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
|
""" Benchmark functions for fftpack.pseudo_diffs module
"""
from __future__ import division, print_function, absolute_import
import sys
from numpy import arange, sin, cos, pi, exp, tanh, sign
from numpy.testing import *
from scipy.fftpack import diff, fft, ifft, tilbert, hilbert, shift, fftfreq
def random(size):
return rand(*size)
def direct_diff(x,k=1,period=None):
fx = fft(x)
n = len(fx)
if period is None:
period = 2*pi
w = fftfreq(n)*2j*pi/period*n
if k < 0:
w = 1 / w**k
w[0] = 0.0
else:
w = w**k
if n > 2000:
w[250:n-250] = 0.0
return ifft(w*fx).real
def direct_tilbert(x,h=1,period=None):
fx = fft(x)
n = len(fx)
if period is None:
period = 2*pi
w = fftfreq(n)*h*2*pi/period*n
w[0] = 1
w = 1j/tanh(w)
w[0] = 0j
return ifft(w*fx)
def direct_hilbert(x):
fx = fft(x)
n = len(fx)
w = fftfreq(n)*n
w = 1j*sign(w)
return ifft(w*fx)
def direct_shift(x,a,period=None):
n = len(x)
if period is None:
k = fftfreq(n)*1j*n
else:
k = fftfreq(n)*2j*pi/period*n
return ifft(fft(x)*exp(k*a)).real
class TestDiff(TestCase):
def bench_random(self):
print()
print('Differentiation of periodic functions')
print('=====================================')
print(' size | convolve | naive')
print('-------------------------------------')
for size,repeat in [(100,1500),(1000,300),
(256,1500),
(512,1000),
(1024,500),
(2048,200),
(2048*2,100),
(2048*4,50),
]:
print('%6s' % size, end=' ')
sys.stdout.flush()
x = arange(size)*2*pi/size
if size < 2000:
f = sin(x)*cos(4*x)+exp(sin(3*x))
else:
f = sin(x)*cos(4*x)
assert_array_almost_equal(diff(f,1),direct_diff(f,1))
assert_array_almost_equal(diff(f,2),direct_diff(f,2))
print('| %9.2f' % measure('diff(f,3)',repeat), end=' ')
sys.stdout.flush()
print('| %9.2f' % measure('direct_diff(f,3)',repeat), end=' ')
sys.stdout.flush()
print(' (secs for %s calls)' % (repeat))
class TestTilbert(TestCase):
def bench_random(self):
print()
print(' Tilbert transform of periodic functions')
print('=========================================')
print(' size | optimized | naive')
print('-----------------------------------------')
for size,repeat in [(100,1500),(1000,300),
(256,1500),
(512,1000),
(1024,500),
(2048,200),
(2048*2,100),
(2048*4,50),
]:
print('%6s' % size, end=' ')
sys.stdout.flush()
x = arange(size)*2*pi/size
if size < 2000:
f = sin(x)*cos(4*x)+exp(sin(3*x))
else:
f = sin(x)*cos(4*x)
assert_array_almost_equal(tilbert(f,1),direct_tilbert(f,1))
print('| %9.2f' % measure('tilbert(f,1)',repeat), end=' ')
sys.stdout.flush()
print('| %9.2f' % measure('direct_tilbert(f,1)',repeat), end=' ')
sys.stdout.flush()
print(' (secs for %s calls)' % (repeat))
class TestHilbert(TestCase):
def bench_random(self):
print()
print(' Hilbert transform of periodic functions')
print('=========================================')
print(' size | optimized | naive')
print('-----------------------------------------')
for size,repeat in [(100,1500),(1000,300),
(256,1500),
(512,1000),
(1024,500),
(2048,200),
(2048*2,100),
(2048*4,50),
]:
print('%6s' % size, end=' ')
sys.stdout.flush()
x = arange(size)*2*pi/size
if size < 2000:
f = sin(x)*cos(4*x)+exp(sin(3*x))
else:
f = sin(x)*cos(4*x)
assert_array_almost_equal(hilbert(f),direct_hilbert(f))
print('| %9.2f' % measure('hilbert(f)',repeat), end=' ')
sys.stdout.flush()
print('| %9.2f' % measure('direct_hilbert(f)',repeat), end=' ')
sys.stdout.flush()
print(' (secs for %s calls)' % (repeat))
class TestShift(TestCase):
def bench_random(self):
print()
print(' Shifting periodic functions')
print('==============================')
print(' size | optimized | naive')
print('------------------------------')
for size,repeat in [(100,1500),(1000,300),
(256,1500),
(512,1000),
(1024,500),
(2048,200),
(2048*2,100),
(2048*4,50),
]:
print('%6s' % size, end=' ')
sys.stdout.flush()
x = arange(size)*2*pi/size
a = 1
if size < 2000:
f = sin(x)*cos(4*x)+exp(sin(3*x))
sf = sin(x+a)*cos(4*(x+a))+exp(sin(3*(x+a)))
else:
f = sin(x)*cos(4*x)
sf = sin(x+a)*cos(4*(x+a))
assert_array_almost_equal(direct_shift(f,1),sf)
assert_array_almost_equal(shift(f,1),sf)
print('| %9.2f' % measure('shift(f,a)',repeat), end=' ')
sys.stdout.flush()
print('| %9.2f' % measure('direct_shift(f,a)',repeat), end=' ')
sys.stdout.flush()
print(' (secs for %s calls)' % (repeat))
if __name__ == "__main__":
run_module_suite()
|
