+ diff < 2*tolerance);
+
+
+pcgm_simple = simple_preconditioned_cgm(A, M, b, x0, tolerance, max_iterations);
+diff = norm(pcgm_simple - pcgm, 'inf');
+
+unit_test_equals("PCGM agrees with Simple PCGM when M != I", ...
+ true, ...
+ diff < 2*tolerance);
+
+
+# Test again Octave's pcg() function.
+for n = [ 5, 10, 25, 50, 100 ]
+ A = random_positive_definite_matrix(n, 100);
+
+ # Use the cholesky factorization as a preconditioner.
+ Ct = perturb(chol(A));
+ C = Ct';
+ M = Ct*C;
+
+ # Assumed by Octave's implementation when you don't supply a
+ # preconditioner.
+ x0 = zeros(n, 1);
+ b = unifrnd(-100, 100, n, 1);
+ g = @(x) A*x - b;
+
+ ## pcg() stops when the /relative/ norm falls below tolerance. To
+ ## eliminate the relativity, we divide the tolerance by the
+ ## quantity that pcg() will divide by.
+ [o_x, o_flag, o_relres, o_iter] = pcg(A, b, tolerance/norm(g(x0)), ...
+ max_iterations, C, C');
+ [x, k] = preconditioned_conjugate_gradient_method(A,
+ M,
+ b,
+ x0,
+ tolerance,
+ max_iterations);
+
+ diff = norm(o_x - x, 'inf');
+ msg = sprintf("Our PCGM agrees with Octave's, n=%d.", n);
+ ## There's no good way to choose the tolerance here, since each
+ ## individual algorithm terminates based on the (2,infinity)-norm of
+ ## the gradient. So we use two orders of magnitude.
+ unit_test_equals(msg, true, diff <= sqrt(tolerance));
+end