# -*- coding: utf-8 -*-
#
#
# TheVirtualBrain-Scientific Package. This package holds all simulators, and
# analysers necessary to run brain-simulations. You can use it stand alone or
# in conjunction with TheVirtualBrain-Framework Package. See content of the
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# CITATION:
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# https://www.thevirtualbrain.org/tvb/zwei/neuroscience-publications
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"""
Calculate the cross spectrum and complex coherence on a TimeSeries datatype and
return a ComplexCoherence datatype.
.. moduleauthor:: Paula Sanz Leon <Paula@tvb.invalid>
"""
import numpy
import tvb.datatypes.spectral as spectral
from scipy import signal as sp_signal
from tvb.basic.logger.builder import get_logger
from tvb.basic.neotraits.info import narray_describe
SUPPORTED_WINDOWING_FUNCTIONS = ("hamming", "bartlett", "blackman", "hanning")
log = get_logger(__name__)
# NOTE: Work only with 2D TimeSeries -- otherwise a MemoryError will raise
# My first attempts made use of itertools on the 4D TimeSeries but they were
# fruitless.
# Nested `for` loops seem a 'good' solution instead of creating enormous ndarrays
# to compute the FFT and derived complex spectra at once
"""
A module for calculating the FFT of a TimeSeries and returning
a ComplexCoherenceSpectrum datatype.
This algorithm is based on the matlab function data2cs_event.m written by Guido Nolte:
.. [Freyer_2012] Freyer, F.; Reinacher, M.; Nolte, G.; Dinse, H. R. and
Ritter, P. *Repetitive tactile stimulation changes resting-state
functional connectivity-implications for treatment of sensorimotor decline*.
Front Hum Neurosci, Bernstein Focus State Dependencies of Learning and
Bernstein Center for Computational Neuroscience Berlin, Germany., 2012, 6, 144
Input:
originally the input could be 2D (tpts x nodes/channels), and it was possible
to give a 3D array (e.g., tpspt x nodes/cahnnels x trials) via the segment_length
attribute.
Current TVB implementation can handle 4D or 2D TimeSeries datatypes.
Be warned: the 4D TimeSeries will be averaged and squeezed.
Output: (main arrays)
- the cross-spectrum
- the complex coherence, from which the imaginary part can be extracted
By default the time series is segmented into 1 second `epoch` blocks and 0.5
second 50% overlapping `segments` to which a Hanning function is applied.
"""
[docs]def calculate_complex_cross_coherence(time_series, epoch_length, segment_length, segment_shift, window_function,
average_segments, subtract_epoch_average, zeropad, detrend_ts, max_freq,
npat):
"""
# type: (TimeSeries, float, float, float, str, bool, bool, int, bool, float, float) -> ComplexCoherenceSpectrum
Calculate the FFT, Cross Coherence and Complex Coherence of time_series
broken into (possibly) epochs and segments of length `epoch_length` and
`segment_length` respectively, filtered by `window_function`.
Parameters
__________
time_series : TimeSeries
The timeseries for which the CrossCoherence and ComplexCoherence is to be computed.
epoch_length : float
In general for lengthy EEG recordings (~30 min), the timeseries are divided into equally
sized segments (~ 20-40s). These contain the event that is to be characterized by means of the
cross coherence. Additionally each epoch block will be further divided into segments to which
the FFT will be applied.
segment_length : float
The segment length determines the frequency resolution of the resulting power spectra --
longer windows produce finer frequency resolution.
segment_shift : float
Time length by which neighboring segments are shifted. e.g.
`segment shift` = `segment_length` / 2 means 50% overlapping segments.
window_function : str
Windowing functions can be applied before the FFT is performed.
average_segments : bool
Flag. If `True`, compute the mean Cross Spectrum across segments.
subtract_epoch_average: bool
Flag. If `True` and if the number of epochs is > 1, you can optionally subtract the
mean across epochs before computing the complex coherence.
zeropad : int
Adds `n` zeros at the end of each segment and at the end of window_function. It is not yet functional.
detrend_ts : bool
Flag. If `True` removes linear trend along the time dimension before applying FFT.
max_freq : float
Maximum frequency points (e.g. 32., 64., 128.) represented in the output. Default is segment_length / 2 + 1.
npat : float
This attribute appears to be related to an input projection matrix... Which is not yet implemented.
