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# Copyright 2018 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.framework import ops
from tensorflow.python.framework import random_seed
from tensorflow.python.ops import array_ops
from tensorflow.python.ops.linalg import linalg as linalg_lib
from tensorflow.python.ops.linalg import linear_operator_kronecker as kronecker
from tensorflow.python.ops.linalg import linear_operator_test_util
from tensorflow.python.ops.linalg import linear_operator_util
from tensorflow.python.platform import test
linalg = linalg_lib
random_seed.set_random_seed(23)
rng = np.random.RandomState(0)
def _kronecker_dense(factors):
"""Convert a list of factors, into a dense Kronecker product."""
product = factors[0]
for factor in factors[1:]:
product = product[..., array_ops.newaxis, :, array_ops.newaxis]
factor_to_mul = factor[..., array_ops.newaxis, :, array_ops.newaxis, :]
product *= factor_to_mul
product = array_ops.reshape(
product,
shape=array_ops.concat(
[array_ops.shape(product)[:-4],
[array_ops.shape(product)[-4] * array_ops.shape(product)[-3],
array_ops.shape(product)[-2] * array_ops.shape(product)[-1]]
], axis=0))
return product
class KroneckerDenseTest(test.TestCase):
def testKroneckerDenseMatrix(self):
x = ops.convert_to_tensor([[2., 3.], [1., 2.]], dtype=dtypes.float32)
y = ops.convert_to_tensor([[1., 2.], [5., -1.]], dtype=dtypes.float32)
# From explicitly writing out the kronecker product of x and y.
z = ops.convert_to_tensor([
[2., 4., 3., 6.],
[10., -2., 15., -3.],
[1., 2., 2., 4.],
[5., -1., 10., -2.]], dtype=dtypes.float32)
# From explicitly writing out the kronecker product of y and x.
w = ops.convert_to_tensor([
[2., 3., 4., 6.],
[1., 2., 2., 4.],
[10., 15., -2., -3.],
[5., 10., -1., -2.]], dtype=dtypes.float32)
with self.cached_session():
self.assertAllClose(_kronecker_dense([x, y]).eval(), z.eval())
self.assertAllClose(_kronecker_dense([y, x]).eval(), w.eval())
class SquareLinearOperatorKroneckerTest(
linear_operator_test_util.SquareLinearOperatorDerivedClassTest):
"""Most tests done in the base class LinearOperatorDerivedClassTest."""
def setUp(self):
# Increase from 1e-6 to 1e-4
self._atol[dtypes.float32] = 1e-4
self._atol[dtypes.complex64] = 1e-4
self._rtol[dtypes.float32] = 1e-4
self._rtol[dtypes.complex64] = 1e-4
@property
def _operator_build_infos(self):
build_info = linear_operator_test_util.OperatorBuildInfo
return [
build_info((1, 1), factors=[(1, 1), (1, 1)]),
build_info((8, 8), factors=[(2, 2), (2, 2), (2, 2)]),
build_info((12, 12), factors=[(2, 2), (3, 3), (2, 2)]),
build_info((1, 3, 3), factors=[(1, 1), (1, 3, 3)]),
build_info((3, 6, 6), factors=[(3, 1, 1), (1, 2, 2), (1, 3, 3)]),
]
@property
def _tests_to_skip(self):
return ["det", "solve", "solve_with_broadcast"]
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_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_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 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_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 test_empty_or_one_operators_raises(self):
with self.assertRaisesRegexp(ValueError, ">=1 operators"):
kronecker.LinearOperatorKronecker([])
if __name__ == "__main__":
test.main()
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