00| chol  1  1 
10|0.961|0.960|3.0e-13|3.4e-09|3.9e-03|-3.958218e+00 -3.962073e+00| 0:0:00| chol  1  1 
11|0.969|0.980|1.8e-14|6.9e-11|1.1e-04|-3.961117e+00 -3.961227e+00| 0:0:00| chol  1  1 
12|0.954|0.987|1.0e-11|1.9e-12|8.3e-06|-3.961201e+00 -3.961209e+00| 0:0:00| chol  2  2 
13|1.000|0.996|3.5e-13|1.5e-12|4.8e-07|-3.961208e+00 -3.961209e+00| 0:0:00| chol  2  2 
14|0.564|1.000|5.9e-13|1.0e-12|2.4e-07|-3.961208e+00 -3.961209e+00| 0:0:00| chol  1  2 
15|0.566|1.000|4.8e-13|1.0e-12|1.3e-07|-3.961209e+00 -3.961209e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 15
 primal objective value = -3.96120861e+00
 dual   objective value = -3.96120873e+00
 gap := trace(XZ)       = 1.27e-07
 relative gap           = 1.43e-08
 actual relative gap    = 1.43e-08
 rel. primal infeas (scaled problem)   = 4.78e-13
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 9.1e-01, 1.1e+01, 4.9e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.1e+00, 7.4e+01
 Total CPU time (secs)  = 0.13  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 5.0e-13  0.0e+00  1.1e-12  0.0e+00  1.4e-08  1.4e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -3.96121
 
sparsity =
     5
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.2e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.622|1.000|1.2e+01|8.8e-03|2.6e+03| 3.692116e+01 -7.565469e+01| 0:0:00| chol  1  1 
 2|0.980|1.000|2.4e-01|8.8e-04|1.1e+02| 2.564122e-01 -5.869759e+01| 0:0:00| chol  1  1 
 3|0.997|0.989|6.2e-04|9.7e-05|1.2e+01|-2.207086e-01 -1.265128e+01| 0:0:00| chol  1  1 
 4|1.000|0.582|1.3e-08|1.7e-04|6.4e+00|-7.623628e-01 -7.136510e+00| 0:0:00| chol  1  1 
 5|0.233|0.399|9.8e-09|1.0e-04|5.4e+00|-1.986725e+00 -7.372695e+00| 0:0:00| chol  1  1 
 6|0.498|0.631|6.7e-09|3.8e-05|3.1e+00|-2.923240e+00 -6.045203e+00| 0:0:00| chol  1  1 
 7|1.000|0.229|3.2e-09|2.9e-05|2.4e+00|-3.156646e+00 -5.557980e+00| 0:0:00| chol  1  1 
 8|0.881|0.718|2.9e-10|8.2e-06|7.7e-01|-4.140086e+00 -4.908344e+00| 0:0:00| chol  1  1 
 9|1.000|0.887|2.0e-11|9.3e-07|1.0e-01|-4.500953e+00 -4.601948e+00| 0:0:00| chol  1  1 
10|0.969|0.967|6.3e-13|3.1e-08|3.3e-03|-4.574669e+00 -4.577955e+00| 0:0:00| chol  1  1 
11|0.978|0.983|3.6e-14|5.3e-10|6.9e-05|-4.577171e+00 -4.577240e+00| 0:0:00| chol  1  1 
12|0.912|0.990|2.2e-11|6.1e-12|7.4e-06|-4.577218e+00 -4.577225e+00| 0:0:00| chol  2  2 
13|0.933|0.983|2.2e-12|1.6e-12|1.0e-06|-4.577223e+00 -4.577224e+00| 0:0:00| chol  2  2 
14|0.551|0.978|1.0e-12|1.0e-12|5.2e-07|-4.577223e+00 -4.577224e+00| 0:0:00| chol  1  2 
15|0.554|1.000|3.3e-13|1.0e-12|2.8e-07|-4.577223e+00 -4.577224e+00| 0:0:00| chol  1  2 
16|0.556|1.000|2.2e-13|1.0e-12|1.5e-07|-4.577223e+00 -4.577224e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 16
 primal objective value = -4.57722349e+00
 dual   objective value = -4.57722364e+00
 gap := trace(XZ)       = 1.49e-07
 relative gap           = 1.47e-08
 actual relative gap    = 1.47e-08
 rel. primal infeas (scaled problem)   = 2.17e-13
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 9.6e-01, 1.1e+01, 4.4e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.1e+00, 7.4e+01
 Total CPU time (secs)  = 0.18  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 2.3e-13  0.0e+00  1.1e-12  0.0e+00  1.5e-08  1.5e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -4.57722
 
sparsity =
     5
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.1e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.624|1.000|1.2e+01|8.8e-03|2.6e+03| 3.687474e+01 -8.499806e+01| 0:0:00| chol  1  1 
 2|0.980|1.000|2.3e-01|8.8e-04|1.1e+02| 2.298584e-01 -6.724294e+01| 0:0:00| chol  1  1 
 3|0.998|0.989|4.2e-04|9.7e-05|1.2e+01|-2.646088e-01 -1.249961e+01| 0:0:00| chol  1  1 
 4|0.916|0.357|3.5e-05|1.5e-04|8.3e+00|-1.255001e+00 -9.523344e+00| 0:0:00| chol  1  1 
 5|0.344|0.493|2.3e-05|8.3e-05|5.9e+00|-2.358470e+00 -8.228647e+00| 0:0:00| chol  1  1 
 6|1.000|0.415|1.2e-09|5.4e-05|3.8e+00|-2.516983e+00 -6.357213e+00| 0:0:00| chol  1  1 
 7|0.698|0.825|3.2e-10|9.4e-06|1.5e+00|-4.215364e+00 -5.714758e+00| 0:0:00| chol  1  1 
 8|1.000|0.869|7.0e-11|1.2e-06|3.1e-01|-4.906456e+00 -5.213147e+00| 0:0:00| chol  1  1 
 9|0.936|0.952|6.6e-11|5.9e-08|2.7e-02|-5.099330e+00 -5.126647e+00| 0:0:00| chol  1  1 
10|0.899|0.931|6.6e-12|4.1e-09|3.0e-03|-5.118851e+00 -5.121897e+00| 0:0:00| chol  1  1 
11|0.873|0.910|8.5e-13|3.7e-10|6.1e-04|-5.120961e+00 -5.121570e+00| 0:0:00| chol  1  1 
12|1.000|1.000|4.5e-12|1.0e-12|8.0e-05|-5.121448e+00 -5.121529e+00| 0:0:00| chol  1  1 
13|0.991|0.997|1.2e-12|1.0e-12|1.5e-06|-5.121522e+00 -5.121523e+00| 0:0:00| chol  1  1 
14|0.563|1.000|5.8e-13|1.0e-12|7.8e-07|-5.121523e+00 -5.121523e+00| 0:0:00| chol  1  1 
15|0.566|1.000|1.6e-13|1.0e-12|4.1e-07|-5.121523e+00 -5.121523e+00| 0:0:00| chol  1  1 
16|0.555|1.000|7.6e-14|1.0e-12|2.2e-07|-5.121523e+00 -5.121523e+00| 0:0:00| chol  1  1 
17|0.557|1.000|1.2e-14|1.0e-12|1.2e-07|-5.121523e+00 -5.121523e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 17
 primal objective value = -5.12152330e+00
 dual   objective value = -5.12152342e+00
 gap := trace(XZ)       = 1.18e-07
 relative gap           = 1.05e-08
 actual relative gap    = 1.05e-08
 rel. primal infeas (scaled problem)   = 1.23e-14
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 1.0e+00, 1.1e+01, 4.0e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.2e+00, 7.4e+01
 Total CPU time (secs)  = 0.11  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 1.3e-14  0.0e+00  1.1e-12  0.0e+00  1.1e-08  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -5.12152
 
