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_eig(spd_matrix, epsilon, method, canonical_signs):
sm, vm = spd_eig(spd_matrix,
epsilon=epsilon,
method=method,
canonical_signs=canonical_signs)
assert_(sm[0] >= sm[1] >= sm[2])
assert_array_almost_equal(vm @ np.diag(sm) @ vm.T, spd_matrix)
assert_array_almost_equal(vm.T @ vm, np.eye(3))
if canonical_signs or True:
# largest element in each column in vm should be positive
for col in range(vm.shape[1]):
assert_(np.max(vm[:, col]) > 0)
def test_spd_eig_invalid_inputs(spd_matrix):
with assert_raises(ValueError):
spd_eig(spd_matrix, method='...')
# not symmetric
with assert_raises(ValueError):
spd_eig(np.arange(9).reshape(3, 3), check_sym=True)
# zero rank
with assert_raises(ZeroRankError):
spd_eig(np.zeros((3, 3)))
def test_spd_inv(spd_matrix, epsilon, method):
W = spd_inv(spd_matrix, epsilon=epsilon, method=method)
sm, _ = spd_eig(spd_matrix)
sminv, _ = spd_eig(W)
assert_array_almost_equal(np.sort(sm), np.sort(1. / sminv))