def test_different_dtypes_raises(self):
operators = [
linalg.LinearOperatorFullMatrix(rng.rand(2, 3, 3)),
linalg.LinearOperatorFullMatrix(rng.rand(2, 3, 3).astype(np.float32))
]
with self.assertRaisesRegexp(TypeError, "same dtype"):
kronecker.LinearOperatorKronecker(operators)
def _operator_and_matrix(self, build_info, dtype, use_placeholder):
shape = list(build_info.shape)
expected_factors = build_info.__dict__["factors"]
matrices = [
linear_operator_test_util.random_positive_definite_matrix(
block_shape, dtype, force_well_conditioned=True)
for block_shape in expected_factors
]
lin_op_matrices = matrices
if use_placeholder:
lin_op_matrices = [
array_ops.placeholder_with_default(m, shape=None) for m in matrices]
operator = kronecker.LinearOperatorKronecker(
[linalg.LinearOperatorFullMatrix(
l, is_square=True) for l in lin_op_matrices])
matrices = linear_operator_util.broadcast_matrix_batch_dims(matrices)
kronecker_dense = _kronecker_dense(matrices)
if not use_placeholder:
kronecker_dense.set_shape(shape)
return operator, kronecker_dense
def test_kronecker_cholesky_type(self):
matrix = [[1., 0.], [0., 1.]]
operator = kronecker.LinearOperatorKronecker(
[
linalg.LinearOperatorFullMatrix(
matrix,
is_positive_definite=True,
is_self_adjoint=True,
),
linalg.LinearOperatorFullMatrix(
matrix,
is_positive_definite=True,
is_self_adjoint=True,
),
],
is_positive_definite=True,
is_self_adjoint=True,
)
cholesky_factor = operator.cholesky()
self.assertIsInstance(cholesky_factor,
kronecker.LinearOperatorKronecker)
self.assertEqual(2, len(cholesky_factor.operators))
self.assertIsInstance(cholesky_factor.operators[0],
lower_triangular.LinearOperatorLowerTriangular)
self.assertIsInstance(cholesky_factor.operators[1],
lower_triangular.LinearOperatorLowerTriangular)
def test_name(self):
matrix = [[11., 0.], [1., 8.]]
operator_1 = linalg.LinearOperatorFullMatrix(matrix, name="left")
operator_2 = linalg.LinearOperatorFullMatrix(matrix, name="right")
operator = kronecker.LinearOperatorKronecker([operator_1, operator_2])
self.assertEqual("left_x_right", operator.name)
def test_is_non_singular_auto_set(self):
# Matrix with two positive eigenvalues, 11 and 8.
# The matrix values do not effect auto-setting of the flags.
matrix = [[11., 0.], [1., 8.]]
operator_1 = linalg.LinearOperatorFullMatrix(matrix, is_non_singular=True)
operator_2 = linalg.LinearOperatorFullMatrix(matrix, is_non_singular=True)
operator = kronecker.LinearOperatorKronecker(
[operator_1, operator_2],
is_positive_definite=False, # No reason it HAS to be False...
is_non_singular=None)
self.assertFalse(operator.is_positive_definite)
self.assertTrue(operator.is_non_singular)
with self.assertRaisesRegexp(ValueError, "always non-singular"):
kronecker.LinearOperatorKronecker(
[operator_1, operator_2], is_non_singular=False)
def _cholesky_kronecker(kronecker_operator):
# Cholesky decomposition of a Kronecker product is the Kronecker product
# of cholesky decompositions.
return linear_operator_kronecker.LinearOperatorKronecker(
operators=[
operator.cholesky() for operator in kronecker_operator.operators],
is_non_singular=True,
is_self_adjoint=False,
is_square=True)
def _inverse_kronecker(kronecker_operator):
# Inverse decomposition of a Kronecker product is the Kronecker product
# of inverse decompositions.
return linear_operator_kronecker.LinearOperatorKronecker(
operators=[
operator.inverse() for operator in kronecker_operator.operators],
is_non_singular=kronecker_operator.is_non_singular,
is_self_adjoint=kronecker_operator.is_self_adjoint,
is_positive_definite=kronecker_operator.is_positive_definite,
is_square=True)
def _adjoint_kronecker(kronecker_operator):
# Adjoint of a Kronecker product is the Kronecker product
# of adjoints.
return linear_operator_kronecker.LinearOperatorKronecker(
operators=[
operator.adjoint() for operator in kronecker_operator.operators],
is_non_singular=kronecker_operator.is_non_singular,
is_self_adjoint=kronecker_operator.is_self_adjoint,
is_positive_definite=kronecker_operator.is_positive_definite,
is_square=True)
def _operator_and_mat_and_feed_dict(self, build_info, dtype,
use_placeholder):
shape = list(build_info.shape)
expected_factors = build_info.__dict__["factors"]
matrices = [
linear_operator_test_util.random_positive_definite_matrix(
block_shape, dtype, force_well_conditioned=True)
for block_shape in expected_factors
]
if use_placeholder:
matrices_ph = [
array_ops.placeholder(dtype=dtype) for _ in expected_factors
]
