def xcorr(self):
"""The cross-correlation between every pairwise combination time-series
in the object. Uses np.correlation('full').
Returns
-------
TimeSeries: the time-dependent cross-correlation, with zero-lag
at time=0"""
tseries_length = self.input.data.shape[0]
t_points = self.input.data.shape[-1]
xcorr = np.zeros((tseries_length,
tseries_length,
t_points*2-1))
for i in xrange(tseries_length):
for j in xrange(i,tseries_length):
xcorr[i][j] = tsu.xcorr(self.input.data[i],self.input.data[j])
idx = tsu.tril_indices(tseries_length,-1)
xcorr[idx[0],idx[1],...] = xcorr[idx[1],idx[0],...]
return ts.TimeSeries(xcorr,
sampling_interval=self.input.sampling_interval,
t0=-self.input.sampling_interval*t_points)
def xcorr_norm(self):
"""The cross-correlation between every pairwise combination time-series
in the object, where the zero lag correlation is normalized to be equal
to the correlation coefficient between the time-series
Returns
-------
TimeSeries: the time-dependent cross-correlation, with zero-lag
at time=0"""
tseries_length = self.input.data.shape[0]
t_points = self.input.data.shape[-1]
xcorr = np.zeros((tseries_length,
tseries_length,
t_points*2-1))
for i in xrange(tseries_length):
for j in xrange(i,tseries_length):
xcorr[i,j] = tsu.xcorr(self.input.data[i],self.input.data[j])
xcorr[i,j] /= (xcorr[i,j,t_points])
xcorr[i,j] *= self.output[i,j]
idx = tsu.tril_indices(tseries_length,-1)
xcorr[idx[0],idx[1],...] = xcorr[idx[1],idx[0],...]
return ts.TimeSeries(xcorr,
sampling_interval=self.input.sampling_interval,
t0=-self.input.sampling_interval*t_points)
def coherence_partial(self):
"""The partial coherence between data[i] and data[j], given data[k], as
a function of frequency band"""
tseries_length = self.input.data.shape[0]
spectrum_length = self.spectrum.shape[-1]
p_coherence=np.zeros((tseries_length,
tseries_length,
tseries_length,
spectrum_length))
for i in xrange(tseries_length):
for j in xrange(tseries_length):
for k in xrange(tseries_length):
if j==k or i==k:
pass
else:
p_coherence[i][j][k]=tsa.coherence_partial_calculate(
self.spectrum[i][j],
self.spectrum[i][i],
self.spectrum[j][j],
self.spectrum[i][k],
self.spectrum[j][k],
self.spectrum[k][k])
idx = tsu.tril_indices(tseries_length,-1)
p_coherence[idx[0],idx[1],...] = p_coherence[idx[1],idx[0],...].conj()
return p_coherence
def coherence(self):
"""
The coherence between the different channels in the input TimeSeries
object
"""
#XXX Calculate this from the standard output, instead of recalculating
#the coherence:
tseries_length = self.input.data.shape[0]
spectrum_length = self.spectrum.shape[-1]
coherence=np.zeros((tseries_length,
tseries_length,
spectrum_length))
for i in xrange(tseries_length):
for j in xrange(i,tseries_length):
coherence[i][j] = tsa.coherence_calculate(self.spectrum[i][j],
self.spectrum[i][i],
self.spectrum[j][j])
idx = tsu.tril_indices(tseries_length,-1)
coherence[idx[0],idx[1],...] = coherence[idx[1],idx[0],...].conj()
return coherence
def coherence(self):
tseries_length = self.input.data.shape[0]
spectrum_length = self.spectrum.shape[-1]
coherence=np.zeros((tseries_length,
tseries_length,
spectrum_length))
for i in xrange(tseries_length):
for j in xrange(i,tseries_length):
coherence[i][j] = tsa.coherence_calculate(self.spectrum[i][j],
self.spectrum[i][i],
self.spectrum[j][j])
idx = tsu.tril_indices(tseries_length,-1)
coherence[idx[0],idx[1],...] = coherence[idx[1],idx[0],...].conj()
return coherence
def output(self):
"""The standard output for this kind of analyzer is the coherency """
data = self.input.data
tseries_length = data.shape[0]
spectrum_length = self.spectrum.shape[-1]
coherency=np.zeros((tseries_length,
tseries_length,
spectrum_length),dtype=complex)
for i in xrange(tseries_length):
for j in xrange(i,tseries_length):
coherency[i][j] = tsa.coherency_calculate(self.spectrum[i][j],
self.spectrum[i][i],
self.spectrum[j][j])
idx = tsu.tril_indices(tseries_length,-1)
coherency[idx[0],idx[1],...] = coherency[idx[1],idx[0],...].conj()
return coherency
tspectra[i], tspectra[i], (w[i], w[i]), sides='onesided'
).real
syy = alg.mtm_cross_spectrum(
tspectra[j], tspectra[j], (w[i], w[j]), sides='onesided'
).real
psd_mat[0,i,j] = sxx
psd_mat[1,i,j] = syy
coh_mat[i,j] = np.abs(sxy)**2
coh_mat[i,j] /= (sxx * syy)
csd_mat[i,j] = sxy
if i != j:
coh_var[i,j] = utils.jackknifed_coh_variance(
tspectra[i], tspectra[j], weights=(w[i], w[j]), last_freq=L
)
upper_idc = utils.triu_indices(nseq, k=1)
lower_idc = utils.tril_indices(nseq, k=-1)
coh_mat[upper_idc] = coh_mat[lower_idc]
coh_var[upper_idc] = coh_var[lower_idc]
# convert this measure with the normalizing function
coh_mat_xform = utils.normalize_coherence(coh_mat, 2*K-2)
t025_limit = coh_mat_xform + dist.t.ppf(.025, K-1)*np.sqrt(coh_var)
t975_limit = coh_mat_xform + dist.t.ppf(.975, K-1)*np.sqrt(coh_var)
utils.normal_coherence_to_unit(t025_limit, 2*K-2, t025_limit)
utils.normal_coherence_to_unit(t975_limit, 2*K-2, t975_limit)
if L < n_samples:
freqs = np.linspace(0, 1/(2*TR), L)