/
test_cross_correlation.py
503 lines (456 loc) · 21.1 KB
/
test_cross_correlation.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
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
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
# -*- coding: utf-8 -*-
"""
The cross correlation test suite.
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
from future.builtins import * # NOQA
import ctypes as C
import numpy as np
import os
import unittest
import warnings
from obspy import UTCDateTime, read
from obspy.core.util.deprecation_helpers import ObsPyDeprecationWarning
from obspy.core.util.libnames import _load_cdll
from obspy.core.util.testing import ImageComparison
from obspy.signal.cross_correlation import (correlate, correlate_template,
xcorr_pick_correction,
xcorr_3c, xcorr_max, xcorr,
_xcorr_padzeros, _xcorr_slice)
class CrossCorrelationTestCase(unittest.TestCase):
"""
Cross corrrelation test case
"""
def setUp(self):
# directory where the test files are located
self.path = os.path.join(os.path.dirname(__file__), 'data')
self.path_images = os.path.join(os.path.dirname(__file__), 'images')
self.a = np.sin(np.linspace(0, 10, 101))
self.b = 5 * np.roll(self.a, 5)
self.c = 5 * np.roll(self.a[:81], 5)
def test_xcorr(self):
"""
This tests the old, deprecated xcorr() function.
"""
with warnings.catch_warnings():
warnings.simplefilter("ignore", category=ObsPyDeprecationWarning)
# example 1 - all samples are equal
np.random.seed(815) # make test reproducible
tr1 = np.random.randn(10000).astype(np.float32)
tr2 = tr1.copy()
shift, corr = xcorr(tr1, tr2, 100)
self.assertEqual(shift, 0)
self.assertAlmostEqual(corr, 1, 2)
# example 2 - all samples are different
tr1 = np.ones(10000, dtype=np.float32)
tr2 = np.zeros(10000, dtype=np.float32)
shift, corr = xcorr(tr1, tr2, 100)
self.assertEqual(shift, 0)
self.assertAlmostEqual(corr, 0, 2)
# example 3 - shift of 10 samples
tr1 = np.random.randn(10000).astype(np.float32)
tr2 = np.concatenate((np.zeros(10), tr1[0:-10]))
shift, corr = xcorr(tr1, tr2, 100)
self.assertEqual(shift, -10)
self.assertAlmostEqual(corr, 1, 2)
shift, corr = xcorr(tr2, tr1, 100)
self.assertEqual(shift, 10)
self.assertAlmostEqual(corr, 1, 2)
# example 4 - shift of 10 samples + small sine disturbance
tr1 = (np.random.randn(10000) * 100).astype(np.float32)
var = np.sin(np.arange(10000, dtype=np.float32) * 0.1)
tr2 = np.concatenate((np.zeros(10), tr1[0:-10])) * 0.9
tr2 += var
shift, corr = xcorr(tr1, tr2, 100)
self.assertEqual(shift, -10)
self.assertAlmostEqual(corr, 1, 2)
shift, corr = xcorr(tr2, tr1, 100)
self.assertEqual(shift, 10)
self.assertAlmostEqual(corr, 1, 2)
def test_correlate_deprecated_domain_keyword(self):
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always", category=ObsPyDeprecationWarning)
a = [1, 2, 3]
b = [1, 2]
correlate(a, b, 5, domain='freq')
correlate(a, b, 5, domain='time')
self.assertEqual(len(w), 2)
def test_correlate_normalize_true_false(self):
a = read()[0].data[500:]
b = a[10:]
shift = 100
cc1 = correlate(a, b, shift, normalize='naive')
cc2 = correlate(a, b, shift, normalize=True)
cc3 = correlate(a, b, shift, normalize=None)
cc4 = correlate(a, b, shift, normalize=False)
np.testing.assert_equal(cc1, cc2)
np.testing.assert_equal(cc3, cc4)
def test_srl_xcorr(self):
"""
Tests if example in ObsPy paper submitted to the Electronic
Seismologist section of SRL is still working. The test shouldn't be
changed because the reference gets wrong.
