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
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
|
# Copyright 2016 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.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.ops import random_ops
from tensorflow.python.platform import test
def _AddTest(test_class, op_name, testcase_name, fn):
test_name = "_".join(["test", op_name, testcase_name])
if hasattr(test_class, test_name):
raise RuntimeError("Test %s defined more than once" % test_name)
setattr(test_class, test_name, fn)
class SelfAdjointEigTest(test.TestCase):
def testWrongDimensions(self):
# The input to self_adjoint_eig should be a tensor of
# at least rank 2.
scalar = constant_op.constant(1.)
with self.assertRaises(ValueError):
linalg_ops.self_adjoint_eig(scalar)
vector = constant_op.constant([1., 2.])
with self.assertRaises(ValueError):
linalg_ops.self_adjoint_eig(vector)
def testConcurrentExecutesWithoutError(self):
all_ops = []
with self.test_session(use_gpu=True) as sess:
for compute_v_ in True, False:
matrix1 = random_ops.random_normal([5, 5], seed=42)
matrix2 = random_ops.random_normal([5, 5], seed=42)
if compute_v_:
e1, v1 = linalg_ops.self_adjoint_eig(matrix1)
e2, v2 = linalg_ops.self_adjoint_eig(matrix2)
all_ops += [e1, v1, e2, v2]
else:
e1 = linalg_ops.self_adjoint_eigvals(matrix1)
e2 = linalg_ops.self_adjoint_eigvals(matrix2)
all_ops += [e1, e2]
val = sess.run(all_ops)
self.assertAllEqual(val[0], val[2])
# The algorithm is slightly different for compute_v being True and False,
# so require approximate equality only here.
self.assertAllClose(val[2], val[4])
self.assertAllEqual(val[4], val[5])
self.assertAllEqual(val[1], val[3])
def testMatrixThatFailsWhenFlushingDenormsToZero(self):
# Test a 32x32 matrix which is known to fail if denorm floats are flushed to
# zero.
matrix = np.genfromtxt(
test.test_src_dir_path(
"python/kernel_tests/testdata/"
"self_adjoint_eig_fail_if_denorms_flushed.txt")).astype(np.float32)
self.assertEqual(matrix.shape, (32, 32))
matrix_tensor = constant_op.constant(matrix)
with self.test_session(use_gpu=True) as sess:
(e, v) = sess.run(linalg_ops.self_adjoint_eig(matrix_tensor))
self.assertEqual(e.size, 32)
self.assertAllClose(
np.matmul(v, v.transpose()), np.eye(32, dtype=np.float32), atol=2e-3)
self.assertAllClose(matrix,
np.matmul(np.matmul(v, np.diag(e)), v.transpose()))
def SortEigenDecomposition(e, v):
if v.ndim < 2:
return e, v
else:
perm = np.argsort(e, -1)
return np.take(e, perm, -1), np.take(v, perm, -1)
def EquilibrateEigenVectorPhases(x, y):
"""Equilibrate the phase of the Eigenvectors in the columns of `x` and `y`.
Eigenvectors are only unique up to an arbitrary phase. This function rotates x
such that it matches y. Precondition: The coluns of x and y differ by a
multiplicative complex phase factor only.
Args:
x: `np.ndarray` with Eigenvectors
y: `np.ndarray` with Eigenvectors
Returns:
`np.ndarray` containing an equilibrated version of x.
"""
phases = np.sum(np.conj(x) * y, -2, keepdims=True)
phases /= np.abs(phases)
return phases * x
def _GetSelfAdjointEigTest(dtype_, shape_, compute_v_):
def CompareEigenVectors(self, x, y, tol):
x = EquilibrateEigenVectorPhases(x, y)
self.assertAllClose(x, y, atol=tol)
def CompareEigenDecompositions(self, x_e, x_v, y_e, y_v, tol):
num_batches = int(np.prod(x_e.shape[:-1]))
n = x_e.shape[-1]
x_e = np.reshape(x_e, [num_batches] + [n])
x_v = np.reshape(x_v, [num_batches] + [n, n])
y_e = np.reshape(y_e, [num_batches] + [n])
y_v = np.reshape(y_v, [num_batches] + [n, n])
for i in range(num_batches):
x_ei, x_vi = SortEigenDecomposition(x_e[i, :], x_v[i, :, :])
y_ei, y_vi = SortEigenDecomposition(y_e[i, :], y_v[i, :, :])
self.assertAllClose(x_ei, y_ei, atol=tol, rtol=tol)
CompareEigenVectors(self, x_vi, y_vi, tol)
def Test(self):
np.random.seed(1)
n = shape_[-1]
batch_shape = shape_[:-2]
np_dtype = dtype_.as_numpy_dtype
a = np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape([n, n]).astype(np_dtype)
if dtype_.is_complex:
a += 1j * np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape([n, n]).astype(np_dtype)
a += np.conj(a.T)
a = np.tile(a, batch_shape + (1, 1))
if dtype_ in (dtypes_lib.float32, dtypes_lib.complex64):
atol = 1e-4
else:
atol = 1e-12
np_e, np_v = np.linalg.eigh(a)
with self.test_session(use_gpu=True):
if compute_v_:
tf_e, tf_v = linalg_ops.self_adjoint_eig(constant_op.constant(a))