sparsity =
     5
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.0e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.625|1.000|1.1e+01|8.8e-03|2.6e+03| 3.682817e+01 -9.428732e+01| 0:0:00| chol  1  1 
 2|0.980|1.000|2.3e-01|8.8e-04|1.2e+02| 2.031008e-01 -7.559645e+01| 0:0:00| chol  1  1 
 3|0.999|0.989|3.3e-04|9.7e-05|1.2e+01|-3.085764e-01 -1.219059e+01| 0:0:00| chol  1  1 
 4|0.406|0.160|2.0e-04|1.5e-04|9.9e+00|-1.267893e+00 -1.118037e+01| 0:0:00| chol  1  1 
 5|0.367|0.471|1.3e-04|1.2e-04|7.0e+00|-2.470977e+00 -9.419035e+00| 0:0:00| chol  1  1 
 6|1.000|0.472|9.3e-10|8.8e-05|4.2e+00|-2.746130e+00 -6.930280e+00| 0:0:00| chol  1  1 
 7|0.706|0.889|3.0e-10|9.8e-06|1.5e+00|-4.652164e+00 -6.191815e+00| 0:0:00| chol  1  1 
 8|0.985|0.816|1.4e-10|1.8e-06|3.6e-01|-5.373578e+00 -5.737083e+00| 0:0:00| chol  1  1 
 9|0.994|0.966|4.1e-11|6.2e-08|4.5e-02|-5.563793e+00 -5.609060e+00| 0:0:00| chol  1  1 
10|0.951|0.955|2.0e-12|2.8e-09|2.3e-03|-5.597314e+00 -5.599609e+00| 0:0:00| chol  1  1 
11|0.869|0.914|2.6e-13|2.4e-10|3.3e-04|-5.598862e+00 -5.599188e+00| 0:0:00| chol  1  1 
12|1.000|0.998|1.3e-12|1.5e-12|4.4e-05|-5.599094e+00 -5.599139e+00| 0:0:00| chol  1  1 
13|1.000|0.995|4.5e-12|1.0e-12|8.6e-07|-5.599133e+00 -5.599134e+00| 0:0:00| chol  1  1 
14|0.560|1.000|1.5e-12|1.0e-12|4.1e-07|-5.599134e+00 -5.599134e+00| 0:0:00| chol  1  1 
15|0.563|1.000|1.1e-12|1.0e-12|2.2e-07|-5.599134e+00 -5.599134e+00| 0:0:00| chol  1  1 
16|0.563|1.000|7.2e-13|1.0e-12|1.2e-07|-5.599134e+00 -5.599134e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 16
 primal objective value = -5.59913411e+00
 dual   objective value = -5.59913422e+00
 gap := trace(XZ)       = 1.15e-07
 relative gap           = 9.44e-09
 actual relative gap    = 9.44e-09
 rel. primal infeas (scaled problem)   = 7.18e-13
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 1.1e+00, 1.1e+01, 3.6e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.2e+00, 7.4e+01
 Total CPU time (secs)  = 0.16  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 8.0e-13  0.0e+00  1.1e-12  0.0e+00  9.4e-09  9.4e-09
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -5.59913
 
sparsity =
     7
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.615|1.000|1.3e+01|8.8e-03|2.6e+03| 3.715084e+01 -2.812188e+01| 0:0:00| chol  1  1 
 2|0.976|1.000|3.1e-01|8.8e-04|7.5e+01| 5.229692e-01 -1.303457e+01| 0:0:00| chol  1  1 
 3|0.986|0.988|4.6e-03|9.8e-05|1.1e+00| 6.376350e-03 -1.783665e-01| 0:0:00| chol  1  1 
 4|0.989|0.989|5.1e-05|2.2e-04|1.3e-02| 7.349197e-05 -1.916682e-03| 0:0:00| chol  1  1 
 5|0.989|0.989|5.6e-07|5.8e-06|1.6e-04| 8.085084e-07 -1.612679e-05| 0:0:00| chol  1  1 
 6|0.945|0.949|1.2e-07|4.9e-07|2.7e-05| 2.224733e-07 -5.608809e-07| 0:0:00| chol  1  1 
 7|0.589|0.958|6.1e-08|4.5e-08|1.2e-05| 1.148759e-07 -6.868319e-08| 0:0:00| chol  1  1 
 8|0.588|1.000|3.1e-08|1.2e-08|6.2e-06| 5.964796e-08 -2.478543e-08| 0:0:00| chol  1  1 
 9|0.584|1.000|1.6e-08|6.3e-09|3.2e-06| 3.109906e-08 -1.278678e-08| 0:0:00| chol  1  1 
10|0.476|1.000|8.5e-09|3.3e-09|2.0e-06| 2.002438e-08 -6.641306e-09| 0:0:00| chol  1  1 
11|0.475|1.000|4.5e-09|1.7e-09|1.2e-06| 1.272938e-08 -4.136969e-09| 0:0:00| chol  1  1 
12|0.474|1.000|2.4e-09|9.0e-10|7.6e-07| 8.015443e-09 -2.559475e-09| 0:0:00| chol  1  1 
13|0.474|1.000|1.2e-09|4.7e-10|4.7e-07| 5.016543e-09 -1.584791e-09| 0:0:00| chol  1  1 
14|0.474|1.000|6.5e-10|2.5e-10|2.9e-07| 3.127565e-09 -9.820450e-10| 0:0:00| chol  1  1 
15|0.473|1.000|3.4e-10|1.3e-10|1.8e-07| 1.945245e-09 -6.089768e-10| 0:0:00| chol  1  1 
16|0.473|1.000|1.8e-10|6.9e-11|1.1e-07| 1.208190e-09 -3.778754e-10| 0:0:00| chol  1  1 
17|0.473|1.000|9.5e-11|3.6e-11|7.0e-08| 7.498492e-10 -2.346075e-10| 0:0:00| chol  1  1 
18|0.473|1.000|5.0e-11|1.9e-11|4.3e-08| 4.652408e-10 -1.457321e-10| 0:0:00| chol  1  1 
19|0.472|1.000|2.7e-11|1.0e-11|2.7e-08| 2.886476e-10 -9.056359e-11| 0:0:00| chol  1  1 
20|0.472|1.000|1.4e-11|5.3e-12|1.7e-08| 1.791104e-10 -5.630091e-11| 0:0:00| chol  1  1 
21|0.472|1.000|7.4e-12|2.8e-12|1.0e-08| 1.111676e-10 -3.501189e-11| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 21
 primal objective value =  1.11167576e-10
 dual   objective value = -3.50118913e-11
 gap := trace(XZ)       = 1.04e-08
 relative gap           = 1.04e-08
 actual relative gap    = 1.46e-10
 rel. primal infeas (scaled problem)   = 7.39e-12
 rel. dual     "        "       "      = 2.79e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 7.1e-01, 6.9e+02, 4.5e+03
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 7.4e+01
 Total CPU time (secs)  = 0.25  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 7.4e-12  0.0e+00  3.0e-12  0.0e+00  1.5e-10  1.0e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +1.11168e-10
 
