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# Copyright 2017 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.gen_linalg_ops.matrix_logarithm."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
from tensorflow.python.client import session
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import ops
from tensorflow.python.ops import control_flow_ops
from tensorflow.python.ops import gen_linalg_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import random_ops
from tensorflow.python.ops import variables
from tensorflow.python.ops.linalg import linalg_impl
from tensorflow.python.platform import benchmark
from tensorflow.python.platform import test
class LogarithmOpTest(test.TestCase):
def _verifyLogarithm(self, x, np_type):
inp = x.astype(np_type)
with self.test_session(use_gpu=True):
# Verify that expm(logm(A)) == A.
tf_ans = linalg_impl.matrix_exponential(
gen_linalg_ops.matrix_logarithm(inp))
out = tf_ans.eval()
self.assertAllClose(inp, out, rtol=1e-4, atol=1e-3)
def _verifyLogarithmComplex(self, x):
for np_type in [np.complex64, np.complex128]:
self._verifyLogarithm(x, np_type)
def _makeBatch(self, matrix1, matrix2):
matrix_batch = np.concatenate(
[np.expand_dims(matrix1, 0),
np.expand_dims(matrix2, 0)])
matrix_batch = np.tile(matrix_batch, [2, 3, 1, 1])
return matrix_batch
def testNonsymmetric(self):
# 2x2 matrices
matrix1 = np.array([[1., 2.], [3., 4.]])
matrix2 = np.array([[1., 3.], [3., 5.]])
matrix1 = matrix1.astype(np.complex64)
matrix1 += 1j * matrix1
matrix2 = matrix2.astype(np.complex64)
matrix2 += 1j * matrix2
self._verifyLogarithmComplex(matrix1)
self._verifyLogarithmComplex(matrix2)
# Complex batch
self._verifyLogarithmComplex(self._makeBatch(matrix1, matrix2))
def testSymmetricPositiveDefinite(self):
# 2x2 matrices
matrix1 = np.array([[2., 1.], [1., 2.]])
matrix2 = np.array([[3., -1.], [-1., 3.]])
matrix1 = matrix1.astype(np.complex64)
matrix1 += 1j * matrix1
matrix2 = matrix2.astype(np.complex64)
matrix2 += 1j * matrix2
self._verifyLogarithmComplex(matrix1)
self._verifyLogarithmComplex(matrix2)
# Complex batch
self._verifyLogarithmComplex(self._makeBatch(matrix1, matrix2))
def testNonSquareMatrix(self):
# When the logarithm of a non-square matrix is attempted we should return
# an error
with self.assertRaises(ValueError):
gen_linalg_ops.matrix_logarithm(
np.array([[1., 2., 3.], [3., 4., 5.]], dtype=np.complex64))
def testWrongDimensions(self):
# The input to the logarithm should be at least a 2-dimensional tensor.
tensor3 = constant_op.constant([1., 2.], dtype=dtypes.complex64)
with self.assertRaises(ValueError):
gen_linalg_ops.matrix_logarithm(tensor3)
def testEmpty(self):
self._verifyLogarithmComplex(np.empty([0, 2, 2], dtype=np.complex64))
self._verifyLogarithmComplex(np.empty([2, 0, 0], dtype=np.complex64))
def testRandomSmallAndLargeComplex64(self):
np.random.seed(42)
for batch_dims in [(), (1,), (3,), (2, 2)]:
for size in 8, 31, 32:
shape = batch_dims + (size, size)
matrix = np.random.uniform(
low=-1.0, high=1.0,
size=np.prod(shape)).reshape(shape).astype(np.complex64)
self._verifyLogarithmComplex(matrix)
def testRandomSmallAndLargeComplex128(self):
np.random.seed(42)
for batch_dims in [(), (1,), (3,), (2, 2)]:
for size in 8, 31, 32:
shape = batch_dims + (size, size)
matrix = np.random.uniform(
low=-1.0, high=1.0,
size=np.prod(shape)).reshape(shape).astype(np.complex128)
self._verifyLogarithmComplex(matrix)
def testConcurrentExecutesWithoutError(self):
with self.test_session(use_gpu=True) as sess:
matrix1 = math_ops.cast(
random_ops.random_normal([5, 5], seed=42), dtypes.complex64)
matrix2 = math_ops.cast(
random_ops.random_normal([5, 5], seed=42), dtypes.complex64)
logm1 = gen_linalg_ops.matrix_logarithm(matrix1)
logm2 = gen_linalg_ops.matrix_logarithm(matrix2)
logm = sess.run([logm1, logm2])
self.assertAllEqual(logm[0], logm[1])
class MatrixLogarithmBenchmark(test.Benchmark):
shapes = [
(4, 4),
(10, 10),
(16, 16),
(101, 101),
(256, 256),
(1000, 1000),
(1024, 1024),
(2048, 2048),
(513, 4, 4),
(513, 16, 16),
(513, 256, 256),
]
def _GenerateMatrix(self, shape):
batch_shape = shape[:-2]
shape = shape[-2:]
assert shape[0] == shape[1]
n = shape[0]
matrix = np.ones(shape).astype(np.complex64) / (
2.0 * n) + np.diag(np.ones(n).astype(np.complex64))
return variables.Variable(np.tile(matrix, batch_shape + (1, 1)))
def benchmarkMatrixLogarithmOp(self):
for shape in self.shapes:
with ops.Graph().as_default(), \
session.Session(config=benchmark.benchmark_config()) as sess, \
ops.device("/cpu:0"):
matrix = self._GenerateMatrix(shape)
logm = gen_linalg_ops.matrix_logarithm(matrix)
variables.global_variables_initializer().run()
self.run_op_benchmark(
sess,
control_flow_ops.group(logm),
min_iters=25,
name="matrix_logarithm_cpu_{shape}".format(
shape=shape))
if __name__ == "__main__":
test.main()
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