author Michael Orlitzky Mon, 25 Mar 2013 16:50:29 +0000 (12:50 -0400) committer Michael Orlitzky Mon, 25 Mar 2013 16:50:29 +0000 (12:50 -0400)

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);
+                                               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);
+                                               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