def test_fast_svd():
n_samples = 100
k = 10
rng = np.random.RandomState(42)
# We need to use n_features > 500 to trigger the randomized_svd
for n_features in (30, 100, 550):
# generate a matrix X of approximate effective rank `rank` and no noise
# component (very structured signal):
U = rng.normal(size=(n_samples, k))
V = rng.normal(size=(k, n_features))
X = np.dot(U, V)
assert_equal(X.shape, (n_samples, n_features))
# compute the singular values of X using the slow exact method
U_, s_, V_ = linalg.svd(X, full_matrices=False)
Ur, Sr, Vr = fast_svd(X, k, random_state=0)
assert_equal(Vr.shape, (k, n_features))
assert_equal(Ur.shape, (n_samples, k))
# check the singular vectors too (while not checking the sign)
assert_array_almost_equal(
np.abs(np.diag(np.corrcoef(V_[:k], Vr)))[:k],
np.ones(k))
def test_fast_svd():
n_samples = 100
k = 10
rng = np.random.RandomState(42)
# We need to use n_features > 500 to trigger the randomized_svd
for n_features in (30, 100, 550):
# generate a matrix X of approximate effective rank `rank` and no noise
# component (very structured signal):
U = rng.normal(size=(n_samples, k))
V = rng.normal(size=(k, n_features))
X = np.dot(U, V)
assert X.shape == (n_samples, n_features)
# compute the singular values of X using the slow exact method
U_, s_, V_ = linalg.svd(X, full_matrices=False)
Ur, Sr, Vr = fast_svd(X, k, random_state=0)
assert Vr.shape == (k, n_features)
assert Ur.shape == (n_samples, k)
# check the singular vectors too (while not checking the sign)
assert_array_almost_equal(
np.abs(np.diag(np.corrcoef(V_[:k], Vr)))[:k], np.ones(k))
def _reduce(self, signals):
"""
Perform temporal dimensionality reduction.
:param signals: single-subject resting state matrix.
:return U: reduced resting state matrix
"""
U, S, V = fast_svd(signals.T, self.n_components)
U = U.T.copy()
U = U * S[:, np.newaxis]
return U