def test_is_special_orthogonal_tolerance():
tol = Tolerance(atol=0.5)
# Pays attention to specified tolerance.
assert cirq.is_special_orthogonal(np.array([[1, 0], [-0.5, 1]]), tol)
assert not cirq.is_special_orthogonal(np.array([[1, 0], [-0.6, 1]]), tol)
# Error isn't accumulated across entries, except for determinant factors.
assert cirq.is_special_orthogonal(
np.array([[1.2, 0, 0], [0, 1.2, 0], [0, 0, 1 / 1.2]]), tol)
assert not cirq.is_special_orthogonal(
np.array([[1.2, 0, 0], [0, 1.2, 0], [0, 0, 1.2]]), tol)
assert not cirq.is_special_orthogonal(
np.array([[1.2, 0, 0], [0, 1.3, 0], [0, 0, 1 / 1.2]]), tol)
def test_is_special_orthogonal():
assert cirq.is_special_orthogonal(np.empty((0, 0)))
assert not cirq.is_special_orthogonal(np.empty((1, 0)))
assert not cirq.is_special_orthogonal(np.empty((0, 1)))
assert cirq.is_special_orthogonal(np.array([[1]]))
assert not cirq.is_special_orthogonal(np.array([[-1]]))
assert not cirq.is_special_orthogonal(np.array([[1j]]))
assert not cirq.is_special_orthogonal(np.array([[5]]))
assert not cirq.is_special_orthogonal(np.array([[3j]]))
assert not cirq.is_special_orthogonal(np.array([[1, 0]]))
assert not cirq.is_special_orthogonal(np.array([[1], [0]]))
assert not cirq.is_special_orthogonal(np.array([[1, 0], [0, -2]]))
assert not cirq.is_special_orthogonal(np.array([[1, 0], [0, -1]]))
assert cirq.is_special_orthogonal(np.array([[-1, 0], [0, -1]]))
assert not cirq.is_special_orthogonal(np.array([[1j, 0], [0, 1]]))
assert not cirq.is_special_orthogonal(np.array([[1, 0], [1, 1]]))
assert not cirq.is_special_orthogonal(np.array([[1, 1], [0, 1]]))
assert not cirq.is_special_orthogonal(np.array([[1, 1], [1, 1]]))
assert not cirq.is_special_orthogonal(np.array([[1, -1], [1, 1]]))
assert cirq.is_special_orthogonal(
np.array([[1, -1], [1, 1]]) * np.sqrt(0.5))
assert not cirq.is_special_orthogonal(
np.array([[1, 1], [1, -1]]) * np.sqrt(0.5))
assert not cirq.is_special_orthogonal(
np.array([[1, 1j], [1j, 1]]) * np.sqrt(0.5))
assert not cirq.is_special_orthogonal(
np.array([[1, -1j], [1j, 1]]) * np.sqrt(0.5))
assert cirq.is_special_orthogonal(np.array([[1, 1e-11], [0, 1 + 1e-11]]))
def test_bidiagonalize_unitary_with_special_orthogonals(mat):
p, d, q = cirq.bidiagonalize_unitary_with_special_orthogonals(mat)
assert cirq.is_special_orthogonal(p)
assert cirq.is_special_orthogonal(q)
assert np.allclose(p.dot(mat).dot(q), np.diag(d))
assert_bidiagonalized_by(mat, p, q)
