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, 0.3, 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'
      [[0.6, -0.1, 1.3, 1.2], [-0.3, 1., -0.4, 1.5], [0.3, 0.8, 1.4, 0.9], [0., 0.1, -0.5, 1.8]]

% Singular values: 4, 2, 1, 0
U*diag([4, 2, 1, 0])*V'
      [[0.65, 0.05, 1.45, 1.65], [-0.25, 1.15, -0.25, 1.95], [0.35, 0.95, 1.55, 1.35], [0.05, 0.25, -0.35, 2.25]]

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

% Singular values: 4, 3, 2, 0
U*diag([4, 3, 2, 0])*V'
      [[0.95, -0.45, 1.85, 1.65], [-0.55, 1.65, -0.65, 1.95], [0.35, 1.35, 2.05, 1.05], [0.05, -0.15, -0.85, 2.55]]

% Singular values: 4, 3, 2, 1
U*diag([4, 3, 2, 1])*V'
      [[1.4, -0.3, 1.7, 1.6], [-0.1, 1.8, -0.8, 1.9], [-0.1, 1.2, 2.2, 1.1], [-0.4, -0.3, -0.7, 2.6]]

% Singular values: 5, 2, 1, 0
U*diag([5, 2, 1, 0])*V'
      [[0.7, 0.2, 1.6, 2.1], [-0.2, 1.3, -0.1, 2.4], [0.4, 1.1, 1.7, 1.8], [0.1, 0.4, -0.2, 2.7]]

% Singular values: 5, 3, 1, 0
U*diag([5, 3, 1, 0])*V'
      [[0.85, 0.15, 2.05, 1.95], [-0.35, 1.35, -0.55, 2.55], [0.55, 1.05, 2.15, 1.65], [-0.05, 0.45, -0.65, 2.85]]

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

% Singular values: 5, 3, 2, 1
U*diag([5, 3, 2, 1])*V'
      [[1.45, -0.15, 1.85, 2.05], [-0.05, 1.95, -0.65, 2.35], [-0.05, 1.35, 2.35, 1.55], [-0.35, -0.15, -0.55, 3.05]]

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

% Singular values: 5, 4, 2, 0
U*diag([5, 4, 2, 0])*V'
      [[1.15, -0.35, 2.45, 1.95], [-0.65, 1.85, -0.95, 2.55], [0.55, 1.45, 2.65, 1.35], [-0.05, 0.05, -1.15, 3.15]]

% Singular values: 5, 4, 2, 1
U*diag([5, 4, 2, 1])*V'
      [[1.6, -0.2, 2.3, 1.9], [-0.2, 2., -1.1, 2.5], [0.1, 1.3, 2.8, 1.4], [-0.5, -0.1, -1., 3.2]]

% Singular values: 5, 4, 3, 0
U*diag([5, 4, 3, 0])*V'
      [[1.3, -0.8, 2.4, 2.1], [-0.8, 2.3, -0.9, 2.4], [0.4, 1.9, 2.7, 1.2], [0.1, -0.4, -1.2, 3.3]]

% Singular values: 5, 4, 3, 1
U*diag([5, 4, 3, 1])*V'
      [[1.75, -0.65, 2.25, 2.05], [-0.35, 2.45, -1.05, 2.35], [-0.05, 1.75, 2.85, 1.25], [-0.35, -0.55, -1.05, 3.35]]

% Singular values: 5, 4, 3, 2
U*diag([5, 4, 3, 2])*V'
      [[2.2, -0.5, 2.1, 2], [0.1, 2.6, -1.2, 2.3], [-0.5, 1.6, 3., 1.3], [-0.8, -0.7, -0.9, 3.4]]