sparsity =
     0
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.616|1.000|1.3e+01|8.8e-03|2.6e+03| 3.712805e+01 -3.293660e+01| 0:0:00| chol  1  1 
 2|0.978|1.000|2.9e-01|8.8e-04|7.5e+01| 4.451251e-01 -1.782510e+01| 0:0:00| chol  1  1 
 3|0.987|0.988|3.9e-03|9.8e-05|4.9e+00|-1.784498e-02 -4.266684e+00| 0:0:00| chol  1  1 
 4|1.000|0.821|4.3e-08|8.1e-04|8.4e-01|-3.283020e-02 -8.632518e-01| 0:0:00| chol  1  1 
 5|0.374|0.067|2.6e-08|7.5e-04|5.7e-01|-3.069281e-01 -8.731642e-01| 0:0:00| chol  1  1 
 6|0.696|0.446|7.2e-09|4.2e-04|2.7e-01|-6.114230e-01 -8.753684e-01| 0:0:00| chol  1  1 
 7|0.714|0.964|2.8e-09|1.5e-05|6.9e-02|-6.798416e-01 -7.492182e-01| 0:0:00| chol  1  1 
 8|0.979|0.933|2.3e-10|1.0e-06|7.9e-03|-7.295291e-01 -7.374458e-01| 0:0:00| chol  1  1 
 9|0.985|0.987|2.5e-11|1.4e-08|1.2e-04|-7.364272e-01 -7.365437e-01| 0:0:00| chol  1  1 
10|0.975|0.988|7.1e-13|1.6e-10|4.1e-06|-7.365266e-01 -7.365307e-01| 0:0:00| chol  1  2 
11|0.571|1.000|3.0e-13|1.0e-12|2.0e-06|-7.365284e-01 -7.365304e-01| 0:0:00| chol  1  2 
12|0.573|1.000|1.3e-13|1.0e-12|1.1e-06|-7.365294e-01 -7.365304e-01| 0:0:00| chol  1  2 
13|0.573|1.000|9.0e-14|1.0e-12|5.7e-07|-7.365299e-01 -7.365304e-01| 0:0:00| chol  1  1 
14|0.572|1.000|6.4e-12|1.0e-12|3.0e-07|-7.365301e-01 -7.365304e-01| 0:0:00| chol  1  2 
15|0.572|1.000|2.7e-12|1.3e-12|1.6e-07|-7.365303e-01 -7.365304e-01| 0:0:00| chol  1  1 
16|0.572|1.000|3.4e-12|1.0e-12|8.3e-08|-7.365303e-01 -7.365304e-01| 0:0:00| chol  1  1 
17|0.572|1.000|2.0e-12|1.0e-12|4.4e-08|-7.365304e-01 -7.365304e-01| 0:0:00| chol  1  1 
18|0.572|1.000|1.5e-12|1.0e-12|2.3e-08|-7.365304e-01 -7.365304e-01| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 18
 primal objective value = -7.36530397e-01
 dual   objective value = -7.36530420e-01
 gap := trace(XZ)       = 2.32e-08
 relative gap           = 9.38e-09
 actual relative gap    = 9.38e-09
 rel. primal infeas (scaled problem)   = 1.55e-12
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 7.1e-01, 1.5e+01, 9.4e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 7.4e+01
 Total CPU time (secs)  = 0.13  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 1.5e-12  0.0e+00  1.1e-12  0.0e+00  9.4e-09  9.4e-09
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -0.73653
 
sparsity =
     1
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.617|1.000|1.3e+01|8.8e-03|2.6e+03| 3.710522e+01 -3.773762e+01| 0:0:00| chol  1  1 
 2|0.979|1.000|2.7e-01|8.8e-04|7.6e+01| 3.856204e-01 -2.256516e+01| 0:0:00| chol  1  1 
 3|0.988|0.988|3.3e-03|9.8e-05|7.5e+00|-4.209956e-02 -7.066708e+00| 0:0:00| chol  1  1 
 4|1.000|0.777|3.6e-08|6.8e-04|1.7e+00|-7.041715e-02 -1.727365e+00| 0:0:00| chol  1  1 
 5|0.210|0.098|2.9e-08|6.1e-04|1.4e+00|-3.480013e-01 -1.740679e+00| 0:0:00| chol  1  1 
 6|0.639|0.245|9.0e-09|4.6e-04|6.8e-01|-1.105946e+00 -1.785494e+00| 0:0:00| chol  1  1 
 7|1.000|0.572|9.7e-10|2.0e-04|3.4e-01|-1.152359e+00 -1.493259e+00| 0:0:00| chol  1  1 
 8|0.960|0.970|1.1e-10|5.9e-06|1.3e-02|-1.375584e+00 -1.388993e+00| 0:0:00| chol  1  1 
 9|0.939|0.983|7.7e-11|1.0e-07|6.6e-04|-1.384729e+00 -1.385393e+00| 0:0:00| chol  1  1 
10|0.862|0.969|1.1e-11|3.1e-09|1.0e-04|-1.385164e+00 -1.385264e+00| 0:0:00| chol  1  1 
11|0.989|0.988|7.6e-12|4.0e-11|6.2e-06|-1.385250e+00 -1.385256e+00| 0:0:00| chol  1  1 
12|0.565|1.000|2.5e-12|1.5e-12|3.2e-06|-1.385253e+00 -1.385256e+00| 0:0:00| chol  1  1 
13|0.558|1.000|4.5e-13|1.0e-12|1.7e-06|-1.385254e+00 -1.385256e+00| 0:0:00| chol  1  1 
14|0.560|1.000|1.3e-13|1.0e-12|9.3e-07|-1.385255e+00 -1.385256e+00| 0:0:00| chol  1  1 
15|0.562|1.000|5.8e-14|1.0e-12|5.0e-07|-1.385256e+00 -1.385256e+00| 0:0:00| chol  1  1 
16|0.563|1.000|1.8e-14|1.0e-12|2.7e-07|-1.385256e+00 -1.385256e+00| 0:0:00| chol  1  1 
17|0.564|1.000|1.4e-14|1.0e-12|1.4e-07|-1.385256e+00 -1.385256e+00| 0:0:00| chol  1  1 
18|0.565|1.000|1.0e-14|1.0e-12|7.6e-08|-1.385256e+00 -1.385256e+00| 0:0:00| chol  1  1 
19|0.566|1.000|8.7e-15|1.0e-12|4.1e-08|-1.385256e+00 -1.385256e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 19
 primal objective value = -1.38525604e+00
 dual   objective value = -1.38525608e+00
 gap := trace(XZ)       = 4.06e-08
 relative gap           = 1.08e-08
 actual relative gap    = 1.08e-08
 rel. primal infeas (scaled problem)   = 8.69e-15
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 7.4e-01, 1.4e+01, 8.3e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 7.4e+01
 Total CPU time (secs)  = 0.13  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 8.7e-15  0.0e+00  1.1e-12  0.0e+00  1.1e-08  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -1.38526
 
