def test_dgapl21l1():
"""Test duality gap for L21 + L1 regularization."""
n_orient = 2
M, G, active_set = _generate_tf_data()
n_times = M.shape[1]
n_sources = G.shape[1]
tstep, wsize = 4, 32
n_steps = int(np.ceil(n_times / float(tstep)))
n_freqs = wsize // 2 + 1
n_coefs = n_steps * n_freqs
phi = _Phi(wsize, tstep, n_coefs)
phiT = _PhiT(tstep, n_freqs, n_steps, n_times)
for l1_ratio in [0.05, 0.1]:
alpha_max = norm_epsilon_inf(G, M, phi, l1_ratio, n_orient)
alpha_space = (1. - l1_ratio) * alpha_max
alpha_time = l1_ratio * alpha_max
Z = np.zeros([n_sources, n_coefs])
shape = (-1, n_steps, n_freqs)
# for alpha = alpha_max, Z = 0 is the solution so the dgap is 0
gap = dgap_l21l1(M, G, Z, np.ones(n_sources, dtype=bool), alpha_space,
alpha_time, phi, phiT, shape, n_orient, -np.inf)[0]
assert_allclose(0., gap)
# check that solution for alpha smaller than alpha_max is non 0:
X_hat_tf, active_set_hat_tf, E, gap = tf_mixed_norm_solver(
M,
G,
alpha_space / 1.01,
alpha_time / 1.01,
maxit=200,
tol=1e-8,
verbose=True,
debias=False,
n_orient=n_orient,
tstep=tstep,
wsize=wsize,
return_gap=True)
# allow possible small numerical errors (negative gap)
assert_array_less(-1e-10, gap)
assert_array_less(gap, 1e-8)
assert_array_less(1, len(active_set_hat_tf))
X_hat_tf, active_set_hat_tf, E, gap = tf_mixed_norm_solver(
M,
G,
alpha_space / 5.,
alpha_time / 5.,
maxit=200,
tol=1e-8,
verbose=True,
debias=False,
n_orient=n_orient,
tstep=tstep,
wsize=wsize,
return_gap=True)
assert_array_less(-1e-10, gap)
assert_array_less(gap, 1e-8)
assert_array_less(1, len(active_set_hat_tf))
def test_dgapl21l1():
"""Test duality gap for L21 + L1 regularization."""
n_orient = 2
M, G, active_set = _generate_tf_data()
n_times = M.shape[1]
n_sources = G.shape[1]
tstep, wsize = np.array([4, 2]), np.array([64, 16])
n_steps = np.ceil(n_times / tstep.astype(float)).astype(int)
n_freqs = wsize // 2 + 1
n_coefs = n_steps * n_freqs
phi = _Phi(wsize, tstep, n_coefs)
phiT = _PhiT(tstep, n_freqs, n_steps, n_times)
for l1_ratio in [0.05, 0.1]:
alpha_max = norm_epsilon_inf(G, M, phi, l1_ratio, n_orient)
alpha_space = (1. - l1_ratio) * alpha_max
alpha_time = l1_ratio * alpha_max
Z = np.zeros([n_sources, phi.n_coefs.sum()])
# for alpha = alpha_max, Z = 0 is the solution so the dgap is 0
gap = dgap_l21l1(M, G, Z, np.ones(n_sources, dtype=bool),
alpha_space, alpha_time, phi, phiT,
n_orient, -np.inf)[0]
assert_allclose(0., gap)
# check that solution for alpha smaller than alpha_max is non 0:
X_hat_tf, active_set_hat_tf, E, gap = tf_mixed_norm_solver(
M, G, alpha_space / 1.01, alpha_time / 1.01, maxit=200, tol=1e-8,
verbose=True, debias=False, n_orient=n_orient, tstep=tstep,
wsize=wsize, return_gap=True)
# allow possible small numerical errors (negative gap)
assert_array_less(-1e-10, gap)
assert_array_less(gap, 1e-8)
assert_array_less(1, len(active_set_hat_tf))
X_hat_tf, active_set_hat_tf, E, gap = tf_mixed_norm_solver(
M, G, alpha_space / 5., alpha_time / 5., maxit=200, tol=1e-8,
verbose=True, debias=False, n_orient=n_orient, tstep=tstep,
wsize=wsize, return_gap=True)
assert_array_less(-1e-10, gap)
assert_array_less(gap, 1e-8)
assert_array_less(1, len(active_set_hat_tf))