1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
|
# 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.math_ops.matrix_inverse."""
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 ops
from tensorflow.python.ops import control_flow_ops
from tensorflow.python.ops import 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.platform import test
class InverseOpTest(test.TestCase):
def _verifyInverse(self, x, np_type):
for adjoint in False, True:
y = x.astype(np_type)
with self.test_session(use_gpu=True):
# Verify that x^{-1} * x == Identity matrix.
inv = linalg_ops.matrix_inverse(y, adjoint=adjoint)
tf_ans = math_ops.matmul(inv, y, adjoint_b=adjoint)
np_ans = np.identity(y.shape[-1])
if x.ndim > 2:
tiling = list(y.shape)
tiling[-2:] = [1, 1]
np_ans = np.tile(np_ans, tiling)
out = tf_ans.eval()
self.assertAllClose(np_ans, out, rtol=1e-4, atol=1e-3)
self.assertShapeEqual(y, tf_ans)
def _verifyInverseReal(self, x):
for np_type in [np.float32, np.float64]:
self._verifyInverse(x, np_type)
def _verifyInverseComplex(self, x):
for np_type in [np.complex64, np.complex128]:
self._verifyInverse(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.]])
self._verifyInverseReal(matrix1)
self._verifyInverseReal(matrix2)
# A multidimensional batch of 2x2 matrices
self._verifyInverseReal(self._makeBatch(matrix1, matrix2))
# Complex
matrix1 = matrix1.astype(np.complex64)
matrix1 += 1j * matrix1
matrix2 = matrix2.astype(np.complex64)
matrix2 += 1j * matrix2
self._verifyInverseComplex(matrix1)
self._verifyInverseComplex(matrix2)
# Complex batch
self._verifyInverseComplex(self._makeBatch(matrix1, matrix2))
def testSymmetricPositiveDefinite(self):
# 2x2 matrices
matrix1 = np.array([[2., 1.], [1., 2.]])
matrix2 = np.array([[3., -1.], [-1., 3.]])
self._verifyInverseReal(matrix1)
self._verifyInverseReal(matrix2)
# A multidimensional batch of 2x2 matrices
self._verifyInverseReal(self._makeBatch(matrix1, matrix2))
# Complex
matrix1 = matrix1.astype(np.complex64)
matrix1 += 1j * matrix1
matrix2 = matrix2.astype(np.complex64)
matrix2 += 1j * matrix2
self._verifyInverseComplex(matrix1)
self._verifyInverseComplex(matrix2)
# Complex batch
self._verifyInverseComplex(self._makeBatch(matrix1, matrix2))
def testNonSquareMatrix(self):
# When the inverse of a non-square matrix is attempted we should return
# an error
with self.assertRaises(ValueError):
linalg_ops.matrix_inverse(np.array([[1., 2., 3.], [3., 4., 5.]]))
def testWrongDimensions(self):
# The input to the inverse should be at least a 2-dimensional tensor.
tensor3 = constant_op.constant([1., 2.])
with self.assertRaises(ValueError):
linalg_ops.matrix_inverse(tensor3)
def testNotInvertible(self):
# The input should be invertible.
with self.cached_session():
with self.assertRaisesOpError("Input is not invertible."):
# All rows of the matrix below add to zero.
tensor3 = constant_op.constant([[1., 0., -1.], [-1., 1., 0.],
[0., -1., 1.]])
linalg_ops.matrix_inverse(tensor3).eval()
def testEmpty(self):
self._verifyInverseReal(np.empty([0, 2, 2]))
self._verifyInverseReal(np.empty([2, 0, 0]))
def testRandomSmallAndLarge(self):
np.random.seed(42)
for dtype in np.float32, np.float64, np.complex64, np.complex128:
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(dtype)
self._verifyInverseReal(matrix)
def testConcurrentExecutesWithoutError(self):
with self.test_session(use_gpu=True) as sess:
all_ops = []
for adjoint_ in True, False:
matrix1 = random_ops.random_normal([5, 5], seed=42)
matrix2 = random_ops.random_normal([5, 5], seed=42)
inv1 = linalg_ops.matrix_inverse(matrix1, adjoint=adjoint_)
inv2 = linalg_ops.matrix_inverse(matrix2, adjoint=adjoint_)
all_ops += [inv1, inv2]
inv = sess.run(all_ops)
self.assertAllEqual(inv[0], inv[1])
self.assertAllEqual(inv[2], inv[3])
class MatrixInverseBenchmark(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 benchmarkMatrixInverseOp(self):
for adjoint in False, True:
for shape in self.shapes:
with ops.Graph().as_default(), \
session.Session() as sess, \
ops.device("/cpu:0"):
matrix = self._GenerateMatrix(shape)
inv = linalg_ops.matrix_inverse(matrix, adjoint=adjoint)
variables.global_variables_initializer().run()
self.run_op_benchmark(
sess,
control_flow_ops.group(inv),
min_iters=25,
name="matrix_inverse_cpu_{shape}_adjoint_{adjoint}".format(
shape=shape, adjoint=adjoint))
if test.is_gpu_available(True):
with ops.Graph().as_default(), \
session.Session() as sess, \
ops.device("/gpu:0"):
matrix = self._GenerateMatrix(shape)
inv = linalg_ops.matrix_inverse(matrix, adjoint=adjoint)
variables.global_variables_initializer().run()
self.run_op_benchmark(
sess,
control_flow_ops.group(inv),
min_iters=25,
name="matrix_inverse_gpu_{shape}_adjoint_{adjoint}".format(
shape=shape, adjoint=adjoint))
if __name__ == "__main__":
test.main()
|
