tests/preconditioned_conjugate_gradient_method_tests.m

   1 A = [5,1,2; ...
   2      1,6,3; ...
   3      2,3,7];
   4
   5 M = eye(3);
   6 b = [1;2;3];
   7 x0 = [1;1;1];
   8
   9 cgm  = conjugate_gradient_method(A, b, x0, 1e-6, 1000);
  10 pcgm = preconditioned_conjugate_gradient_method(A, M, b, x0, 1e-6, 1000);
  11 diff = norm(cgm - pcgm);
  12
  13 unit_test_equals("PCGM agrees with CGM when M == I", ...
  14                  true, ...
  15                  norm(diff) < 1e-6);
  16
  17 pcgm_simple = simple_preconditioned_cgm(A, M, b, x0, 1e-6, 1000);
  18 diff = norm(pcgm_simple - pcgm);
  19
  20 unit_test_equals("PCGM agrees with SimplePCGM when M == I", ...
  21                  true, ...
  22                  norm(diff) < 1e-6);
  23
  24 ## Needs to be symmetric!
  25 M = [0.97466, 0.24345, 0.54850; ...
  26      0.24345, 0.73251, 0.76639; ...
  27      0.54850, 0.76639, 1.47581];
  28
  29 pcgm = preconditioned_conjugate_gradient_method(A, M, b, x0, 1e-6, 1000);
  30 diff = norm(cgm - pcgm);
  31
  32 unit_test_equals("PCGM agrees with CGM when M != I", ...
  33                  true, ...
  34                  norm(diff) < 1e-6);
  35
  36
  37 pcgm_simple = simple_preconditioned_cgm(A, M, b, x0, 1e-6, 1000);
  38 diff = norm(pcgm_simple - pcgm);
  39
  40 unit_test_equals("PCGM agrees with Simple PCGM when M != I", ...
  41                  true, ...
  42                  norm(diff) < 1e-6);
  43
  44
  45 # Test again Octave's pcg() function.
  46 max_iterations = 100000;
  47 tolerance = 1e-11;
  48 C = random_positive_definite_matrix(5, 1000);
  49 M = C*C';
  50
  51 for n = [ 5, 10, 25, 50, 100 ]
  52   A = random_positive_definite_matrix(5, 1000);
  53
  54   # Assumed by Octave's implementation when you don't supply a
  55   # preconditioner.
  56   x0 = zeros(5, 1);
  57   b  = unifrnd(-1000, 1000, 5, 1);
  58   [o_x, o_flag, o_relres, o_iter] = pcg(A, b, tolerance, max_iterations, C, C');
  59   [x, k] = preconditioned_conjugate_gradient_method(A,
  60                                                     M,
  61                                                     b,
  62                                                     x0,
  63                                                     tolerance,
  64                                                     max_iterations);
  65   diff = norm(o_x - x);
  66   msg = sprintf("Our PCGM agrees with Octave's, n=%d.", n);
  67   unit_test_equals(msg, true, norm(diff) < 1e-10);
  68 end