def test_conjgrad_martens_termination_criterion(self):
"""Tests conjugate gradient method with martens termination criterion."""
n = 500
mat = get_pd_mat(
np.array([[((i + j) % n) for j in range(n)] for i in range(n)]))
b = np.linspace(1, n, n) / n
x0 = np.zeros(n)
test_mvm_fn = lambda x: mat @ x
x = hessian_free.mf_conjgrad_solver(
test_mvm_fn, b, x0, n, 1e-6, 500, None,
'relative_per_iteration_progress_test')
f_value = np.dot(x, test_mvm_fn(x) - 2 * b) / 2
self.assertAlmostEqual(f_value, -0.223612323, places=8)
def test_conjgrad(self):
"""Tests conjugate gradient method."""
n = 5
mat = get_pd_mat(
np.array([[2., 4., 5., 2., 8.], [0., 4., 3., 5., 3.],
[-2., -2., 9., -2., -6.], [4., 1., -11., 1., 4.],
[-5., 4., -9., 3., -2.]]))
b = np.array([-3, 2, 0, 3, -4])
x0 = np.ones(n)
test_matmul_fn = lambda x: mat @ x
x = hessian_free.mf_conjgrad_solver(test_matmul_fn, b, x0, n, 1e-6, 10,
None, 'residual_norm_test')
self.assertAlmostEqual(np.linalg.norm(test_matmul_fn(x) - b),
0,
places=3)
def test_conjgrad_preconditioning(self):
"""Tests conjugate gradient method with preconditioning."""
n = 5
mat = get_pd_mat(
np.array([[2., 4., 5., 2., 8.], [0., 4., 3., 5., 3.],
[-2., -2., 9., -2., -6.], [4., 1., -11., 1., 4.],
[-5., 4., -9., 3., -2.]]))
precond_mat = get_pd_mat(
np.array([[4., 2., 0., 2., 4.], [-2., 4., 4., 2., 6.],
[4., 4., -8., -2., -4.], [-2., 2., 4., 0., -2.],
[2., 2., -6., 4., 0.]]))
b = np.array([-3, 2, 0, 3, -4])
x0 = np.ones(n)
test_matmul_fn = lambda x: mat @ x
test_precond_fn = lambda x: precond_mat @ x
x_arr, x_arr_idx = mf_conjgrad_solver(test_matmul_fn, b, x0, n, 1e-6,
10, test_precond_fn,
'residual_norm_test')
x = x_arr[x_arr_idx]
self.assertAlmostEqual(np.linalg.norm(test_matmul_fn(x) - b),
0,
places=3)