def myCorr(data, maxlag, plot=False):
"""This function takes ndimensional *data* array, computes the cross-correlation in the frequency domain
and returns the cross-correlation function between [-*maxlag*:*maxlag*].
:type data: :class:`numpy.ndarray`
:param data: This array contains the fft of each timeseries to be cross-correlated.
:type maxlag: int
:param maxlag: This number defines the number of samples (N=2*maxlag + 1) of the CCF that will be returned.
:rtype: :class:`numpy.ndarray`
:returns: The cross-correlation function between [-maxlag:maxlag]
"""
normalized = True
allCpl = False
maxlag = np.round(maxlag)
#~ print "np.shape(data)",np.shape(data)
if data.shape[0] == 2:
#~ print "2 matrix to correlate"
if allCpl:
# Skipped this unused part
pass
else:
K = data.shape[0]
#couples de stations
couples = np.concatenate((np.arange(0, K), K + np.arange(0, K)))
Nt = data.shape[1]
Nc = 2 * Nt - 1
Nfft = 2 ** nextpow2(Nc)
# corr = scipy.fftpack.fft(data,int(Nfft),axis=1)
corr = data
if plot:
plt.subplot(211)
plt.plot(np.arange(len(corr[0])) * 0.05, np.abs(corr[0]))
plt.subplot(212)
plt.plot(np.arange(len(corr[1])) * 0.05, np.abs(corr[1]))
corr = np.conj(corr[couples[0]]) * corr[couples[1]]
corr = np.real(scipy.fftpack.ifft(corr)) / Nt
corr = np.concatenate((corr[-Nt + 1:], corr[:Nt + 1]))
if plot:
plt.figure()
plt.plot(corr)
E = np.sqrt(np.mean(scipy.fftpack.ifft(data, axis=1) ** 2, axis=1))
normFact = E[0] * E[1]
if normalized:
corr /= np.real(normFact)
if maxlag != Nt:
tcorr = np.arange(-Nt + 1, Nt)
dN = np.where(np.abs(tcorr) <= maxlag)[0]
corr = corr[dN]
del data
return corr
def mwcs(ccCurrent,
ccReference,
fmin,
fmax,
sampRate,
tmin,
windL,
step,
plot=False):
"""...
:type ccCurrent: :class:`numpy.ndarray`
:param ccCurrent: The "Current" timeseries
:type ccReference: :class:`numpy.ndarray`
:param ccReference: The "Reference" timeseries
:type fmin: float
:param fmin: The lower frequency bound to compute the dephasing
:type fmax: float
:param fmax: The higher frequency bound to compute the dephasing
:type sampRate: float
:param sampRate: The sample rate of the input timeseries
:type tmin: float
:param tmin: The leftmost time lag (used to compute the "time lags array")
:type windL: float
:param windL: The moving window length
:type step: float
:param step: The step to jump for the moving window
:type plot: bool
:param plot: If True, plots the MWCS result for each window. Defaults to
False
:rtype: :class:`numpy.ndarray`
:returns: [Taxis,deltaT,deltaErr,deltaMcoh]. Taxis contains the central
times of the windows. The three other columns contain dt, error and
mean coherence for each window.
