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spectral.py
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spectral.py
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# Authors: Martin Luessi <mluessi@nmr.mgh.harvard.edu>
#
# License: BSD (3-clause)
from functools import partial
from inspect import getmembers
import numpy as np
from scipy.fftpack import fftfreq
from .utils import check_indices
from ..fixes import _get_args
from ..parallel import parallel_func
from ..source_estimate import _BaseSourceEstimate
from ..epochs import BaseEpochs
from ..time_frequency.multitaper import (dpss_windows, _mt_spectra,
_psd_from_mt, _csd_from_mt,
_psd_from_mt_adaptive)
from ..time_frequency.tfr import morlet, cwt
from ..utils import logger, verbose, _time_mask, warn
from ..externals.six import string_types
########################################################################
# Various connectivity estimators
class _AbstractConEstBase(object):
"""ABC for connectivity estimators."""
def start_epoch(self):
raise RuntimeError('start_epoch method not implemented')
def accumulate(self, con_idx, csd_xy):
raise RuntimeError('accumulate method not implemented')
def combine(self, other):
raise RuntimeError('combine method not implemented')
def compute_con(self, con_idx, n_epochs):
raise RuntimeError('compute_con method not implemented')
class _EpochMeanConEstBase(_AbstractConEstBase):
"""Base class for methods that estimate connectivity as mean epoch-wise."""
def __init__(self, n_cons, n_freqs, n_times):
self.n_cons = n_cons
self.n_freqs = n_freqs
self.n_times = n_times
if n_times == 0:
self.csd_shape = (n_cons, n_freqs)
else:
self.csd_shape = (n_cons, n_freqs, n_times)
self.con_scores = None
def start_epoch(self): # noqa: D401
"""Called at the start of each epoch."""
pass # for this type of con. method we don't do anything
def combine(self, other):
"""Include con. accumated for some epochs in this estimate."""
self._acc += other._acc
class _CohEstBase(_EpochMeanConEstBase):
"""Base Estimator for Coherence, Coherency, Imag. Coherence."""
def __init__(self, n_cons, n_freqs, n_times):
super(_CohEstBase, self).__init__(n_cons, n_freqs, n_times)
# allocate space for accumulation of CSD
self._acc = np.zeros(self.csd_shape, dtype=np.complex128)
def accumulate(self, con_idx, csd_xy):
"""Accumulate CSD for some connections."""
self._acc[con_idx] += csd_xy
class _CohEst(_CohEstBase):
"""Coherence Estimator."""
name = 'Coherence'
def compute_con(self, con_idx, n_epochs, psd_xx, psd_yy):
"""Compute final con. score for some connections."""
if self.con_scores is None:
self.con_scores = np.zeros(self.csd_shape)
csd_mean = self._acc[con_idx] / n_epochs
self.con_scores[con_idx] = np.abs(csd_mean) / np.sqrt(psd_xx * psd_yy)
class _CohyEst(_CohEstBase):
"""Coherency Estimator."""
name = 'Coherency'
def compute_con(self, con_idx, n_epochs, psd_xx, psd_yy):
"""Compute final con. score for some connections."""
if self.con_scores is None:
self.con_scores = np.zeros(self.csd_shape,
dtype=np.complex128)
csd_mean = self._acc[con_idx] / n_epochs
self.con_scores[con_idx] = csd_mean / np.sqrt(psd_xx * psd_yy)
class _ImCohEst(_CohEstBase):
"""Imaginary Coherence Estimator."""
name = 'Imaginary Coherence'
def compute_con(self, con_idx, n_epochs, psd_xx, psd_yy):
"""Compute final con. score for some connections."""
if self.con_scores is None:
self.con_scores = np.zeros(self.csd_shape)
csd_mean = self._acc[con_idx] / n_epochs
self.con_scores[con_idx] = np.imag(csd_mean) / np.sqrt(psd_xx * psd_yy)
class _PLVEst(_EpochMeanConEstBase):
"""PLV Estimator."""
name = 'PLV'
def __init__(self, n_cons, n_freqs, n_times):
super(_PLVEst, self).__init__(n_cons, n_freqs, n_times)
# allocate accumulator
self._acc = np.zeros(self.csd_shape, dtype=np.complex128)
def accumulate(self, con_idx, csd_xy):
"""Accumulate some connections."""
