def test_xcorr_xcorrt(self):
N = 1001
data1 = np.sin(np.arange(N // 2 + 1) / 100.)
data2 = np.e**(-(np.arange(N) - 500)**2 / 100.) - np.e**(
-(np.arange(N) - 50)**2 /
100.) + 5 * np.e**(-(np.arange(N) - 950)**2 / 100.)
cor1 = correlate(data1 - np.mean(data1), data2 - np.mean(data2),
'full')
cor2 = xcorrt(data2, data1, 750, window=N, ndat2d=N // 2 + 1)[::-1]
cor3 = xcorrt(data1, data2, 750, window=N,
ndat1d=N // 2 + 1) #@UnusedVariable
cor3b = xcorrt(data1, data2, 750, window=0) #@UnusedVariable
cor3c = xcorrt(data2, data1, 750, window=0)[::-1] #@UnusedVariable
cor1 *= max(cor2) / max(cor1)
cor4 = correlate(data2, data1, 'full')
cor5 = xcorrt(data2, data1, 750, demean=False)
cor5b = xcorrt(data2, data1, 750, shift_zero=-100, demean=False)
cor5c = xcorrt(data2, data1, 750, shift_zero=100, demean=False)
cor4 *= max(cor5) / max(cor4)
cor7 = correlate(data1, data2, 'full')
cor8 = xcorrt(data1, data2, 750, demean=False, normalize=False)
cor10 = xcorrt(data1,
data2,
750,
oneside=True,
demean=False,
normalize=False) #@UnusedVariable
# from pylab import plot, show, subplot, legend
# subplot(411)
# plot(data1)
# plot(data2)
# subplot(412)
# plot(cor1, label='scipy.signal all demeaned and normalized')
# plot(cor2, label='xcorrt ndat1 > ndat2 ndatxd')
# plot(cor3, label='xcorrt ndat1 < ndat2 ndatxd')
# plot(cor3b, label='xcorrt ndat1 > ndat2 window = 0')
# plot(cor3c, label='xcorrt ndat1 < ndat2 window = 0')
# legend()
# subplot(413)
# plot(cor4, label='scipy.signal all normalized')
# plot(cor5, label='xcorrt')
# plot(cor5b, label='xcorrt shifted -100')
# plot(cor5c, label='xcorrt shifted 100')
# legend()
# subplot(414)
# plot(cor7, label='scipy.signal')
# plot(cor8, label='xcorrt')
# plot(cor10, label='xcorrt oneside=True')
# legend()
# show()
np.testing.assert_array_almost_equal(cor1, cor2)
np.testing.assert_array_almost_equal(cor4, cor5)
np.testing.assert_array_almost_equal(cor7, cor8)
np.testing.assert_array_almost_equal(cor5[200:300], cor5b[100:200])
np.testing.assert_array_almost_equal(cor5[200:300], cor5c[300:400])
def test_xcorr_all_again(self):
seed(42)
data1 = random(1200) * np.sin(np.arange(1200)) * np.arange(1200) - 0.5
data2 = random(1000) * np.sin(np.arange(1000) * 0.4) * 500 - 0.5
data1 -= np.mean(data1[100:1100])
data2 -= np.mean(data2)
data2_pad = np.hstack((np.zeros(100), data2, np.zeros(100)))
cor1a = correlate(data1, data2, 'valid')
cor1a2 = xcorr_obspy(data1, data2_pad, 100)
cor1b = xcorrt(data1, data2, 100)
cor1c = xcorrf(data1, data2, 100)
cor1a *= max(cor1b) / max(cor1a)
cor1a2 *= max(cor1b) / max(cor1a2)
cor3 = xcorrf(data2, data1, 100)[::-1] #@UnusedVariable
cor4 = xcorrt(data1, data2, 100, demean=False, normalize=False)
cor5 = xcorrf(data1, data2, 100, demean=False, normalize=False)
val = max (cor4)
cor4 /= val
cor5 /= val
cor6 = xcorrt(data1, data2, 100, shift_zero=100)
cor7 = xcorrf(data1, data2, 100, shift_zero=100)
cor8 = xcorrt(data1, data2, 500, window=200)
cor9 = xcorrf(data1, data2, 500, window=200)