"""
np.random.seed(815)
data1 = np.random.randn(1000).astype(np.float32)
data2 = data1.copy()
window_len = 100
corp = np.empty(2 * window_len + 1, dtype=np.float64)
lib = _load_cdll("signal")
#
shift = C.c_int()
coe_p = C.c_double()
res = lib.X_corr(data1.ctypes.data_as(C.c_void_p),
data2.ctypes.data_as(C.c_void_p),
corp.ctypes.data_as(C.c_void_p),
window_len, len(data1), len(data2),
C.byref(shift), C.byref(coe_p))
self.assertEqual(0, res)
self.assertAlmostEqual(0.0, shift.value)
self.assertAlmostEqual(1.0, coe_p.value)
def test_xcorr_vs_old_implementation(self):
"""
Test against output of xcorr from ObsPy<1.1
"""
# Results of xcorr(self.a, self.b, 15, full_xcorr=True)
# for ObsPy==1.0.2:
# -5, 0.9651607597888241
x = [0.53555336, 0.60748967, 0.67493495, 0.73707491, 0.79313226,
0.84237607, 0.88413089, 0.91778536, 0.94280034, 0.95871645,
0.96516076, 0.96363672, 0.95043933, 0.92590109, 0.89047807,
0.84474328, 0.78377236, 0.71629895, 0.64316805, 0.56526677,
0.48351386, 0.39884904, 0.31222231, 0.22458339, 0.13687123,
0.05000401, -0.03513057, -0.11768441, -0.19685756, -0.27190599,
-0.34214866]
corr_fun = correlate(self.a, self.b, shift=15)
shift, corr = xcorr_max(corr_fun)
np.testing.assert_allclose(corr_fun, x)
self.assertAlmostEqual(corr, 0.96516076)
self.assertEqual(shift, -5)
def test_correlate_different_length_of_signals(self):
# Signals are aligned around the middle
cc = correlate(self.a, self.c, 50)
shift, _ = xcorr_max(cc)
self.assertEqual(shift, -5 - (len(self.a) - len(self.c)) // 2)
def test_correlate(self):
# simple test
a, b = [0, 1], [20, 10]
cc = correlate(a, b, 1, demean=False, normalize=False)
shift, value = xcorr_max(cc)
self.assertEqual(shift, 1)
self.assertAlmostEqual(value, 20.)
np.testing.assert_allclose(cc, [0., 10., 20.], atol=1e-14)
# test symetry and different length of a and b
a, b = [0, 1, 2], [20, 10]
cc1 = correlate(a, b, 1, demean=False, normalize=False, method='fft')
cc2 = correlate(a, b, 1, demean=False, normalize=False,
method='direct')
cc3 = correlate(b, a, 1, demean=False, normalize=False, method='fft')
cc4 = correlate(b, a, 1, demean=False, normalize=False,
method='direct')
shift1, _ = xcorr_max(cc1)
shift2, _ = xcorr_max(cc2)
shift3, _ = xcorr_max(cc3)
shift4, _ = xcorr_max(cc4)
self.assertEqual(shift1, 0.5)
self.assertEqual(shift2, 0.5)
self.assertEqual(shift3, -0.5)
self.assertEqual(shift4, -0.5)
np.testing.assert_allclose(cc1, cc2)
np.testing.assert_allclose(cc3, cc4)
np.testing.assert_allclose(cc1, cc3[::-1])
# test sysmetry for method='direct' and len(a) - len(b) - 2 * num > 0
a, b = [0, 1, 2, 3, 4, 5, 6, 7], [20, 10]
cc1 = correlate(a, b, 2, method='direct')
cc2 = correlate(b, a, 2, method='direct')
np.testing.assert_allclose(cc1, cc2[::-1])
def test_correlate_different_implementations(self):
"""
Test correct length and different implementations against each other
"""
xcorrs1 = []
xcorrs2 = []
for xcorr_func in (_xcorr_padzeros, _xcorr_slice):
for method in ('auto', 'fft', 'direct'):
x = xcorr_func(self.a, self.b, 40, method)
y = xcorr_func(self.a, self.b[:-1], 40, method)
self.assertEqual((len(self.a) - len(self.b)) % 2, 0)
self.assertEqual(len(x), 2 * 40 + 1)
self.assertEqual(len(y), 2 * 40)
xcorrs1.append(x)
xcorrs2.append(y)
for x_other in xcorrs1[1:]:
np.testing.assert_allclose(x_other, xcorrs1[0])
for x_other in xcorrs2[1:]:
np.testing.assert_allclose(x_other, xcorrs2[0])
def test_correlate_extreme_shifts_for_freq_xcorr(self):
"""
Also test shift=None
"""
a, b = [1, 2, 3], [1, 2, 3]
n = len(a) + len(b) - 1
cc1 = correlate(a, b, 2, method='fft')
cc2 = correlate(a, b, 3, method='fft')
cc3 = correlate(a, b, None, method='fft')
cc4 = correlate(a, b, None, method='direct')
self.assertEqual(len(cc1), n)
self.assertEqual(len(cc2), 2 + n)
self.assertEqual(len(cc3), n)
self.assertEqual(len(cc4), n)
a, b = [1, 2, 3], [1, 2]
n = len(a) + len(b) - 1
cc1 = correlate(a, b, 2, method='fft')
cc2 = correlate(a, b, 3, method='fft')
cc3 = correlate(a, b, None, method='fft')
cc4 = correlate(a, b, None, method='direct')
self.assertEqual(len(cc1), n)
self.assertEqual(len(cc2), 2 + n)
self.assertEqual(len(cc3), n)
self.assertEqual(len(cc4), n)
def test_xcorr_max(self):
shift, value = xcorr_max((1, 3, -5))
self.assertEqual(shift, 1)
self.assertEqual(value, -5)
shift, value = xcorr_max((3., -5.), abs_max=False)
self.assertEqual(shift, -0.5)
self.assertEqual(value, 3.)
