def test_spd_inv_split_nocutoff():
x = np.random.normal(size=(5, 5))
unitary = np.linalg.qr(x)[0]
assert_array_almost_equal(unitary @ unitary.T, np.eye(5))
spd = unitary @ np.diag([1., 2., 3., 4., 5.]) @ unitary.T
w, _ = np.linalg.eigh(spd)
L = spd_inv_split(spd, epsilon=0)
spd_inv = L @ L.T
assert_array_almost_equal(spd_inv, np.linalg.pinv(spd))
def test_spd_inv_split(spd_matrix, epsilon, method, canonical_signs):
split = spd_inv_split(spd_matrix,
epsilon=epsilon,
method=method,
canonical_signs=canonical_signs)
spd_matrix_inv = split @ split.T
sminv, _ = spd_eig(spd_matrix_inv)
sm, _ = spd_eig(spd_matrix)
assert_array_almost_equal(np.sort(sm), np.sort(1. / sminv)[-3:])
if canonical_signs:
for i in range(3):
assert_(np.max(split[:, i]) > 0)
def test_spd_inv_splid_1d():
W = np.array([[.5]])
assert_almost_equal(spd_inv_split(W).squeeze(), 1. / np.sqrt(.5))
with assert_raises(ZeroRankError):
spd_inv_split(np.array([[.001]]), epsilon=.01)