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
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
|
import numpy as num
import _correlate
import numpy.fft as dft
import iraf_frame
VALID = 0
SAME = 1
FULL = 2
PASS = 3
convolution_modes = {
"valid":0,
"same":1,
"full":2,
"pass":3,
}
def _condition_inputs(data, kernel):
data, kernel = num.asarray(data), num.asarray(kernel)
if num.rank(data) == 0:
data.shape = (1,)
if num.rank(kernel) == 0:
kernel.shape = (1,)
if num.rank(data) > 1 or num.rank(kernel) > 1:
raise ValueError("arrays must be 1D")
if len(data) < len(kernel):
data, kernel = kernel, data
return data, kernel
def correlate(data, kernel, mode=FULL):
"""correlate(data, kernel, mode=FULL)
>>> correlate(num.arange(8), [1, 2], mode=VALID)
array([ 2, 5, 8, 11, 14, 17, 20])
>>> correlate(num.arange(8), [1, 2], mode=SAME)
array([ 0, 2, 5, 8, 11, 14, 17, 20])
>>> correlate(num.arange(8), [1, 2], mode=FULL)
array([ 0, 2, 5, 8, 11, 14, 17, 20, 7])
>>> correlate(num.arange(8), [1, 2, 3], mode=VALID)
array([ 8, 14, 20, 26, 32, 38])
>>> correlate(num.arange(8), [1, 2, 3], mode=SAME)
array([ 3, 8, 14, 20, 26, 32, 38, 20])
>>> correlate(num.arange(8), [1, 2, 3], mode=FULL)
array([ 0, 3, 8, 14, 20, 26, 32, 38, 20, 7])
>>> correlate(num.arange(8), [1, 2, 3, 4, 5, 6], mode=VALID)
array([ 70, 91, 112])
>>> correlate(num.arange(8), [1, 2, 3, 4, 5, 6], mode=SAME)
array([ 17, 32, 50, 70, 91, 112, 85, 60])
>>> correlate(num.arange(8), [1, 2, 3, 4, 5, 6], mode=FULL)
array([ 0, 6, 17, 32, 50, 70, 91, 112, 85, 60, 38, 20, 7])
>>> correlate(num.arange(8), 1+1j)
Traceback (most recent call last):
...
TypeError: array cannot be safely cast to required type
"""
data, kernel = _condition_inputs(data, kernel)
lenk = len(kernel)
halfk = int(lenk/2)
even = (lenk % 2 == 0)
kdata = [0] * lenk
if mode in convolution_modes.keys():
mode = convolution_modes[ mode ]
result_type = max(kernel.dtype.name, data.dtype.name)
if mode == VALID:
wdata = num.concatenate((kdata, data, kdata))
result = wdata.astype(result_type)
_correlate.Correlate1d(kernel, wdata, result)
return result[lenk+halfk:-lenk-halfk+even]
elif mode == SAME:
wdata = num.concatenate((kdata, data, kdata))
result = wdata.astype(result_type)
_correlate.Correlate1d(kernel, wdata, result)
return result[lenk:-lenk]
elif mode == FULL:
wdata = num.concatenate((kdata, data, kdata))
result = wdata.astype(result_type)
_correlate.Correlate1d(kernel, wdata, result)
return result[halfk+1:-halfk-1+even]
elif mode == PASS:
result = data.astype(result_type)
_correlate.Correlate1d(kernel, data, result)
return result
else:
raise ValueError("Invalid convolution mode.")
cross_correlate = correlate
pix_modes = {
"nearest" : 0,
"reflect": 1,
"wrap" : 2,
"constant": 3
}
def convolve(data, kernel, mode=FULL):
"""convolve(data, kernel, mode=FULL)
Returns the discrete, linear convolution of 1-D
sequences a and v; mode can be 0 (VALID), 1 (SAME), or 2 (FULL)
to specify size of the resulting sequence.
