def test_non_symmetric_matrix_raises(self):
"""Checks that if a non symmetric matrix is given to
components_from_metric, an error is thrown"""
rng = np.random.RandomState(42)
M = rng.randn(10, 10)
with pytest.raises(ValueError) as raised_error:
components_from_metric(M)
assert str(raised_error.value) == "The input metric should be symmetric."
def test_non_psd_raises(self):
"""Checks that a non PSD matrix (i.e. with negative eigenvalues) will
raise an error when passed to components_from_metric"""
rng = np.random.RandomState(42)
D = np.diag([1, 5, 3, 4.2, -4, -2, 1])
P = ortho_group.rvs(7, random_state=rng)
M = P.dot(D).dot(P.T)
msg = ("Matrix is not positive semidefinite (PSD).")
with pytest.raises(NonPSDError) as raised_error:
components_from_metric(M)
assert str(raised_error.value) == msg
with pytest.raises(NonPSDError) as raised_error:
components_from_metric(D)
assert str(raised_error.value) == msg
def test_components_from_metric_edge_cases(self):
"""Test that components_from_metric returns the right result in various
edge cases"""
rng = np.random.RandomState(42)
# an orthonormal matrix useful for creating matrices with given
# eigenvalues:
P = ortho_group.rvs(7, random_state=rng)
# matrix with all its coefficients very low (to check that the algorithm
# does not consider it as a diagonal matrix)(non regression test for
# https://github.com/scikit-learn-contrib/metric-learn/issues/175)
M = np.diag([1e-15, 2e-16, 3e-15, 4e-16, 5e-15, 6e-16, 7e-15])
M = P.dot(M).dot(P.T)
L = components_from_metric(M)
assert_allclose(L.T.dot(L), M)
# diagonal matrix
M = np.diag(np.abs(rng.randn(5)))
L = components_from_metric(M)
assert_allclose(L.T.dot(L), M)
# low-rank matrix (with zeros)
M = np.zeros((7, 7))
small_random = rng.randn(3, 3)
M[:3, :3] = small_random.T.dot(small_random)
L = components_from_metric(M)
assert_allclose(L.T.dot(L), M)
# low-rank matrix (without necessarily zeros)
R = np.abs(rng.randn(7, 7))
M = R.dot(np.diag([1, 5, 3, 2, 0, 0, 0])).dot(R.T)
L = components_from_metric(M)
assert_allclose(L.T.dot(L), M)
# matrix with a determinant still high but which is
# undefinite w.r.t to numpy standards
M = np.diag([1e5, 1e5, 1e5, 1e5, 1e5, 1e5, 1e-20])
M = P.dot(M).dot(P.T)
assert np.abs(np.linalg.det(M)) > 10
assert np.linalg.slogdet(M)[1] > 1 # (just to show that the computed
# determinant is far from null)
assert np.linalg.matrix_rank(M) < M.shape[0]
# (just to show that this case is indeed considered by numpy as an
# indefinite case)
L = components_from_metric(M)
assert_allclose(L.T.dot(L), M)
# matrix with lots of small nonzeros that make a big zero when multiplied
M = np.diag([1e-3, 1e-3, 1e-3, 1e-3, 1e-3, 1e-3, 1e-3])
L = components_from_metric(M)
assert_allclose(L.T.dot(L), M)
# full rank matrix
M = rng.randn(10, 10)
M = M.T.dot(M)
assert np.linalg.matrix_rank(M) == 10
L = components_from_metric(M)
assert_allclose(L.T.dot(L), M)
def test_almost_psd_dont_raise(self): """Checks that if the metric is almost PSD (i.e. it has some negative eigenvalues very close to zero), then components_from_metric will still work""" rng = np.random.RandomState(42) D = np.diag([1, 5, 3, 4.2, -1e-20, -2e-20, -1e-20]) P = ortho_group.rvs(7, random_state=rng) M = P.dot(D).dot(P.T) L = components_from_metric(M) assert_allclose(L.T.dot(L), M)
