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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
import numpy as np
from tensorflow.python.framework import dtypes
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import math_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
class SquareLinearOperatorFullMatrixTest(
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)
matrix = linear_operator_test_util.random_positive_definite_matrix(
shape, dtype)
lin_op_matrix = matrix
if use_placeholder:
lin_op_matrix = array_ops.placeholder_with_default(matrix, shape=None)
operator = linalg.LinearOperatorFullMatrix(lin_op_matrix, is_square=True)
return operator, matrix
def test_is_x_flags(self):
# Matrix with two positive eigenvalues.
matrix = [[1., 0.], [1., 11.]]
operator = 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)
# Auto-detected.
self.assertTrue(operator.is_square)
def test_assert_non_singular_raises_if_cond_too_big_but_finite(self):
with self.cached_session():
tril = linear_operator_test_util.random_tril_matrix(
shape=(50, 50), dtype=np.float32)
diag = np.logspace(-2, 2, 50).astype(np.float32)
tril = array_ops.matrix_set_diag(tril, diag)
matrix = math_ops.matmul(tril, tril, transpose_b=True).eval()
operator = linalg.LinearOperatorFullMatrix(matrix)
with self.assertRaisesOpError("Singular matrix"):
# Ensure that we have finite condition number...just HUGE.
cond = np.linalg.cond(matrix)
self.assertTrue(np.isfinite(cond))
self.assertGreater(cond, 1e12)
operator.assert_non_singular().run()
def test_assert_non_singular_raises_if_cond_infinite(self):
with self.cached_session():
matrix = [[1., 1.], [1., 1.]]
# We don't pass the is_self_adjoint hint here, which means we take the
# generic code path.
operator = linalg.LinearOperatorFullMatrix(matrix)
with self.assertRaisesOpError("Singular matrix"):
operator.assert_non_singular().run()
def test_assert_self_adjoint(self):
matrix = [[0., 1.], [0., 1.]]
operator = linalg.LinearOperatorFullMatrix(matrix)
with self.cached_session():
with self.assertRaisesOpError("not equal to its adjoint"):
operator.assert_self_adjoint().run()
def test_assert_positive_definite(self):
matrix = [[1., 1.], [1., 1.]]
operator = linalg.LinearOperatorFullMatrix(matrix, is_self_adjoint=True)
with self.cached_session():
with self.assertRaisesOpError("Cholesky decomposition was not success"):
operator.assert_positive_definite().run()
class SquareLinearOperatorFullMatrixSymmetricPositiveDefiniteTest(
linear_operator_test_util.SquareLinearOperatorDerivedClassTest):
"""Most tests done in the base class LinearOperatorDerivedClassTest.
In this test, the operator is constructed with hints that invoke the use of
a Cholesky decomposition for solves/determinant.
"""
def setUp(self):
# Increase from 1e-6 to 1e-5. This reduction in tolerance happens,
# presumably, because we are taking a different code path in the operator
# and the matrix. The operator uses a Choleksy, the matrix uses standard
# solve.
self._atol[dtypes.float32] = 1e-5
self._rtol[dtypes.float32] = 1e-5
self._atol[dtypes.float64] = 1e-10
self._rtol[dtypes.float64] = 1e-10
@property
def _dtypes_to_test(self):
return [dtypes.float32, dtypes.float64]
def _operator_and_matrix(self, build_info, dtype, use_placeholder):
shape = list(build_info.shape)
matrix = linear_operator_test_util.random_positive_definite_matrix(
shape, dtype, force_well_conditioned=True)
lin_op_matrix = matrix
if use_placeholder:
lin_op_matrix = array_ops.placeholder_with_default(matrix, shape=None)
operator = linalg.LinearOperatorFullMatrix(lin_op_matrix, is_square=True)
return operator, matrix
def test_is_x_flags(self):
# Matrix with two positive eigenvalues.
matrix = [[1., 0.], [0., 7.]]
operator = linalg.LinearOperatorFullMatrix(
matrix, is_positive_definite=True, is_self_adjoint=True)
self.assertTrue(operator.is_positive_definite)
self.assertTrue(operator.is_self_adjoint)
# Should be auto-set
self.assertTrue(operator.is_non_singular)
self.assertTrue(operator._can_use_cholesky)
self.assertTrue(operator.is_square)
def test_assert_non_singular(self):
matrix = [[1., 1.], [1., 1.]]
operator = linalg.LinearOperatorFullMatrix(
matrix, is_self_adjoint=True, is_positive_definite=True)
with self.cached_session():
# Cholesky decomposition may fail, so the error is not specific to
# non-singular.
with self.assertRaisesOpError(""):
operator.assert_non_singular().run()
def test_assert_self_adjoint(self):
matrix = [[0., 1.], [0., 1.]]
operator = linalg.LinearOperatorFullMatrix(
matrix, is_self_adjoint=True, is_positive_definite=True)
with self.cached_session():
with self.assertRaisesOpError("not equal to its adjoint"):
operator.assert_self_adjoint().run()
def test_assert_positive_definite(self):
matrix = [[1., 1.], [1., 1.]]
operator = linalg.LinearOperatorFullMatrix(
matrix, is_self_adjoint=True, is_positive_definite=True)
with self.cached_session():
# Cholesky decomposition may fail, so the error is not specific to
# non-singular.
with self.assertRaisesOpError(""):
operator.assert_positive_definite().run()
class NonSquareLinearOperatorFullMatrixTest(
linear_operator_test_util.NonSquareLinearOperatorDerivedClassTest):
"""Most tests done in the base class LinearOperatorDerivedClassTest."""
def _operator_and_matrix(self, build_info, dtype, use_placeholder):
shape = list(build_info.shape)
matrix = linear_operator_test_util.random_normal(shape, dtype=dtype)
lin_op_matrix = matrix
if use_placeholder:
lin_op_matrix = array_ops.placeholder_with_default(matrix, shape=None)
operator = linalg.LinearOperatorFullMatrix(lin_op_matrix, is_square=True)
return operator, matrix
def test_is_x_flags(self):
matrix = [[3., 2., 1.], [1., 1., 1.]]
operator = linalg.LinearOperatorFullMatrix(
matrix,
is_self_adjoint=False)
self.assertEqual(operator.is_positive_definite, None)
self.assertEqual(operator.is_non_singular, None)
self.assertFalse(operator.is_self_adjoint)
self.assertFalse(operator.is_square)
def test_matrix_must_have_at_least_two_dims_or_raises(self):
with self.assertRaisesRegexp(ValueError, "at least 2 dimensions"):
linalg.LinearOperatorFullMatrix([1.])
if __name__ == "__main__":
test.main()
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