# from pylab import plot, show, subplot, legend
# subplot(411)
# plot(data1)
# plot(data2)
# subplot(412)
# plot(cor1a, label='convolve')
# plot(cor1b, label='xcorrt')
# plot(cor1c, label='xcorrf')
# plot(cor1a2, label='xcorr_obspy')
# plot(cor6, label='xcorrt shift')
# plot(cor7, label='xcorrf shift')
# legend()
# subplot(413)
# plot(cor4, label='xcorrt all not demeaned not normalized')
# plot(cor5, label='xcorrf')
# legend()
# subplot(414)
# plot(cor8, label='xcorrt window')
# plot(cor9, label='xcorrf window')
# legend()
# show()
np.testing.assert_array_almost_equal(cor1a, cor1b)
np.testing.assert_array_almost_equal(cor1a, cor1a2)
np.testing.assert_array_almost_equal(cor1b, cor1c)
np.testing.assert_array_almost_equal(cor1c[20:30], cor7[120:130])
np.testing.assert_array_almost_equal(cor4, cor5)
np.testing.assert_array_almost_equal(cor6, cor7)
np.testing.assert_array_almost_equal(cor8, cor9)
def test_xcorr_all_again(self):
seed(42)
data1 = random(1200) * np.sin(np.arange(1200)) * np.arange(1200) - 0.5
data2 = random(1000) * np.sin(np.arange(1000) * 0.4) * 500 - 0.5
data1 -= np.mean(data1[100:1100])
data2 -= np.mean(data2)
data2_pad = np.hstack((np.zeros(100), data2, np.zeros(100)))
cor1a = correlate(data1, data2, 'valid')
cor1a2 = xcorr_obspy(data1, data2_pad, 100)
cor1b = xcorrt(data1, data2, 100)
cor1c = xcorrf(data1, data2, 100)
cor1a *= max(cor1b) / max(cor1a)
cor1a2 *= max(cor1b) / max(cor1a2)
cor3 = xcorrf(data2, data1, 100)[::-1] #@UnusedVariable
cor4 = xcorrt(data1, data2, 100, demean=False, normalize=False)
cor5 = xcorrf(data1, data2, 100, demean=False, normalize=False)
val = max(cor4)
cor4 /= val
cor5 /= val
cor6 = xcorrt(data1, data2, 100, shift_zero=100)
cor7 = xcorrf(data1, data2, 100, shift_zero=100)
cor8 = xcorrt(data1, data2, 500, window=200)
cor9 = xcorrf(data1, data2, 500, window=200)
# from pylab import plot, show, subplot, legend
# subplot(411)
# plot(data1)
# plot(data2)
# subplot(412)
# plot(cor1a, label='convolve')
# plot(cor1b, label='xcorrt')
# plot(cor1c, label='xcorrf')
# plot(cor1a2, label='xcorr_obspy')
# plot(cor6, label='xcorrt shift')
# plot(cor7, label='xcorrf shift')
# legend()
# subplot(413)
# plot(cor4, label='xcorrt all not demeaned not normalized')
# plot(cor5, label='xcorrf')
# legend()
# subplot(414)
# plot(cor8, label='xcorrt window')
# plot(cor9, label='xcorrf window')
# legend()
# show()
np.testing.assert_array_almost_equal(cor1a, cor1b)
np.testing.assert_array_almost_equal(cor1a, cor1a2)
np.testing.assert_array_almost_equal(cor1b, cor1c)
np.testing.assert_array_almost_equal(cor1c[20:30], cor7[120:130])
np.testing.assert_array_almost_equal(cor4, cor5)
np.testing.assert_array_almost_equal(cor6, cor7)
np.testing.assert_array_almost_equal(cor8, cor9)
def test_xcorr_xcorrt(self):
N = 1001
data1 = np.sin(np.arange(N // 2 + 1) / 100.)
data2 = np.e ** (-(np.arange(N) - 500) ** 2 / 100.) - np.e ** (-(np.arange(N) - 50) ** 2 / 100.) + 5 * np.e ** (-(np.arange(N) - 950) ** 2 / 100.)
