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
|
# 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 DCT operations."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import importlib
import numpy as np
from tensorflow.python.ops import spectral_ops
from tensorflow.python.ops import spectral_ops_test_util
from tensorflow.python.platform import test
from tensorflow.python.platform import tf_logging
def try_import(name): # pylint: disable=invalid-name
module = None
try:
module = importlib.import_module(name)
except ImportError as e:
tf_logging.warning("Could not import %s: %s" % (name, str(e)))
return module
fftpack = try_import("scipy.fftpack")
def _np_dct2(signals, norm=None):
"""Computes the DCT-II manually with NumPy."""
# X_k = sum_{n=0}^{N-1} x_n * cos(\frac{pi}{N} * (n + 0.5) * k) k=0,...,N-1
dct_size = signals.shape[-1]
dct = np.zeros_like(signals)
for k in range(dct_size):
phi = np.cos(np.pi * (np.arange(dct_size) + 0.5) * k / dct_size)
dct[..., k] = np.sum(signals * phi, axis=-1)
# SciPy's `dct` has a scaling factor of 2.0 which we follow.
# https://github.com/scipy/scipy/blob/v0.15.1/scipy/fftpack/src/dct.c.src
if norm == "ortho":
# The orthonormal scaling includes a factor of 0.5 which we combine with
# the overall scaling of 2.0 to cancel.
dct[..., 0] *= np.sqrt(1.0 / dct_size)
dct[..., 1:] *= np.sqrt(2.0 / dct_size)
else:
dct *= 2.0
return dct
def _np_dct3(signals, norm=None):
"""Computes the DCT-III manually with NumPy."""
# SciPy's `dct` has a scaling factor of 2.0 which we follow.
# https://github.com/scipy/scipy/blob/v0.15.1/scipy/fftpack/src/dct.c.src
dct_size = signals.shape[-1]
signals = np.array(signals) # make a copy so we can modify
if norm == "ortho":
signals[..., 0] *= np.sqrt(4.0 / dct_size)
signals[..., 1:] *= np.sqrt(2.0 / dct_size)
else:
signals *= 2.0
dct = np.zeros_like(signals)
# X_k = 0.5 * x_0 +
# sum_{n=1}^{N-1} x_n * cos(\frac{pi}{N} * n * (k + 0.5)) k=0,...,N-1
half_x0 = 0.5 * signals[..., 0]
for k in range(dct_size):
phi = np.cos(np.pi * np.arange(1, dct_size) * (k + 0.5) / dct_size)
dct[..., k] = half_x0 + np.sum(signals[..., 1:] * phi, axis=-1)
return dct
NP_DCT = {2: _np_dct2, 3: _np_dct3}
NP_IDCT = {2: _np_dct3, 3: _np_dct2}
class DCTOpsTest(test.TestCase):
def _compare(self, signals, norm, dct_type, atol=5e-4, rtol=5e-4):
"""Compares (I)DCT to SciPy (if available) and a NumPy implementation."""
np_dct = NP_DCT[dct_type](signals, norm)
tf_dct = spectral_ops.dct(signals, type=dct_type, norm=norm).eval()
self.assertAllClose(np_dct, tf_dct, atol=atol, rtol=rtol)
np_idct = NP_IDCT[dct_type](signals, norm)
tf_idct = spectral_ops.idct(signals, type=dct_type, norm=norm).eval()
self.assertAllClose(np_idct, tf_idct, atol=atol, rtol=rtol)
if fftpack:
scipy_dct = fftpack.dct(signals, type=dct_type, norm=norm)
self.assertAllClose(scipy_dct, tf_dct, atol=atol, rtol=rtol)
scipy_idct = fftpack.idct(signals, type=dct_type, norm=norm)
self.assertAllClose(scipy_idct, tf_idct, atol=atol, rtol=rtol)
# Verify inverse(forward(s)) == s, up to a normalization factor.
tf_idct_dct = spectral_ops.idct(
tf_dct, type=dct_type, norm=norm).eval()
tf_dct_idct = spectral_ops.dct(
tf_idct, type=dct_type, norm=norm).eval()
if norm is None:
tf_idct_dct *= 0.5 / signals.shape[-1]
tf_dct_idct *= 0.5 / signals.shape[-1]
self.assertAllClose(signals, tf_idct_dct, atol=atol, rtol=rtol)
self.assertAllClose(signals, tf_dct_idct, atol=atol, rtol=rtol)
def test_random(self):
"""Test randomly generated batches of data."""
with spectral_ops_test_util.fft_kernel_label_map():
with self.test_session(use_gpu=True):
for shape in ([1], [2], [3], [10], [2, 20], [2, 3, 25]):
signals = np.random.rand(*shape).astype(np.float32)
for norm in (None, "ortho"):
self._compare(signals, norm, 2)
self._compare(signals, norm, 3)
def test_error(self):
signals = np.random.rand(10)
# Unsupported type.
with self.assertRaises(ValueError):
spectral_ops.dct(signals, type=1)
# Unknown normalization.
with self.assertRaises(ValueError):
spectral_ops.dct(signals, norm="bad")
with self.assertRaises(NotImplementedError):
spectral_ops.dct(signals, n=10)
with self.assertRaises(NotImplementedError):
spectral_ops.dct(signals, axis=0)
if __name__ == "__main__":
test.main()
|