# Check that V*diag(E)*V^T is close to A.
a_ev = math_ops.matmul(
math_ops.matmul(tf_v, array_ops.matrix_diag(tf_e)),
tf_v,
adjoint_b=True)
self.assertAllClose(a_ev.eval(), a, atol=atol)
# Compare to numpy.linalg.eigh.
CompareEigenDecompositions(self, np_e, np_v,
tf_e.eval(), tf_v.eval(), atol)
else:
tf_e = linalg_ops.self_adjoint_eigvals(constant_op.constant(a))
self.assertAllClose(
np.sort(np_e, -1), np.sort(tf_e.eval(), -1), atol=atol)
return Test
class SelfAdjointEigGradTest(test.TestCase):
pass # Filled in below
def _GetSelfAdjointEigGradTest(dtype_, shape_, compute_v_):
def Test(self):
np.random.seed(1)
n = shape_[-1]
batch_shape = shape_[:-2]
np_dtype = dtype_.as_numpy_dtype
a = np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape([n, n]).astype(np_dtype)
if dtype_.is_complex:
a += 1j * np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape([n, n]).astype(np_dtype)
a += np.conj(a.T)
a = np.tile(a, batch_shape + (1, 1))
# Optimal stepsize for central difference is O(epsilon^{1/3}).
epsilon = np.finfo(np_dtype).eps
delta = 0.1 * epsilon**(1.0 / 3.0)
# tolerance obtained by looking at actual differences using
# np.linalg.norm(theoretical-numerical, np.inf) on -mavx build
if dtype_ in (dtypes_lib.float32, dtypes_lib.complex64):
tol = 1e-2
else:
tol = 1e-7
with self.test_session(use_gpu=True):
tf_a = constant_op.constant(a)
if compute_v_:
tf_e, tf_v = linalg_ops.self_adjoint_eig(tf_a)
# (complex) Eigenvectors are only unique up to an arbitrary phase
# We normalize the vectors such that the first component has phase 0.
top_rows = tf_v[..., 0:1, :]
if tf_a.dtype.is_complex:
angle = -math_ops.angle(top_rows)
phase = math_ops.complex(math_ops.cos(angle), math_ops.sin(angle))
else:
phase = math_ops.sign(top_rows)
tf_v *= phase
outputs = [tf_e, tf_v]
else:
tf_e = linalg_ops.self_adjoint_eigvals(tf_a)
outputs = [tf_e]
for b in outputs:
x_init = np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape([n, n]).astype(np_dtype)
if dtype_.is_complex:
x_init += 1j * np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape([n, n]).astype(np_dtype)
x_init += np.conj(x_init.T)
x_init = np.tile(x_init, batch_shape + (1, 1))
theoretical, numerical = gradient_checker.compute_gradient(
tf_a,
tf_a.get_shape().as_list(),
b,
b.get_shape().as_list(),
x_init_value=x_init,
delta=delta)
self.assertAllClose(theoretical, numerical, atol=tol, rtol=tol)
return Test
if __name__ == "__main__":
for compute_v in True, False:
for dtype in (dtypes_lib.float32, dtypes_lib.float64, dtypes_lib.complex64,
dtypes_lib.complex128):
for size in 1, 2, 5, 10:
for batch_dims in [(), (3,)] + [(3, 2)] * (max(size, size) < 10):
shape = batch_dims + (size, size)
name = "%s_%s_%s" % (dtype, "_".join(map(str, shape)), compute_v)
_AddTest(SelfAdjointEigTest, "SelfAdjointEig", name,
_GetSelfAdjointEigTest(dtype, shape, compute_v))
_AddTest(SelfAdjointEigGradTest, "SelfAdjointEigGrad", name,
_GetSelfAdjointEigGradTest(dtype, shape, compute_v))
test.main()
|
