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# 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 numpy as np
from six.moves import xrange # pylint: disable=redefined-builtin
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import dtypes as dtypes_lib
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import gradient_checker
from tensorflow.python.ops import linalg_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.platform import test
from tensorflow.python.platform import tf_logging
class CholeskyOpTest(test.TestCase):
def _verifyCholeskyBase(self, sess, x, chol, verification):
chol_np, verification_np = sess.run([chol, verification])
self.assertAllClose(x, verification_np)
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))
self.assertTrue((np.diag(chol_matrix) > 0.0).all())
def _verifyCholesky(self, x):
# Verify that LL^T == x.
with self.test_session() as sess:
chol = linalg_ops.cholesky(x)
verification = math_ops.matmul(chol, chol, adjoint_b=True)
self._verifyCholeskyBase(sess, x, chol, verification)
def testBasic(self):
self._verifyCholesky(np.array([[4., -1., 2.], [-1., 6., 0], [2., 0., 5.]]))
def testBatch(self):
simple_array = np.array([[[1., 0.], [0., 5.]]]) # 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.]]])
self._verifyCholesky(np.vstack((odd_sized_array, odd_sized_array)))
# Generate random positive-definite matrices.
matrices = np.random.rand(10, 5, 5)
for i in xrange(10):
matrices[i] = np.dot(matrices[i].T, matrices[i])
self._verifyCholesky(matrices)
def testNonSquareMatrix(self):
with self.assertRaises(ValueError):
linalg_ops.cholesky(np.array([[1., 2., 3.], [3., 4., 5.]]))
with self.assertRaises(ValueError):
linalg_ops.cholesky(
np.array([[[1., 2., 3.], [3., 4., 5.]], [[1., 2., 3.], [3., 4., 5.]]
]))
def testWrongDimensions(self):
tensor3 = constant_op.constant([1., 2.])
with self.assertRaises(ValueError):
linalg_ops.cholesky(tensor3)
with self.assertRaises(ValueError):
linalg_ops.cholesky(tensor3)
def testNotInvertible(self):
# The input should be invertible.
with self.test_session():
with self.assertRaisesOpError("LLT decomposition was not successful. The"
" input might not be valid."):
# All rows of the matrix below add to zero
self._verifyCholesky(
np.array([[1., -1., 0.], [-1., 1., -1.], [0., -1., 1.]]))
def testEmpty(self):
self._verifyCholesky(np.empty([0, 2, 2]))
self._verifyCholesky(np.empty([2, 0, 0]))
class CholeskyGradTest(test.TestCase):
_backprop_block_size = 32
def getShapes(self, shapeList):
return ((elem, int(np.floor(1.2 * elem))) for elem in shapeList)
def testSmallMatrices(self):
np.random.seed(0)
shapes = self.getShapes([1, 2, 10])
self.runFiniteDifferences(shapes)
def testOneBlockMatrices(self):
np.random.seed(0)
shapes = self.getShapes([self._backprop_block_size + 1])
self.runFiniteDifferences(
shapes,
dtypes=(dtypes_lib.float32, dtypes_lib.float64),
scalarTest=True)
def testTwoBlockMatrixFloat(self):
np.random.seed(0)
shapes = self.getShapes([2 * self._backprop_block_size + 1])
self.runFiniteDifferences(
shapes, dtypes=(dtypes_lib.float32,), scalarTest=True)
def testTwoBlockMatrixDouble(self):
np.random.seed(0)
shapes = self.getShapes([2 * self._backprop_block_size + 1])
self.runFiniteDifferences(
shapes, dtypes=(dtypes_lib.float64,), scalarTest=True)
def runFiniteDifferences(self,
shapes,
dtypes=(dtypes_lib.float32, dtypes_lib.float64),
scalarTest=False):
with self.test_session(use_gpu=False):
for shape in shapes:
for batch in False, True:
for dtype in dtypes:
if not scalarTest:
x = constant_op.constant(
np.random.randn(shape[0], shape[1]), dtype)
tensor = math_ops.matmul(x, array_ops.transpose(x)) / shape[0]
else:
# This is designed to be a faster test for larger matrices.
x = constant_op.constant(np.random.randn(), dtype)
R = constant_op.constant(
np.random.randn(shape[0], shape[1]), dtype)
e = math_ops.multiply(R, x)
tensor = math_ops.matmul(e, array_ops.transpose(e)) / shape[0]
# Inner-most matrices in tensor are positive definite.
if batch:
tensor = array_ops.tile(
array_ops.expand_dims(tensor, 0), [4, 1, 1])
y = linalg_ops.cholesky(tensor)
if scalarTest:
y = math_ops.reduce_mean(y)
error = gradient_checker.compute_gradient_error(x,
x._shape_as_list(),
y,
y._shape_as_list())
tf_logging.info("error = %f", error)
if dtype == dtypes_lib.float64:
self.assertLess(error, 1e-5)
else:
self.assertLess(error, 3e-3)
if __name__ == "__main__":
test.main()