def test_gram_schmidt_biorth(vector_arrays):
U1, U2 = vector_arrays
V1 = U1.copy()
V2 = U2.copy()
# this is the default used in gram_schmidt_biorth
check_tol = 1e-3
with log_levels(
{'pymor.algorithms.gram_schmidt.gram_schmidt_biorth': 'ERROR'}):
A1, A2 = gram_schmidt_biorth(U1, U2, copy=True, check_tol=check_tol)
assert np.all(almost_equal(U1, V1))
assert np.all(almost_equal(U2, V2))
assert np.allclose(A2.dot(A1), np.eye(len(A1)), atol=check_tol)
c = np.linalg.cond(A1.to_numpy()) * np.linalg.cond(A2.to_numpy())
assert np.all(almost_equal(U1, A1.lincomb(A2.dot(U1).T), rtol=c * 1e-14))
assert np.all(almost_equal(U2, A2.lincomb(A1.dot(U2).T), rtol=c * 1e-14))
with log_levels(
{'pymor.algorithms.gram_schmidt.gram_schmidt_biorth': 'ERROR'}):
B1, B2 = gram_schmidt_biorth(U1, U2, copy=False)
assert np.all(almost_equal(A1, B1))
assert np.all(almost_equal(A2, B2))
assert np.all(almost_equal(A1, U1))
assert np.all(almost_equal(A2, U2))
def test_pod_with_product(operator_with_arrays_and_products, method):
_, _, A, _, p, _ = operator_with_arrays_and_products
B = A.copy()
with log_levels({"pymor.algorithms": "ERROR"}):
U, s = pod(A, product=p, method=method)
assert np.all(almost_equal(A, B))
assert len(U) == len(s)
assert np.allclose(U.gramian(p), np.eye(len(s)))
def test_log_levels():
logger = NumpyMatrixOperator._logger
before_name = 'INFO'
logger.setLevel(before_name)
before = logger.level
with log_levels({logger.name: 'DEBUG'}):
assert 'DEBUG' == logging.getLevelName(logger.level)
assert logger.level != before
assert logger.level == before
assert before_name == logging.getLevelName(logger.level)
def test_method_of_snapshots_with_product(operator_with_arrays_and_products,
method):
_, _, A, _, p, _ = operator_with_arrays_and_products
B = A.copy()
with log_levels({"pymor.algorithms": "ERROR"}):
U, s, Vh = method(A, product=p)
assert np.all(almost_equal(A, B))
assert len(U) == len(s) == Vh.shape[0]
assert Vh.shape[1] == len(A)
assert np.allclose(Vh @ Vh.T.conj(), np.eye(len(s)))
U.scal(s)
UsVh = U.lincomb(Vh.T)
assert np.all(almost_equal(A, UsVh, rtol=4e-8))
def test_method_of_snapshots(vector_array, method):
A = vector_array[0]
# TODO assumption here masks a potential issue with the algorithm
# where it fails in internal lapack instead of a proper error
assume(len(A) > 1 or A.dim > 1)
assume(not contains_zero_vector(A, rtol=1e-13, atol=1e-13))
B = A.copy()
with log_levels({"pymor.algorithms": "ERROR"}):
U, s, Vh = method(A)
assert np.all(almost_equal(A, B))
assert len(U) == len(s) == Vh.shape[0]
assert Vh.shape[1] == len(A)
assert np.allclose(Vh @ Vh.T.conj(), np.eye(len(s)))
U.scal(s)
UsVh = U.lincomb(Vh.T)
assert np.all(almost_equal(A, UsVh, rtol=4e-8))