# Evaluate here because (i) you cannot feed a tensor, and (ii)
# values are random and we want the same value used for both mat and
# feed_dict.
matrices = self.evaluate(matrices)
operator = kronecker.LinearOperatorKronecker([
linalg.LinearOperatorFullMatrix(m_ph, is_square=True)
for m_ph in matrices_ph
],
is_square=True)
feed_dict = {m_ph: m for (m_ph, m) in zip(matrices_ph, matrices)}
else:
operator = kronecker.LinearOperatorKronecker([
linalg.LinearOperatorFullMatrix(m, is_square=True)
for m in matrices
])
feed_dict = None
# Should be auto-set.
self.assertTrue(operator.is_square)
matrices = linear_operator_util.broadcast_matrix_batch_dims(matrices)
kronecker_dense = _kronecker_dense(matrices)
if not use_placeholder:
kronecker_dense.set_shape(shape)
return operator, kronecker_dense, feed_dict
def test_kronecker_inverse_type(self):
matrix = [[1., 0.], [0., 1.]]
operator = kronecker.LinearOperatorKronecker(
[
linalg.LinearOperatorFullMatrix(matrix, is_non_singular=True),
linalg.LinearOperatorFullMatrix(matrix, is_non_singular=True),
],
is_non_singular=True,
)
inverse = operator.inverse()
self.assertIsInstance(inverse, kronecker.LinearOperatorKronecker)
self.assertEqual(2, len(inverse.operators))
def test_kronecker_adjoint_type(self):
matrix = [[1., 0.], [0., 1.]]
operator = kronecker.LinearOperatorKronecker(
[
linalg.LinearOperatorFullMatrix(matrix, is_non_singular=True),
linalg.LinearOperatorFullMatrix(matrix, is_non_singular=True),
],
is_non_singular=True,
)
adjoint = operator.adjoint()
self.assertIsInstance(adjoint, kronecker.LinearOperatorKronecker)
self.assertEqual(2, len(adjoint.operators))
def test_is_x_flags(self):
# Matrix with two positive eigenvalues, 1, and 1.
# The matrix values do not effect auto-setting of the flags.
matrix = [[1., 0.], [1., 1.]]
operator = kronecker.LinearOperatorKronecker(
[linalg.LinearOperatorFullMatrix(matrix),
linalg.LinearOperatorFullMatrix(matrix)],
is_positive_definite=True,
is_non_singular=True,
is_self_adjoint=False)
self.assertTrue(operator.is_positive_definite)
self.assertTrue(operator.is_non_singular)
self.assertFalse(operator.is_self_adjoint)
def test_tape_safe(self):
matrix_1 = variables_module.Variable([[1., 0.], [0., 1.]])
matrix_2 = variables_module.Variable([[2., 0.], [0., 2.]])
operator = kronecker.LinearOperatorKronecker(
[
linalg.LinearOperatorFullMatrix(matrix_1,
is_non_singular=True),
linalg.LinearOperatorFullMatrix(matrix_2,
is_non_singular=True),
],
is_non_singular=True,
)
self.check_tape_safe(operator)
def test_convert_variables_to_tensors(self):
matrix_1 = variables_module.Variable([[1., 0.], [0., 1.]])
matrix_2 = variables_module.Variable([[2., 0.], [0., 2.]])
operator = kronecker.LinearOperatorKronecker(
[
linalg.LinearOperatorFullMatrix(matrix_1,
is_non_singular=True),
linalg.LinearOperatorFullMatrix(matrix_2,
is_non_singular=True),
],
is_non_singular=True,
)
with self.cached_session() as sess:
sess.run([x.initializer for x in operator.variables])
self.check_convert_variables_to_tensors(operator)
def operator_and_matrix(self,
build_info,
dtype,
use_placeholder,
ensure_self_adjoint_and_pd=False):
# Kronecker products constructed below will be from symmetric
# positive-definite matrices.
del ensure_self_adjoint_and_pd
shape = list(build_info.shape)
expected_factors = build_info.__dict__["factors"]
matrices = [
linear_operator_test_util.random_positive_definite_matrix(
block_shape, dtype, force_well_conditioned=True)
for block_shape in expected_factors
]
lin_op_matrices = matrices
if use_placeholder:
lin_op_matrices = [
array_ops.placeholder_with_default(m, shape=None)
for m in matrices
]
operator = kronecker.LinearOperatorKronecker([
linalg.LinearOperatorFullMatrix(l,
is_square=True,
is_self_adjoint=True,
is_positive_definite=True)
for l in lin_op_matrices
])
matrices = linear_operator_util.broadcast_matrix_batch_dims(matrices)
kronecker_dense = _kronecker_dense(matrices)
if not use_placeholder:
kronecker_dense.set_shape(shape)
return operator, kronecker_dense
def test_empty_or_one_operators_raises(self):
with self.assertRaisesRegexp(ValueError, ">=1 operators"):
kronecker.LinearOperatorKronecker([])