text: # Copyright 2015 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.
  # ==============================================================================
  """Tests for tensorflow.ops.tf.Cholesky."""
  
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  import unittest
  
  import numpy as np
  from six.moves import xrange  # pylint: disable=redefined-builtin
  
  from tensorflow.compiler.tests import xla_test
  from tensorflow.python.framework import constant_op
  from tensorflow.python.framework import dtypes
  from tensorflow.python.ops import array_ops
  from tensorflow.python.ops import linalg_ops
  from tensorflow.python.ops import math_ops
  from tensorflow.python.platform import test
  
  
  class CholeskyOpTest(xla_test.XLATestCase):
  
    # Cholesky defined for float64, float32, complex64, complex128
    # (https://www.tensorflow.org/api_docs/python/tf/cholesky)
    @property
    def float_types(self):
      return set(super(CholeskyOpTest, self).float_types).intersection(
          (np.float64, np.float32, np.complex64, np.complex128))
  
    def _verifyCholeskyBase(self, sess, placeholder, x, chol, verification, atol):
      chol_np, verification_np = sess.run([chol, verification], {placeholder: x})
      self.assertAllClose(x, verification_np, atol=atol)
      self.assertShapeEqual(x, chol)
      # Check that the cholesky is lower triangular, and has positive diagonal
      # elements.
      if chol_np.shape[-1] > 0:
        chol_reshaped = np.reshape(chol_np, (-1, chol_np.shape[-2],
                                             chol_np.shape[-1]))
        for chol_matrix in chol_reshaped:
          self.assertAllClose(chol_matrix, np.tril(chol_matrix), atol=atol)
          self.assertTrue((np.diag(chol_matrix) > 0.0).all())
  
    def _verifyCholesky(self, x, atol=1e-6):
      # Verify that LL^T == x.
      with self.test_session() as sess:
        placeholder = array_ops.placeholder(
            dtypes.as_dtype(x.dtype), shape=x.shape)
        with self.test_scope():
          chol = linalg_ops.cholesky(placeholder)
        verification = math_ops.matmul(chol, chol, adjoint_b=True)
        self._verifyCholeskyBase(sess, placeholder, x, chol, verification, atol)
  
    def testBasic(self):
      data = np.array([[4., -1., 2.], [-1., 6., 0], [2., 0., 5.]])
      for dtype in self.float_types:
        self._verifyCholesky(data.astype(dtype))
  
    def testBatch(self):
      for dtype in self.float_types:
        simple_array = np.array(
            [[[1., 0.], [0., 5.]]], dtype=dtype)  # shape (1, 2, 2)
        self._verifyCholesky(simple_array)
        self._verifyCholesky(np.vstack((simple_array, simple_array)))
        odd_sized_array = np.array(
            [[[4., -1., 2.], [-1., 6., 0], [2., 0., 5.]]], dtype=dtype)
        self._verifyCholesky(np.vstack((odd_sized_array, odd_sized_array)))
  
        # Generate random positive-definite matrices.
        matrices = np.random.rand(10, 5, 5).astype(dtype)
        for i in xrange(10):
          matrices[i] = np.dot(matrices[i].T, matrices[i])
        self._verifyCholesky(matrices, atol=1e-4)
  
    def testNonSquareMatrix(self):
      for dtype in self.float_types:
        with self.assertRaises(ValueError):
          linalg_ops.cholesky(np.array([[1., 2., 3.], [3., 4., 5.]], dtype=dtype))
        with self.assertRaises(ValueError):
          linalg_ops.cholesky(
              np.array(
                  [[[1., 2., 3.], [3., 4., 5.]], [[1., 2., 3.], [3., 4., 5.]]],
                  dtype=dtype))
  
    def testWrongDimensions(self):
      for dtype in self.float_types:
        tensor3 = constant_op.constant([1., 2.], dtype=dtype)
        with self.assertRaises(ValueError):
          linalg_ops.cholesky(tensor3)
        with self.assertRaises(ValueError):
          linalg_ops.cholesky(tensor3)
  
    @unittest.skip("Test is slow")
    def testLarge(self):
      n = 200
      shape = (n, n)
      data = np.ones(shape).astype(np.float32) / (2.0 * n) + np.diag(
          np.ones(n).astype(np.float32))
      self._verifyCholesky(data, atol=1e-4)
  
    def testMatrixConditionNumbers(self):
      for dtype in self.float_types:
        condition_number = 1000
        size = 20
  
        # Generate random positive-definite symmetric matrices, and take their
        # Eigendecomposition.
        matrix = np.random.rand(size, size)
        matrix = np.dot(matrix.T, matrix)
        _, w = np.linalg.eigh(matrix)
  
        # Build new Eigenvalues exponentially distributed between 1 and
        # 1/condition_number
        v = np.exp(-np.log(condition_number) * np.linspace(0, size, size) / size)
        matrix = np.dot(np.dot(w, np.diag(v)), w.T).astype(dtype)
        self._verifyCholesky(matrix, atol=1e-4)
  
  
  if __name__ == "__main__":
    test.main()
  