cor1 = correlate(data1 - np.mean(data1), data2 - np.mean(data2), 'full')
cor2 = xcorrt(data2, data1, 750, window=N, ndat2d=N // 2 + 1)[::-1]
cor3 = xcorrt(data1, data2, 750, window=N, ndat1d=N // 2 + 1) #@UnusedVariable
cor3b = xcorrt(data1, data2, 750, window=0) #@UnusedVariable
cor3c = xcorrt(data2, data1, 750, window=0)[::-1] #@UnusedVariable
cor1 *= max(cor2) / max(cor1)
cor4 = correlate(data2, data1, 'full')
cor5 = xcorrt(data2, data1, 750, demean=False)
cor5b = xcorrt(data2, data1, 750, shift_zero= -100, demean=False)
cor5c = xcorrt(data2, data1, 750, shift_zero=100, demean=False)
cor4 *= max(cor5) / max(cor4)
cor7 = correlate(data1, data2, 'full')
cor8 = xcorrt(data1, data2, 750, demean=False, normalize=False)
cor10 = xcorrt(data1, data2, 750, oneside=True, demean=False, normalize=False) #@UnusedVariable
# from pylab import plot, show, subplot, legend
# subplot(411)
# plot(data1)
# plot(data2)
# subplot(412)
# plot(cor1, label='scipy.signal all demeaned and normalized')
# plot(cor2, label='xcorrt ndat1 > ndat2 ndatxd')
# plot(cor3, label='xcorrt ndat1 < ndat2 ndatxd')
# plot(cor3b, label='xcorrt ndat1 > ndat2 window = 0')
# plot(cor3c, label='xcorrt ndat1 < ndat2 window = 0')
# legend()
# subplot(413)
# plot(cor4, label='scipy.signal all normalized')
# plot(cor5, label='xcorrt')
# plot(cor5b, label='xcorrt shifted -100')
# plot(cor5c, label='xcorrt shifted 100')
# legend()
# subplot(414)
# plot(cor7, label='scipy.signal')
# plot(cor8, label='xcorrt')
# plot(cor10, label='xcorrt oneside=True')
# legend()
# show()
np.testing.assert_array_almost_equal(cor1, cor2)
np.testing.assert_array_almost_equal(cor4, cor5)
np.testing.assert_array_almost_equal(cor7, cor8)
np.testing.assert_array_almost_equal(cor5[200:300], cor5b[100:200])
np.testing.assert_array_almost_equal(cor5[200:300], cor5c[300:400])
def test_xcorr_realdata(self):
stream = self.stream.copy()
data = stream.select(component='Z')[0].data
shift = 100
cor1 = xcorrf(data, data[shift:-shift], shift)
cor2 = xcorrt(data, data[shift:-shift], shift)
# from pylab import plot, show
# plot(cor1)
# plot(cor2)
# show()
np.testing.assert_array_almost_equal(cor1, cor2)
def test_xcorr_realdata(self):
stream = self.stream.copy()
data = stream.select(component='Z')[0].data
shift = 100
cor1 = xcorrf(data, data[shift:-shift], shift)
cor2 = xcorrt(data, data[shift:-shift], shift)
# from pylab import plot, show
# plot(cor1)
# plot(cor2)
# show()
np.testing.assert_array_almost_equal(cor1, cor2)
def test_xcorr_xcorrf(self):
N = 1001
data1 = np.sin(np.arange(N // 2 + 1) / 100.)
data2 = np.e**(-(np.arange(N) - 500)**2 / 100.) - np.e**(
-(np.arange(N) - 50)**2 /
100.) + 5 * np.e**(-(np.arange(N) - 950)**2 / 100.)
cor1 = xcorrt(data1, data2, 750)
cor2 = xcorrf(data1, data2, 750)
cor3 = xcorrf(data2, data1, 750)[::-1]
cor4 = xcorrt(data1, data2, 750, demean=False, normalize=False)
cor5 = xcorrf(data1, data2, 750, demean=False, normalize=False)
cor6 = xcorrt(data1, data2, 750, shift_zero=100)
cor7 = xcorrf(data1, data2, 750, shift_zero=100)
cor8 = xcorrt(data1, data2, 750, window=200)
cor9 = xcorrf(data1, data2, 750, window=200)
# from pylab import plot, show, subplot, legend
# subplot(411)
# plot(data1)
# plot(data2)
# subplot(412)
# plot(cor1, label='xcorrt')
# plot(cor2, label='xcorrf ndat1 > ndat2')
# plot(cor3, label='xcorrf ndat2 > ndat1')
# legend()
# subplot(413)
# plot(cor4, label='xcorrt all not demeaned not normalized')
# plot(cor5, label='xcorrf')
# legend()
# subplot(414)
# plot(cor6, label='xcorrt shift')
# plot(cor7, label='xcorrf shift')
# plot(cor8, label='xcorrt window')
# plot(cor9, label='xcorrf window')
# legend()
# show()
np.testing.assert_array_almost_equal(cor1, cor2)
np.testing.assert_array_almost_equal(cor1, cor3)
np.testing.assert_array_almost_equal(cor4, cor5, 5)
np.testing.assert_array_almost_equal(cor6, cor7)
np.testing.assert_array_almost_equal(cor8, cor9)
def test_xcorr_acorrt(self):
data1 = np.sin(np.arange(1001) * 2 * np.pi / 500.)