"""
windL = np.int(windL * sampRate)
step = np.int(step * sampRate)
count = 0
deltaT = []
deltaErr = []
deltaMcoh = []
Taxis = []
padd = 2**(nextpow2(windL) + 2)
# Tentative checking if enough point are used to compute the FFT
freqVec = scipy.fftpack.fftfreq(int(padd), 1. / sampRate)[:int(padd) / 2]
indRange = np.argwhere(np.logical_and(freqVec >= fmin, freqVec <= fmax))
if len(indRange) < 2:
padd = 2**(nextpow2(windL) + 3)
tp = cosTaper(windL, .85)
timeaxis = (np.arange(len(ccCurrent)) / float(sampRate)) + tmin
minind = 0
maxind = windL
while maxind <= len(ccCurrent):
ind = minind
cci = ccCurrent[ind:(ind + windL)].copy()
cci = scipy.signal.detrend(cci, type='linear')
cci -= cci.min()
cci /= cci.max()
cci -= np.mean(cci)
cci *= tp
cri = ccReference[ind:(ind + windL)].copy()
cri = scipy.signal.detrend(cri, type='linear')
cri -= cri.min()
cri /= cri.max()
cri -= np.mean(cri)
cri *= tp
Fcur = scipy.fftpack.fft(cci, n=int(padd))[:int(padd) / 2]
Fref = scipy.fftpack.fft(cri, n=int(padd))[:int(padd) / 2]
Fcur2 = np.real(Fcur)**2 + np.imag(Fcur)**2
Fref2 = np.real(Fref)**2 + np.imag(Fref)**2
smoother = 5
dcur = np.sqrt(smooth(Fcur2, window='hanning', half_win=smoother))
dref = np.sqrt(smooth(Fref2, window='hanning', half_win=smoother))
# Calculate the cross-spectrum
X = Fref * (Fcur.conj())
X = smooth(X, window='hanning', half_win=smoother)
dcs = np.abs(X)
# Find the values the frequency range of interest
freqVec = scipy.fftpack.fftfreq(len(X) * 2,
1. / sampRate)[:int(padd) / 2]
indRange = np.argwhere(np.logical_and(freqVec >= fmin,
freqVec <= fmax))
# Get Coherence and its mean value
coh = getCoherence(dcs, dref, dcur)
mcoh = np.mean(coh[indRange])
# Get Weights
w = 1.0 / (1.0 / (coh[indRange]**2) - 1.0)
w[coh[indRange] >= 0.99] = 1.0 / (1.0 / 0.9801 - 1.0)
w = np.sqrt(w * np.sqrt(dcs[indRange]))
# w /= (np.sum(w)/len(w)) #normalize
w = np.real(w)
# Frequency array:
v = np.real(freqVec[indRange]) * 2 * np.pi
vo = np.real(freqVec) * 2 * np.pi
# Phase:
phi = np.angle(X)
phi[0] = 0.
phi = np.unwrap(phi)
#phio = phi.copy()
phi = phi[indRange]
# Calculate the slope with a weighted least square linear regression
# forced through the origin
# weights for the WLS must be the variance !
res = sm.regression.linear_model.WLS(phi, v, w**2).fit()
# print "forced", np.real(res.params[0])
# print "!forced", np.real(res2.params[0])
m = np.real(res.params[0])
deltaT.append(m)
# print phi.shape, v.shape, w.shape
e = np.sum((phi - m * v)**2) / (np.size(v) - 1)
s2x2 = np.sum(v**2 * w**2)
sx2 = np.sum(w * v**2)
e = np.sqrt(e * s2x2 / sx2**2)
# print w.shape
if plot:
plt.figure()
plt.suptitle('%.1fs' % (timeaxis[ind + windL / 2]))
plt.subplot(311)
plt.plot(cci)
plt.plot(cri)
ax = plt.subplot(312)
plt.plot(vo / (2 * np.pi), phio)
plt.scatter(v / (2 * np.pi),
phi,
c=w,
edgecolor='none',
vmin=0.6,
vmax=1)
plt.subplot(313, sharex=ax)
plt.plot(v / (2 * np.pi), coh[indRange])
plt.axhline(mcoh, c='r')
plt.axhline(1.0, c='k', ls='--')
plt.xlim(-0.1, 1.5)
plt.ylim(0, 1.5)
plt.show()
deltaErr.append(e)
deltaMcoh.append(np.real(mcoh))
Taxis.append(timeaxis[ind + windL / 2])
count += 1
minind += step
maxind += step
del Fcur, Fref
del X
del freqVec
del indRange
del w, v, e, s2x2
del res
if maxind > len(ccCurrent) + step:
logging.warning("The last window was too small, but was computed")
return np.array([Taxis, deltaT, deltaErr, deltaMcoh]).T
def myCorr(data, maxlag, plot=False):
"""This function takes ndimensional *data* array, computes the cross-correlation in the frequency domain
and returns the cross-correlation function between [-*maxlag*:*maxlag*].
