U =
      [[0.5, 0.5, 0.5, 0.5], [0.5, -0.5, -0.5, 0.5], [0.5, 0.5, -0.5, -0.5], [0.5, -0.5, 0.5, -0.5]]

V =
      [[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]]

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

% Singular values: 3, 2, 1, 0
U*diag([3, 2, 1, 0])*V'
      [[0.9, 0.3, 1.4, 0.8], [-0.6, 1.2, 0.1, 1.3], [0.4, 1., 1.5, 0.3], [-0.1, 0.5, 0., 1.8]]

% Singular values: 4, 2, 1, 0
U*diag([4, 2, 1, 0])*V'
      [[0.95, 0.55, 1.65, 1.15], [-0.55, 1.45, 0.35, 1.65], [0.45, 1.25, 1.75, 0.65], [-0.05, 0.75, 0.25, 2.15]]

% Singular values: 4, 3, 1, 0
U*diag([4, 3, 1, 0])*V'
      [[1.2, 0.5, 2., 0.9], [-0.8, 1.5, 0., 1.9], [0.7, 1.2, 2.1, 0.4], [-0.3, 0.8, -0.1, 2.4]]

% Singular values: 4, 3, 2, 0
U*diag([4, 3, 2, 0])*V'
      [[1.45, 0.15, 1.95, 1.15], [-1.05, 1.85, 0.05, 1.65], [0.45, 1.55, 2.15, 0.15], [-0.05, 0.45, -0.15, 2.65]]

% Singular values: 4, 3, 2, 1
U*diag([4, 3, 2, 1])*V'
      [[1.8, 0.4, 1.7, 1.1], [-0.7, 2.1, -0.2, 1.6], [0.1, 1.3, 2.4, 0.2], [-0.4, 0.2, 0.1, 2.7]]

% Singular values: 5, 2, 1, 0
U*diag([5, 2, 1, 0])*V'
      [[1., 0.8, 1.9, 1.5], [-0.5, 1.7, 0.6, 2], [0.5, 1.5, 2., 1], [0., 1., 0.5, 2.5]]

% Singular values: 5, 3, 1, 0
U*diag([5, 3, 1, 0])*V'
      [[1.25, 0.75, 2.25, 1.25], [-0.75, 1.75, 0.25, 2.25], [0.75, 1.45, 2.35, 0.75], [-0.25, 1.05, 0.15, 2.75]]

% Singular values: 5, 3, 2, 0
U*diag([5, 3, 2, 0])*V'
      [[1.5, 0.4, 2.2, 1.5], [-1., 2.1, 0.3, 2], [0.5, 1.8, 2.4, 0.5], [0., 0.7, 0.1, 3]]

% Singular values: 5, 3, 2, 1
U*diag([5, 3, 2, 1])*V'
      [[1.85, 0.65, 1.95, 1.45], [-0.65, 2.35, 0.05, 1.95], [0.15, 1.55, 2.65, 0.55], [-0.35, 0.45, 0.35, 3.05]]

% Singular values: 5, 4, 1, 0
U*diag([5, 4, 1, 0])*V'
      [[1.5, 0.7, 2.6, 1], [-1., 1.8, -0.1, 2.5], [1., 1.4, 2.7, 0.5], [-0.5, 1.1, -0.2, 3]]

% Singular values: 5, 4, 2, 0
U*diag([5, 4, 2, 0])*V'
      [[1.75, 0.35, 2.55, 1.25], [-1.25, 2.15, -0.05, 2.25], [0.75, 1.75, 2.75, 0.25], [-0.25, 0.75, -0.25, 3.25]]

% Singular values: 5, 4, 2, 1
U*diag([5, 4, 2, 1])*V'
      [[2.1, 0.6, 2.3, 1.2], [-0.9, 2.4, -0.3, 2.2], [0.4, 1.5, 3., 0.3], [-0.6, 0.5, 0., 3.3]]

% Singular values: 5, 4, 3, 0
U*diag([5, 4, 3, 0])*V'
      [[2., 0., 2.5, 1.5], [-1.5, 2.5, 0., 2], [0.5, 2.1, 2.8, 0], [0., 0.4, -0.3, 3.5]]

% Singular values: 5, 4, 3, 1
U*diag([5, 4, 3, 1])*V'
      [[2.35, 0.25, 2.25, 1.45], [-1.15, 2.75, -0.25, 1.95], [0.15, 1.85, 3.05, 0.05], [-0.35, 0.15, -0.05, 3.55]]

% Singular values: 5, 4, 3, 2
U*diag([5, 4, 3, 2])*V'
      [[2.7, 0.5, 2., 1.4], [-0.8, 3., -0.5, 1.9], [-0.2, 1.6, 3.3, 0.1], [-0.7, -0.1, 0.2, 3.6]]