U =
      [[0.1, 0.5, 0.5, 0.7], [0.5, -0.1, -0.7, 0.5], [0.5, 0.7, -0.1, -0.5], [0.7, -0.5, 0.5, -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'
      [[0.48, -0.46, 0.94, 0.12], [-0.12, 1.1, 0.34, 1.2], [0.54, 0.4, 1.72, 0.9], [0.06, 0.28, -0.32, 2.34]]

% Singular values: 4, 2, 1, 0
U*diag([4, 2, 1, 0])*V'
      [[0.49, -0.43, 0.97, 0.21], [-0.07, 1.25, 0.49, 1.65], [0.59, 0.55, 1.87, 1.35], [0.13, 0.49, -0.11, 2.97]]

% Singular values: 4, 3, 1, 0
U*diag([4, 3, 1, 0])*V'
      [[0.64, -0.48, 1.42, 0.06], [-0.1, 1.26, 0.4, 1.68], [0.8, 0.48, 2.5, 1.14], [-0.02, 0.54, -0.56, 3.12]]

% Singular values: 4, 3, 2, 0
U*diag([4, 3, 2, 0])*V'
      [[0.79, -0.93, 1.37, 0.21], [-0.31, 1.89, 0.47, 1.47], [0.77, 0.57, 2.51, 1.11], [0.13, 0.09, -0.61, 3.27]]

% Singular values: 4, 3, 2, 1
U*diag([4, 3, 2, 1])*V'
      [[1.42, -0.72, 1.16, 0.14], [0.14, 2.04, 0.32, 1.42], [0.32, 0.42, 2.66, 1.16], [0.04, 0.06, -0.58, 3.28]]

% Singular values: 5, 2, 1, 0
U*diag([5, 2, 1, 0])*V'
      [[0.5, -0.4, 1., 0.3], [-0.02, 1.4, 0.64, 2.1], [0.64, 0.7, 2.02, 1.8], [0.2, 0.7, 0.1, 3.6]]

% Singular values: 5, 3, 1, 0
U*diag([5, 3, 1, 0])*V'
      [[0.65, -0.45, 1.45, 0.15], [-0.05, 1.41, 0.55, 2.13], [0.85, 0.63, 2.65, 1.59], [0.05, 0.75, -0.35, 3.75]]

% Singular values: 5, 3, 2, 0
U*diag([5, 3, 2, 0])*V'
      [[0.8, -0.9, 1.4, 0.3], [-0.26, 2.04, 0.62, 1.92], [0.82, 0.72, 2.66, 1.56], [0.2, 0.3, -0.4, 3.9]]

% Singular values: 5, 3, 2, 1
U*diag([5, 3, 2, 1])*V'
      [[1.43, -0.69, 1.19, 0.23], [0.19, 2.19, 0.47, 1.87], [0.37, 0.57, 2.81, 1.61], [0.11, 0.27, -0.37, 3.91]]

% Singular values: 5, 4, 1, 0
U*diag([5, 4, 1, 0])*V'
      [[0.8, -0.5, 1.9, 0], [-0.08, 1.42, 0.46, 2.16], [1.06, 0.56, 3.28, 1.38], [-0.1, 0.8, -0.8, 3.9]]

% Singular values: 5, 4, 2, 0
U*diag([5, 4, 2, 0])*V'
      [[0.95, -0.95, 1.85, 0.15], [-0.29, 2.05, 0.53, 1.95], [1.03, 0.65, 3.29, 1.35], [0.05, 0.35, -0.85, 4.05]]

% Singular values: 5, 4, 2, 1
U*diag([5, 4, 2, 1])*V'
      [[1.58, -0.74, 1.64, 0.08], [0.16, 2.2, 0.38, 1.9], [0.58, 0.5, 3.44, 1.4], [-0.04, 0.32, -0.82, 4.06]]

% Singular values: 5, 4, 3, 0
U*diag([5, 4, 3, 0])*V'
      [[1.1, -1.4, 1.8, 0.3], [-0.5, 2.68, 0.6, 1.74], [1., 0.74, 3.3, 1.32], [0.2, -0.1, -0.9, 4.2]]

% Singular values: 5, 4, 3, 1
U*diag([5, 4, 3, 1])*V'
      [[1.73, -1.19, 1.59, 0.23], [-0.05, 2.83, 0.45, 1.69], [0.55, 0.59, 3.45, 1.37], [0.11, -0.13, -0.87, 4.21]]

% Singular values: 5, 4, 3, 2
U*diag([5, 4, 3, 2])*V'
      [[2.36, -0.98, 1.38, 0.16], [0.4, 2.98, 0.3, 1.64], [0.1, 0.44, 3.6, 1.42], [0.02, -0.16, -0.84, 4.22]]