:type data: :class:`numpy.ndarray`
:param data: This array contains the fft of each timeseries to be cross-correlated.
:type maxlag: int
:param maxlag: This number defines the number of samples (N=2*maxlag + 1) of the CCF that will be returned.
:rtype: :class:`numpy.ndarray`
:returns: The cross-correlation function between [-maxlag:maxlag]
"""
normalized = True
allCpl = False
maxlag = np.round(maxlag)
#~ print "np.shape(data)",np.shape(data)
if data.shape[0] == 2:
#~ print "2 matrix to correlate"
if allCpl:
# Skipped this unused part
pass
else:
K = data.shape[0]
#couples de stations
couples = np.concatenate((np.arange(0, K), K + np.arange(0, K)))
Nt = data.shape[1]
Nc = 2 * Nt - 1
Nfft = 2**nextpow2(Nc)
# corr = scipy.fftpack.fft(data,int(Nfft),axis=1)
corr = data
if plot:
plt.subplot(211)
plt.plot(np.arange(len(corr[0])) * 0.05, np.abs(corr[0]))
plt.subplot(212)
plt.plot(np.arange(len(corr[1])) * 0.05, np.abs(corr[1]))
corr = np.conj(corr[couples[0]]) * corr[couples[1]]
corr = np.real(scipy.fftpack.ifft(corr)) / Nt
corr = np.concatenate((corr[-Nt + 1:], corr[:Nt + 1]))
if plot:
plt.figure()
plt.plot(corr)
E = np.sqrt(np.mean(scipy.fftpack.ifft(data, axis=1)**2, axis=1))
normFact = E[0] * E[1]
if normalized:
corr /= np.real(normFact)
if maxlag != Nt:
tcorr = np.arange(-Nt + 1, Nt)
dN = np.where(np.abs(tcorr) <= maxlag)[0]
corr = corr[dN]
del data
return corr
def mwcs(ccCurrent, ccReference, fmin, fmax, sampRate, tmin, windL, step,
plot=False):
"""...
:type ccCurrent: :class:`numpy.ndarray`
:param ccCurrent: The "Current" timeseries
:type ccReference: :class:`numpy.ndarray`
:param ccReference: The "Reference" timeseries
:type fmin: float
:param fmin: The lower frequency bound to compute the dephasing
:type fmax: float
:param fmax: The higher frequency bound to compute the dephasing
:type sampRate: float
:param sampRate: The sample rate of the input timeseries
:type tmin: float
:param tmin: The leftmost time lag (used to compute the "time lags array")
:type windL: float
:param windL: The moving window length
:type step: float
:param step: The step to jump for the moving window
:type plot: bool
:param plot: If True, plots the MWCS result for each window. Defaults to
False
:rtype: :class:`numpy.ndarray`
:returns: [Taxis,deltaT,deltaErr,deltaMcoh]. Taxis contains the central
times of the windows. The three other columns contain dt, error and
mean coherence for each window.
