U =
      [[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]]

V =
      [[0.1, 0.3, 0.3, 0.9], [0.3, -0.1, -0.9, 0.3], [0.3, 0.9, -0.1, -0.3], [0.9, -0.3, 0.3, -0.1]]

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

% Singular values: 3, 2, 1, 0
U*diag(3, 2, 1, 0])*V'
      [[0.3, -0.56, 0.2, 0.42], [-0.24, 0.74, -0.02, 0.12], [0.6, 0.58, 1.9, 1.44], [-0.18, 0.68, -0.64, 2.34]]

% Singular values: 4, 2, 1, 0
U*diag([4, 2, 1, 0])*V'
      [[0.31, -0.53, 0.23, 0.51], [-0.23, 0.77, 0.01, 0.21], [0.67, 0.79, 2.11, 2.07], [-0.11, 0.89, -0.43, 2.97]]

% Singular values: 4, 3, 1, 0
U*diag([4, 3, 1, 0])*V'
      [[0.34, -0.54, 0.32, 0.48], [-0.26, 0.78, -0.08, 0.24], [0.88, 0.72, 2.74, 1.86], [-0.32, 0.96, -1.06, 3.18]]

% Singular values: 4, 3, 2, 0
U*diag([4, 3, 2, 0])*V'
      [[0.55, -1.17, 0.25, 0.69], [-0.47, 1.41, -0.01, 0.03], [0.85, 0.81, 2.75, 1.83], [-0.29, 0.87, -1.07, 3.21]]

% Singular values: 4, 3, 2, 1
U*diag([4, 3, 2, 1])*V'
      [[1.18, -0.96, 0.04, 0.62], [0.16, 1.62, -0.22, -0.04], [0.76, 0.78, 2.78, 1.84], [-0.38, 0.84, -1.04, 3.22]]

% Singular values: 5, 2, 1, 0
U*diag([5, 2, 1, 0])*V'
      [[0.32, -0.5, 0.26, 0.6], [-0.22, 0.8, 0.04, 0.3], [0.74, 1., 2.32, 2.7], [-0.04, 1.1, -0.22, 3.6]]

% Singular values: 5, 3, 1, 0
U*diag([5, 3, 1, 0])*V'
      [[0.35, -0.51, 0.35, 0.57], [-0.25, 0.81, -0.05, 0.33], [0.95, 0.93, 2.95, 2.49], [-0.25, 1.17, -0.85, 3.81]]

% Singular values: 5, 3, 2, 0
U*diag([5, 3, 2, 0])*V'
      [[0.56, -1.14, 0.28, 0.78], [-0.46, 1.44, 0.02, 0.12], [0.92, 1.02, 2.96, 2.46], [-0.22, 1.08, -0.86, 3.84]]

% Singular values: 5, 3, 2, 1
U*diag([5, 3, 2, 1])*V'
      [[1.19, -0.93, 0.07, 0.71], [0.17, 1.65, -0.19, 0.05], [0.83, 0.99, 2.99, 2.47], [-0.31, 1.05, -0.83, 3.85]]

% Singular values: 5, 4, 1, 0
U*diag([5, 4, 1, 0])*V'
      [[0.38, -0.52, 0.44, 0.54], [-0.28, 0.82, -0.14, 0.36], [1.16, 0.86, 3.58, 2.28], [-0.46, 1.24, -1.48, 4.02]]

% Singular values: 5, 4, 2, 0
U*diag([5, 4, 2, 0])*V'
      [[0.59, -1.15, 0.37, 0.75], [-0.49, 1.45, -0.07, 0.15], [1.13, 0.95, 3.59, 2.25], [-0.43, 1.15, -1.49, 4.05]]

% Singular values: 5, 4, 2, 1
U*diag([5, 4, 2, 1])*V'
      [[1.22, -0.94, 0.16, 0.68], [0.14, 1.66, -0.28, 0.08], [1.04, 0.92, 3.62, 2.26], [-0.52, 1.12, -1.46, 4.06]]

% Singular values: 5, 4, 3, 0
U*diag([5, 4, 3, 0])*V'
      [[0.8, -1.78, 0.3, 0.96], [-0.7, 2.08, -0., -0.06], [1.1, 1.04, 3.6, 2.22], [-0.4, 1.06, -1.5, 4.08]]

% Singular values: 5, 4, 3, 1
U*diag([5, 4, 3, 1])*V'
      [[1.43, -1.57, 0.09, 0.89], [-0.07, 2.29, -0.21, -0.13], [1.01, 1.01, 3.63, 2.23], [-0.49, 1.03, -1.47, 4.09]]

% Singular values: 5, 4, 3, 2
U*diag([5, 4, 3, 2])*V'
      [[2.06, -1.36, -0.12, 0.82], [0.56, 2.5, -0.42, -0.2], [0.92, 0.98, 3.66, 2.24], [-0.58, 1., -1.44, 4.1]]