A = [5,1,2; ... 1,6,3; 2,3,7]; b = [1;2;3]; 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); 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