self._acc[con_idx] += csd_xy / np.abs(csd_xy)
def compute_con(self, con_idx, n_epochs):
"""Compute final con. score for some connections."""
if self.con_scores is None:
self.con_scores = np.zeros(self.csd_shape)
plv = np.abs(self._acc / n_epochs)
self.con_scores[con_idx] = plv
class _PLIEst(_EpochMeanConEstBase):
"""PLI Estimator."""
name = 'PLI'
def __init__(self, n_cons, n_freqs, n_times):
super(_PLIEst, self).__init__(n_cons, n_freqs, n_times)
# allocate accumulator
self._acc = np.zeros(self.csd_shape)
def accumulate(self, con_idx, csd_xy):
"""Accumulate some connections."""
self._acc[con_idx] += np.sign(np.imag(csd_xy))
def compute_con(self, con_idx, n_epochs):
"""Compute final con. score for some connections."""
if self.con_scores is None:
self.con_scores = np.zeros(self.csd_shape)
pli_mean = self._acc[con_idx] / n_epochs
self.con_scores[con_idx] = np.abs(pli_mean)
class _PLIUnbiasedEst(_PLIEst):
"""Unbiased PLI Square Estimator."""
name = 'Unbiased PLI Square'
def compute_con(self, con_idx, n_epochs):
"""Compute final con. score for some connections."""
if self.con_scores is None:
self.con_scores = np.zeros(self.csd_shape)
pli_mean = self._acc[con_idx] / n_epochs
# See Vinck paper Eq. (30)
con = (n_epochs * pli_mean ** 2 - 1) / (n_epochs - 1)
self.con_scores[con_idx] = con
class _WPLIEst(_EpochMeanConEstBase):
"""WPLI Estimator."""
name = 'WPLI'
def __init__(self, n_cons, n_freqs, n_times):
super(_WPLIEst, self).__init__(n_cons, n_freqs, n_times)
# store both imag(csd) and abs(imag(csd))
acc_shape = (2,) + self.csd_shape
self._acc = np.zeros(acc_shape)
def accumulate(self, con_idx, csd_xy):
"""Accumulate some connections."""
im_csd = np.imag(csd_xy)
self._acc[0, con_idx] += im_csd
self._acc[1, con_idx] += np.abs(im_csd)
def compute_con(self, con_idx, n_epochs):
"""Compute final con. score for some connections."""
if self.con_scores is None:
self.con_scores = np.zeros(self.csd_shape)
num = np.abs(self._acc[0, con_idx])
denom = self._acc[1, con_idx]
# handle zeros in denominator
z_denom = np.where(denom == 0.)
denom[z_denom] = 1.
con = num / denom
# where we had zeros in denominator, we set con to zero
con[z_denom] = 0.
self.con_scores[con_idx] = con
class _WPLIDebiasedEst(_EpochMeanConEstBase):
"""Debiased WPLI Square Estimator."""
name = 'Debiased WPLI Square'
def __init__(self, n_cons, n_freqs, n_times):
super(_WPLIDebiasedEst, self).__init__(n_cons, n_freqs, n_times)
# store imag(csd), abs(imag(csd)), imag(csd)^2
acc_shape = (3,) + self.csd_shape
self._acc = np.zeros(acc_shape)
def accumulate(self, con_idx, csd_xy):
"""Accumulate some connections."""
im_csd = np.imag(csd_xy)
self._acc[0, con_idx] += im_csd
self._acc[1, con_idx] += np.abs(im_csd)
self._acc[2, con_idx] += im_csd ** 2
def compute_con(self, con_idx, n_epochs):
"""Compute final con. score for some connections."""
if self.con_scores is None:
self.con_scores = np.zeros(self.csd_shape)
# note: we use the trick from fieldtrip to compute the
# the estimate over all pairwise epoch combinations
sum_im_csd = self._acc[0, con_idx]
sum_abs_im_csd = self._acc[1, con_idx]
sum_sq_im_csd = self._acc[2, con_idx]
denom = sum_abs_im_csd ** 2 - sum_sq_im_csd
# handle zeros in denominator
z_denom = np.where(denom == 0.)
denom[z_denom] = 1.
con = (sum_im_csd ** 2 - sum_sq_im_csd) / denom
# where we had zeros in denominator, we set con to zero
con[z_denom] = 0.
self.con_scores[con_idx] = con
class _PPCEst(_EpochMeanConEstBase):
"""Pairwise Phase Consistency (PPC) Estimator."""