def test_xcorr_3c(self):
st = read()
st2 = read()
for tr in st2:
tr.data = -5 * np.roll(tr.data, 50)
shift, value, x = xcorr_3c(st, st2, 200, full_xcorr=True)
self.assertEqual(shift, -50)
self.assertAlmostEqual(value, -0.998, 3)
def test_xcorr_pick_correction(self):
"""
Test cross correlation pick correction on a set of two small local
earthquakes.
"""
st1 = read(os.path.join(self.path,
'BW.UH1._.EHZ.D.2010.147.a.slist.gz'))
st2 = read(os.path.join(self.path,
'BW.UH1._.EHZ.D.2010.147.b.slist.gz'))
tr1 = st1.select(component="Z")[0]
tr2 = st2.select(component="Z")[0]
tr1_copy = tr1.copy()
tr2_copy = tr2.copy()
t1 = UTCDateTime("2010-05-27T16:24:33.315000Z")
t2 = UTCDateTime("2010-05-27T16:27:30.585000Z")
dt, coeff = xcorr_pick_correction(t1, tr1, t2, tr2, 0.05, 0.2, 0.1)
self.assertAlmostEqual(dt, -0.014459080288833711)
self.assertAlmostEqual(coeff, 0.91542878457939791)
dt, coeff = xcorr_pick_correction(t2, tr2, t1, tr1, 0.05, 0.2, 0.1)
self.assertAlmostEqual(dt, 0.014459080288833711)
self.assertAlmostEqual(coeff, 0.91542878457939791)
dt, coeff = xcorr_pick_correction(
t1, tr1, t2, tr2, 0.05, 0.2, 0.1, filter="bandpass",
filter_options={'freqmin': 1, 'freqmax': 10})
self.assertAlmostEqual(dt, -0.013025086360067755)
self.assertAlmostEqual(coeff, 0.98279277273758803)
self.assertEqual(tr1, tr1_copy)
self.assertEqual(tr2, tr2_copy)
def test_xcorr_pick_correction_images(self):
"""
Test cross correlation pick correction on a set of two small local
earthquakes.
"""
st1 = read(os.path.join(self.path,
'BW.UH1._.EHZ.D.2010.147.a.slist.gz'))
st2 = read(os.path.join(self.path,
'BW.UH1._.EHZ.D.2010.147.b.slist.gz'))
tr1 = st1.select(component="Z")[0]
tr2 = st2.select(component="Z")[0]
t1 = UTCDateTime("2010-05-27T16:24:33.315000Z")
t2 = UTCDateTime("2010-05-27T16:27:30.585000Z")
with ImageComparison(self.path_images, 'xcorr_pick_corr.png') as ic:
dt, coeff = xcorr_pick_correction(
t1, tr1, t2, tr2, 0.05, 0.2, 0.1, plot=True, filename=ic.name)
def test_correlate_template_eqcorrscan(self):
"""
Test for moving window correlations with "full" normalisation.