sparsity =
     1
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.618|1.000|1.3e+01|8.8e-03|2.6e+03| 3.708236e+01 -4.252497e+01| 0:0:00| chol  1  1 
 2|0.979|1.000|2.7e-01|8.8e-04|7.9e+01| 3.672945e-01 -2.725496e+01| 0:0:00| chol  1  1 
 3|0.989|0.988|2.8e-03|9.8e-05|9.3e+00|-6.505316e-02 -9.039969e+00| 0:0:00| chol  1  1 
 4|1.000|0.749|3.1e-08|6.0e-04|2.5e+00|-1.112442e-01 -2.560012e+00| 0:0:00| chol  1  1 
 5|0.172|0.102|2.6e-08|5.4e-04|2.1e+00|-4.578602e-01 -2.585712e+00| 0:0:00| chol  1  1 
 6|0.553|0.356|1.1e-08|3.5e-04|1.3e+00|-1.346139e+00 -2.617018e+00| 0:0:00| chol  1  1 
 7|1.000|0.231|1.4e-09|2.7e-04|1.8e+00|-3.803495e-01 -2.162967e+00| 0:0:00| chol  1  1 
 8|0.855|0.921|2.3e-10|2.1e-05|3.5e-01|-1.720544e+00 -2.066512e+00| 0:0:00| chol  1  1 
 9|0.965|0.977|1.2e-10|4.9e-07|1.1e-02|-1.938997e+00 -1.949887e+00| 0:0:00| chol  1  1 
10|0.741|0.965|3.0e-11|1.7e-08|2.5e-03|-1.944424e+00 -1.946879e+00| 0:0:00| chol  1  1 
11|0.999|0.878|1.5e-12|2.1e-09|4.4e-04|-1.945787e+00 -1.946229e+00| 0:0:00| chol  1  1 
12|0.984|0.987|3.3e-14|2.8e-11|6.9e-06|-1.946171e+00 -1.946178e+00| 0:0:00| chol  1  1 
13|0.580|0.970|1.9e-12|1.8e-12|3.3e-06|-1.946174e+00 -1.946177e+00| 0:0:00| chol  1  2 
14|0.580|1.000|7.9e-13|1.0e-12|1.7e-06|-1.946175e+00 -1.946177e+00| 0:0:00| chol  1  2 
15|0.578|1.000|3.2e-13|1.0e-12|8.9e-07|-1.946176e+00 -1.946177e+00| 0:0:00| chol  1  2 
16|0.537|1.000|7.0e-14|1.0e-12|5.0e-07|-1.946176e+00 -1.946177e+00| 0:0:00| chol  1  2 
17|0.539|1.000|6.0e-14|1.0e-12|2.8e-07|-1.946177e+00 -1.946177e+00| 0:0:00| chol  2  2 
18|0.541|1.000|8.7e-14|1.0e-12|1.5e-07|-1.946177e+00 -1.946177e+00| 0:0:00| chol  1  2 
19|0.543|1.000|3.8e-14|1.0e-12|8.4e-08|-1.946177e+00 -1.946177e+00| 0:0:00| chol  1  2 
20|0.545|1.000|1.6e-13|1.0e-12|4.6e-08|-1.946177e+00 -1.946177e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 20
 primal objective value = -1.94617693e+00
 dual   objective value = -1.94617698e+00
 gap := trace(XZ)       = 4.64e-08
 relative gap           = 9.48e-09
 actual relative gap    = 9.48e-09
 rel. primal infeas (scaled problem)   = 1.58e-13
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 7.7e-01, 1.3e+01, 7.2e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 7.4e+01
 Total CPU time (secs)  = 0.13  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 1.6e-13  0.0e+00  1.1e-12  0.0e+00  9.5e-09  9.5e-09
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -1.94618
 
sparsity =
     1
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.4e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.618|1.000|1.3e+01|8.8e-03|2.6e+03| 3.705945e+01 -4.729866e+01| 0:0:00| chol  1  1 
 2|0.979|1.000|2.6e-01|8.8e-04|8.3e+01| 3.488943e-01 -3.189471e+01| 0:0:00| chol  1  1 
 3|0.991|0.988|2.4e-03|9.8e-05|1.1e+01|-8.771356e-02 -1.040015e+01| 0:0:00| chol  1  1 
 4|1.000|0.724|2.7e-08|5.1e-04|3.2e+00|-1.573150e-01 -3.365236e+00| 0:0:00| chol  1  1 
 5|0.157|0.102|2.3e-08|4.6e-04|2.8e+00|-5.906943e-01 -3.411351e+00| 0:0:00| chol  1  1 
 6|0.461|0.609|1.2e-08|1.8e-04|1.9e+00|-1.456507e+00 -3.330016e+00| 0:0:00| chol  1  1 
 7|1.000|0.248|8.2e-10|1.3e-04|2.7e+00| 8.158339e-02 -2.579418e+00| 0:0:00| chol  1  1 
 8|0.435|0.547|4.0e-10|6.1e-05|1.7e+00|-1.301198e+00 -2.966672e+00| 0:0:00| chol  1  1 
 9|0.955|0.830|1.7e-10|1.0e-05|2.4e-01|-2.300562e+00 -2.535701e+00| 0:0:00| chol  1  1 
10|0.634|0.785|6.1e-11|2.2e-06|9.2e-02|-2.371520e+00 -2.463146e+00| 0:0:00| chol  1  1 
11|0.883|0.933|7.2e-12|1.5e-07|1.6e-02|-2.418083e+00 -2.434172e+00| 0:0:00| chol  1  1 
12|0.978|0.959|1.5e-13|6.1e-09|4.8e-04|-2.430701e+00 -2.431184e+00| 0:0:00| chol  1  1 
13|0.985|0.975|2.3e-15|1.6e-10|8.7e-06|-2.431047e+00 -2.431056e+00| 0:0:00| chol  1  1 
14|0.606|0.876|4.2e-14|2.0e-11|3.3e-06|-2.431050e+00 -2.431053e+00| 0:0:00| chol  1  1 
15|0.587|0.972|3.3e-13|1.6e-12|1.6e-06|-2.431052e+00 -2.431053e+00| 0:0:00| chol  1  1 
16|0.578|1.000|4.9e-12|1.0e-12|8.2e-07|-2.431052e+00 -2.431053e+00| 0:0:00| chol  1  2 
17|0.576|1.000|2.1e-12|1.0e-12|4.3e-07|-2.431053e+00 -2.431053e+00| 0:0:00| chol  1  1 
18|0.575|1.000|1.4e-11|1.0e-12|2.3e-07|-2.431053e+00 -2.431053e+00| 0:0:00| chol  1  2 
19|0.574|1.000|6.2e-12|1.5e-12|1.2e-07|-2.431053e+00 -2.431053e+00| 0:0:00| chol  1  1 
20|0.573|1.000|3.2e-12|1.2e-12|6.3e-08|-2.431053e+00 -2.431053e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 20
 primal objective value = -2.43105307e+00
 dual   objective value = -2.43105314e+00
 gap := trace(XZ)       = 6.26e-08
 relative gap           = 1.07e-08
 actual relative gap    = 1.07e-08
 rel. primal infeas (scaled problem)   = 3.15e-12
 rel. dual     "        "       "      = 1.23e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 8.0e-01, 1.2e+01, 6.5e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 7.4e+01
 Total CPU time (secs)  = 0.12  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 3.2e-12  0.0e+00  1.3e-12  0.0e+00  1.1e-08  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -2.43105
 
