X-Git-Url: http://gitweb.michael.orlitzky.com/?p=octave.git;a=blobdiff_plain;f=tests%2Fpreconditioned_conjugate_gradient_method_tests.m;h=a27d3e206b4de1ebe4e48f77fe9cae6d55e6c27b;hp=2c8ff84044fb9c3ffce03259a3d6af2cb4265366;hb=606266fd6248aa04a256a3fe23e98a83b1397c9e;hpb=e1b71b4ca7cfa08ac76744a17a3778d4ccfaa7e2

diff --git a/tests/preconditioned_conjugate_gradient_method_tests.m b/tests/preconditioned_conjugate_gradient_method_tests.m
index 2c8ff84..a27d3e2 100644
--- a/tests/preconditioned_conjugate_gradient_method_tests.m
+++ b/tests/preconditioned_conjugate_gradient_method_tests.m
@@ -1,3 +1,9 @@
+## 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];
@@ -6,63 +12,83 @@ M = eye(3);
 b = [1;2;3];
 x0 = [1;1;1];
 
-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, 1e-6, 1000);
-diff = norm(pcgm_simple - pcgm);
+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, ...
-		 norm(diff) < 1e-6);
+		 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, 1e-6, 1000);
-diff = norm(pcgm_simple - pcgm);
+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, ...
-		 norm(diff) < 1e-6);
+		 diff < 2*tolerance);
 
 
 # Test again Octave's pcg() function.
-max_iterations = 100000;
-tolerance = 1e-11;
-C = random_positive_definite_matrix(5, 1000);
-M = C*C';
-
 for n = [ 5, 10, 25, 50, 100 ]
-  A = random_positive_definite_matrix(5, 1000);
+  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(5, 1);
-  b  = unifrnd(-1000, 1000, 5, 1);
-  [o_x, o_flag, o_relres, o_iter] = pcg(A, b, tolerance, max_iterations, C, C');
+  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);
+   						    b,
+   						    x0,
+   						    tolerance,
+   						    max_iterations);
+
+  diff = norm(o_x - x, 'inf');
   msg = sprintf("Our PCGM agrees with Octave's, n=%d.", n);
-  unit_test_equals(msg, true, norm(diff) < 1e-10);
+  ## 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