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test_cross_correlation.py
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test_cross_correlation.py
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# -*- 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, 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_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)
cc2 = correlate(a, b, 1, demean=False, normalize=False, domain='time')
cc3 = correlate(b, a, 1, demean=False, normalize=False)
cc4 = correlate(b, a, 1, demean=False, normalize=False, domain='time')
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 domain='time' 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, domain='time')
cc2 = correlate(b, a, 2, domain='time')
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 domain in ('freq', 'time'):
x = xcorr_func(self.a, self.b, 40, domain=domain)
y = xcorr_func(self.a, self.b[:-1], 40, domain=domain)
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, domain='freq')
cc2 = correlate(a, b, 3, domain='freq')
cc3 = correlate(a, b, None, domain='freq')
cc4 = correlate(a, b, None, domain='time')
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, domain='freq')
cc2 = correlate(a, b, 3, domain='freq')
cc3 = correlate(a, b, None, domain='freq')
cc4 = correlate(a, b, None, domain='time')
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_template_matching(self):
"""
Test for moving window correlations with "full" normalisation.
Comparison result is from EQcorrscan v.0.2.7.
"""
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]
shift = 20
cc = correlate(data, template, shift, normalize="full", domain="freq")
# TODO: This doesn't match closely enough
np.testing.assert_allclose(cc, result, atol=0.00001)
shift, corr = xcorr_max(cc)
# TODO: This is not close enough to 1.0
self.assertAlmostEqual(corr, 1.0, 7)
self.assertEqual(shift, 0)
def test_template_matching_time(self):
"""
Test full normalization in time domain.
"""
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]
shift = 20
cc = correlate(data, template, shift, normalize="full", domain="time")
# TODO: Not close enough
np.testing.assert_allclose(cc, result, atol=0.000001)
shift, corr = xcorr_max(cc)
# TODO: Not close enough
self.assertAlmostEqual(corr, 1.0, 7)
self.assertEqual(shift, 0)
def test_template_matching_normalization_equality(self):
"""
Test that, for data of the same length, naive and full normalization
give the same result.
"""
naive_xcorr = correlate(self.a, self.b, shift=15)
full_xcorr = correlate(self.a, self.b, shift=15, normalize='full')
self.assertEqual(naive_xcorr, full_xcorr)
def test_template_matching_reversed_order(self):
"""
Check that arguments can be given in whichever order the user fancies.
"""
forwards_xcorr = correlate(self.a, self.b[0:-20], normalize='full')
reversed_xcorr = correlate(self.b[0:-20], self.a, normalize='full')
self.assertEqual(forwards_xcorr, reversed_xcorr)
"""
We need a test that does this, but the only way to do it with long duration
data - EQcorrscan tests against Kaikoura data, which we know causes issues
for a lot of cross-correlation implementations.
"""
# def test_normalisation_extreme_amplitudes(self):
# """
# Test full normalisation method with extreme amplitudes
# (e.g. large EQ)
#
# Comparison result is from EQcorrscan v.0.2.7.
# """
# result =
# data = read()[0].data
# # Add a large amplitude thing in the data
# template = data[400:600]
# data = data[200:800]
# shift = 1000
# cc = correlate(data, template, shift, normalize="full")
# np.testing.assert_allclose(cc, result)
# shift, corr = xcorr_max(cc)
# self.assertAlmostEqual(corr, 0.96516076)
# self.assertEqual(shift, -5)
def suite():
return unittest.makeSuite(CrossCorrelationTestCase, 'test')
if __name__ == '__main__':
unittest.main(defaultTest='suite')