name = 'PPC'
def __init__(self, n_cons, n_freqs, n_times):
super(_PPCEst, self).__init__(n_cons, n_freqs, n_times)
# store csd / abs(csd)
self._acc = np.zeros(self.csd_shape, dtype=np.complex128)
def accumulate(self, con_idx, csd_xy):
"""Accumulate some connections."""
denom = np.abs(csd_xy)
z_denom = np.where(denom == 0.)
denom[z_denom] = 1.
this_acc = csd_xy / denom
this_acc[z_denom] = 0. # handle division by zero
self._acc[con_idx] += this_acc
def compute_con(self, con_idx, n_epochs):
"""Compute final con. score for some connections."""
if self.con_scores is None:
self.con_scores = np.zeros(self.csd_shape)
# note: we use the trick from fieldtrip to compute the
# the estimate over all pairwise epoch combinations
con = ((self._acc[con_idx] * np.conj(self._acc[con_idx]) - n_epochs) /
(n_epochs * (n_epochs - 1.)))
self.con_scores[con_idx] = np.real(con)
###############################################################################
def _epoch_spectral_connectivity(data, sig_idx, tmin_idx, tmax_idx, sfreq,
mode, window_fun, eigvals, wavelets,
freq_mask, mt_adaptive, idx_map, block_size,
psd, accumulate_psd, con_method_types,
con_methods, n_signals, n_times,
accumulate_inplace=True):
"""Estimate connectivity for one epoch (see spectral_connectivity)."""
n_cons = len(idx_map[0])
if wavelets is not None:
n_times_spectrum = n_times
n_freqs = len(wavelets)
else:
n_times_spectrum = 0
n_freqs = np.sum(freq_mask)
if not accumulate_inplace:
# instantiate methods only for this epoch (used in parallel mode)
con_methods = [mtype(n_cons, n_freqs, n_times_spectrum)
for mtype in con_method_types]
if len(sig_idx) == n_signals:
# we use all signals: use a slice for faster indexing
sig_idx = slice(None, None)
# compute tapered spectra
if mode in ['multitaper', 'fourier']:
x_mt = list()
this_psd = list()
sig_pos_start = 0
for this_data in data:
this_n_sig = this_data.shape[0]
sig_pos_end = sig_pos_start + this_n_sig
if not isinstance(sig_idx, slice):
this_sig_idx = sig_idx[(sig_idx >= sig_pos_start) &
(sig_idx < sig_pos_end)] - sig_pos_start
else:
this_sig_idx = sig_idx
if isinstance(this_data, _BaseSourceEstimate):
_mt_spectra_partial = partial(_mt_spectra, dpss=window_fun,
sfreq=sfreq)
this_x_mt = this_data.transform_data(
_mt_spectra_partial, idx=this_sig_idx, tmin_idx=tmin_idx,
tmax_idx=tmax_idx)
else:
this_x_mt, _ = _mt_spectra(this_data[this_sig_idx,
tmin_idx:tmax_idx],
window_fun, sfreq)
if mt_adaptive:
# compute PSD and adaptive weights
_this_psd, weights = _psd_from_mt_adaptive(
this_x_mt, eigvals, freq_mask, return_weights=True)
# only keep freqs of interest
this_x_mt = this_x_mt[:, :, freq_mask]
else:
# do not use adaptive weights
this_x_mt = this_x_mt[:, :, freq_mask]
if mode == 'multitaper':
weights = np.sqrt(eigvals)[np.newaxis, :, np.newaxis]
else:
# hack to so we can sum over axis=-2
weights = np.array([1.])[:, None, None]
if accumulate_psd:
_this_psd = _psd_from_mt(this_x_mt, weights)
x_mt.append(this_x_mt)
if accumulate_psd:
this_psd.append(_this_psd)
x_mt = np.concatenate(x_mt, axis=0)
if accumulate_psd:
this_psd = np.concatenate(this_psd, axis=0)
# advance position
sig_pos_start = sig_pos_end
elif mode == 'cwt_morlet':
# estimate spectra using CWT
x_cwt = list()
this_psd = list()
sig_pos_start = 0
for this_data in data:
this_n_sig = this_data.shape[0]
sig_pos_end = sig_pos_start + this_n_sig
if not isinstance(sig_idx, slice):
this_sig_idx = sig_idx[(sig_idx >= sig_pos_start) &
(sig_idx < sig_pos_end)] - sig_pos_start
else:
this_sig_idx = sig_idx
if isinstance(this_data, _BaseSourceEstimate):
cwt_partial = partial(cwt, Ws=wavelets, use_fft=True,
