Mangle the PCGM tests, commit something that just might work even when we fail to...

[octave.git] / tests / preconditioned_conjugate_gradient_method_tests.m

diff --git a/tests/preconditioned_conjugate_gradient_method_tests.m b/tests/preconditioned_conjugate_gradient_method_tests.m
index c58eb55edb206042c80477deb3ad41d964133334..a27d3e206b4de1ebe4e48f77fe9cae6d55e6c27b 100644 (file)
--- a/tests/preconditioned_conjugate_gradient_method_tests.m
+++ b/tests/preconditioned_conjugate_gradient_method_tests.m
@@ -1,31 +1,94 @@
+## Used throughout. The PCGM uses the infinity norm as the stopping
+## condition, so we had better also.
+max_iterations = 10000;
+tolerance = 1e-10;
+
+## First a simple example.
 A = [5,1,2; ...
      1,6,3; ...
      2,3,7];
 
 M = eye(3);
-
 b = [1;2;3];
-
 x0 = [1;1;1];
 
-## Solved over the rationals.
-cgm  = conjugate_gradient_method(A, b, x0, 1e-6, 1000);
-pcgm = preconditioned_conjugate_gradient_method(A, M, b, x0, 1e-6, 1000);
-diff = norm(cgm - pcgm);
+cgm  = conjugate_gradient_method(A, b, x0, tolerance, max_iterations);
+pcgm = preconditioned_conjugate_gradient_method(A, ...
+                                               M, ...
+                                               b, ...
+                                               x0, ...
+                                               tolerance, ...
+                                               max_iterations);
+diff = norm(cgm - pcgm, 'inf');
 
 unit_test_equals("PCGM agrees with CGM when M == I", ...
                 true, ...
-                norm(diff) < 1e-6);
+                diff < 2*tolerance);
+
+pcgm_simple = simple_preconditioned_cgm(A, M, b, x0, tolerance, max_iterations);
+diff = norm(pcgm_simple - pcgm, 'inf');
 
+unit_test_equals("PCGM agrees with SimplePCGM when M == I", ...
+                true, ...
+                diff < 2*tolerance);
 
 ## Needs to be symmetric!
 M = [0.97466, 0.24345, 0.54850; ...
      0.24345, 0.73251, 0.76639; ...
      0.54850, 0.76639, 1.47581];
 
-pcgm = preconditioned_conjugate_gradient_method(A, M, b, x0, 1e-6, 1000);
-diff = norm(cgm - pcgm);
+pcgm = preconditioned_conjugate_gradient_method(A, ...
+                                               M, ...
+                                               b, ...
+                                               x0, ...
+                                               tolerance, ...
+                                               max_iterations);
+diff = norm(cgm - pcgm, 'inf');
 
 unit_test_equals("PCGM agrees with CGM when M != I", ...
                 true, ...
-                norm(diff) < 1e-6);
+                diff < 2*tolerance);
+
+
+pcgm_simple = simple_preconditioned_cgm(A, M, b, x0, tolerance, max_iterations);
+diff = norm(pcgm_simple - pcgm, 'inf');
+
+unit_test_equals("PCGM agrees with Simple PCGM when M != I", ...
+                true, ...
+                diff < 2*tolerance);
+
+
+# Test again Octave's pcg() function.
+for n = [ 5, 10, 25, 50, 100 ]
+  A = random_positive_definite_matrix(n, 100);
+
+  # Use the cholesky factorization as a preconditioner.
+  Ct = perturb(chol(A));
+  C = Ct';
+  M = Ct*C;
+
+  # Assumed by Octave's implementation when you don't supply a
+  # preconditioner.
+  x0 = zeros(n, 1);
+  b  = unifrnd(-100, 100, n, 1);
+  g = @(x) A*x - b;
+
+  ## pcg() stops when the /relative/ norm falls below tolerance. To
+  ## eliminate the relativity, we divide the tolerance by the
+  ## quantity that pcg() will divide by.
+  [o_x, o_flag, o_relres, o_iter] = pcg(A, b, tolerance/norm(g(x0)), ...
+                                       max_iterations, C, C');
+  [x, k] = preconditioned_conjugate_gradient_method(A,
+                                                   M,
+                                                   b,
+                                                   x0,
+                                                   tolerance,
+                                                   max_iterations);
+
+  diff = norm(o_x - x, 'inf');
+  msg = sprintf("Our PCGM agrees with Octave's, n=%d.", n);
+  ## There's no good way to choose the tolerance here, since each
+  ## individual algorithm terminates based on the (2,infinity)-norm of
+  ## the gradient. So we use two orders of magnitude.
+  unit_test_equals(msg, true, diff <= sqrt(tolerance));
+end