"""
# self.time_series.trait["data"].log_debug(owner=cls_attr_name)
tpts = time_series.data.shape[0]
time_series_length = tpts * time_series.sample_period
if len(time_series.data.shape) > 2:
time_series_data = numpy.squeeze((time_series.data.mean(axis=-1)).mean(axis=1))
# Divide time-series into epochs, no overlapping
if epoch_length > 0.0:
nepochs = int(numpy.floor(time_series_length / epoch_length))
epoch_tpts = int(epoch_length / time_series.sample_period)
time_series_length = epoch_length
tpts = epoch_tpts
else:
epoch_length = time_series_length
nepochs = int(numpy.ceil(time_series_length / epoch_length))
# Segment time-series, overlapping if necessary
nseg = int(numpy.floor(time_series_length / segment_length))
if nseg > 1:
seg_tpts = int(segment_length / time_series.sample_period)
seg_shift_tpts = int(segment_shift / time_series.sample_period)
nseg = int(numpy.floor((tpts - seg_tpts) / seg_shift_tpts) + 1)
else:
segment_length = time_series_length
seg_tpts = time_series_data.shape[0]
# Frequency
nfreq = int(numpy.min([max_freq, numpy.floor((seg_tpts + zeropad) / 2.0) + 1]))
resulted_shape, av_result_shape = complex_coherence_result_shape(time_series.data.shape, max_freq, epoch_length,
segment_length, segment_shift,
time_series.sample_period, zeropad,
average_segments)
cs = numpy.zeros(resulted_shape, dtype=numpy.complex128)
av = numpy.zeros(av_result_shape, dtype=numpy.complex128)
coh = numpy.zeros(resulted_shape, dtype=numpy.complex128)
# Apply windowing function
if window_function is not None:
if window_function not in SUPPORTED_WINDOWING_FUNCTIONS:
log.error("Windowing function is: %s" % window_function)
log.error("Must be in: %s" % str(SUPPORTED_WINDOWING_FUNCTIONS))
window_func = eval("".join(("numpy.", window_function)))
win = window_func(seg_tpts)
window_mask = (numpy.kron(numpy.ones((time_series_data.shape[1], 1)), win)).T
nave = 0
for j in numpy.arange(nepochs):
data = time_series_data[j * epoch_tpts:(j + 1) * epoch_tpts, :]
for i in numpy.arange(nseg): # average over all segments;
ts = data[i * seg_shift_tpts: i * seg_shift_tpts + seg_tpts, :]
if detrend_ts:
ts = sp_signal.detrend(ts, axis=0)
datalocfft = numpy.fft.fft(ts * window_mask, axis=0)
datalocfft = numpy.matrix(datalocfft)
for f in numpy.arange(nfreq): # for all frequencies
if npat == 1:
if not average_segments:
cs[:, :, f, i] += numpy.conjugate(datalocfft[f, :].conj().T * datalocfft[f, :])
av[:, f, i] += numpy.conjugate(datalocfft[f, :].conj().T)
else:
cs[:, :, f] += numpy.conjugate(datalocfft[f, :].conj().T * datalocfft[f, :])
av[:, f] += numpy.conjugate(datalocfft[f, :].conj().T)
else:
if not average_segments:
cs[:, :, f, j, i] = numpy.conjugate(datalocfft[f, :].conj().T * datalocfft[f, :])
av[:, f, j, i] = numpy.conjugate(datalocfft[f, :].conj().T)
else:
cs[:, :, f, j] += numpy.conjugate(datalocfft[f, :].conj().T * datalocfft[f, :])
av[:, f, j] += numpy.conjugate(datalocfft[f, :].conj().T)
del datalocfft
nave += 1.0
# End of FORs
if not average_segments:
cs = cs / nave
av = av / nave
else:
nave = nave * nseg
cs = cs / nave
av = av / nave
# Subtract average
for f in numpy.arange(nfreq):
if subtract_epoch_average:
if npat == 1:
if not average_segments:
for i in numpy.arange(nseg):
cs[:, :, f, i] = cs[:, :, f, i] - av[:, f, i] * av[:, f, i].conj().T
else:
cs[:, :, f] = cs[:, :, f] - av[:, f] * av[:, f].conj().T
else:
if not average_segments:
for i in numpy.arange(nseg):
for j in numpy.arange(nepochs):
cs[:, :, f, j, i] = cs[:, :, f, j, i] - av[:, f, j, i] * av[:, f, j, i].conj().T
else:
for j in numpy.arange(nepochs):
cs[:, :, f, j] = cs[:, :, f, j] - av[:, f, j] * av[:, f, j].conj().T
# Compute Complex Coherence
ndim = len(cs.shape)
if ndim == 3:
for i in numpy.arange(cs.shape[2]):
temp = numpy.array(cs[:, :, i])
coh[:, :, i] = cs[:, :, i] / numpy.sqrt(temp.diagonal().conj().T * temp.diagonal())
elif ndim == 4:
for i in numpy.arange(cs.shape[2]):
for j in numpy.arange(cs.shape[3]):
temp = numpy.array(numpy.squeeze(cs[:, :, i, j]))
coh[:, :, i, j] = temp / numpy.sqrt(temp.diagonal().conj().T * temp.diagonal().T)
log.debug("result")
log.debug(narray_describe(cs))
spectra = spectral.ComplexCoherenceSpectrum(source=time_series,
array_data=coh,
cross_spectrum=cs,
epoch_length=epoch_length,
segment_length=segment_length,
windowing_function=window_function)
return spectra
[docs]def complex_coherence_result_shape(input_shape, max_freq, epoch_length, segment_length, segment_shift, sample_period,
zeropad,
average_segments):
"""
Returns the shape of the main result and the average over epochs
"""
# this is useless here unless the input could actually be a 2D TimeSeries
nchan = input_shape[2] if len(input_shape) > 2 else input_shape[1]
seg_tpts = segment_length / sample_period
seg_shift_tpts = segment_shift / sample_period
tpts = (epoch_length / sample_period) if epoch_length > 0.0 else input_shape[0]
nfreq = int(numpy.min([max_freq, numpy.floor((seg_tpts + zeropad) / 2.0) + 1]))
nseg = int(numpy.floor((tpts - seg_tpts) / seg_shift_tpts) + 1)
if not average_segments:
result_shape = (nchan, nchan, nfreq, nseg)
av_result_shape = (nchan, nfreq, nseg)
else:
result_shape = (nchan, nchan, nfreq)
av_result_shape = (nchan, nfreq)
return [result_shape, av_result_shape]