mode='same')
this_x_cwt = this_data.transform_data(
cwt_partial, idx=this_sig_idx, tmin_idx=tmin_idx,
tmax_idx=tmax_idx)
else:
this_x_cwt = cwt(this_data[this_sig_idx, tmin_idx:tmax_idx],
wavelets, use_fft=True, mode='same')
if accumulate_psd:
this_psd.append((this_x_cwt * this_x_cwt.conj()).real)
x_cwt.append(this_x_cwt)
# advance position
sig_pos_start = sig_pos_end
x_cwt = np.concatenate(x_cwt, axis=0)
if accumulate_psd:
this_psd = np.concatenate(this_psd, axis=0)
else:
raise RuntimeError('invalid mode')
# accumulate or return psd
if accumulate_psd:
if accumulate_inplace:
psd += this_psd
else:
psd = this_psd
else:
psd = None
# tell the methods that a new epoch starts
for method in con_methods:
method.start_epoch()
# accumulate connectivity scores
if mode in ['multitaper', 'fourier']:
for i in range(0, n_cons, block_size):
con_idx = slice(i, i + block_size)
if mt_adaptive:
csd = _csd_from_mt(x_mt[idx_map[0][con_idx]],
x_mt[idx_map[1][con_idx]],
weights[idx_map[0][con_idx]],
weights[idx_map[1][con_idx]])
else:
csd = _csd_from_mt(x_mt[idx_map[0][con_idx]],
x_mt[idx_map[1][con_idx]],
weights, weights)
for method in con_methods:
method.accumulate(con_idx, csd)
else:
# cwt_morlet mode
for i in range(0, n_cons, block_size):
con_idx = slice(i, i + block_size)
csd = x_cwt[idx_map[0][con_idx]] * \
np.conjugate(x_cwt[idx_map[1][con_idx]])
for method in con_methods:
method.accumulate(con_idx, csd)
return con_methods, psd
def _get_n_epochs(epochs, n):
"""Generate lists with at most n epochs."""
epochs_out = []
for e in epochs:
if not isinstance(e, (list, tuple)):
e = (e,)
epochs_out.append(e)
if len(epochs_out) >= n:
yield epochs_out
epochs_out = []
yield epochs_out
def _check_method(method):
"""Test if a method implements the required interface."""
interface_members = [m[0] for m in getmembers(_AbstractConEstBase)
if not m[0].startswith('_')]
method_members = [m[0] for m in getmembers(method)
if not m[0].startswith('_')]
for member in interface_members:
if member not in method_members:
return False, member
return True, None
def _get_and_verify_data_sizes(data, n_signals=None, n_times=None, times=None):
"""Get and/or verify the data sizes and time scales."""
if not isinstance(data, (list, tuple)):
raise ValueError('data has to be a list or tuple')
n_signals_tot = 0
for this_data in data:
this_n_signals, this_n_times = this_data.shape
if n_times is not None:
if this_n_times != n_times:
raise ValueError('all input time series must have the same '
'number of time points')
else:
n_times = this_n_times
n_signals_tot += this_n_signals
if hasattr(this_data, 'times'):
this_times = this_data.times
if times is not None:
if np.any(times != this_times):
warn('time scales of input time series do not match')
else:
times = this_times
if n_signals is not None:
if n_signals != n_signals_tot:
raise ValueError('the number of time series has to be the same in '
'each epoch')
n_signals = n_signals_tot
return n_signals, n_times, times
# map names to estimator types
_CON_METHOD_MAP = {'coh': _CohEst, 'cohy': _CohyEst, 'imcoh': _ImCohEst,
'plv': _PLVEst, 'ppc': _PPCEst, 'pli': _PLIEst,
'pli2_unbiased': _PLIUnbiasedEst, 'wpli': _WPLIEst,
'wpli2_debiased': _WPLIDebiasedEst}
@verbose
def spectral_connectivity(data, method='coh', indices=None, sfreq=2 * np.pi,
mode='multitaper', fmin=None, fmax=np.inf,
fskip=0, faverage=False, tmin=None, tmax=None,
mt_bandwidth=None, mt_adaptive=False,
mt_low_bias=True, cwt_frequencies=None,
cwt_n_cycles=7, block_size=1000, n_jobs=1,
verbose=None):
"""Compute frequency- and time-frequency-domain connectivity measures.
