Put back the redundant step_length_positive_definite() parameter.

[octave.git] / tests / steepest_descent_tests.m

diff --git a/tests/steepest_descent_tests.m b/tests/steepest_descent_tests.m
index 7b9982d7d72510d47864ead036234d5abeb3de06..d6de1ccaf4b013539d45833a70c3e293bb0ad6b6 100644 (file)
--- a/tests/steepest_descent_tests.m
+++ b/tests/steepest_descent_tests.m
@@ -6,7 +6,7 @@
 ## stopping condition, so we should too.
 ##
 max_iterations = 100000;
-tolerance = 1e-11;
+tolerance = 1e-8;
 
 ## First a simple example.
 Q = [5,1,2; ...
@@ -34,13 +34,13 @@ unit_test_equals("Steepest descent agrees with CGM", ...
 
 ## Test again Octave's pcg() function.
 for n = [ 5, 10, 25, 50, 100 ]
-  Q = random_positive_definite_matrix(5, 1000);
-  C = random_positive_definite_matrix(5, 1000);
+  Q = random_positive_definite_matrix(n, 100);
+  C = 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);
+  x0 = zeros(n, 1);
+  b  = unifrnd(-100, 100, n, 1);
 
   q = @(x) (1/2)*x'*Q*x - b'*x;
   g = @(x) Q*x - b; % The gradient of q at x.
@@ -48,15 +48,22 @@ for n = [ 5, 10, 25, 50, 100 ]
   % The step size algorithm to use in the steepest descent method.
   step_size = @(x) step_length_positive_definite(g(x), Q, -g(x));
 
+  ## 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.
   [x_pcg, o_flag, o_relres, o_iter] = pcg(Q, ...
                                          b, ...
-                                         tolerance, ...
+                                         tolerance/norm(g(x0)), ...
                                          max_iterations, ...
                                          C, ...
                                          C');
-  x_sd = steepest_descent(g, x0, step_size, tolerance, max_iterations);
+  [x_sd, k] = steepest_descent(g, x0, step_size, tolerance, max_iterations);
 
   diff = norm(x_pcg - x_sd, 'inf');
   msg = sprintf("Our steepest descent agrees with Octave's pcg, 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.
+  unit_test_equals(msg, true, diff <= sqrt(tolerance));
 end