# Authors: Adam Li <adam2392@gmail.com>
# Santeri Ruuskanen <santeriruuskanen@gmail.com>
#
# License: BSD (3-clause)
import numpy as np
import xarray as xr
from mne.epochs import BaseEpochs
from mne.parallel import parallel_func
from mne.time_frequency import (tfr_array_morlet, tfr_array_multitaper,
dpss_windows)
from mne.utils import (logger, verbose)
from ..base import (SpectralConnectivity, EpochSpectralConnectivity)
from .epochs import _compute_freq_mask
from .smooth import _create_kernel, _smooth_spectra
from ..utils import check_indices, fill_doc
[docs]@verbose
@fill_doc
def spectral_connectivity_time(data, freqs, method='coh', average=False,
indices=None, sfreq=None, fmin=None,
fmax=None, fskip=0, faverage=False, sm_times=0,
sm_freqs=1, sm_kernel='hanning', padding=0,
mode='cwt_morlet', mt_bandwidth=None,
n_cycles=7, decim=1, n_jobs=1, verbose=None):
"""Compute time-frequency-domain connectivity measures.
This function computes spectral connectivity over time from epoched data.
The data may consist of a single epoch.
The connectivity method(s) are specified using the ``method`` parameter.
All methods are based on time-resolved estimates of the cross- and
power spectral densities (CSD/PSD) Sxy and Sxx, Syy.
Parameters
----------
data : array_like, shape (n_epochs, n_signals, n_times) | Epochs
The data from which to compute connectivity.
freqs : array_like
Array of frequencies of interest for time-frequency decomposition.
Only the frequencies within the range specified by ``fmin`` and
``fmax`` are used.
method : str | list of str
Connectivity measure(s) to compute. These can be
``['coh', 'plv', 'ciplv', 'pli', 'wpli']``. These are:
* 'coh' : Coherence
* 'plv' : Phase-Locking Value (PLV)
* 'ciplv' : Corrected imaginary Phase-Locking Value
* 'pli' : Phase-Lag Index
* 'wpli' : Weighted Phase-Lag Index
average : bool
Average connectivity scores over epochs. If ``True``, output will be
an instance of :class:`SpectralConnectivity`, otherwise
:class:`EpochSpectralConnectivity`.
indices : tuple of array_like | None
Two arrays with indices of connections for which to compute
connectivity. I.e. it is a ``(n_pairs, 2)`` array essentially.
If `None`, all connections are computed.
sfreq : float
The sampling frequency. Required if data is not
:class:`Epochs <mne.Epochs>`.
fmin : float | tuple of float | None
The lower frequency of interest. Multiple bands are defined using
a tuple, e.g., ``(8., 20.)`` for two bands with 8 Hz and 20 Hz lower
bounds. If `None`, the lowest frequency in ``freqs`` is used.
fmax : float | tuple of float | None
The upper frequency of interest. Multiple bands are defined using
a tuple, e.g. ``(13., 30.)`` for two band with 13 Hz and 30 Hz upper
bounds. If `None`, the highest frequency in ``freqs`` is used.
fskip : int
Omit every ``(fskip + 1)``-th frequency bin to decimate in frequency
domain.
faverage : bool
Average connectivity scores for each frequency band. If `True`,
the output ``freqs`` will be an array of the median frequencies of each
band.
sm_times : float
Amount of time to consider for the temporal smoothing in seconds.
If zero, no temporal smoothing is applied.
sm_freqs : int
Number of points for frequency smoothing. By default, 1 is used which
is equivalent to no smoothing.
sm_kernel : {'square', 'hanning'}
Smoothing kernel type. Choose either 'square' or 'hanning'.
padding : float
Amount of time to consider as padding at the beginning and end of each
epoch in seconds. See Notes for more information.
mode : str
Time-frequency decomposition method. Can be either: 'multitaper', or
'cwt_morlet'. See :func:`mne.time_frequency.tfr_array_multitaper` and
:func:`mne.time_frequency.tfr_array_morlet` for reference.
mt_bandwidth : float | None
Product between the temporal window length (in seconds) and the full
frequency bandwidth (in Hz). This product can be seen as the surface
of the window on the time/frequency plane and controls the frequency
bandwidth (thus the frequency resolution) and the number of good
tapers. See :func:`mne.time_frequency.tfr_array_multitaper`
documentation.
n_cycles : float | array_like of float
Number of cycles in the wavelet, either a fixed number or one per
frequency. The number of cycles ``n_cycles`` and the frequencies of
interest ``cwt_freqs`` define the temporal window length. For details,
see :func:`mne.time_frequency.tfr_array_morlet` documentation.
decim : int
To reduce memory usage, decimation factor after time-frequency
decomposition. Returns ``tfr[…, ::decim]``.
n_jobs : int
Number of connections to compute in parallel. Memory mapping must be
activated. Please see the Notes section for details.
