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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 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_block_diag as block_diag
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 _block_diag_dense(expected_shape, blocks):
"""Convert a list of blocks, into a dense block diagonal matrix."""
rows = []
num_cols = 0
for block in blocks:
# Get the batch shape for the block.
batch_row_shape = array_ops.shape(block)[:-1]
zeros_to_pad_before_shape = array_ops.concat(
[batch_row_shape, [num_cols]], axis=-1)
zeros_to_pad_before = array_ops.zeros(
shape=zeros_to_pad_before_shape, dtype=block.dtype)
num_cols += array_ops.shape(block)[-1]
zeros_to_pad_after_shape = array_ops.concat(
[batch_row_shape, [expected_shape[-2] - num_cols]], axis=-1)
zeros_to_pad_after = array_ops.zeros(
zeros_to_pad_after_shape, dtype=block.dtype)
rows.append(array_ops.concat(
[zeros_to_pad_before, block, zeros_to_pad_after], axis=-1))
return array_ops.concat(rows, axis=-2)
class SquareLinearOperatorBlockDiagTest(
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((0, 0)),
build_info((1, 1)),
build_info((1, 3, 3)),
build_info((5, 5), blocks=[(2, 2), (3, 3)]),
build_info((3, 7, 7), blocks=[(1, 2, 2), (3, 2, 2), (1, 3, 3)]),
build_info((2, 1, 5, 5), blocks=[(2, 1, 2, 2), (1, 3, 3)]),
]
def _operator_and_matrix(self, build_info, dtype, use_placeholder):
shape = list(build_info.shape)
expected_blocks = (
build_info.__dict__["blocks"] if "blocks" in build_info.__dict__
else [shape])
matrices = [
linear_operator_test_util.random_positive_definite_matrix(
block_shape, dtype, force_well_conditioned=True)
for block_shape in expected_blocks
]
lin_op_matrices = matrices
if use_placeholder:
lin_op_matrices = [
array_ops.placeholder_with_default(
matrix, shape=None) for matrix in matrices]
operator = block_diag.LinearOperatorBlockDiag(
[linalg.LinearOperatorFullMatrix(
l, is_square=True) for l in lin_op_matrices])
# Should be auto-set.
self.assertTrue(operator.is_square)
# Broadcast the shapes.
expected_shape = list(build_info.shape)
matrices = linear_operator_util.broadcast_matrix_batch_dims(matrices)
block_diag_dense = _block_diag_dense(expected_shape, matrices)
if not use_placeholder:
block_diag_dense.set_shape(
expected_shape[:-2] + [expected_shape[-1], expected_shape[-1]])
return operator, block_diag_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 = block_diag.LinearOperatorBlockDiag(
[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 = block_diag.LinearOperatorBlockDiag(
[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"):
block_diag.LinearOperatorBlockDiag(
[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 = block_diag.LinearOperatorBlockDiag([operator_1, operator_2])
self.assertEqual("left_ds_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"):
block_diag.LinearOperatorBlockDiag(operators)
def test_non_square_operator_raises(self):
operators = [
linalg.LinearOperatorFullMatrix(rng.rand(3, 4), is_square=False),
linalg.LinearOperatorFullMatrix(rng.rand(3, 3))
]
with self.assertRaisesRegexp(ValueError, "square matrices"):
block_diag.LinearOperatorBlockDiag(operators)
def test_empty_operators_raises(self):
with self.assertRaisesRegexp(ValueError, "non-empty"):
block_diag.LinearOperatorBlockDiag([])
if __name__ == "__main__":
test.main()
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