A = [5,1,2; ... 1,6,3; ... 2,3,7]; M = eye(3); b = [1;2;3]; x0 = [1;1;1]; ## Solved over the rationals. 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); ## 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);