The connectivity method(s) are specified using the "method" parameter.
All methods are based on estimates of the cross- and power spectral
densities (CSD/PSD) Sxy and Sxx, Syy.
The spectral densities can be estimated using a multitaper method with
digital prolate spheroidal sequence (DPSS) windows, a discrete Fourier
transform with Hanning windows, or a continuous wavelet transform using
Morlet wavelets. The spectral estimation mode is specified using the
"mode" parameter.
By default, the connectivity between all signals is computed (only
connections corresponding to the lower-triangular part of the
connectivity matrix). If one is only interested in the connectivity
between some signals, the "indices" parameter can be used. For example,
to compute the connectivity between the signal with index 0 and signals
"2, 3, 4" (a total of 3 connections) one can use the following::
indices = (np.array([0, 0, 0]), # row indices
np.array([2, 3, 4])) # col indices
con_flat = spectral_connectivity(data, method='coh',
indices=indices, ...)
In this case con_flat.shape = (3, n_freqs). The connectivity scores are
in the same order as defined indices.
**Supported Connectivity Measures**
The connectivity method(s) is specified using the "method" parameter. The
following methods are supported (note: ``E[]`` denotes average over
epochs). Multiple measures can be computed at once by using a list/tuple,
e.g., ``['coh', 'pli']`` to compute coherence and PLI.
'coh' : Coherence given by::
| E[Sxy] |
C = ---------------------
sqrt(E[Sxx] * E[Syy])
'cohy' : Coherency given by::
E[Sxy]
C = ---------------------
sqrt(E[Sxx] * E[Syy])
'imcoh' : Imaginary coherence [1]_ given by::
Im(E[Sxy])
C = ----------------------
sqrt(E[Sxx] * E[Syy])
'plv' : Phase-Locking Value (PLV) [2]_ given by::
PLV = |E[Sxy/|Sxy|]|
'ppc' : Pairwise Phase Consistency (PPC), an unbiased estimator
of squared PLV [3]_.
'pli' : Phase Lag Index (PLI) [4]_ given by::
PLI = |E[sign(Im(Sxy))]|
'pli2_unbiased' : Unbiased estimator of squared PLI [5]_.
'wpli' : Weighted Phase Lag Index (WPLI) [5]_ given by::
|E[Im(Sxy)]|
WPLI = ------------------
E[|Im(Sxy)|]
'wpli2_debiased' : Debiased estimator of squared WPLI [5]_.
Parameters
----------
data : array-like, shape=(n_epochs, n_signals, n_times) | Epochs
The data from which to compute connectivity. Note that it is also
possible to combine multiple signals by providing a list of tuples,
e.g., data = [(arr_0, stc_0), (arr_1, stc_1), (arr_2, stc_2)],
corresponds to 3 epochs, and arr_* could be an array with the same
number of time points as stc_*. The array-like object can also
be a list/generator of array, shape =(n_signals, n_times),
or a list/generator of SourceEstimate or VolSourceEstimate objects.
method : string | list of string
Connectivity measure(s) to compute.
indices : tuple of arrays | None
Two arrays with indices of connections for which to compute
connectivity. If None, all connections are computed.
sfreq : float
The sampling frequency.
mode : str
Spectrum estimation mode can be either: 'multitaper', 'fourier', or
'cwt_morlet'.
fmin : float | tuple of floats
The lower frequency of interest. Multiple bands are defined using
a tuple, e.g., (8., 20.) for two bands with 8Hz and 20Hz lower freq.
If None the frequency corresponding to an epoch length of 5 cycles
is used.
fmax : float | tuple of floats
The upper frequency of interest. Multiple bands are dedined using
a tuple, e.g. (13., 30.) for two band with 13Hz and 30Hz upper freq.
fskip : int
Omit every "(fskip + 1)-th" frequency bin to decimate in frequency
domain.
faverage : boolean
Average connectivity scores for each frequency band. If True,
the output freqs will be a list with arrays of the frequencies
that were averaged.
tmin : float | None
Time to start connectivity estimation. Note: when "data" is an array,
the first sample is assumed to be at time 0. For other types
(Epochs, etc.), the time information contained in the object is used
to compute the time indices.
tmax : float | None
Time to end connectivity estimation. Note: when "data" is an array,
the first sample is assumed to be at time 0. For other types
(Epochs, etc.), the time information contained in the object is used
to compute the time indices.
mt_bandwidth : float | None
The bandwidth of the multitaper windowing function in Hz.