Comparison result is from EQcorrscan v.0.2.7, using the following:
from eqcorrscan.utils.correlate import get_array_xcorr
from obspy import read
data = read()[0].data
template = data[400:600]
data = data[380:620]
eqcorrscan_func = get_array_xcorr("fftw")
result = eqcorrscan_func(
stream=data, templates=template.reshape(1, len(template)),
pads=[0])[0][0]
"""
result = [
-2.24548906e-01, 7.10350871e-02, 2.68642932e-01, 2.75941312e-01,
1.66854098e-01, 1.66086946e-02, -1.29057273e-01, -1.96172655e-01,
-1.41613603e-01, -6.83271606e-03, 1.45768464e-01, 2.42143899e-01,
1.98310092e-01, 2.16377302e-04, -2.41576880e-01, -4.00586188e-01,
-4.32240069e-01, -2.88735539e-01, 1.26461715e-01, 7.09268868e-01,
9.99999940e-01, 7.22769439e-01, 1.75955653e-01, -2.46459037e-01,
-4.34027880e-01, -4.32590246e-01, -2.67131507e-01, -6.78363896e-04,
2.08171085e-01, 2.32197508e-01, 8.64804164e-02, -1.14158235e-01,
-2.53621429e-01, -2.62945205e-01, -1.40505865e-01, 3.35594788e-02,
1.77415669e-01, 2.72263527e-01, 2.81718552e-01, 1.38080209e-01,
-1.27307668e-01]
data = read()[0].data
template = data[400:600]
data = data[380:620]
cc = correlate_template(data, template)
np.testing.assert_allclose(cc, result, atol=1e-7)
shift, corr = xcorr_max(cc)
self.assertAlmostEqual(corr, 1.0)
self.assertEqual(shift, 0)
def test_correlate_template_eqcorrscan_time(self):
"""
Test full normalization for method='direct'.
"""
result = [
-2.24548906e-01, 7.10350871e-02, 2.68642932e-01, 2.75941312e-01,
1.66854098e-01, 1.66086946e-02, -1.29057273e-01, -1.96172655e-01,
-1.41613603e-01, -6.83271606e-03, 1.45768464e-01, 2.42143899e-01,
1.98310092e-01, 2.16377302e-04, -2.41576880e-01, -4.00586188e-01,
-4.32240069e-01, -2.88735539e-01, 1.26461715e-01, 7.09268868e-01,
9.99999940e-01, 7.22769439e-01, 1.75955653e-01, -2.46459037e-01,
-4.34027880e-01, -4.32590246e-01, -2.67131507e-01, -6.78363896e-04,
2.08171085e-01, 2.32197508e-01, 8.64804164e-02, -1.14158235e-01,
-2.53621429e-01, -2.62945205e-01, -1.40505865e-01, 3.35594788e-02,
1.77415669e-01, 2.72263527e-01, 2.81718552e-01, 1.38080209e-01,
-1.27307668e-01]
data = read()[0].data
template = data[400:600]
data = data[380:620]
cc = correlate_template(data, template, method='direct')
np.testing.assert_allclose(cc, result, atol=1e-7)
shift, corr = xcorr_max(cc)
self.assertAlmostEqual(corr, 1.0)
self.assertEqual(shift, 0)
def test_correlate_template_different_normalizations(self):
data = read()[0].data
template = data[400:600]
data = data[380:700]
max_index = 20
ct = correlate_template
full_xcorr = ct(data, template, demean=False)
naive_xcorr = ct(data, template, demean=False, normalize='naive')
nonorm_xcorr = ct(data, template, demean=False, normalize=None)
self.assertEqual(np.argmax(full_xcorr), max_index)
self.assertEqual(np.argmax(naive_xcorr), max_index)
self.assertEqual(np.argmax(nonorm_xcorr), max_index)
self.assertAlmostEqual(full_xcorr[max_index], 1.0)
self.assertLess(naive_xcorr[max_index], full_xcorr[max_index])
np.testing.assert_allclose(nonorm_xcorr, np.correlate(data, template))
def test_correlate_template_correct_alignment_of_normalization(self):
data = read()[0].data
template = data[400:600]
data = data[380:620]
# test for all combinations of odd and even length input data
for i1, i2 in ((0, 0), (0, 1), (1, 1), (1, 0)):
for mode in ('valid', 'same', 'full'):
for demean in (True, False):
xcorr = correlate_template(data[i1:], template[i2:],
mode=mode, demean=demean)
self.assertAlmostEqual(np.max(xcorr), 1)
def test_correlate_template_versus_correlate(self):
data = read()[0].data
template = data[400:600]
data = data[380:620]
xcorr1 = correlate_template(data, template, normalize='naive')
xcorr2 = correlate(data, template, 20)
