From e1b71b4ca7cfa08ac76744a17a3778d4ccfaa7e2 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 22 Mar 2013 03:48:56 -0400
Subject: [PATCH] Test our (P)CGM implementation against Octave's.

---
 tests/conjugate_gradient_method_tests.m       | 20 ++++++++++++++
 ...ditioned_conjugate_gradient_method_tests.m | 26 +++++++++++++++++++
 2 files changed, 46 insertions(+)

diff --git a/tests/conjugate_gradient_method_tests.m b/tests/conjugate_gradient_method_tests.m
index 59e137a..e04b2e2 100644
--- a/tests/conjugate_gradient_method_tests.m
+++ b/tests/conjugate_gradient_method_tests.m
@@ -14,3 +14,23 @@ diff = norm(actual - expected);
 unit_test_equals("CGM works on an example", ...
 		 true, ...
 		 norm(diff) < 1e-6);
+
+
+# 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);
+
+  # 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);
+  msg = sprintf("Our CGM agrees with Octave's, n=%d.", n);
+  unit_test_equals(msg, true, norm(diff) < 1e-10);
+end
diff --git a/tests/preconditioned_conjugate_gradient_method_tests.m b/tests/preconditioned_conjugate_gradient_method_tests.m
index d44ee42..2c8ff84 100644
--- a/tests/preconditioned_conjugate_gradient_method_tests.m
+++ b/tests/preconditioned_conjugate_gradient_method_tests.m
@@ -40,3 +40,29 @@ diff = norm(pcgm_simple - pcgm);
 unit_test_equals("PCGM agrees with Simple PCGM when M != I", ...
 		 true, ...
 		 norm(diff) < 1e-6);
+
+
+# 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);
+
+  # 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');
+  [x, k] = preconditioned_conjugate_gradient_method(A,
+						    M,
+						    b,
+						    x0,
+						    tolerance,
+						    max_iterations);
+  diff = norm(o_x - x);
+  msg = sprintf("Our PCGM agrees with Octave's, n=%d.", n);
+  unit_test_equals(msg, true, norm(diff) < 1e-10);
+end
-- 
2.43.2