tests/rank_k_approximation_tests.m

   1 U = [ 0, 0, 1; ...
   2       0, 1, 0; ...
   3       1, 0, 0 ];
   4
   5 S = [ 3, 0, 0; ...
   6       0, 2, 0; ...
   7       0, 0, 1 ];
   8
   9 V = [ 0, 1, 0; ...
  10       1, 0, 0; ...
  11       0, 0, 1 ];
  12
  13 A = U*S*V';
  14
  15 expected = A;
  16 % This should be exact.
  17 actual = rank_k_approximation(A, 3);
  18
  19 unit_test_equals("Full rank approximation of a matrix is itself", ...
  20                  actual, ...
  21                  expected);
  22
  23
  24
  25 % This too.
  26 actual = rank_k_approximation(A, 13);
  27
  28 unit_test_equals("Full rank approximation of a matrix is itself", ...
  29                  actual, ...
  30                  expected);
  31
  32
  33 S2 = S;
  34 S2(3,3) = 0;
  35 expected = U*S2*V';
  36 actual = rank_k_approximation(A, 2);
  37 unit_test_equals("Rank 2 approximation of a matrix is correct", ...
  38                  true, ...
  39                  (norm(actual - expected) <= 1e-10));
  40
  41
  42 S1 = S2;
  43 S1(2,2) = 0;
  44 expected = U*S1*V';
  45 actual = rank_k_approximation(A, 1);
  46 unit_test_equals("Rank 1 approximation of a matrix is correct", ...
  47                  true, ...
  48                  (norm(actual - expected) <= 1e-10));