/
helper.py
277 lines (221 loc) · 8.85 KB
/
helper.py
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
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
from __future__ import division, print_function, absolute_import
import operator
from numpy import (arange, array, asarray, atleast_1d, intc, integer,
isscalar, issubdtype, take, unique, where)
from numpy.fft.helper import fftshift, ifftshift, fftfreq
from bisect import bisect_left
__all__ = ['fftshift', 'ifftshift', 'fftfreq', 'rfftfreq', 'next_fast_len']
def rfftfreq(n, d=1.0):
"""DFT sample frequencies (for usage with rfft, irfft).
The returned float array contains the frequency bins in
cycles/unit (with zero at the start) given a window length `n` and a
sample spacing `d`::
f = [0,1,1,2,2,...,n/2-1,n/2-1,n/2]/(d*n) if n is even
f = [0,1,1,2,2,...,n/2-1,n/2-1,n/2,n/2]/(d*n) if n is odd
Parameters
----------
n : int
Window length.
d : scalar, optional
Sample spacing. Default is 1.
Returns
-------
out : ndarray
The array of length `n`, containing the sample frequencies.
Examples
--------
>>> from scipy import fftpack
>>> sig = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
>>> sig_fft = fftpack.rfft(sig)
>>> n = sig_fft.size
>>> timestep = 0.1
>>> freq = fftpack.rfftfreq(n, d=timestep)
>>> freq
array([ 0. , 1.25, 1.25, 2.5 , 2.5 , 3.75, 3.75, 5. ])
"""
n = operator.index(n)
if n < 0:
raise ValueError("n = %s is not valid. "
"n must be a nonnegative integer." % n)
return (arange(1, n + 1, dtype=int) // 2) / float(n * d)
def next_fast_len(target):
"""
Find the next fast size of input data to `fft`, for zero-padding, etc.
SciPy's FFTPACK has efficient functions for radix {2, 3, 4, 5}, so this
returns the next composite of the prime factors 2, 3, and 5 which is
greater than or equal to `target`. (These are also known as 5-smooth
numbers, regular numbers, or Hamming numbers.)
Parameters
----------
target : int
Length to start searching from. Must be a positive integer.
Returns
-------
out : int
The first 5-smooth number greater than or equal to `target`.
Notes
-----
.. versionadded:: 0.18.0
Examples
--------
On a particular machine, an FFT of prime length takes 133 ms:
>>> from scipy import fftpack
>>> min_len = 10007 # prime length is worst case for speed
>>> a = np.random.randn(min_len)
>>> b = fftpack.fft(a)
Zero-padding to the next 5-smooth length reduces computation time to
211 us, a speedup of 630 times:
>>> fftpack.helper.next_fast_len(min_len)
10125
>>> b = fftpack.fft(a, 10125)
Rounding up to the next power of 2 is not optimal, taking 367 us to
compute, 1.7 times as long as the 5-smooth size:
>>> b = fftpack.fft(a, 16384)
"""
hams = (8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48,
50, 54, 60, 64, 72, 75, 80, 81, 90, 96, 100, 108, 120, 125, 128,
135, 144, 150, 160, 162, 180, 192, 200, 216, 225, 240, 243, 250,
256, 270, 288, 300, 320, 324, 360, 375, 384, 400, 405, 432, 450,
480, 486, 500, 512, 540, 576, 600, 625, 640, 648, 675, 720, 729,
750, 768, 800, 810, 864, 900, 960, 972, 1000, 1024, 1080, 1125,
1152, 1200, 1215, 1250, 1280, 1296, 1350, 1440, 1458, 1500, 1536,
1600, 1620, 1728, 1800, 1875, 1920, 1944, 2000, 2025, 2048, 2160,
2187, 2250, 2304, 2400, 2430, 2500, 2560, 2592, 2700, 2880, 2916,
3000, 3072, 3125, 3200, 3240, 3375, 3456, 3600, 3645, 3750, 3840,
3888, 4000, 4050, 4096, 4320, 4374, 4500, 4608, 4800, 4860, 5000,
5120, 5184, 5400, 5625, 5760, 5832, 6000, 6075, 6144, 6250, 6400,
6480, 6561, 6750, 6912, 7200, 7290, 7500, 7680, 7776, 8000, 8100,
8192, 8640, 8748, 9000, 9216, 9375, 9600, 9720, 10000)
target = int(target)
if target <= 6:
return target
# Quickly check if it's already a power of 2
if not (target & (target-1)):