Only used in 'multitaper' mode.
mt_adaptive : bool
Use adaptive weights to combine the tapered spectra into PSD.
Only used in 'multitaper' mode.
mt_low_bias : bool
Only use tapers with more than 90% spectral concentration within
bandwidth. Only used in 'multitaper' mode.
cwt_frequencies : array
Array of frequencies of interest. Only used in 'cwt_morlet' mode.
cwt_n_cycles: float | array of float
Number of cycles. Fixed number or one per frequency. Only used in
'cwt_morlet' mode.
block_size : int
How many connections to compute at once (higher numbers are faster
but require more memory).
n_jobs : int
How many epochs to process in parallel.
verbose : bool, str, int, or None
If not None, override default verbose level (see :func:`mne.verbose`
and :ref:`Logging documentation <tut_logging>` for more).
Returns
-------
con : array | list of arrays
Computed connectivity measure(s). The shape of each array is either
(n_signals, n_signals, n_frequencies) mode: 'multitaper' or 'fourier'
(n_signals, n_signals, n_frequencies, n_times) mode: 'cwt_morlet'
when "indices" is None, or
(n_con, n_frequencies) mode: 'multitaper' or 'fourier'
(n_con, n_frequencies, n_times) mode: 'cwt_morlet'
when "indices" is specified and "n_con = len(indices[0])".
freqs : array
Frequency points at which the connectivity was computed.
times : array
Time points for which the connectivity was computed.
n_epochs : int
Number of epochs used for computation.
n_tapers : int
The number of DPSS tapers used. Only defined in 'multitaper' mode.
Otherwise None is returned.
References
----------
.. [1] Nolte et al. "Identifying true brain interaction from EEG data using
the imaginary part of coherency" Clinical neurophysiology, vol. 115,
no. 10, pp. 2292-2307, Oct. 2004.
.. [2] Lachaux et al. "Measuring phase synchrony in brain signals" Human
brain mapping, vol. 8, no. 4, pp. 194-208, Jan. 1999.
.. [3] Vinck et al. "The pairwise phase consistency: a bias-free measure of
rhythmic neuronal synchronization" NeuroImage, vol. 51, no. 1,
pp. 112-122, May 2010.
.. [4] Stam et al. "Phase lag index: assessment of functional connectivity
from multi channel EEG and MEG with diminished bias from common
sources" Human brain mapping, vol. 28, no. 11, pp. 1178-1193,
Nov. 2007.
.. [5] Vinck et al. "An improved index of phase-synchronization for
electro-physiological data in the presence of volume-conduction,
noise and sample-size bias" NeuroImage, vol. 55, no. 4,
pp. 1548-1565, Apr. 2011.
"""
if n_jobs != 1:
parallel, my_epoch_spectral_connectivity, _ = \
parallel_func(_epoch_spectral_connectivity, n_jobs,
verbose=verbose)
# format fmin and fmax and check inputs
if fmin is None:
fmin = -np.inf # set it to -inf, so we can adjust it later
fmin = np.asarray((fmin,)).ravel()
fmax = np.asarray((fmax,)).ravel()
if len(fmin) != len(fmax):
raise ValueError('fmin and fmax must have the same length')
if np.any(fmin > fmax):
raise ValueError('fmax must be larger than fmin')
n_bands = len(fmin)
# assign names to connectivity methods
if not isinstance(method, (list, tuple)):
method = [method] # make it a list so we can iterate over it
n_methods = len(method)
con_method_types = []
for m in method:
if m in _CON_METHOD_MAP:
method = _CON_METHOD_MAP[m]
con_method_types.append(method)
elif isinstance(m, string_types):
raise ValueError('%s is not a valid connectivity method' % m)
else:
# add custom method
method_valid, msg = _check_method(m)
if not method_valid:
raise ValueError('The supplied connectivity method does '
'not have the method %s' % msg)
con_method_types.append(m)
# determine how many arguments the compute_con_function needs
n_comp_args = [len(_get_args(mtype.compute_con))
for mtype in con_method_types]
# we only support 3 or 5 arguments
if any(n not in (3, 5) for n in n_comp_args):
raise ValueError('The compute_con function needs to have either '
'3 or 5 arguments')
# if none of the comp_con functions needs the PSD, we don't estimate it
accumulate_psd = any(n == 5 for n in n_comp_args)
if isinstance(data, BaseEpochs):
times_in = data.times # input times for Epochs input type
sfreq = data.info['sfreq']
# loop over data; it could be a generator that returns
# (n_signals x n_times) arrays or SourceEstimates
epoch_idx = 0
logger.info('Connectivity computation...')
