def test_svd_lapack_err():
"""Test that svd raises an exception when LAPACK fails with nan input."""
n = 10
mat = np.zeros((n, n)) * np.nan
with np.testing.assert_raises_regex(Exception, 'LAPACK'):
svd.svd(mat)
def test_svd_non_sqr_err():
"""Test that svd raises an exception when a non-square matrix is passed."""
n = 10
mat = np.zeros((n, n + 1))
with np.testing.assert_raises_regex(Exception, 'square'):
svd.svd(mat)
def test_svd_dim_err():
"""Test that svd raises an exception when a non-2D array is passed."""
n = 10
mat = np.zeros((n, n, n))
with np.testing.assert_raises_regex(Exception, '2D'):
svd.svd(mat)
def test_svd_rand():
"""Test that the SVD of a random matrix recovers the original matrix."""
n = 10
mat = np.random.uniform(size=(n, n))
U, S, VT = svd.svd(mat)
np.testing.assert_almost_equal(U @ np.diag(S) @ VT, mat)
def test_svd_eye():
"""Test that the SVD of the identity matrix is the identity matrix."""
n = 10
mat = np.eye(n)
U, S, VT = svd.svd(mat)
np.testing.assert_almost_equal(U, np.eye(n))
np.testing.assert_almost_equal(S, 1)
np.testing.assert_almost_equal(VT, np.eye(n))
def test_svd_diag():
"""Test that the SVD of a sorted diagonal matrix is the original diagonal matrix."""
n = 10
diag_elem = np.flip(np.sort(np.random.uniform(size=n)))
mat = np.diag(diag_elem)
U, S, VT = svd.svd(mat)
np.testing.assert_almost_equal(U, np.eye(n))
np.testing.assert_almost_equal(S, diag_elem)
np.testing.assert_almost_equal(VT, np.eye(n))