return target
# Get result quickly for small sizes, since FFT itself is similarly fast.
if target <= hams[-1]:
return hams[bisect_left(hams, target)]
match = float('inf') # Anything found will be smaller
p5 = 1
while p5 < target:
p35 = p5
while p35 < target:
# Ceiling integer division, avoiding conversion to float
# (quotient = ceil(target / p35))
quotient = -(-target // p35)
# Quickly find next power of 2 >= quotient
p2 = 2**((quotient - 1).bit_length())
N = p2 * p35
if N == target:
return N
elif N < match:
match = N
p35 *= 3
if p35 == target:
return p35
if p35 < match:
match = p35
p5 *= 5
if p5 == target:
return p5
if p5 < match:
match = p5
return match
def _init_nd_shape_and_axes(x, shape, axes):
"""Handle shape and axes arguments for n-dimensional transforms.
Returns the shape and axes in a standard form, taking into account negative
values and checking for various potential errors.
Parameters
----------
x : array_like
The input array.
shape : int or array_like of ints or None
The shape of the result. If both `shape` and `axes` (see below) are
None, `shape` is ``x.shape``; if `shape` is None but `axes` is
not None, then `shape` is ``scipy.take(x.shape, axes, axis=0)``.
If `shape` is -1, the size of the corresponding dimension of `x` is
used.
axes : int or array_like of ints or None
Axes along which the calculation is computed.
The default is over all axes.
Negative indices are automatically converted to their positive
counterpart.
Returns
-------
shape : array
The shape of the result. It is a 1D integer array.
axes : array
The shape of the result. It is a 1D integer array.
"""
x = asarray(x)
noshape = shape is None
noaxes = axes is None
if noaxes:
axes = arange(x.ndim, dtype=intc)
else:
axes = atleast_1d(axes)
if axes.size == 0:
axes = axes.astype(intc)
if not axes.ndim == 1:
raise ValueError("when given, axes values must be a scalar or vector")
if not issubdtype(axes.dtype, integer):
raise ValueError("when given, axes values must be integers")
axes = where(axes < 0, axes + x.ndim, axes)
if axes.size != 0 and (axes.max() >= x.ndim or axes.min() < 0):
raise ValueError("axes exceeds dimensionality of input")
if axes.size != 0 and unique(axes).shape != axes.shape:
raise ValueError("all axes must be unique")
if not noshape:
shape = atleast_1d(shape)
elif isscalar(x):
shape = array([], dtype=intc)
elif noaxes:
shape = array(x.shape, dtype=intc)
else:
shape = take(x.shape, axes)
if shape.size == 0:
shape = shape.astype(intc)
if shape.ndim != 1:
raise ValueError("when given, shape values must be a scalar or vector")
if not issubdtype(shape.dtype, integer):
raise ValueError("when given, shape values must be integers")
if axes.shape != shape.shape:
raise ValueError("when given, axes and shape arguments"
" have to be of the same length")
shape = where(shape == -1, array(x.shape)[axes], shape)
if shape.size != 0 and (shape < 1).any():
raise ValueError(
"invalid number of data points ({0}) specified".format(shape))
return shape, axes
def _init_nd_shape_and_axes_sorted(x, shape, axes):
"""Handle and sort shape and axes arguments for n-dimensional transforms.
This is identical to `_init_nd_shape_and_axes`, except the axes are
returned in sorted order and the shape is reordered to match.
Parameters
----------
x : array_like
The input array.
shape : int or array_like of ints or None
The shape of the result. If both `shape` and `axes` (see below) are
None, `shape` is ``x.shape``; if `shape` is None but `axes` is
not None, then `shape` is ``scipy.take(x.shape, axes, axis=0)``.
If `shape` is -1, the size of the corresponding dimension of `x` is
used.
axes : int or array_like of ints or None
Axes along which the calculation is computed.
The default is over all axes.
Negative indices are automatically converted to their positive
counterpart.
Returns
-------
shape : array
The shape of the result. It is a 1D integer array.
axes : array
The shape of the result. It is a 1D integer array.
"""
noaxes = axes is None
shape, axes = _init_nd_shape_and_axes(x, shape, axes)
if not noaxes:
shape = shape[axes.argsort()]
axes.sort()
return shape, axes