text: # 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.framework import ops
  from tensorflow.python.framework import random_seed
  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
  random_seed.set_random_seed(23)
  rng = np.random.RandomState(0)
  
  
  class SquareLinearOperatorCompositionTest(
      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
  
    def _operator_and_matrix(self, build_info, dtype, use_placeholder):
      sess = ops.get_default_session()
      shape = list(build_info.shape)
  
      # Either 1 or 2 matrices, depending.
      num_operators = rng.randint(low=1, high=3)
      matrices = [
          linear_operator_test_util.random_positive_definite_matrix(
              shape, dtype, force_well_conditioned=True)
          for _ in range(num_operators)
      ]
  
      lin_op_matrices = matrices
  
      if use_placeholder:
        lin_op_matrices = [
            array_ops.placeholder_with_default(
                matrix, shape=None) for matrix in matrices]
  
      operator = linalg.LinearOperatorComposition(
          [linalg.LinearOperatorFullMatrix(l) for l in lin_op_matrices],
          is_square=True)
  
      matmul_order_list = list(reversed(matrices))
      mat = matmul_order_list[0]
      for other_mat in matmul_order_list[1:]:
        mat = math_ops.matmul(other_mat, mat)
  
      return operator, mat
  
    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 = linalg.LinearOperatorComposition(
          [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 = linalg.LinearOperatorComposition(
          [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"):
        linalg.LinearOperatorComposition(
            [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 = linalg.LinearOperatorComposition([operator_1, operator_2])
  
      self.assertEqual("left_o_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"):
        linalg.LinearOperatorComposition(operators)
  
    def test_empty_operators_raises(self):
      with self.assertRaisesRegexp(ValueError, "non-empty"):
        linalg.LinearOperatorComposition([])
  
  
  class NonSquareLinearOperatorCompositionTest(
      linear_operator_test_util.NonSquareLinearOperatorDerivedClassTest):
    """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
  
    def _operator_and_matrix(self, build_info, dtype, use_placeholder):
      sess = ops.get_default_session()
      shape = list(build_info.shape)
  
      # Test only the case of 2 matrices.
      # The Square test uses either 1 or 2, so we have tested the case of 1 matrix
      # sufficiently.
      num_operators = 2
  
      # Create 2 matrices/operators, A1, A2, which becomes A = A1 A2.
      # Use inner dimension of 2.
      k = 2
      batch_shape = shape[:-2]
      shape_1 = batch_shape + [shape[-2], k]
      shape_2 = batch_shape + [k, shape[-1]]
  
      matrices = [
          linear_operator_test_util.random_normal(
              shape_1, dtype=dtype), linear_operator_test_util.random_normal(
                  shape_2, dtype=dtype)
      ]
  
      lin_op_matrices = matrices
  
      if use_placeholder:
        lin_op_matrices = [
            array_ops.placeholder_with_default(
                matrix, shape=None) for matrix in matrices]
  
      operator = linalg.LinearOperatorComposition(
          [linalg.LinearOperatorFullMatrix(l) for l in lin_op_matrices])
  
      matmul_order_list = list(reversed(matrices))
      mat = matmul_order_list[0]
      for other_mat in matmul_order_list[1:]:
        mat = math_ops.matmul(other_mat, mat)
  
      return operator, mat
  
    def test_static_shapes(self):
      operators = [
          linalg.LinearOperatorFullMatrix(rng.rand(2, 3, 4)),
          linalg.LinearOperatorFullMatrix(rng.rand(2, 4, 5))
      ]
      operator = linalg.LinearOperatorComposition(operators)
      self.assertAllEqual((2, 3, 5), operator.shape)
  
    def test_shape_tensors_when_statically_available(self):
      operators = [
          linalg.LinearOperatorFullMatrix(rng.rand(2, 3, 4)),
          linalg.LinearOperatorFullMatrix(rng.rand(2, 4, 5))
      ]
      operator = linalg.LinearOperatorComposition(operators)
      with self.cached_session():
        self.assertAllEqual((2, 3, 5), operator.shape_tensor().eval())
  
    def test_shape_tensors_when_only_dynamically_available(self):
      mat_1 = rng.rand(1, 2, 3, 4)
      mat_2 = rng.rand(1, 2, 4, 5)
      mat_ph_1 = array_ops.placeholder(dtypes.float64)
      mat_ph_2 = array_ops.placeholder(dtypes.float64)
      feed_dict = {mat_ph_1: mat_1, mat_ph_2: mat_2}
  
      operators = [
          linalg.LinearOperatorFullMatrix(mat_ph_1),
          linalg.LinearOperatorFullMatrix(mat_ph_2)
      ]
      operator = linalg.LinearOperatorComposition(operators)
      with self.cached_session():
        self.assertAllEqual(
            (1, 2, 3, 5), operator.shape_tensor().eval(feed_dict=feed_dict))
  
  
  if __name__ == "__main__":
    test.main()
  