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# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from tensorflow.python.framework import random_seed
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import linalg_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import random_ops
from tensorflow.python.ops.linalg import linalg as linalg_lib
from tensorflow.python.ops.linalg import linear_operator_test_util
from tensorflow.python.platform import test
linalg = linalg_lib
random_seed.set_random_seed(23)
class LinearOperatorDiagTest(
linear_operator_test_util.SquareLinearOperatorDerivedClassTest):
"""Most tests done in the base class LinearOperatorDerivedClassTest."""
def _operator_and_matrix(self, build_info, dtype, use_placeholder):
shape = list(build_info.shape)
diag = linear_operator_test_util.random_sign_uniform(
shape[:-1], minval=1., maxval=2., dtype=dtype)
lin_op_diag = diag
if use_placeholder:
lin_op_diag = array_ops.placeholder_with_default(diag, shape=None)
operator = linalg.LinearOperatorDiag(lin_op_diag)
matrix = array_ops.matrix_diag(diag)
return operator, matrix
def test_assert_positive_definite_raises_for_zero_eigenvalue(self):
# Matrix with one positive eigenvalue and one zero eigenvalue.
with self.cached_session():
diag = [1.0, 0.0]
operator = linalg.LinearOperatorDiag(diag)
# is_self_adjoint should be auto-set for real diag.
self.assertTrue(operator.is_self_adjoint)
with self.assertRaisesOpError("non-positive.*not positive definite"):
operator.assert_positive_definite().run()
def test_assert_positive_definite_raises_for_negative_real_eigvalues(self):
with self.cached_session():
diag_x = [1.0, -2.0]
diag_y = [0., 0.] # Imaginary eigenvalues should not matter.
diag = math_ops.complex(diag_x, diag_y)
operator = linalg.LinearOperatorDiag(diag)
# is_self_adjoint should not be auto-set for complex diag.
self.assertTrue(operator.is_self_adjoint is None)
with self.assertRaisesOpError("non-positive real.*not positive definite"):
operator.assert_positive_definite().run()
def test_assert_positive_definite_does_not_raise_if_pd_and_complex(self):
with self.cached_session():
x = [1., 2.]
y = [1., 0.]
diag = math_ops.complex(x, y) # Re[diag] > 0.
# Should not fail
linalg.LinearOperatorDiag(diag).assert_positive_definite().run()
def test_assert_non_singular_raises_if_zero_eigenvalue(self):
# Singlular matrix with one positive eigenvalue and one zero eigenvalue.
with self.cached_session():
diag = [1.0, 0.0]
operator = linalg.LinearOperatorDiag(diag, is_self_adjoint=True)
with self.assertRaisesOpError("Singular operator"):
operator.assert_non_singular().run()
def test_assert_non_singular_does_not_raise_for_complex_nonsingular(self):
with self.cached_session():
x = [1., 0.]
y = [0., 1.]
diag = math_ops.complex(x, y)
# Should not raise.
linalg.LinearOperatorDiag(diag).assert_non_singular().run()
def test_assert_self_adjoint_raises_if_diag_has_complex_part(self):
with self.cached_session():
x = [1., 0.]
y = [0., 1.]
diag = math_ops.complex(x, y)
operator = linalg.LinearOperatorDiag(diag)
with self.assertRaisesOpError("imaginary.*not self-adjoint"):
operator.assert_self_adjoint().run()
def test_assert_self_adjoint_does_not_raise_for_diag_with_zero_imag(self):
with self.cached_session():
x = [1., 0.]
y = [0., 0.]
diag = math_ops.complex(x, y)
operator = linalg.LinearOperatorDiag(diag)
# Should not raise
operator.assert_self_adjoint().run()
def test_scalar_diag_raises(self):
with self.assertRaisesRegexp(ValueError, "must have at least 1 dimension"):
linalg.LinearOperatorDiag(1.)
def test_broadcast_matmul_and_solve(self):
# These cannot be done in the automated (base test class) tests since they
# test shapes that tf.matmul cannot handle.
# In particular, tf.matmul does not broadcast.
with self.cached_session() as sess:
x = random_ops.random_normal(shape=(2, 2, 3, 4))
# This LinearOperatorDiag will be broadcast to (2, 2, 3, 3) during solve
# and matmul with 'x' as the argument.
diag = random_ops.random_uniform(shape=(2, 1, 3))
operator = linalg.LinearOperatorDiag(diag, is_self_adjoint=True)
self.assertAllEqual((2, 1, 3, 3), operator.shape)
# Create a batch matrix with the broadcast shape of operator.
diag_broadcast = array_ops.concat((diag, diag), 1)
mat = array_ops.matrix_diag(diag_broadcast)
self.assertAllEqual((2, 2, 3, 3), mat.get_shape()) # being pedantic.
operator_matmul = operator.matmul(x)
mat_matmul = math_ops.matmul(mat, x)
self.assertAllEqual(operator_matmul.get_shape(), mat_matmul.get_shape())
self.assertAllClose(*sess.run([operator_matmul, mat_matmul]))
operator_solve = operator.solve(x)
mat_solve = linalg_ops.matrix_solve(mat, x)
self.assertAllEqual(operator_solve.get_shape(), mat_solve.get_shape())
self.assertAllClose(*sess.run([operator_solve, mat_solve]))
if __name__ == "__main__":
test.main()
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