Source code for tvb.analyzers.node_complex_coherence

# -*- coding: utf-8 -*-
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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 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
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
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 =[0] time_series_length = tpts * time_series.sample_period if len( > 2: time_series_data = numpy.squeeze(( # 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(, 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]