def random_bi_diagonalizable_pair(
n: int,
d1: Optional[int] = None,
d2: Optional[int] = None) -> Tuple[np.ndarray, np.ndarray]:
u = testing.random_orthogonal(n)
s = random_real_diagonal_matrix(n, d1)
z = random_real_diagonal_matrix(n, d2)
v = testing.random_orthogonal(n)
a = combinators.dot(u, s, v)
b = combinators.dot(u, z, v)
return a, b
def test_random_orthogonal():
o1 = random_orthogonal(2)
o2 = random_orthogonal(2)
assert is_orthogonal(o1)
assert is_orthogonal(o2)
assert not np.allclose(o1, o2)
def test_bidiagonalize_real_matrix_pair_with_symmetric_products(a, b):
a = np.array(a)
b = np.array(b)
p, q = diagonalize.bidiagonalize_real_matrix_pair_with_symmetric_products(
a, b)
assert_bidiagonalized_by(a, p, q)
assert_bidiagonalized_by(b, p, q)
@pytest.mark.parametrize('a,b', [
[X, Z],
[Y, np.eye(2)],
[np.eye(2), Y],
[np.eye(5), np.eye(4)],
[
e * testing.random_orthogonal(4)
for e in random_bi_diagonalizable_pair(4)
],
[
testing.random_orthogonal(4) * e
for e in random_bi_diagonalizable_pair(4)
],
])
def test_bidiagonalize_real_fails(a, b):
a = np.array(a)
b = np.array(b)
with pytest.raises(ValueError):
diagonalize.bidiagonalize_real_matrix_pair_with_symmetric_products(
a, b)
def test_random_orthogonal_deterministic_given_seed():
o1 = random_orthogonal(2, random_state=1234)
o2 = random_orthogonal(2, random_state=1234)
np.testing.assert_equal(o1, o2)