for epoch_block in _get_n_epochs(data, n_jobs):
if epoch_idx == 0:
# initialize everything
first_epoch = epoch_block[0]
# get the data size and time scale
n_signals, n_times_in, times_in = \
_get_and_verify_data_sizes(first_epoch)
if times_in is None:
# we are not using Epochs or SourceEstimate(s) as input
times_in = np.linspace(0.0, n_times_in / sfreq, n_times_in,
endpoint=False)
n_times_in = len(times_in)
mask = _time_mask(times_in, tmin, tmax, sfreq=sfreq)
tmin_idx, tmax_idx = np.where(mask)[0][[0, -1]]
tmax_idx += 1
tmin_true = times_in[tmin_idx]
tmax_true = times_in[tmax_idx - 1] # time of last point used
times = times_in[tmin_idx:tmax_idx]
n_times = len(times)
if indices is None:
# only compute r for lower-triangular region
indices_use = np.tril_indices(n_signals, -1)
else:
indices_use = check_indices(indices)
# number of connectivities to compute
n_cons = len(indices_use[0])
logger.info(' computing connectivity for %d connections'
% n_cons)
logger.info(' using t=%0.3fs..%0.3fs for estimation (%d points)'
% (tmin_true, tmax_true, n_times))
# get frequencies of interest for the different modes
if mode in ['multitaper', 'fourier']:
# fmin fmax etc is only supported for these modes
# decide which frequencies to keep
freqs_all = fftfreq(n_times, 1. / sfreq)
freqs_all = freqs_all[freqs_all >= 0]
elif mode == 'cwt_morlet':
# cwt_morlet mode
if cwt_frequencies is None:
raise ValueError('define frequencies of interest using '
'cwt_frequencies')
else:
cwt_frequencies = cwt_frequencies.astype(np.float)
if any(cwt_frequencies > (sfreq / 2.)):
raise ValueError('entries in cwt_frequencies cannot be '
'larger than Nyquist (sfreq / 2)')
freqs_all = cwt_frequencies
else:
raise ValueError('mode has an invalid value')
# check that fmin corresponds to at least 5 cycles
five_cycle_freq = 5. * sfreq / float(n_times)
if len(fmin) == 1 and fmin[0] == -np.inf:
# we use the 5 cycle freq. as default
fmin = [five_cycle_freq]
else:
if any(fmin < five_cycle_freq):
warn('fmin corresponds to less than 5 cycles, '
'spectrum estimate will be unreliable')
# create a frequency mask for all bands
freq_mask = np.zeros(len(freqs_all), dtype=np.bool)
for f_lower, f_upper in zip(fmin, fmax):
freq_mask |= ((freqs_all >= f_lower) & (freqs_all <= f_upper))
# possibly skip frequency points
for pos in range(fskip):
freq_mask[pos + 1::fskip + 1] = False
# the frequency points where we compute connectivity
freqs = freqs_all[freq_mask]
n_freqs = len(freqs)
# get the freq. indices and points for each band
freq_idx_bands = [np.where((freqs >= fl) & (freqs <= fu))[0]
for fl, fu in zip(fmin, fmax)]
freqs_bands = [freqs[freq_idx] for freq_idx in freq_idx_bands]
# make sure we don't have empty bands
for i, n_f_band in enumerate([len(f) for f in freqs_bands]):
if n_f_band == 0:
raise ValueError('There are no frequency points between '
'%0.1fHz and %0.1fHz. Change the band '
'specification (fmin, fmax) or the '
'frequency resolution.'
