9 ## Solved over the rationals.
10 expected = [2/73; 11/73; 26/73];
11 actual = conjugate_gradient_method(A, b, x0, 1e-6, 1000);
12 diff = norm(actual - expected);
14 unit_test_equals("CGM works on an example", ...
19 # Let's test Octave's pcg() against our method on some easy matrices.
20 max_iterations = 100000;
23 for n = [ 5, 10, 25, 50, 100 ]
24 A = random_positive_definite_matrix(5, 1000);
26 # Assumed by Octave's implementation when you don't supply a
29 b = unifrnd(-1000, 1000, 5, 1);
30 [o_x, o_flag, o_relres, o_iter] = pcg(A, b, tolerance, max_iterations);
31 [x, k] = conjugate_gradient_method(A, b, x0, tolerance, max_iterations);
34 msg = sprintf("Our CGM agrees with Octave's, n=%d.", n);
35 unit_test_equals(msg, true, norm(diff) < 1e-10);