A = [5,1,2; ... 1,6,3; ... 2,3,7]; M = eye(3); b = [1;2;3]; x0 = [1;1;1]; cgm = conjugate_gradient_method(A, b, x0, 1e-6, 1000); pcgm = preconditioned_conjugate_gradient_method(A, M, b, x0, 1e-6, 1000); diff = norm(cgm - pcgm); unit_test_equals("PCGM agrees with CGM when M == I", ... true, ... norm(diff) < 1e-6); pcgm_simple = simple_preconditioned_cgm(A, M, b, x0, 1e-6, 1000); diff = norm(pcgm_simple - pcgm); unit_test_equals("PCGM agrees with SimplePCGM when M == I", ... true, ... norm(diff) < 1e-6); ## Needs to be symmetric! M = [0.97466, 0.24345, 0.54850; ... 0.24345, 0.73251, 0.76639; ... 0.54850, 0.76639, 1.47581]; pcgm = preconditioned_conjugate_gradient_method(A, M, b, x0, 1e-6, 1000); diff = norm(cgm - pcgm); unit_test_equals("PCGM agrees with CGM when M != I", ... true, ... norm(diff) < 1e-6); pcgm_simple = simple_preconditioned_cgm(A, M, b, x0, 1e-6, 1000); 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