sparsity =
     2
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.3e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.619|1.000|1.3e+01|8.8e-03|2.6e+03| 3.703650e+01 -5.205869e+01| 0:0:00| chol  1  1 
 2|0.980|1.000|2.6e-01|8.8e-04|8.7e+01| 3.304194e-01 -3.648463e+01| 0:0:00| chol  1  1 
 3|0.993|0.989|1.9e-03|9.8e-05|1.1e+01|-1.102025e-01 -1.131577e+01| 0:0:00| chol  1  1 
 4|1.000|0.701|2.3e-08|4.2e-04|3.9e+00|-2.106965e-01 -4.139797e+00| 0:0:00| chol  1  1 
 5|0.153|0.104|2.0e-08|3.8e-04|3.5e+00|-7.457136e-01 -4.208719e+00| 0:0:00| chol  1  1 
 6|0.416|0.761|1.2e-08|9.1e-05|2.3e+00|-1.594982e+00 -3.882395e+00| 0:0:00| chol  1  1 
 7|1.000|0.417|3.3e-10|5.3e-05|1.6e+00|-1.392213e+00 -3.034517e+00| 0:0:00| chol  1  1 
 8|0.904|1.000|5.6e-11|9.5e-10|2.4e-01|-2.697584e+00 -2.941886e+00| 0:0:00| chol  1  1 
 9|0.922|0.969|2.8e-11|1.3e-10|1.9e-02|-2.855420e+00 -2.874667e+00| 0:0:00| chol  1  1 
10|0.877|0.973|3.5e-12|1.8e-11|2.2e-03|-2.868923e+00 -2.871132e+00| 0:0:00| chol  1  1 
11|0.921|0.973|5.8e-13|2.3e-12|2.4e-04|-2.870692e+00 -2.870936e+00| 0:0:00| chol  1  1 
12|0.976|0.982|9.7e-13|1.0e-12|5.9e-06|-2.870921e+00 -2.870927e+00| 0:0:00| chol  1  1 
13|0.989|0.970|6.7e-12|1.0e-12|1.4e-07|-2.870927e+00 -2.870927e+00| 0:0:00| chol  1  1 
14|0.557|1.000|6.6e-12|1.3e-12|7.3e-08|-2.870927e+00 -2.870927e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 14
 primal objective value = -2.87092688e+00
 dual   objective value = -2.87092695e+00
 gap := trace(XZ)       = 7.33e-08
 relative gap           = 1.09e-08
 actual relative gap    = 1.09e-08
 rel. primal infeas (scaled problem)   = 6.63e-12
 rel. dual     "        "       "      = 1.34e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 8.3e-01, 1.2e+01, 6.0e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 7.4e+01
 Total CPU time (secs)  = 0.11  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 6.7e-12  0.0e+00  1.5e-12  0.0e+00  1.1e-08  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -2.87093
 
sparsity =
     2
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.3e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.620|1.000|1.3e+01|8.8e-03|2.6e+03| 3.701351e+01 -5.680510e+01| 0:0:00| chol  1  1 
 2|0.980|1.000|2.6e-01|8.8e-04|9.1e+01| 3.118696e-01 -4.102492e+01| 0:0:00| chol  1  1 
 3|0.994|0.989|1.5e-03|9.7e-05|1.2e+01|-1.325978e-01 -1.190502e+01| 0:0:00| chol  1  1 
 4|1.000|0.680|2.0e-08|3.5e-04|4.6e+00|-2.745905e-01 -4.876896e+00| 0:0:00| chol  1  1 
 5|0.158|0.108|1.7e-08|3.1e-04|4.0e+00|-9.274815e-01 -4.964263e+00| 0:0:00| chol  1  1 
 6|0.396|0.982|1.1e-08|5.7e-06|2.4e+00|-1.767127e+00 -4.207890e+00| 0:0:00| chol  1  1 
 7|1.000|0.468|2.6e-10|3.0e-06|1.3e+00|-2.197188e+00 -3.510812e+00| 0:0:00| chol  1  1 
 8|0.880|0.785|8.2e-11|6.5e-07|3.0e-01|-3.051626e+00 -3.354118e+00| 0:0:00| chol  1  1 
 9|0.985|0.891|2.4e-11|7.1e-08|3.9e-02|-3.235598e+00 -3.274895e+00| 0:0:00| chol  1  1 
10|0.955|0.938|1.1e-12|4.4e-09|2.1e-03|-3.265750e+00 -3.267828e+00| 0:0:00| chol  1  1 
11|0.937|0.951|8.7e-14|2.2e-10|1.3e-04|-3.267333e+00 -3.267468e+00| 0:0:00| chol  1  1 
12|0.934|0.974|3.5e-13|6.7e-12|8.6e-06|-3.267442e+00 -3.267451e+00| 0:0:00| chol  2  1 
13|0.986|0.992|6.8e-12|1.1e-12|4.8e-07|-3.267450e+00 -3.267450e+00| 0:0:00| chol  2  2 
14|0.533|1.000|3.2e-12|1.4e-12|2.6e-07|-3.267450e+00 -3.267450e+00| 0:0:00| chol  1  2 
15|0.536|1.000|1.6e-12|1.0e-12|1.4e-07|-3.267450e+00 -3.267450e+00| 0:0:00| chol  1  1 
16|0.537|1.000|7.6e-13|1.0e-12|8.0e-08|-3.267450e+00 -3.267450e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 16
 primal objective value = -3.26745029e+00
 dual   objective value = -3.26745037e+00
 gap := trace(XZ)       = 8.03e-08
 relative gap           = 1.07e-08
 actual relative gap    = 1.07e-08
 rel. primal infeas (scaled problem)   = 7.57e-13
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 8.7e-01, 1.2e+01, 5.5e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.0e+00, 7.4e+01
 Total CPU time (secs)  = 0.11  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 7.7e-13  0.0e+00  1.1e-12  0.0e+00  1.1e-08  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -3.26745
 
sparsity =
     2
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.3e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.620|1.000|1.3e+01|8.8e-03|2.6e+03| 3.699048e+01 -6.153789e+01| 0:0:00| chol  1  1 
 2|0.980|1.000|2.5e-01|8.8e-04|9.4e+01| 2.958625e-01 -4.551615e+01| 0:0:00| chol  1  1 
 3|0.995|0.989|1.2e-03|9.7e-05|1.2e+01|-1.548032e-01 -1.228095e+01| 0:0:00| chol  1  1 
 4|1.000|0.660|1.8e-08|2.8e-04|5.2e+00|-3.532909e-01 -5.566570e+00| 0:0:00| chol  1  1 
 5|0.173|0.118|1.4e-08|2.5e-04|4.5e+00|-1.142136e+00 -5.659000e+00| 0:0:00| chol  1  1 
 6|0.397|1.000|9.8e-09|9.1e-08|2.5e+00|-1.980648e+00 -4.522863e+00| 0:0:00| chol  1  1 
 7|1.000|0.435|3.5e-10|5.7e-08|1.2e+00|-2.923495e+00 -4.084279e+00| 0:0:00| chol  1  1 
 8|0.843|0.764|1.4e-10|1.4e-08|3.7e-01|-3.393270e+00 -3.760220e+00| 0:0:00| chol  1  1 
 9|1.000|0.809|2.1e-11|2.8e-09|8.0e-02|-3.568708e+00 -3.649084e+00| 0:0:00| chol  1  1 
10|0.969|0.952|6.4e-13|1.5e-10|3.1e-03|-3.623852e+00 -3.626977e+00| 0:0:00| chol  1  1 
11|0.966|0.963|2.2e-14|7.3e-12|1.1e-04|-3.625854e+00 -3.625966e+00| 0:0:00| chol  1  1 
12|0.975|0.986|4.8e-15|1.1e-12|4.3e-06|-3.625926e+00 -3.625930e+00| 0:0:00| chol  1  1 
13|0.571|0.967|1.0e-11|1.0e-12|1.9e-06|-3.625927e+00 -3.625929e+00| 0:0:00| chol  1  2 
14|0.572|1.000|4.0e-12|1.5e-12|1.0e-06|-3.625928e+00 -3.625929e+00| 0:0:00| chol  1  2 
15|0.571|1.000|1.8e-12|1.0e-12|5.3e-07|-3.625929e+00 -3.625929e+00| 0:0:00| chol  1  2 
16|0.529|1.000|8.5e-13|1.0e-12|3.0e-07|-3.625929e+00 -3.625929e+00| 0:0:00| chol  1  1 
17|0.530|1.000|5.2e-12|1.0e-12|1.7e-07|-3.625929e+00 -3.625929e+00| 0:0:00| chol  1  2 
18|0.531|1.000|2.5e-12|1.0e-12|9.2e-08|-3.625929e+00 -3.625929e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 18
 primal objective value = -3.62592913e+00
 dual   objective value = -3.62592922e+00
 gap := trace(XZ)       = 9.23e-08
 relative gap           = 1.12e-08
 actual relative gap    = 1.12e-08
 rel. primal infeas (scaled problem)   = 2.47e-12
 rel. dual     "        "       "      = 1.05e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 8.9e-01, 1.2e+01, 5.1e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.1e+00, 7.4e+01
 Total CPU time (secs)  = 0.15  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 2.5e-12  0.0e+00  1.1e-12  0.0e+00  1.1e-08  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -3.62593
 
