tests/conjugate_gradient_method_tests.m

   1 A = [5,1,2; ...
   2      1,6,3;
   3      2,3,7];
   4
   5 b = [1;2;3];
   6
   7 x0 = [1;1;1];
   8
   9 ## Solved over the rationals.
  10 expected = [2/73; 11/73; 26/73];
  11 actual = conjugate_gradient_method(A, b, x0, 1e-6, 1000);
  12 diff = norm(actual - expected);
  13
  14 unit_test_equals("CGM works on an example", ...
  15                  true, ...
  16                  norm(diff) < 1e-6);
  17
  18
  19 # Let's test Octave's pcg() against our method on some easy matrices.
  20 max_iterations = 100000;
  21 tolerance = 1e-11;
  22
  23 for n = [ 5, 10, 25, 50, 100 ]
  24   A = random_positive_definite_matrix(5, 1000);
  25
  26   # Assumed by Octave's implementation when you don't supply a
  27   # preconditioner.
  28   x0 = zeros(5, 1);
  29   b  = unifrnd(-1000, 1000, 5, 1);
  30   [o_x, o_flag, o_relres, o_iter] = pcg(A, b, tolerance, max_iterations);
  31   [x, k] = conjugate_gradient_method(A, b, x0, tolerance, max_iterations);
  32
  33   diff = norm(o_x - x);
  34   msg = sprintf("Our CGM agrees with Octave's, n=%d.", n);
  35   unit_test_equals(msg, true, norm(diff) < 1e-10);
  36 end