% (fmin[i], fmax[i]))
if n_bands == 1:
logger.info(' frequencies: %0.1fHz..%0.1fHz (%d points)'
% (freqs_bands[0][0], freqs_bands[0][-1],
n_freqs))
else:
logger.info(' computing connectivity for the bands:')
for i, bfreqs in enumerate(freqs_bands):
logger.info(' band %d: %0.1fHz..%0.1fHz '
'(%d points)' % (i + 1, bfreqs[0],
bfreqs[-1], len(bfreqs)))
if faverage:
logger.info(' connectivity scores will be averaged for '
'each band')
# get the window function, wavelets, etc for different modes
if mode == 'multitaper':
# compute standardized half-bandwidth
if mt_bandwidth is not None:
half_nbw = float(mt_bandwidth) * n_times / (2 * sfreq)
else:
half_nbw = 4
# compute dpss windows
n_tapers_max = int(2 * half_nbw)
window_fun, eigvals = dpss_windows(n_times, half_nbw,
n_tapers_max,
low_bias=mt_low_bias)
n_tapers = len(eigvals)
logger.info(' using multitaper spectrum estimation with '
'%d DPSS windows' % n_tapers)
if mt_adaptive and len(eigvals) < 3:
warn('Not adaptively combining the spectral estimators '
'due to a low number of tapers.')
mt_adaptive = False
n_times_spectrum = 0 # this method only uses the freq. domain
wavelets = None
elif mode == 'fourier':
logger.info(' using FFT with a Hanning window to estimate '
'spectra')
window_fun = np.hanning(n_times)
mt_adaptive = False
eigvals = 1.
n_tapers = None
n_times_spectrum = 0 # this method only uses the freq. domain
wavelets = None
elif mode == 'cwt_morlet':
logger.info(' using CWT with Morlet wavelets to estimate '
'spectra')
# reformat cwt_n_cycles if we have removed some frequencies
# using fmin, fmax, fskip
cwt_n_cycles = np.asarray((cwt_n_cycles,)).ravel()
if len(cwt_n_cycles) > 1:
if len(cwt_n_cycles) != len(cwt_frequencies):
raise ValueError('cwt_n_cycles must be float or an '
'array with the same size as '
'cwt_frequencies')
cwt_n_cycles = cwt_n_cycles[freq_mask]
# get the Morlet wavelets
wavelets = morlet(sfreq, freqs, n_cycles=cwt_n_cycles,
zero_mean=True)
eigvals = None
n_tapers = None
window_fun = None
n_times_spectrum = n_times
else:
raise ValueError('mode has an invalid value')
# unique signals for which we actually need to compute PSD etc.
sig_idx = np.unique(np.r_[indices_use[0], indices_use[1]])
# map indices to unique indices
idx_map = [np.searchsorted(sig_idx, ind) for ind in indices_use]
# allocate space to accumulate PSD
if accumulate_psd:
if n_times_spectrum == 0:
psd_shape = (len(sig_idx), n_freqs)
else:
psd_shape = (len(sig_idx), n_freqs, n_times_spectrum)
psd = np.zeros(psd_shape)
else:
psd = None
# create instances of the connectivity estimators
con_methods = [mtype(n_cons, n_freqs, n_times_spectrum)
for mtype in con_method_types]
sep = ', '
metrics_str = sep.join([meth.name for meth in con_methods])
logger.info(' the following metrics will be computed: %s'
% metrics_str)
# check dimensions and time scale
for this_epoch in epoch_block:
_get_and_verify_data_sizes(this_epoch, n_signals, n_times_in,
times_in)
if n_jobs == 1:
# no parallel processing
for this_epoch in epoch_block:
logger.info(' computing connectivity for epoch %d'
% (epoch_idx + 1))
# con methods and psd are updated inplace
_epoch_spectral_connectivity(
this_epoch, sig_idx, tmin_idx,
tmax_idx, sfreq, mode, window_fun, eigvals, wavelets,
freq_mask, mt_adaptive, idx_map, block_size, psd,
accumulate_psd, con_method_types, con_methods,
n_signals, n_times, accumulate_inplace=True)
epoch_idx += 1
else:
# process epochs in parallel
logger.info(' computing connectivity for epochs %d..%d'
% (epoch_idx + 1, epoch_idx + len(epoch_block)))
out = parallel(my_epoch_spectral_connectivity(
this_epoch, sig_idx,
tmin_idx, tmax_idx, sfreq, mode, window_fun, eigvals,
wavelets, freq_mask, mt_adaptive, idx_map, block_size, psd,
accumulate_psd, con_method_types, None, n_signals, n_times,
accumulate_inplace=False) for this_epoch in epoch_block)