U =
      [[0.2, 0.4, 0.4, 0.8], [0.4, -0.2, -0.8, 0.4], [0.4, 0.8, -0.2, -0.4], [0.8, -0.4, 0.4, -0.2]]

V =
      [[0.1, 0.1, 0.7, 0.7], [0.1, -0.1, -0.7, 0.7], [0.7, 0.7, -0.1, -0.1], [0.7, -0.7, 0.1, -0.1]]

%%%%%%%%%%%%%%%%%%%%%%%%%
% Matrices with integer %
%    singular values    %
%%%%%%%%%%%%%%%%%%%%%%%%%

% Singular values: 3, 2, 1, 0
U*diag([3, 2, 1, 0])*V'
      [[0.42, -0.3, 0.94, -0.1], [-0.48, 0.72, 0.64, 1.04], [0.14, 0.1, 1.98, -0.3], [0.44, 0.04, 1.08, 2.28]]

% Singular values: 4, 2, 1, 0
U*diag([4, 2, 1, 0])*V'
      [[0.44, -0.28, 1.08, 0.04], [-0.44, 0.76, 0.92, 1.32], [0.18, 0.14, 2.26, -0.02], [0.52, 0.12, 1.64, 2.84]]

% Singular values: 4, 3, 1, 0
U*diag([4, 3, 1, 0])*V'
      [[0.48, -0.32, 1.36, -0.24], [-0.46, 0.78, 0.78, 1.46], [0.26, 0.06, 2.82, -0.58], [0.48, 0.16, 1.36, 3.12]]

% Singular values: 4, 3, 2, 0
U*diag([4, 3, 2, 0])*V'
      [[0.76, -0.6, 1.32, -0.2], [-1.02, 1.34, 0.86, 1.38], [0.12, 0.2, 2.84, -0.6], [0.76, -0.12, 1.32, 3.16]]

% Singular values: 4, 3, 2, 1
U*diag([4, 3, 2, 1])*V'
      [[1.32, -0.04, 1.24, -0.28], [-0.74, 1.62, 0.82, 1.34], [-0.16, -0.08, 2.88, -0.56], [0.62, -0.26, 1.34, 3.18]]

% Singular values: 5, 2, 1, 0
U*diag([5, 2, 1, 0])*V'
      [[0.46, -0.26, 1.22, 0.18], [-0.4, 0.8, 1.2, 1.6], [0.22, 0.18, 2.54, 0.26], [0.6, 0.2, 2.2, 3.4]]

% Singular values: 5, 3, 1, 0
U*diag([5, 3, 1, 0])*V'
      [[0.5, -0.3, 1.5, -0.1], [-0.42, 0.82, 1.06, 1.74], [0.3, 0.1, 3.1, -0.3], [0.56, 0.24, 1.92, 3.68]]

% Singular values: 5, 3, 2, 0
U*diag([5, 3, 2, 0])*V'
      [[0.78, -0.58, 1.46, -0.06], [-0.98, 1.38, 1.14, 1.66], [0.16, 0.24, 3.12, -0.32], [0.84, -0.04, 1.88, 3.72]]

% Singular values: 5, 3, 2, 1
U*diag([5, 3, 2, 1])*V'
      [[1.34, -0.02, 1.38, -0.14], [-0.7, 1.66, 1.1, 1.62], [-0.12, -0.04, 3.16, -0.28], [0.7, -0.18, 1.9, 3.74]]

% Singular values: 5, 4, 1, 0
U*diag([5, 4, 1, 0])*V'
      [[0.54, -0.34, 1.78, -0.38], [-0.44, 0.84, 0.92, 1.88], [0.38, 0.02, 3.66, -0.86], [0.52, 0.28, 1.64, 3.96]]

% Singular values: 5, 4, 2, 0
U*diag([5, 4, 2, 0])*V'
      [[0.82, -0.62, 1.74, -0.34], [-1., 1.4, 1., 1.8], [0.24, 0.16, 3.68, -0.88], [0.8, 0., 1.6, 4]]

% Singular values: 5, 4, 2, 1
U*diag([5, 4, 2, 1])*V'
      [[1.38, -0.06, 1.66, -0.42], [-0.72, 1.68, 0.96, 1.76], [-0.04, -0.12, 3.72, -0.84], [0.66, -0.14, 1.62, 4.02]]

% Singular values: 5, 4, 3, 0
U*diag([5, 4, 3, 0])*V'
      [[1.1, -0.9, 1.7, -0.3], [-1.56, 1.96, 1.08, 1.72], [0.1, 0.3, 3.7, -0.9], [1.08, -0.28, 1.56, 4.04]]

% Singular values: 5, 4, 3, 1
U*diag([5, 4, 3, 1])*V'
      [[1.66, -0.34, 1.62, -0.38], [-1.28, 2.24, 1.04, 1.68], [-0.18, 0.02, 3.74, -0.86], [0.94, -0.42, 1.58, 4.06]]

% Singular values: 5, 4, 3, 2
U*diag([5, 4, 3, 2])*V'
      [[2.22, 0.22, 1.54, -0.46], [-1., 2.52, 1., 1.64], [-0.46, -0.26, 3.78, -0.82], [0.8, -0.56, 1.6, 4.08]]