def test_arnoldi(j, rng, seed):
d = 11
A = random.random_spsd_matrix(d=d, random_state=rng)
b = random.random_vector(d=d, random_state=rng)
with Timer(text='Arnoldi done in {:.4f} seconds', logger=_logger.info):
v = arnoldi.arnoldi(A, b, j=j)
np.testing.assert_almost_equal(np.eye(v.shape[0]), v @ v.T)
def test_conjugate_gradient(d, rng, seed):
minimiser = cg.ConjugateGradient(A=random.random_spsd_matrix(
d=d, random_state=rng),
b=random.random_vector(d=d,
random_state=rng))
with Timer(text='Conjugate gradient minimiser done in {:.4f} seconds',
logger=_logger.info):
x_star = minimiser()
_logger.info('Conjugate gradient minimiser took %d iterations.',
minimiser.niter)
np.testing.assert_allclose(minimiser.A @ x_star, minimiser.b)
def test_rayleigh_iteration(rng, seed):
A = random.random_spsd_matrix(d=10, random_state=rng)
w_eigh, v_eigh = la.eigh(A)
weighting = .9
lambda_ = weighting * w_eigh[-1] + (1 - weighting) * w_eigh[-2]
w_power = inverse_iteration.rayleigh_iteration(A,
lambda_,
niter=100,
random_state=rng)
np.testing.assert_allclose(w_eigh[-1], w_power)
def test_power_method(rng, seed):
print(rng.uniform())
A = random.random_spsd_matrix(d=10, random_state=rng)
w_power, v_power, sigma_power = power.power_method(A,
niter=100,
random_state=rng)
w_eigh, v_eigh = la.eigh(A)
np.testing.assert_allclose(v_eigh[:, -1], v_power)
np.testing.assert_allclose(w_eigh[-1], w_power)