cor1 = xcorrt(data1, data1, 1000)
cor2 = acorrt(data1, 1000, oneside=False, clipdata=False)
# from pylab import plot, show, subplot, legend
# subplot(211)
# plot(data1)
# subplot(212)
# plot(cor1, label='xcorrt')
# plot(cor2, label='acorr clip=False')
# legend()
# show()
np.testing.assert_array_almost_equal(cor1, cor2)
def test_xcorr_acorrt(self):
data1 = np.sin(np.arange(1001) * 2 * np.pi / 500.)
cor1 = xcorrt(data1, data1, 1000)
cor2 = acorrt(data1, 1000, oneside=False, clipdata=False)
# from pylab import plot, show, subplot, legend
# subplot(211)
# plot(data1)
# subplot(212)
# plot(cor1, label='xcorrt')
# plot(cor2, label='acorr clip=False')
# legend()
# show()
np.testing.assert_array_almost_equal(cor1, cor2)
def test_xcorr_xcorrf(self):
N = 1001
data1 = np.sin(np.arange(N // 2 + 1) / 100.)
data2 = np.e ** (-(np.arange(N) - 500) ** 2 / 100.) - np.e ** (-(np.arange(N) - 50) ** 2 / 100.) + 5 * np.e ** (-(np.arange(N) - 950) ** 2 / 100.)
cor1 = xcorrt(data1, data2, 750)
cor2 = xcorrf(data1, data2, 750)
cor3 = xcorrf(data2, data1, 750)[::-1]
cor4 = xcorrt(data1, data2, 750, demean=False, normalize=False)
cor5 = xcorrf(data1, data2, 750, demean=False, normalize=False)
cor6 = xcorrt(data1, data2, 750, shift_zero=100)
cor7 = xcorrf(data1, data2, 750, shift_zero=100)
cor8 = xcorrt(data1, data2, 750, window=200)
cor9 = xcorrf(data1, data2, 750, window=200)
# from pylab import plot, show, subplot, legend
# subplot(411)
# plot(data1)
# plot(data2)
# subplot(412)
# plot(cor1, label='xcorrt')
# plot(cor2, label='xcorrf ndat1 > ndat2')
# plot(cor3, label='xcorrf ndat2 > ndat1')
# legend()
# subplot(413)
# plot(cor4, label='xcorrt all not demeaned not normalized')
# plot(cor5, label='xcorrf')
# legend()
# subplot(414)
# plot(cor6, label='xcorrt shift')
# plot(cor7, label='xcorrf shift')
# plot(cor8, label='xcorrt window')
# plot(cor9, label='xcorrf window')
# legend()
# show()
np.testing.assert_array_almost_equal(cor1, cor2)
np.testing.assert_array_almost_equal(cor1, cor3)
np.testing.assert_array_almost_equal(cor4, cor5, 5)
np.testing.assert_array_almost_equal(cor6, cor7)
np.testing.assert_array_almost_equal(cor8, cor9)
def deconvt(rsp_list, src, spiking, shift, length=None, normalize=True):
"""
Time domain deconvolution.
Calculate Toeplitz auto-correlation matrix of source, invert it, add noise
and multiply it with cross-correlation vector of response and source.
In a formula:
RF = (STS + spiking*I)^-1 * STR
This function calculates RF.
