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# Author: Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
# Daniel Strohmeier <daniel.strohmeier@gmail.com>
#
# License: Simplified BSD
import numpy as np
import warnings
from numpy.testing import assert_array_equal, assert_array_almost_equal
from numpy.testing import assert_allclose
from mne.inverse_sparse.mxne_optim import (mixed_norm_solver,
tf_mixed_norm_solver,
iterative_mixed_norm_solver)
warnings.simplefilter('always') # enable b/c these tests throw warnings
def _generate_tf_data():
n, p, t = 30, 40, 64
rng = np.random.RandomState(0)
G = rng.randn(n, p)
G /= np.std(G, axis=0)[None, :]
X = np.zeros((p, t))
active_set = [0, 4]
times = np.linspace(0, 2 * np.pi, t)
X[0] = np.sin(times)
X[4] = -2 * np.sin(4 * times)
X[4, times <= np.pi / 2] = 0
X[4, times >= np.pi] = 0
M = np.dot(G, X)
M += 1 * rng.randn(*M.shape)
return M, G, active_set
def test_l21_mxne():
"""Test convergence of MxNE solver"""
n, p, t, alpha = 30, 40, 20, 1.
rng = np.random.RandomState(0)
G = rng.randn(n, p)
G /= np.std(G, axis=0)[None, :]
X = np.zeros((p, t))
X[0] = 3
X[4] = -2
M = np.dot(G, X)
args = (M, G, alpha, 1000, 1e-8)
X_hat_prox, active_set, _ = mixed_norm_solver(
*args, active_set_size=None,
debias=True, solver='prox')
assert_array_equal(np.where(active_set)[0], [0, 4])
X_hat_cd, active_set, _ = mixed_norm_solver(
*args, active_set_size=None,
debias=True, solver='cd')
assert_array_equal(np.where(active_set)[0], [0, 4])
X_hat_bcd, active_set, _ = mixed_norm_solver(
M, G, alpha, maxit=1000, tol=1e-8, active_set_size=None,
debias=True, solver='bcd')
assert_array_equal(np.where(active_set)[0], [0, 4])
assert_allclose(X_hat_prox, X_hat_cd, rtol=1e-2)
assert_allclose(X_hat_prox, X_hat_bcd, rtol=1e-2)
assert_allclose(X_hat_bcd, X_hat_cd, rtol=1e-2)
X_hat_prox, active_set, _ = mixed_norm_solver(
*args, active_set_size=2, debias=True, solver='prox')
assert_array_equal(np.where(active_set)[0], [0, 4])
X_hat_cd, active_set, _ = mixed_norm_solver(
*args, active_set_size=2, debias=True, solver='cd')
assert_array_equal(np.where(active_set)[0], [0, 4])
X_hat_bcd, active_set, _ = mixed_norm_solver(
*args, active_set_size=2, debias=True, solver='bcd')
assert_array_equal(np.where(active_set)[0], [0, 4])
assert_allclose(X_hat_bcd, X_hat_cd, rtol=1e-2)
assert_allclose(X_hat_bcd, X_hat_prox, rtol=1e-2)
X_hat_prox, active_set, _ = mixed_norm_solver(
*args, active_set_size=2, debias=True, n_orient=2, solver='prox')
assert_array_equal(np.where(active_set)[0], [0, 1, 4, 5])
X_hat_bcd, active_set, _ = mixed_norm_solver(
*args, active_set_size=2, debias=True, n_orient=2, solver='bcd')
assert_array_equal(np.where(active_set)[0], [0, 1, 4, 5])
# suppress a coordinate-descent warning here
with warnings.catch_warnings(record=True):
X_hat_cd, active_set, _ = mixed_norm_solver(
*args, active_set_size=2, debias=True, n_orient=2, solver='cd')
assert_array_equal(np.where(active_set)[0], [0, 1, 4, 5])
assert_allclose(X_hat_bcd, X_hat_prox, rtol=1e-2)
assert_allclose(X_hat_bcd, X_hat_cd, rtol=1e-2)
X_hat_bcd, active_set, _ = mixed_norm_solver(
*args, active_set_size=2, debias=True, n_orient=5, solver='bcd')
assert_array_equal(np.where(active_set)[0], [0, 1, 2, 3, 4])
X_hat_prox, active_set, _ = mixed_norm_solver(
*args, active_set_size=2, debias=True, n_orient=5, solver='prox')
assert_array_equal(np.where(active_set)[0], [0, 1, 2, 3, 4])
with warnings.catch_warnings(record=True): # coordinate-ascent warning
X_hat_cd, active_set, _ = mixed_norm_solver(
*args, active_set_size=2, debias=True, n_orient=5, solver='cd')
assert_array_equal(np.where(active_set)[0], [0, 1, 2, 3, 4])
assert_array_equal(X_hat_bcd, X_hat_cd)
assert_allclose(X_hat_bcd, X_hat_prox, rtol=1e-2)
def test_tf_mxne():
"""Test convergence of TF-MxNE solver"""
alpha_space = 10.