"""
windL = np.int(windL*sampRate)
step = np.int(step*sampRate)
count = 0
deltaT = []
deltaErr = []
deltaMcoh = []
Taxis = []
padd = 2**(nextpow2(windL)+2)
# Tentative checking if enough point are used to compute the FFT
freqVec = scipy.fftpack.fftfreq(int(padd), 1./sampRate)[:int(padd)/2]
indRange = np.argwhere(np.logical_and(freqVec >= fmin,
freqVec <= fmax))
if len(indRange) < 2:
padd = 2**(nextpow2(windL)+3)
tp = cosTaper(windL, .85)
timeaxis = (np.arange(len(ccCurrent)) / float(sampRate))+tmin
minind = 0
maxind = windL
while maxind <= len(ccCurrent):
ind = minind
cci = ccCurrent[ind:(ind+windL)].copy()
cci = scipy.signal.detrend(cci, type='linear')
cci -= cci.min()
cci /= cci.max()
cci -= np.mean(cci)
cci *= tp
cri = ccReference[ind:(ind+windL)].copy()
cri = scipy.signal.detrend(cri, type='linear')
cri -= cri.min()
cri /= cri.max()
cri -= np.mean(cri)
cri *= tp
Fcur = scipy.fftpack.fft(cci, n=int(padd))[:int(padd)/2]
Fref = scipy.fftpack.fft(cri, n=int(padd))[:int(padd)/2]
Fcur2 = np.real(Fcur)**2 + np.imag(Fcur)**2
Fref2 = np.real(Fref)**2 + np.imag(Fref)**2
smoother = 5
dcur = np.sqrt(smooth(Fcur2, window='hanning', half_win=smoother))
dref = np.sqrt(smooth(Fref2, window='hanning', half_win=smoother))
# Calculate the cross-spectrum
X = Fref*(Fcur.conj())
X = smooth(X, window='hanning', half_win=smoother)
dcs = np.abs(X)
# Find the values the frequency range of interest
freqVec = scipy.fftpack.fftfreq(len(X)*2, 1./sampRate)[:int(padd)/2]
indRange = np.argwhere(np.logical_and(freqVec >= fmin,
freqVec <= fmax))
# Get Coherence and its mean value
coh = getCoherence(dcs, dref, dcur)
mcoh = np.mean(coh[indRange])
# Get Weights
w = 1.0 / (1.0 / (coh[indRange]**2) - 1.0)
w[coh[indRange] >= 0.99] = 1.0 / (1.0 / 0.9801 - 1.0)
w = np.sqrt(w * np.sqrt(dcs[indRange]))
# w /= (np.sum(w)/len(w)) #normalize
w = np.real(w)
# Frequency array:
v = np.real(freqVec[indRange]) * 2 * np.pi
vo = np.real(freqVec) * 2 * np.pi
# Phase:
phi = np.angle(X)
phi[0] = 0.
phi = np.unwrap(phi)
#phio = phi.copy()
phi = phi[indRange]
# Calculate the slope with a weighted least square linear regression
# forced through the origin
# weights for the WLS must be the variance !
res = sm.regression.linear_model.WLS(phi, v, w**2).fit()
# print "forced", np.real(res.params[0])
# print "!forced", np.real(res2.params[0])
m = np.real(res.params[0])
deltaT.append(m)
# print phi.shape, v.shape, w.shape
e = np.sum((phi-m*v)**2) / (np.size(v)-1)
s2x2 = np.sum(v**2 * w**2)
sx2 = np.sum(w * v**2)
e = np.sqrt(e*s2x2 / sx2**2)
# print w.shape
if plot:
plt.figure()
plt.suptitle('%.1fs' % (timeaxis[ind + windL/2]))
plt.subplot(311)
plt.plot(cci)
plt.plot(cri)
ax = plt.subplot(312)
plt.plot(vo/(2*np.pi), phio)
plt.scatter(v/(2*np.pi), phi, c=w, edgecolor='none',
vmin=0.6, vmax=1)
plt.subplot(313, sharex=ax)
plt.plot(v/(2*np.pi), coh[indRange])
plt.axhline(mcoh, c='r')
plt.axhline(1.0, c='k', ls='--')
plt.xlim(-0.1, 1.5)
plt.ylim(0, 1.5)
plt.show()
deltaErr.append(e)
deltaMcoh.append(np.real(mcoh))
Taxis.append(timeaxis[ind + windL/2])
count += 1
minind += step
maxind += step
del Fcur, Fref
del X
del freqVec
del indRange
del w, v, e, s2x2
del res
if maxind > len(ccCurrent)+step:
logging.warning("The last window was too small, but was computed")
return np.array([Taxis, deltaT, deltaErr, deltaMcoh]).T