N... length
( S0 S-1 S-2 ... S-N+1 )
( S1 S0 S-1 ... S-N+2 )
S = ( S2 ... )
( ... )
( SN-1 ... S0 )
R = (R0 R1 ... RN-1)^T
RF = (RF0 RF1 ... RFN-1)^T
S... source matrix (shape N*N)
R... response vector (length N)
RF... receiver function (deconvolution) vector (length N)
STS = S^T*S = Toeplitz autocorrelation matrix
STR = S^T*R = cross-correlation vector
I... Identity
:parameters:
rsp_list (list of) data containing the response
src data of source
spiking random noise added to autocorrelation (eg. 1.0, 0.1)
shift shift the source by that amount of samples to the left side to get onset in RF at the right time
(negative -> shift source to the right side)
shift = (middle of rsp window - middle of src window) + (0 - middle rf window)
length number of data points of deconvolution
normalize if True normalize all deconvolutions so that the maximum of the
first deconvolution is 1
:return: (list of) deconvolutions (length N)
"""
# time_rf = winrf[1]-winrf[0] = length / samp
# shift_zero=int(samp*(
# (winrsp[1] - winrsp[0] - winsrc[1] + winsrc[0] - time_rf) / 2
# + winrsp[0] - winsrc[0] - winrf[0]))
# = shift_zero=int(samp*(
# (winrsp[1] + winrsp[0] - winsrc[1] - winsrc[0] -winrf[1] - winrf[0]) / 2
#
#
if length == None:
length = len(src)
flag = False
RF_list = []
STS = acorrt(src, length, demean=False, clipdata=False)
STS[0] += spiking
#print shift, len(src), len(rsp_list), spiking, length
if not isinstance(rsp_list, (list, tuple)):
flag = True
rsp_list = [rsp_list]
for rsp in rsp_list:
STR = xcorrt(rsp, src, length // 2, shift, demean=False)
if len(STR) > len(STS):
STR = np.delete(STR, -1)
RF = toeplitz(STS, STR)
RF_list.append(RF)
if normalize:
norm = 1 / np.max(np.abs(RF_list[0]))
for RF in RF_list:
RF *= norm
if flag:
return RF
else:
return RF_list
# comment return commands for testing
samp = 50.
from pylab import plot, subplot, show
subplot(411)
plot(np.arange(len(src)) / samp, src)
plot(np.arange(len(rsp)) / samp, rsp)
subplot(412)
plot(np.arange(len(STS)) / samp, STS)
subplot(413)
plot(np.arange(len(STR)) / samp, STR)
subplot(414)
plot(np.arange(len(RF)) / samp, RF_list[0])
show()
def deconvt(rsp_list, src, spiking, shift, length=None, normalize=True):
"""
Time domain deconvolution.
Calculate Toeplitz auto-correlation matrix of source, invert it, add noise
and multiply it with cross-correlation vector of response and source.
In a formula:
RF = (STS + spiking*I)^-1 * STR
This function calculates RF.
N... length
( S0 S-1 S-2 ... S-N+1 )
( S1 S0 S-1 ... S-N+2 )
S = ( S2 ... )
( ... )
( SN-1 ... S0 )
R = (R0 R1 ... RN-1)^T
RF = (RF0 RF1 ... RFN-1)^T
S... source matrix (shape N*N)
R... response vector (length N)
RF... receiver function (deconvolution) vector (length N)
STS = S^T*S = Toeplitz autocorrelation matrix
STR = S^T*R = cross-correlation vector
I... Identity
:parameters:
rsp_list (list of) data containing the response
src data of source
spiking random noise added to autocorrelation (eg. 1.0, 0.1)
shift shift the source by that amount of samples to the left side to get onset in RF at the right time
(negative -> shift source to the right side)
shift = (middle of rsp window - middle of src window) + (0 - middle rf window)
length number of data points of deconvolution
normalize if True normalize all deconvolutions so that the maximum of the
first deconvolution is 1
:return: (list of) deconvolutions (length N)
"""
# time_rf = winrf[1]-winrf[0] = length / samp
# shift_zero=int(samp*(
# (winrsp[1] - winrsp[0] - winsrc[1] + winsrc[0] - time_rf) / 2
# + winrsp[0] - winsrc[0] - winrf[0]))
# = shift_zero=int(samp*(
# (winrsp[1] + winrsp[0] - winsrc[1] - winsrc[0] -winrf[1] - winrf[0]) / 2
#
#
if length == None:
length = len(src)
flag = False
RF_list = []
STS = acorrt(src, length, demean=False, clipdata=False)
STS[0] += spiking
#print shift, len(src), len(rsp_list), spiking, length
if not isinstance(rsp_list, (list, tuple)):
flag = True
rsp_list = [rsp_list]
for rsp in rsp_list:
STR = xcorrt(rsp, src, length // 2, shift, demean=False)
if len(STR) > len(STS):
STR = np.delete(STR, -1)
RF = toeplitz(STS, STR)
RF_list.append(RF)
if normalize:
norm = 1 / np.max(np.abs(RF_list[0]))
for RF in RF_list:
RF *= norm
if flag:
return RF
else:
return RF_list
# comment return commands for testing
samp = 50.
from pylab import plot, subplot, show
subplot(411)
plot(np.arange(len(src)) / samp, src)
plot(np.arange(len(rsp)) / samp, rsp)
subplot(412)
plot(np.arange(len(STS)) / samp, STS)
subplot(413)
plot(np.arange(len(STR)) / samp, STR)
subplot(414)
plot(np.arange(len(RF)) / samp, RF_list[0])
show()