np.testing.assert_equal(xcorr1, xcorr2)
def test_correlate_template_zeros_in_input(self):
template = np.zeros(10)
data = read()[0].data[380:420]
xcorr = correlate_template(data, template)
np.testing.assert_equal(xcorr, np.zeros(len(xcorr)))
template[:] = data[:10]
data[5:20] = 0
xcorr = correlate_template(data, template)
np.testing.assert_equal(xcorr[5:11], np.zeros(6))
data[:] = 0
xcorr = correlate_template(data, template)
np.testing.assert_equal(xcorr, np.zeros(len(xcorr)))
xcorr = correlate_template(data, template, normalize='naive')
np.testing.assert_equal(xcorr, np.zeros(len(xcorr)))
def test_correlate_template_different_amplitudes(self):
"""
Check that correlations are the same independent of template amplitudes
"""
data = np.random.randn(20000)
template = data[1000:1200]
template_large = template * 10e10
template_small = template * 10e-10
cc = correlate_template(data, template)
cc_large = correlate_template(data, template_large)
cc_small = correlate_template(data, template_small)
np.testing.assert_allclose(cc, cc_large)
np.testing.assert_allclose(cc, cc_small)
def test_correlate_template_nodemean_fastmatchedfilter(self):
"""
Compare non-demeaned result against FMF derived result.
FMF result obtained by the following:
import copy
import numpy as np
from fast_matched_filter import matched_filter
from obspy import read
data = read()[0].data
template = copy.deepcopy(data[400:600])
data = data[380:620]
result = matched_filter(
templates=template.reshape(1, 1, 1, len(template)),
moveouts=np.array(0).reshape(1, 1, 1),
weights=np.array(1).reshape(1, 1, 1),
data=data.reshape(1, 1, len(data)),
step=1, arch='cpu')[0]
.. note::
FastMatchedFilter doesn't use semver, but result generated by Calum
Chamberlain on 18 Jan 2018 using up-to-date code, with the patch
in https://github.com/beridel/fast_matched_filter/pull/12
"""
result = [
-1.48108244e-01, 4.71532270e-02, 1.82797655e-01,
1.92574233e-01, 1.18700281e-01, 1.18958903e-02,
-9.23405439e-02, -1.40047163e-01, -1.00863703e-01,
-4.86961426e-03, 1.04124829e-01, 1.72662303e-01,
1.41110823e-01, 1.53776666e-04, -1.71214968e-01,
-2.83201426e-01, -3.04899812e-01, -2.03215942e-01,
8.88349637e-02, 5.00749528e-01, 7.18140483e-01,
5.29728174e-01, 1.30591258e-01, -1.83402568e-01,
-3.22406143e-01, -3.20676118e-01, -1.98054180e-01,
-5.06028766e-04, 1.56253457e-01, 1.74580097e-01,
6.49696961e-02, -8.56237561e-02, -1.89858019e-01,
-1.96504310e-01, -1.04968190e-01, 2.51029599e-02,
1.32686019e-01, 2.03692451e-01, 2.11983219e-01,
0.00000000e+00, 0.00000000e+00]
data = read()[0].data
template = data[400:600]
data = data[380:620]
# FMF demeans template but does not locally demean data for
# normalization
template = template - template.mean()
cc = correlate_template(data, template, demean=False)
# FMF misses the last two elements?
np.testing.assert_allclose(cc[0:-2], result[0:-2], atol=1e-7)
shift, corr = xcorr_max(cc)
self.assertEqual(shift, 0)
def test_integer_input_equals_float_input(self):
a = [-3, 0, 4]
b = [-3, 4]
c = np.array(a, dtype=float)
d = np.array(b, dtype=float)
for demean in (True, False):
for normalize in (None, 'naive'):
cc1 = correlate(a, b, 3, demean=demean, normalize=normalize,
method='direct')
cc2 = correlate(c, d, 3, demean=demean, normalize=normalize)
np.testing.assert_allclose(cc1, cc2)
for normalize in (None, 'naive', 'full'):
cc3 = correlate_template(a, b, demean=demean,
normalize=normalize, method='direct')
cc4 = correlate_template(c, d, demean=demean,
normalize=normalize)
np.testing.assert_allclose(cc3, cc4)
def suite():
return unittest.makeSuite(CrossCorrelationTestCase, 'test')
if __name__ == '__main__':
unittest.main(defaultTest='suite')