alpha_time = 5.
M, G, active_set = _generate_tf_data()
X_hat_tf, active_set_hat_tf, E = tf_mixed_norm_solver(
M, G, alpha_space, alpha_time, maxit=200, tol=1e-8, verbose=True,
n_orient=1, tstep=4, wsize=32)
assert_array_equal(np.where(active_set_hat_tf)[0], active_set)
def test_tf_mxne_vs_mxne():
"""Test equivalence of TF-MxNE (with alpha_time=0) and MxNE"""
alpha_space = 60.
alpha_time = 0.
M, G, active_set = _generate_tf_data()
X_hat_tf, active_set_hat_tf, E = tf_mixed_norm_solver(
M, G, alpha_space, alpha_time, maxit=200, tol=1e-8, verbose=True,
debias=False, n_orient=1, tstep=4, wsize=32)
# Also run L21 and check that we get the same
X_hat_l21, _, _ = mixed_norm_solver(
M, G, alpha_space, maxit=200, tol=1e-8, verbose=False, n_orient=1,
active_set_size=None, debias=False)
assert_allclose(X_hat_tf, X_hat_l21, rtol=1e-1)
def test_iterative_reweighted_mxne():
"""Test convergence of irMxNE solver"""
n, p, t, alpha = 30, 40, 20, 1
rng = np.random.RandomState(0)
G = rng.randn(n, p)
G /= np.std(G, axis=0)[None, :]
X = np.zeros((p, t))
X[0] = 3
X[4] = -2
M = np.dot(G, X)
X_hat_l21, _, _ = mixed_norm_solver(
M, G, alpha, maxit=1000, tol=1e-8, verbose=False, n_orient=1,
active_set_size=None, debias=False, solver='bcd')
X_hat_bcd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 1, maxit=1000, tol=1e-8, active_set_size=None,
debias=False, solver='bcd')
X_hat_prox, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 1, maxit=1000, tol=1e-8, active_set_size=None,
debias=False, solver='prox')
assert_allclose(X_hat_bcd, X_hat_l21, rtol=1e-3)
assert_allclose(X_hat_prox, X_hat_l21, rtol=1e-3)
X_hat_prox, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=None,
debias=True, solver='prox')
assert_array_equal(np.where(active_set)[0], [0, 4])
X_hat_bcd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=2,
debias=True, solver='bcd')
assert_array_equal(np.where(active_set)[0], [0, 4])
X_hat_cd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=None,
debias=True, solver='cd')
assert_array_equal(np.where(active_set)[0], [0, 4])
assert_array_almost_equal(X_hat_prox, X_hat_cd, 5)
assert_array_almost_equal(X_hat_bcd, X_hat_cd, 5)
X_hat_bcd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=2,
debias=True, n_orient=2, solver='bcd')
assert_array_equal(np.where(active_set)[0], [0, 1, 4, 5])
# suppress a coordinate-descent warning here
with warnings.catch_warnings(record=True):
X_hat_cd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=2,
debias=True, n_orient=2, solver='cd')
assert_array_equal(np.where(active_set)[0], [0, 1, 4, 5])
assert_array_equal(X_hat_bcd, X_hat_cd, 5)
X_hat_bcd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=2, debias=True,
n_orient=5)
assert_array_equal(np.where(active_set)[0], [0, 1, 2, 3, 4])
with warnings.catch_warnings(record=True): # coordinate-ascent warning
X_hat_cd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=2,
debias=True, n_orient=5, solver='cd')
assert_array_equal(np.where(active_set)[0], [0, 1, 2, 3, 4])
assert_array_equal(X_hat_bcd, X_hat_cd, 5)
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