Use the infinity norm in the PCGM tests.
authorMichael Orlitzky <michael@orlitzky.com>
Mon, 25 Mar 2013 16:50:29 +0000 (12:50 -0400)
committerMichael Orlitzky <michael@orlitzky.com>
Mon, 25 Mar 2013 16:50:29 +0000 (12:50 -0400)
tests/preconditioned_conjugate_gradient_method_tests.m

index 2c8ff84044fb9c3ffce03259a3d6af2cb4265366..6a11a63efd743df7fa7a73349de80fff3f488827 100644 (file)
@@ -1,3 +1,9 @@
+## Used throughout. The PCGM uses the infinity norm as the stopping
+## condition, so we had better also.
+max_iterations = 100000;
+tolerance = 1e-11;
+
+## First a simple example.
 A = [5,1,2; ...
      1,6,3; ...
      2,3,7];
@@ -6,50 +12,57 @@ 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);
+  C = random_positive_definite_matrix(5, 1000);
+  M = C*C';
 
   # Assumed by Octave's implementation when you don't supply a
   # preconditioner.
@@ -62,7 +75,7 @@ for n = [ 5, 10, 25, 50, 100 ]
                                                    x0,
                                                    tolerance,
                                                    max_iterations);
-  diff = norm(o_x - x);
+  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);
+  unit_test_equals(msg, true, diff < 2*tolerance);
 end