>>> convolve(num.arange(8), [1, 2], mode=VALID)
array([ 1, 4, 7, 10, 13, 16, 19])
>>> convolve(num.arange(8), [1, 2], mode=SAME)
array([ 0, 1, 4, 7, 10, 13, 16, 19])
>>> convolve(num.arange(8), [1, 2], mode=FULL)
array([ 0, 1, 4, 7, 10, 13, 16, 19, 14])
>>> convolve(num.arange(8), [1, 2, 3], mode=VALID)
array([ 4, 10, 16, 22, 28, 34])
>>> convolve(num.arange(8), [1, 2, 3], mode=SAME)
array([ 1, 4, 10, 16, 22, 28, 34, 32])
>>> convolve(num.arange(8), [1, 2, 3], mode=FULL)
array([ 0, 1, 4, 10, 16, 22, 28, 34, 32, 21])
>>> convolve(num.arange(8), [1, 2, 3, 4, 5, 6], mode=VALID)
array([35, 56, 77])
>>> convolve(num.arange(8), [1, 2, 3, 4, 5, 6], mode=SAME)
array([ 4, 10, 20, 35, 56, 77, 90, 94])
>>> convolve(num.arange(8), [1, 2, 3, 4, 5, 6], mode=FULL)
array([ 0, 1, 4, 10, 20, 35, 56, 77, 90, 94, 88, 71, 42])
>>> convolve([1.,2.], num.arange(10.))
array([ 0., 1., 4., 7., 10., 13., 16., 19., 22., 25., 18.])
"""
data, kernel = _condition_inputs(data, kernel)
if len(data) >= len(kernel):
return correlate(data, kernel[::-1], mode)
else:
return correlate(kernel, data[::-1], mode)
def _gaussian(sigma, mew, npoints, sigmas):
ox = num.arange(mew-sigmas*sigma,
mew+sigmas*sigma,
2*sigmas*sigma/npoints, type=num.float64)
x = ox-mew
x /= sigma
x = x * x
x *= -1/2
x = num.exp(x)
return ox, 1/(sigma * num.sqrt(2*num.pi)) * x
def _correlate2d_fft(data0, kernel0, output=None, mode="nearest", cval=0.0):
"""_correlate2d_fft does 2d correlation of 'data' with 'kernel', storing
the result in 'output' using the FFT to perform the correlation.
supported 'mode's include:
'nearest' elements beyond boundary come from nearest edge pixel.
'wrap' elements beyond boundary come from the opposite array edge.
'reflect' elements beyond boundary come from reflection on same array edge.
'constant' elements beyond boundary are set to 'cval'
"""
shape = data0.shape
kshape = kernel0.shape
oversized = (num.array(shape) + num.array(kshape))
dy = kshape[0] // 2
dx = kshape[1] // 2
kernel = num.zeros(oversized, dtype=num.float64)
kernel[:kshape[0], :kshape[1]] = kernel0[::-1,::-1] # convolution <-> correlation
data = iraf_frame.frame(data0, oversized, mode=mode, cval=cval)
complex_result = (isinstance(data, num.complexfloating) or
isinstance(kernel, num.complexfloating))
Fdata = dft.fft2(data)
del data
Fkernel = dft.fft2(kernel)
del kernel
num.multiply(Fdata, Fkernel, Fdata)
del Fkernel
if complex_result:
convolved = dft.irfft2( Fdata, s=oversized)
else:
convolved = dft.irfft2( Fdata, s=oversized)
result = convolved[ kshape[0]-1:shape[0]+kshape[0]-1, kshape[1]-1:shape[1]+kshape[1]-1 ]
if output is not None:
output._copyFrom( result )
else:
return result
def _correlate2d_naive(data, kernel, output=None, mode="nearest", cval=0.0):
return _correlate.Correlate2d(kernel, data, output, pix_modes[mode], cval)
def _fix_data_kernel(data, kernel):
"""The _correlate.Correlate2d C-code can only handle kernels which
fit inside the data array. Since convolution and correlation are
commutative, _fix_data_kernel reverses kernel and data if necessary
and panics if there's no good order.