sparsity =
     4
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.3e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.621|1.000|1.2e+01|8.8e-03|2.6e+03| 3.696741e+01 -6.625707e+01| 0:0:00| chol  1  1 
 2|0.980|1.000|2.5e-01|8.8e-04|9.8e+01| 2.827630e-01 -4.995870e+01| 0:0:00| chol  1  1 
 3|0.996|0.989|9.7e-04|9.7e-05|1.2e+01|-1.767987e-01 -1.251835e+01| 0:0:00| chol  1  1 
 4|1.000|0.627|1.6e-08|2.4e-04|5.7e+00|-4.559533e-01 -6.197793e+00| 0:0:00| chol  1  1 
 5|0.208|0.140|1.3e-08|2.0e-04|4.8e+00|-1.405663e+00 -6.252294e+00| 0:0:00| chol  1  1 
 6|0.425|0.939|8.6e-09|1.3e-05|2.6e+00|-2.259360e+00 -4.846833e+00| 0:0:00| chol  1  1 
 7|0.518|0.747|4.2e-09|3.2e-06|1.6e+00|-3.187921e+00 -4.751887e+00| 0:0:00| chol  1  1 
 8|1.000|0.505|8.6e-11|1.6e-06|8.1e-01|-3.389311e+00 -4.195811e+00| 0:0:00| chol  1  1 
 9|0.960|0.947|7.6e-12|8.3e-08|9.4e-02|-3.888837e+00 -3.982717e+00| 0:0:00| chol  1  1 
10|0.961|0.960|3.0e-13|3.4e-09|3.9e-03|-3.958218e+00 -3.962073e+00| 0:0:00| chol  1  1 
11|0.969|0.980|5.2e-14|6.9e-11|1.1e-04|-3.961117e+00 -3.961227e+00| 0:0:00| chol  1  1 
12|0.954|0.987|4.7e-14|1.9e-12|8.3e-06|-3.961201e+00 -3.961209e+00| 0:0:00| chol  1  2 
13|1.000|0.996|2.7e-13|1.0e-12|4.8e-07|-3.961208e+00 -3.961209e+00| 0:0:00| chol  2  2 
14|0.564|1.000|4.2e-13|1.0e-12|2.4e-07|-3.961208e+00 -3.961209e+00| 0:0:00| chol  1  1 
15|0.566|1.000|5.8e-12|1.0e-12|1.3e-07|-3.961209e+00 -3.961209e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 15
 primal objective value = -3.96120861e+00
 dual   objective value = -3.96120873e+00
 gap := trace(XZ)       = 1.27e-07
 relative gap           = 1.43e-08
 actual relative gap    = 1.43e-08
 rel. primal infeas (scaled problem)   = 5.82e-12
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 9.1e-01, 1.1e+01, 4.9e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.1e+00, 7.4e+01
 Total CPU time (secs)  = 0.11  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 6.0e-12  0.0e+00  1.1e-12  0.0e+00  1.4e-08  1.4e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -3.96121
 
sparsity =
     5
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.2e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.622|1.000|1.2e+01|8.8e-03|2.6e+03| 3.694431e+01 -7.096267e+01| 0:0:00| chol  1  1 
 2|0.980|1.000|2.4e-01|8.8e-04|1.0e+02| 2.696129e-01 -5.435244e+01| 0:0:00| chol  1  1 
 3|0.997|0.989|7.7e-04|9.7e-05|1.2e+01|-1.987611e-01 -1.263137e+01| 0:0:00| chol  1  1 
 4|1.000|0.599|1.4e-08|2.0e-04|6.2e+00|-5.878611e-01 -6.740432e+00| 0:0:00| chol  1  1 
 5|0.248|0.190|1.1e-08|1.6e-04|5.0e+00|-1.715158e+00 -6.752188e+00| 0:0:00| chol  1  1 
 6|0.470|0.672|7.6e-09|5.3e-05|2.9e+00|-2.586317e+00 -5.530371e+00| 0:0:00| chol  1  1 
 7|0.693|1.000|2.6e-09|1.0e-08|1.2e+00|-3.544270e+00 -4.739656e+00| 0:0:00| chol  1  1 
 8|1.000|0.555|1.7e-10|5.6e-09|5.1e-01|-3.910104e+00 -4.417163e+00| 0:0:00| chol  1  1 
 9|0.932|0.873|2.1e-11|8.3e-10|5.6e-02|-4.242096e+00 -4.297851e+00| 0:0:00| chol  1  1 
10|0.974|0.934|5.5e-13|6.7e-11|2.3e-03|-4.276984e+00 -4.279303e+00| 0:0:00| chol  1  1 
11|0.980|0.934|2.2e-14|6.2e-12|1.0e-04|-4.278133e+00 -4.278234e+00| 0:0:00| chol  1  1 
12|0.980|0.929|1.3e-13|1.4e-12|9.3e-06|-4.278175e+00 -4.278184e+00| 0:0:00| chol  1  1 
13|0.958|0.983|1.5e-11|1.0e-12|5.5e-07|-4.278180e+00 -4.278181e+00| 0:0:00| chol  2  2 
14|0.566|0.974|7.1e-12|1.5e-12|2.4e-07|-4.278180e+00 -4.278181e+00| 0:0:00| chol  2  2 
15|0.566|1.000|3.1e-12|1.4e-12|1.3e-07|-4.278180e+00 -4.278181e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 15
 primal objective value = -4.27818045e+00
 dual   objective value = -4.27818057e+00
 gap := trace(XZ)       = 1.27e-07
 relative gap           = 1.33e-08
 actual relative gap    = 1.33e-08
 rel. primal infeas (scaled problem)   = 3.11e-12
 rel. dual     "        "       "      = 1.42e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 9.3e-01, 1.1e+01, 4.6e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.1e+00, 7.4e+01
 Total CPU time (secs)  = 0.10  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 3.3e-12  0.0e+00  1.5e-12  0.0e+00  1.3e-08  1.3e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -4.27818
 
