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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.linalg.linalg_impl.matrix_exponential."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import itertools
import numpy as np
from tensorflow.python.client import session
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import ops
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import control_flow_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
def np_expm(x): # pylint: disable=invalid-name
"""Slow but accurate Taylor series matrix exponential."""
y = np.zeros(x.shape, dtype=x.dtype)
xn = np.eye(x.shape[0], dtype=x.dtype)
for n in range(40):
if n > 0:
xn /= float(n)
y += xn
xn = np.dot(xn, x)
return y
class ExponentialOpTest(test.TestCase):
def _verifyExponential(self, x, np_type):
inp = x.astype(np_type)
with self.test_session(use_gpu=True):
tf_ans = linalg_impl.matrix_exponential(inp)
if x.size == 0:
np_ans = np.empty(x.shape, dtype=np_type)
else:
if x.ndim > 2:
np_ans = np.zeros(inp.shape, dtype=np_type)
for i in itertools.product(*[range(x) for x in inp.shape[:-2]]):
np_ans[i] = np_expm(inp[i])
else:
np_ans = np_expm(inp)
out = tf_ans.eval()
self.assertAllClose(np_ans, out, rtol=1e-4, atol=1e-3)
def _verifyExponentialReal(self, x):
for np_type in [np.float32, np.float64]:
self._verifyExponential(x, np_type)
def _verifyExponentialComplex(self, x):
for np_type in [np.complex64, np.complex128]:
self._verifyExponential(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 testNonsymmetricReal(self):
# 2x2 matrices
matrix1 = np.array([[1., 2.], [3., 4.]])
matrix2 = np.array([[1., 3.], [3., 5.]])
self._verifyExponentialReal(matrix1)
self._verifyExponentialReal(matrix2)
# A multidimensional batch of 2x2 matrices
self._verifyExponentialReal(self._makeBatch(matrix1, matrix2))
def testNonsymmetricComplex(self):
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._verifyExponentialComplex(matrix1)
self._verifyExponentialComplex(matrix2)
# Complex batch
self._verifyExponentialComplex(self._makeBatch(matrix1, matrix2))
def testSymmetricPositiveDefiniteReal(self):
# 2x2 matrices
matrix1 = np.array([[2., 1.], [1., 2.]])
matrix2 = np.array([[3., -1.], [-1., 3.]])
self._verifyExponentialReal(matrix1)
self._verifyExponentialReal(matrix2)
# A multidimensional batch of 2x2 matrices
self._verifyExponentialReal(self._makeBatch(matrix1, matrix2))
def testSymmetricPositiveDefiniteComplex(self):
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._verifyExponentialComplex(matrix1)
self._verifyExponentialComplex(matrix2)
# Complex batch
self._verifyExponentialComplex(self._makeBatch(matrix1, matrix2))
def testNonSquareMatrix(self):
# When the exponential of a non-square matrix is attempted we should return
# an error
with self.assertRaises(ValueError):
linalg_impl.matrix_exponential(np.array([[1., 2., 3.], [3., 4., 5.]]))
def testWrongDimensions(self):
# The input to the exponential should be at least a 2-dimensional tensor.
tensor3 = constant_op.constant([1., 2.])
with self.assertRaises(ValueError):
linalg_impl.matrix_exponential(tensor3)
def testEmpty(self):
self._verifyExponentialReal(np.empty([0, 2, 2]))
self._verifyExponentialReal(np.empty([2, 0, 0]))
def testDynamic(self):
with self.test_session(use_gpu=True) as sess:
inp = array_ops.placeholder(ops.dtypes.float32)
expm = linalg_impl.matrix_exponential(inp)
matrix = np.array([[1., 2.], [3., 4.]])
sess.run(expm, feed_dict={inp: matrix})
def testConcurrentExecutesWithoutError(self):
with self.test_session(use_gpu=True) as sess:
matrix1 = random_ops.random_normal([5, 5], seed=42)
matrix2 = random_ops.random_normal([5, 5], seed=42)
expm1 = linalg_impl.matrix_exponential(matrix1)
expm2 = linalg_impl.matrix_exponential(matrix2)
expm = sess.run([expm1, expm2])
self.assertAllEqual(expm[0], expm[1])
class MatrixExponentialBenchmark(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.float32) / (
2.0 * n) + np.diag(np.ones(n).astype(np.float32))
return variables.Variable(np.tile(matrix, batch_shape + (1, 1)))
def benchmarkMatrixExponentialOp(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)
expm = linalg_impl.matrix_exponential(matrix)
variables.global_variables_initializer().run()
self.run_op_benchmark(
sess,
control_flow_ops.group(expm),
min_iters=25,
name="matrix_exponential_cpu_{shape}".format(
shape=shape))
if test.is_gpu_available(True):
with ops.Graph().as_default(), \
session.Session(config=benchmark.benchmark_config()) as sess, \
ops.device("/gpu:0"):
matrix = self._GenerateMatrix(shape)
expm = linalg_impl.matrix_exponential(matrix)
variables.global_variables_initializer().run()
self.run_op_benchmark(
sess,
control_flow_ops.group(expm),
min_iters=25,
name="matrix_exponential_gpu_{shape}".format(
shape=shape))
def _TestRandomSmall(dtype, batch_dims, size):
def Test(self):
np.random.seed(42)
shape = batch_dims + (size, size)
matrix = np.random.uniform(
low=-1.0, high=1.0,
size=shape).astype(dtype)
self._verifyExponentialReal(matrix)
return Test
def _TestL1Norms(dtype, shape, scale):
def Test(self):
np.random.seed(42)
matrix = np.random.uniform(
low=-1.0, high=1.0,
size=np.prod(shape)).reshape(shape).astype(dtype)
print(dtype, shape, scale, matrix)
l1_norm = np.max(np.sum(np.abs(matrix), axis=matrix.ndim-2))
matrix /= l1_norm
self._verifyExponentialReal(scale * matrix)
return Test
if __name__ == "__main__":
for dtype_ in [np.float32, np.float64, np.complex64, np.complex128]:
for batch_ in [(), (2,), (2, 2)]:
for size_ in [4, 7]:
name = "%s_%d_%d" % (dtype_.__name__, len(batch_), size_)
setattr(ExponentialOpTest, "testL1Norms_" + name,
_TestRandomSmall(dtype_, batch_, size_))
for shape_ in [(3, 3), (2, 3, 3)]:
for dtype_ in [np.float32, np.complex64]:
for scale_ in [0.1, 1.5, 5.0, 20.0]:
name = "%s_%d_%d" % (dtype_.__name__, len(shape_), int(scale_*10))
setattr(ExponentialOpTest, "testL1Norms_" + name,
_TestL1Norms(dtype_, shape_, scale_))
for dtype_ in [np.float64, np.complex128]:
for scale_ in [0.01, 0.2, 0.5, 1.5, 6.0, 25.0]:
name = "%s_%d_%d" % (dtype_.__name__, len(shape_), int(scale_*100))
setattr(ExponentialOpTest, "testL1Norms_" + name,
_TestL1Norms(dtype_, shape_, scale_))
test.main()
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