"""
data, kernel = map(num.asarray, [data, kernel])
if num.rank(data) == 0:
data.shape = (1,1)
elif num.rank(data) == 1:
data.shape = (1,) + data.shape
if num.rank(kernel) == 0:
kernel.shape = (1,1)
elif num.rank(kernel) == 1:
kernel.shape = (1,) + kernel.shape
if (kernel.shape[0] > data.shape[0] and
kernel.shape[1] > data.shape[1]):
kernel, data = data, kernel
elif (kernel.shape[0] <= data.shape[0] and
kernel.shape[1] <= data.shape[1]):
pass
return data, kernel
def correlate2d(data, kernel, output=None, mode="nearest", cval=0.0, fft=0):
"""correlate2d does 2d correlation of 'data' with 'kernel', storing
the result in 'output'.
supported 'mode's include:
'nearest' elements beyond boundary come from nearest edge pixel.
'wrap' elements beyond boundary come from the opposite array edge.
'reflect' elements beyond boundary come from reflection on same array edge.
'constant' elements beyond boundary are set to 'cval'
If fft is True, the correlation is performed using the FFT, else the
correlation is performed using the naive approach.
>>> a = num.arange(20*20)
>>> a = a.reshape((20,20))
>>> b = num.ones((5,5), dtype=num.float64)
>>> rn = correlate2d(a, b, fft=0)
>>> rf = correlate2d(a, b, fft=1)
>>> num.alltrue(num.ravel(rn-rf<1e-10))
True
"""
data, kernel = _fix_data_kernel(data, kernel)
if fft:
return _correlate2d_fft(data, kernel, output, mode, cval)
else:
a = _correlate2d_naive(data, kernel, output, mode, cval)
#a = a.byteswap()
return a
def convolve2d(data, kernel, output=None, mode="nearest", cval=0.0, fft=0):
"""convolve2d does 2d convolution of 'data' with 'kernel', storing
the result in 'output'.
supported 'mode's include:
'nearest' elements beyond boundary come from nearest edge pixel.
'wrap' elements beyond boundary come from the opposite array edge.
'reflect' elements beyond boundary come from reflection on same array edge.
'constant' elements beyond boundary are set to 'cval'
>>> a = num.arange(20*20)
>>> a = a.reshape((20,20))
>>> b = num.ones((5,5), dtype=num.float64)
>>> rn = convolve2d(a, b, fft=0)
>>> rf = convolve2d(a, b, fft=1)
>>> num.alltrue(num.ravel(rn-rf<1e-10))
True
"""
data, kernel = _fix_data_kernel(data, kernel)
kernel = kernel[::-1,::-1] # convolution -> correlation
if fft:
return _correlate2d_fft(data, kernel, output, mode, cval)
else:
return _correlate2d_naive(data, kernel, output, mode, cval)
def _boxcar(data, output, boxshape, mode, cval):
if len(boxshape) == 1:
_correlate.Boxcar2d(data[num.newaxis,...], 1, boxshape[0],
output[num.newaxis,...], mode, cval)
elif len(boxshape) == 2:
_correlate.Boxcar2d(data, boxshape[0], boxshape[1], output, mode, cval)
else:
raise ValueError("boxshape must be a 1D or 2D shape.")
def boxcar(data, boxshape, output=None, mode="nearest", cval=0.0):
"""boxcar computes a 1D or 2D boxcar filter on every 1D or 2D subarray of data.
'boxshape' is a tuple of integers specifying the dimensions of the filter: e.g. (3,3)
if 'output' is specified, it should be the same shape as 'data' and
None will be returned.
supported 'mode's include:
'nearest' elements beyond boundary come from nearest edge pixel.
'wrap' elements beyond boundary come from the opposite array edge.
'reflect' elements beyond boundary come from reflection on same array edge.
