author Michael Orlitzky Tue, 26 Mar 2013 00:58:54 +0000 (20:58 -0400) committer Michael Orlitzky Tue, 26 Mar 2013 00:58:54 +0000 (20:58 -0400)

index 6a11a63efd743df7fa7a73349de80fff3f488827..a27d3e206b4de1ebe4e48f77fe9cae6d55e6c27b 100644 (file)
@@ -1,7 +1,7 @@
## Used throughout. The PCGM uses the infinity norm as the stopping
## condition, so we had better also.
-max_iterations = 100000;
-tolerance = 1e-11;
+max_iterations = 10000;
+tolerance = 1e-10;

## First a simple example.
A = [5,1,2; ...
@@ -60,22 +60,35 @@ unit_test_equals("PCGM agrees with Simple PCGM when M != I", ...

# Test again Octave's pcg() function.
for n = [ 5, 10, 25, 50, 100 ]
-  A = random_positive_definite_matrix(5, 1000);
-  C = random_positive_definite_matrix(5, 1000);
-  M = C*C';
+  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');
M,
-                                                   b,
-                                                   x0,
-                                                   tolerance,
-                                                   max_iterations);
+                                                   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, diff < 2*tolerance);
+  ## 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