def test_reg_pinv(ndim):
"""Test regularization and inversion of covariance matrix."""
# create rank-deficient array
a = np.array([[1., 0., 1.], [0., 1., 0.], [1., 0., 1.]])
for _ in range(ndim - 2):
a = a[np.newaxis]
# Test if rank-deficient matrix without regularization throws
# specific warning
with pytest.warns(RuntimeWarning, match='deficient'):
_reg_pinv(a, reg=0.)
# Test inversion with explicit rank
a_inv_np = np.linalg.pinv(a, hermitian=True)
a_inv_mne, loading_factor, rank = _reg_pinv(a, rank=2)
assert loading_factor == 0
assert rank == 2
assert_allclose(a_inv_np, a_inv_mne, atol=1e-14)
# Test inversion with automatic rank detection
a_inv_mne, _, estimated_rank = _reg_pinv(a, rank=None)
assert_allclose(a_inv_np, a_inv_mne, atol=1e-14)
assert estimated_rank == 2
# Test adding regularization
a_inv_mne, loading_factor, estimated_rank = _reg_pinv(a, reg=2)
# Since A has a diagonal of all ones, loading_factor should equal the
# regularization parameter
assert loading_factor == 2
# The estimated rank should be that of the non-regularized matrix
assert estimated_rank == 2
# Test result against the NumPy version
a_inv_np = np.linalg.pinv(a + loading_factor * np.eye(3), hermitian=True)
assert_allclose(a_inv_np, a_inv_mne, atol=1e-14)
# Test setting rcond
a_inv_np = np.linalg.pinv(a, rcond=0.5)
a_inv_mne, _, estimated_rank = _reg_pinv(a, rcond=0.5)
assert_allclose(a_inv_np, a_inv_mne, atol=1e-14)
assert estimated_rank == 1
# Test inverting an all zero cov
a_inv, loading_factor, estimated_rank = _reg_pinv(np.zeros((3, 3)), reg=2)
assert_array_equal(a_inv, 0)
assert loading_factor == 0
assert estimated_rank == 0
def test_reg_pinv():
"""Test regularization and inversion of covariance matrix."""
# create rank-deficient array
a = np.array([[1., 0., 1.], [0., 1., 0.], [1., 0., 1.]])
# Test if rank-deficient matrix without regularization throws
# specific warning
with pytest.warns(RuntimeWarning, match='deficient'):
_reg_pinv(a, reg=0.)
# Test inversion with explicit rank
a_inv_np = np.linalg.pinv(a)
a_inv_mne, loading_factor, rank = _reg_pinv(a, rank=2)
assert loading_factor == 0
assert rank == 2
assert_array_equal(a_inv_np, a_inv_mne)
# Test inversion with automatic rank detection
a_inv_mne, _, estimated_rank = _reg_pinv(a, rank=None)
assert_array_equal(a_inv_np, a_inv_mne)
assert estimated_rank == 2
# Test adding regularization
a_inv_mne, loading_factor, estimated_rank = _reg_pinv(a, reg=2)
# Since A has a diagonal of all ones, loading_factor should equal the
# regularization parameter
assert loading_factor == 2
# The estimated rank should be that of the non-regularized matrix
assert estimated_rank == 2
# Test result against the NumPy version
a_inv_np = np.linalg.pinv(a + loading_factor * np.eye(3))
assert_array_equal(a_inv_np, a_inv_mne)
# Test setting rcond
a_inv_np = np.linalg.pinv(a, rcond=0.5)
a_inv_mne, _, estimated_rank = _reg_pinv(a, rcond=0.5)
assert_array_equal(a_inv_np, a_inv_mne)
assert estimated_rank == 1
# Test inverting an all zero cov
a_inv, loading_factor, estimated_rank = _reg_pinv(np.zeros((3, 3)), reg=2)
assert_array_equal(a_inv, 0)
assert loading_factor == 0
assert estimated_rank == 0