'constant' elements beyond boundary are set to 'cval'
>>> boxcar(num.array([10, 0, 0, 0, 0, 0, 1000]), (3,), mode="nearest").astype(num.longlong)
array([ 6, 3, 0, 0, 0, 333, 666], dtype=int64)
>>> boxcar(num.array([10, 0, 0, 0, 0, 0, 1000]), (3,), mode="wrap").astype(num.longlong)
array([336, 3, 0, 0, 0, 333, 336], dtype=int64)
>>> boxcar(num.array([10, 0, 0, 0, 0, 0, 1000]), (3,), mode="reflect").astype(num.longlong)
array([ 6, 3, 0, 0, 0, 333, 666], dtype=int64)
>>> boxcar(num.array([10, 0, 0, 0, 0, 0, 1000]), (3,), mode="constant").astype(num.longlong)
array([ 3, 3, 0, 0, 0, 333, 333], dtype=int64)
>>> a = num.zeros((10,10))
>>> a[0,0] = 100
>>> a[5,5] = 1000
>>> a[9,9] = 10000
>>> boxcar(a, (3,3)).astype(num.longlong)
array([[ 44, 22, 0, 0, 0, 0, 0, 0, 0, 0],
[ 22, 11, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 111, 111, 111, 0, 0, 0],
[ 0, 0, 0, 0, 111, 111, 111, 0, 0, 0],
[ 0, 0, 0, 0, 111, 111, 111, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1111, 2222],
[ 0, 0, 0, 0, 0, 0, 0, 0, 2222, 4444]], dtype=int64)
>>> boxcar(a, (3,3), mode="wrap").astype(num.longlong)
array([[1122, 11, 0, 0, 0, 0, 0, 0, 1111, 1122],
[ 11, 11, 0, 0, 0, 0, 0, 0, 0, 11],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 111, 111, 111, 0, 0, 0],
[ 0, 0, 0, 0, 111, 111, 111, 0, 0, 0],
[ 0, 0, 0, 0, 111, 111, 111, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1111, 0, 0, 0, 0, 0, 0, 0, 1111, 1111],
[1122, 11, 0, 0, 0, 0, 0, 0, 1111, 1122]], dtype=int64)
>>> boxcar(a, (3,3), mode="reflect").astype(num.longlong)
array([[ 44, 22, 0, 0, 0, 0, 0, 0, 0, 0],
[ 22, 11, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 111, 111, 111, 0, 0, 0],
[ 0, 0, 0, 0, 111, 111, 111, 0, 0, 0],
[ 0, 0, 0, 0, 111, 111, 111, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1111, 2222],
[ 0, 0, 0, 0, 0, 0, 0, 0, 2222, 4444]], dtype=int64)
>>> boxcar(a, (3,3), mode="constant").astype(num.longlong)
array([[ 11, 11, 0, 0, 0, 0, 0, 0, 0, 0],
[ 11, 11, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 111, 111, 111, 0, 0, 0],
[ 0, 0, 0, 0, 111, 111, 111, 0, 0, 0],
[ 0, 0, 0, 0, 111, 111, 111, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1111, 1111],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1111, 1111]], dtype=int64)
>>> a = num.zeros((10,10))
>>> a[3:6,3:6] = 111
>>> boxcar(a, (3,3)).astype(num.longlong)
array([[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 12, 24, 37, 24, 12, 0, 0, 0],
[ 0, 0, 24, 49, 74, 49, 24, 0, 0, 0],
[ 0, 0, 37, 74, 111, 74, 37, 0, 0, 0],
[ 0, 0, 24, 49, 74, 49, 24, 0, 0, 0],
[ 0, 0, 12, 24, 37, 24, 12, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=int64)
"""
mode = pix_modes[ mode ]
if output is None:
woutput = data.astype(num.float64)
else:
woutput = output
_fbroadcast(_boxcar, len(boxshape), data.shape,
(data, woutput), (boxshape, mode, cval))
if output is None:
return woutput
def _fbroadcast(f, N, shape, args, params=()):
"""_fbroadcast(f, N, args, shape, params=()) calls 'f' for each of the
'N'-dimensional inner subnumarray of 'args'. Each subarray has
.shape == 'shape'[-N:]. There are a total of product(shape[:-N],axis=0)
calls to 'f'.
"""
if len(shape) == N:
apply(f, tuple(args)+params)
else:
for i in range(shape[0]):
_fbroadcast(f, N, shape[1:], [x[i] for x in args], params)
def test():
import doctest, Convolve
return doctest.testmod(Convolve)
if __name__ == "__main__":
print test()
|