sparsity =
     5
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.2e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.622|1.000|1.2e+01|8.8e-03|2.6e+03| 3.692116e+01 -7.565469e+01| 0:0:00| chol  1  1 
 2|0.980|1.000|2.4e-01|8.8e-04|1.1e+02| 2.564122e-01 -5.869759e+01| 0:0:00| chol  1  1 
 3|0.997|0.989|6.2e-04|9.7e-05|1.2e+01|-2.207086e-01 -1.265128e+01| 0:0:00| chol  1  1 
 4|1.000|0.582|1.3e-08|1.7e-04|6.4e+00|-7.623628e-01 -7.136510e+00| 0:0:00| chol  1  1 
 5|0.233|0.399|9.8e-09|1.0e-04|5.4e+00|-1.986725e+00 -7.372695e+00| 0:0:00| chol  1  1 
 6|0.498|0.631|6.7e-09|3.8e-05|3.1e+00|-2.923240e+00 -6.045203e+00| 0:0:00| chol  1  1 
 7|1.000|0.229|3.2e-09|2.9e-05|2.4e+00|-3.156646e+00 -5.557980e+00| 0:0:00| chol  1  1 
 8|0.881|0.718|2.9e-10|8.2e-06|7.7e-01|-4.140086e+00 -4.908344e+00| 0:0:00| chol  1  1 
 9|1.000|0.887|2.0e-11|9.3e-07|1.0e-01|-4.500953e+00 -4.601948e+00| 0:0:00| chol  1  1 
10|0.969|0.967|6.3e-13|3.1e-08|3.3e-03|-4.574669e+00 -4.577955e+00| 0:0:00| chol  1  1 
11|0.978|0.983|2.9e-14|5.3e-10|6.9e-05|-4.577171e+00 -4.577240e+00| 0:0:00| chol  1  1 
12|0.912|0.990|3.1e-11|6.1e-12|7.4e-06|-4.577218e+00 -4.577225e+00| 0:0:00| chol  2  2 
13|0.933|0.983|1.9e-12|1.6e-12|1.0e-06|-4.577223e+00 -4.577224e+00| 0:0:00| chol  2  2 
14|0.551|0.978|6.7e-13|1.0e-12|5.2e-07|-4.577223e+00 -4.577224e+00| 0:0:00| chol  1  2 
15|0.554|1.000|3.0e-13|1.0e-12|2.8e-07|-4.577223e+00 -4.577224e+00| 0:0:00| chol  1  1 
16|0.556|1.000|9.4e-12|1.0e-12|1.5e-07|-4.577223e+00 -4.577224e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 16
 primal objective value = -4.57722349e+00
 dual   objective value = -4.57722364e+00
 gap := trace(XZ)       = 1.49e-07
 relative gap           = 1.47e-08
 actual relative gap    = 1.47e-08
 rel. primal infeas (scaled problem)   = 9.37e-12
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 9.6e-01, 1.1e+01, 4.4e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.1e+00, 7.4e+01
 Total CPU time (secs)  = 0.12  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 9.9e-12  0.0e+00  1.1e-12  0.0e+00  1.5e-08  1.5e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -4.57722
 
sparsity =
     5
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.2e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.623|1.000|1.2e+01|8.8e-03|2.6e+03| 3.689797e+01 -8.033315e+01| 0:0:00| chol  1  1 
 2|0.980|1.000|2.4e-01|8.8e-04|1.1e+02| 2.431607e-01 -6.299435e+01| 0:0:00| chol  1  1 
 3|0.998|0.989|5.0e-04|9.7e-05|1.2e+01|-2.426544e-01 -1.260147e+01| 0:0:00| chol  1  1 
 4|1.000|0.494|1.2e-08|1.5e-04|7.2e+00|-1.001759e+00 -8.166146e+00| 0:0:00| chol  1  1 
 5|0.224|0.860|9.4e-09|2.2e-05|5.7e+00|-2.060321e+00 -7.760913e+00| 0:0:00| chol  1  1 
 6|0.532|0.415|6.1e-09|1.3e-05|3.7e+00|-3.237348e+00 -6.946629e+00| 0:0:00| chol  1  1 
 7|1.000|0.245|1.7e-09|9.9e-06|3.7e+00|-2.325169e+00 -5.990625e+00| 0:0:00| chol  1  1 
 8|0.890|0.976|1.3e-10|2.4e-07|9.0e-01|-4.267062e+00 -5.170663e+00| 0:0:00| chol  1  1 
 9|0.937|0.897|1.5e-11|2.5e-08|9.8e-02|-4.784255e+00 -4.882371e+00| 0:0:00| chol  1  1 
10|0.978|0.931|3.3e-13|1.7e-09|5.3e-03|-4.854458e+00 -4.859736e+00| 0:0:00| chol  1  1 
11|0.972|0.983|9.5e-15|3.1e-11|1.3e-04|-4.858231e+00 -4.858363e+00| 0:0:00| chol  1  1 
12|0.968|0.986|2.6e-12|1.4e-12|3.8e-06|-4.858335e+00 -4.858339e+00| 0:0:00| chol  2  2 
13|0.568|0.994|1.1e-12|1.0e-12|1.7e-06|-4.858336e+00 -4.858338e+00| 0:0:00| chol  2  2 
14|0.548|1.000|7.6e-13|1.0e-12|9.1e-07|-4.858337e+00 -4.858338e+00| 0:0:00| chol  2  2 
15|0.539|1.000|4.4e-13|1.0e-12|5.0e-07|-4.858337e+00 -4.858338e+00| 0:0:00| chol  2  2 
16|0.540|1.000|6.4e-13|1.0e-12|2.8e-07|-4.858338e+00 -4.858338e+00| 0:0:00| chol  2  2 
17|0.542|1.000|5.4e-13|1.0e-12|1.5e-07|-4.858338e+00 -4.858338e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 17
 primal objective value = -4.85833777e+00
 dual   objective value = -4.85833792e+00
 gap := trace(XZ)       = 1.51e-07
 relative gap           = 1.41e-08
 actual relative gap    = 1.41e-08
 rel. primal infeas (scaled problem)   = 5.39e-13
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 9.8e-01, 1.1e+01, 4.2e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.1e+00, 7.4e+01
 Total CPU time (secs)  = 0.12  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 5.8e-13  0.0e+00  1.1e-12  0.0e+00  1.4e-08  1.4e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -4.85834
 
