Fix a ton of crap in the CGM tests.

diff --git a/tests/conjugate_gradient_method_tests.m b/tests/conjugate_gradient_method_tests.m
index e04b2e2a0e9a28afab3a0f083872303775471100..3f068ae9f6c93cc678b6db038650d9772deda6b8 100644 (file)
--- a/tests/conjugate_gradient_method_tests.m
+++ b/tests/conjugate_gradient_method_tests.m
@@ -1,3 +1,8 @@
+## Used throughout. The CGM uses the infinity norm as the stopping
+## condition, so we had better also.
+max_iterations = 10000;
+tolerance = 1e-10;
+
 A = [5,1,2; ...
      1,6,3;
      2,3,7];
@@ -8,29 +13,38 @@ x0 = [1;1;1];
 
 ## Solved over the rationals.
 expected = [2/73; 11/73; 26/73];
-actual = conjugate_gradient_method(A, b, x0, 1e-6, 1000);
-diff = norm(actual - expected);
+actual = conjugate_gradient_method(A, b, x0, tolerance, max_iterations);
+diff = norm(actual - expected, 'inf');
 
 unit_test_equals("CGM works on an example", ...
                 true, ...
-                norm(diff) < 1e-6);
+                diff < tolerance);
 
 
 # Let's test Octave's pcg() against our method on some easy matrices.
-max_iterations = 100000;
-tolerance = 1e-11;
 
 for n = [ 5, 10, 25, 50, 100 ]
-  A = random_positive_definite_matrix(5, 1000);
+  A = random_positive_definite_matrix(n, 100);
 
   # 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);
-  [x, k] = conjugate_gradient_method(A, b, x0, tolerance, max_iterations);
-
-  diff = norm(o_x - x);
+  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);
+  [x, k] = conjugate_gradient_method(A, b, x0, tolerance, ...
+                                    max_iterations);
+
+  diff = norm(o_x - x, 'inf');
   msg = sprintf("Our CGM 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