def test_ista():
"""Test that objective goes down in ISTA for a simple problem."""
# || Ax - b ||_2^2
n, p = 100, 10
x = np.random.randn(p)
x /= np.linalg.norm(x)
A = np.random.randn(n, p)
b = np.dot(A, x)
def obj(x):
res = A.dot(x) - b
return 0.5 * np.dot(res.ravel(), res.ravel())
def grad(x):
return A.T.dot(A.dot(x) - b)
def prox(x, step_size=0):
return x / max(np.linalg.norm(x), 1.)
x0 = np.random.rand(p)
L = power_iteration(A.dot(A.T))
step_size = 0.99 / L
x_hat, pobj = fista(obj,
grad,
prox,
step_size,
x0,
max_iter=600,
momentum=False,
eps=None,
debug=True,
verbose=0)
np.testing.assert_array_almost_equal(x, x_hat)
assert np.all(np.diff(pobj) <= 0)
def test_linear_operator():
"""Test linear operator."""
n_times, n_atoms, n_times_atom = 64, 16, 32
n_times_valid = n_times - n_times_atom + 1
rng = check_random_state(42)
ds = rng.randn(n_atoms, n_times_atom)
some_sample_weights = np.abs(rng.randn(n_times))
for sample_weights in [None, some_sample_weights]:
gbc = partial(gram_block_circulant, ds=ds, n_times_valid=n_times_valid,
sample_weights=sample_weights)
DTD_full = gbc(method='full')
DTD_scipy = gbc(method='scipy')
DTD_custom = gbc(method='custom')
z = rng.rand(DTD_full.shape[1])
assert np.allclose(DTD_full.dot(z), DTD_scipy.dot(z))
assert np.allclose(DTD_full.dot(z), DTD_custom.dot(z))
# test power iterations with linear operator
mu, _ = linalg.eigh(DTD_full)
for DTD in [DTD_full, DTD_scipy, DTD_custom]:
mu_hat = power_iteration(DTD)
assert np.allclose(np.max(mu), mu_hat, rtol=1e-2)
def test_power_iterations():
"""Test power iteration."""
A = np.diag((1, 2, 3))
mu, b = np.linalg.eig(A)
mu_hat = power_iteration(A)
assert np.isclose(mu_hat, mu.max())