sparsity =
     5
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.1e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.624|1.000|1.2e+01|8.8e-03|2.6e+03| 3.687474e+01 -8.499806e+01| 0:0:00| chol  1  1 
 2|0.980|1.000|2.3e-01|8.8e-04|1.1e+02| 2.298584e-01 -6.724294e+01| 0:0:00| chol  1  1 
 3|0.998|0.989|4.2e-04|9.7e-05|1.2e+01|-2.646088e-01 -1.249961e+01| 0:0:00| chol  1  1 
 4|0.916|0.357|3.5e-05|1.5e-04|8.3e+00|-1.255001e+00 -9.523344e+00| 0:0:00| chol  1  1 
 5|0.344|0.493|2.3e-05|8.3e-05|5.9e+00|-2.358470e+00 -8.228647e+00| 0:0:00| chol  1  1 
 6|1.000|0.415|1.2e-09|5.4e-05|3.8e+00|-2.516983e+00 -6.357213e+00| 0:0:00| chol  1  1 
 7|0.698|0.825|3.2e-10|9.4e-06|1.5e+00|-4.215364e+00 -5.714758e+00| 0:0:00| chol  1  1 
 8|1.000|0.869|7.0e-11|1.2e-06|3.1e-01|-4.906456e+00 -5.213147e+00| 0:0:00| chol  1  1 
 9|0.936|0.952|6.6e-11|5.9e-08|2.7e-02|-5.099330e+00 -5.126647e+00| 0:0:00| chol  1  1 
10|0.899|0.931|6.6e-12|4.1e-09|3.0e-03|-5.118851e+00 -5.121897e+00| 0:0:00| chol  1  1 
11|0.873|0.910|8.5e-13|3.7e-10|6.1e-04|-5.120961e+00 -5.121570e+00| 0:0:00| chol  1  1 
12|1.000|1.000|4.5e-12|1.0e-12|8.0e-05|-5.121448e+00 -5.121529e+00| 0:0:00| chol  1  1 
13|0.991|0.997|1.2e-12|1.0e-12|1.5e-06|-5.121522e+00 -5.121523e+00| 0:0:00| chol  1  1 
14|0.563|1.000|5.8e-13|1.0e-12|7.8e-07|-5.121523e+00 -5.121523e+00| 0:0:00| chol  1  1 
15|0.566|1.000|1.6e-13|1.0e-12|4.1e-07|-5.121523e+00 -5.121523e+00| 0:0:00| chol  1  1 
16|0.555|1.000|7.6e-14|1.0e-12|2.2e-07|-5.121523e+00 -5.121523e+00| 0:0:00| chol  1  1 
17|0.557|1.000|1.2e-14|1.0e-12|1.2e-07|-5.121523e+00 -5.121523e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 17
 primal objective value = -5.12152330e+00
 dual   objective value = -5.12152342e+00
 gap := trace(XZ)       = 1.18e-07
 relative gap           = 1.05e-08
 actual relative gap    = 1.05e-08
 rel. primal infeas (scaled problem)   = 1.23e-14
 rel. dual     "        "       "      = 1.00e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 1.0e+00, 1.1e+01, 4.0e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.2e+00, 7.4e+01
 Total CPU time (secs)  = 0.12  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 1.3e-14  0.0e+00  1.1e-12  0.0e+00  1.1e-08  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -5.12152
 
sparsity =
     5
 
Calling SDPT3 4.0: 126 variables, 43 equality constraints
------------------------------------------------------------

 num. of constraints = 43
 dim. of socp   var  = 125,   num. of socp blk  = 42
 dim. of linear var  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
    NT      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.1e+01|6.5e+00|4.9e+03| 5.432900e+01  0.000000e+00| 0:0:00| chol  1  1 
 1|0.625|1.000|1.2e+01|8.8e-03|2.6e+03| 3.685147e+01 -8.964945e+01| 0:0:00| chol  1  1 
 2|0.980|1.000|2.3e-01|8.8e-04|1.2e+02| 2.165052e-01 -7.144357e+01| 0:0:00| chol  1  1 
 3|0.998|0.989|3.7e-04|9.7e-05|1.2e+01|-2.865804e-01 -1.235920e+01| 0:0:00| chol  1  1 
 4|0.595|0.244|1.5e-04|1.5e-04|9.3e+00|-1.225605e+00 -1.053506e+01| 0:0:00| chol  1  1 
 5|0.366|0.439|9.4e-05|1.1e-04|6.7e+00|-2.399742e+00 -9.059759e+00| 0:0:00| chol  1  1 
 6|1.000|0.437|1.2e-09|8.3e-05|4.4e+00|-2.318365e+00 -6.698419e+00| 0:0:00| chol  1  1 
 7|0.671|0.920|3.3e-10|6.6e-06|1.7e+00|-4.345743e+00 -6.075238e+00| 0:0:00| chol  1  1 
 8|0.907|0.868|1.1e-10|8.8e-07|4.3e-01|-5.089489e+00 -5.522306e+00| 0:0:00| chol  1  1 
 9|0.987|0.967|1.1e-10|2.9e-08|6.8e-02|-5.313743e+00 -5.382220e+00| 0:0:00| chol  1  1 
10|0.961|0.953|4.2e-12|1.4e-09|3.8e-03|-5.364702e+00 -5.368462e+00| 0:0:00| chol  1  1 
11|0.983|0.980|8.7e-14|3.0e-11|6.6e-05|-5.367747e+00 -5.367813e+00| 0:0:00| chol  1  1 
12|0.989|0.990|1.5e-14|1.3e-12|9.7e-07|-5.367799e+00 -5.367800e+00| 0:0:00| chol  2  1 
13|0.560|0.991|1.5e-11|1.0e-12|4.4e-07|-5.367799e+00 -5.367800e+00| 0:0:00| chol  2  2 
14|0.537|1.000|6.5e-12|1.5e-12|2.4e-07|-5.367800e+00 -5.367800e+00| 0:0:00| chol  1  2 
15|0.539|1.000|3.1e-12|1.3e-12|1.3e-07|-5.367800e+00 -5.367800e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 15
 primal objective value = -5.36779971e+00
 dual   objective value = -5.36779984e+00
 gap := trace(XZ)       = 1.34e-07
 relative gap           = 1.15e-08
 actual relative gap    = 1.15e-08
 rel. primal infeas (scaled problem)   = 3.07e-12
 rel. dual     "        "       "      = 1.31e-12
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 1.0e+00, 1.1e+01, 3.8e+01
 norm(A), norm(b), norm(C) = 2.2e+01, 2.2e+00, 7.4e+01
 Total CPU time (secs)  = 0.12  
 CPU time per iteration = 0.01  
 termination code       =  0
 DIMACS: 3.4e-12  0.0e+00  1.4e-12  0.0e+00  1.1e-08  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -5.3678
 
sparsity =
     6

Visualization of results

Two types of plots are used to show the performance of the detector. The first is the Receiver Operating Characteristics (ROC) that characterize the tradeoff between the probability of attack detection vs. the probability of false alarm. In addition, the Attacker Operating Characteristics (AOC)is plotted. The AOC charaterizes the tradeoff between the probability of being detected vs. resulting (extra) mean-square error at the state estimator (for a fixed probability of false alarm)

%1- ROC & AOC of GLRT for 2 sparsity case
%ROC: MSE with attack is 8db,SNR=10db
%AOC: Flase alarm rate=0.05, SNR=10db

k=2;SNR=10; ROC(a_1,Co_z1,Co_x1,Co_e1,k,SNR,z,H); % Sparsity k=2, SNR=10
k=3;SNR=10; ROC(a_2,Co_z1,Co_x2,Co_e2,k,SNR,z,H); % Sparsity k=3, SNR=10
k=3;SNR=6 ; ROC(a_3,Co_z1,Co_x3,Co_e3,k,SNR,z,H); % Sparsity k=3, SNR=6
k=6;SNR=10; ROC(a_4,Co_z1,Co_x4,Co_e4,k,SNR,z,H); % Sparsity k=6, SNR=10

Analysis and conclusions

A list of source files/functions necessary for algorithm implementation

1- DC power state estimation data is obtained from: WLS.m in Power Flow folder, the results are stored in Power_DC.mat to be used

2- main.m uses two functions: 1- GLRT.m: contains optimization problem code for the given case of sparsity and SNR 2- ROC.m: plot the ROC and AOC curves for the given case of sparsity and SNR

References

[1] Abur, Ali, and Antonio Gomez Exposito. Power system state estimation: theory and implementation. CRC press, 2004. [2] Kosut, Oliver, et al. "Malicious data attacks on the smart grid." IEEE Transactions on Smart Grid 2.4 (2011): 645-658.


Published with MATLAB® R2015b