%(verbose)s
Returns
-------
con : instance of Connectivity | list
Computed connectivity measure(s). An instance of
:class:`EpochSpectralConnectivity`, :class:`SpectralConnectivity`
or a list of instances corresponding to connectivity measures if
several connectivity measures are specified.
The shape of each connectivity dataset is
(n_epochs, n_signals, n_signals, n_freqs) when ``indices`` is `None`
and (n_epochs, n_nodes, n_nodes, n_freqs) when ``indices`` is specified
and ``n_nodes = len(indices[0])``.
See Also
--------
mne_connectivity.spectral_connectivity_epochs
mne_connectivity.SpectralConnectivity
mne_connectivity.EpochSpectralConnectivity
Notes
-----
Please note that the interpretation of the measures in this function
depends on the data and underlying assumptions and does not necessarily
reflect a causal relationship between brain regions.
The connectivity measures are computed over time within each epoch and
optionally averaged over epochs. High connectivity values indicate that
the phase coupling (interpreted as estimated connectivity) differences
between signals stay consistent over time.
The spectral densities can be estimated using a multitaper method with
digital prolate spheroidal sequence (DPSS) windows, or a continuous wavelet
transform using Morlet wavelets. The spectral estimation mode is specified
using the ``mode`` parameter.
When using the multitaper spectral estimation method, the
cross-spectral density is computed separately for each taper and aggregated
using a weighted average, where the weights correspond to the concentration
ratios between the DPSS windows.
Spectral estimation using multitaper or Morlet wavelets introduces edge
effects that depend on the length of the wavelet. To remove edge effects,
the parameter ``padding`` can be used to prune the edges of the signal.
Please see the documentation of
:func:`mne.time_frequency.tfr_array_multitaper` and
:func:`mne.time_frequency.tfr_array_morlet` for details on wavelet length
(i.e., time window length).
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 = spectral_connectivity_time(data, method='coh',
indices=indices, ...)
In this case ``con.get_data().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])
'plv' : Phase-Locking Value (PLV) :footcite:`LachauxEtAl1999` given
by::
PLV = |E[Sxy/|Sxy|]|
'ciplv' : Corrected imaginary PLV (icPLV) :footcite:`BrunaEtAl2018`
given by::
|E[Im(Sxy/|Sxy|)]|
ciPLV = ------------------------------------
sqrt(1 - |E[real(Sxy/|Sxy|)]| ** 2)
'pli' : Phase Lag Index (PLI) :footcite:`StamEtAl2007` given by::
PLI = |E[sign(Im(Sxy))]|
'wpli' : Weighted Phase Lag Index (WPLI) :footcite:`VinckEtAl2011`
given by::
|E[Im(Sxy)]|
WPLI = ------------------
E[|Im(Sxy)|]
Parallel computation can be activated by setting the ``n_jobs`` parameter.
Under the hood, this utilizes the ``joblib`` library. For effective
parallelization, you should activate memory mapping in MNE-Python by
setting ``MNE_MEMMAP_MIN_SIZE`` and ``MNE_CACHE_DIR``. Activating memory
mapping will make ``joblib`` store arrays greater than the minimum size on
disc, and forego direct RAM access for more efficient processing.
For example, in your code, run
mne.set_config('MNE_MEMMAP_MIN_SIZE', '10M')
mne.set_config('MNE_CACHE_DIR', '/dev/shm')
When ``MNE_MEMMAP_MIN_SIZE=None``, the underlying joblib implementation
results in pickling and unpickling the whole array each time a pair of
indices is accessed, which is slow, compared to memory mapping the array.
This function is based on the ``frites.conn.conn_spec`` implementation in
Frites.
.. versionadded:: 0.3
References
----------
.. footbibliography::
"""
events = None
event_id = None
# extract data from Epochs object
if isinstance(data, BaseEpochs):
names = data.ch_names
sfreq = data.info['sfreq']
events = data.events
event_id = data.event_id
n_epochs, n_signals, n_times = data.get_data().shape
# Extract metadata from the Epochs data structure.
# Make Annotations persist through by adding them to the metadata.
metadata = data.metadata
if metadata is None:
annots_in_metadata = False
else:
annots_in_metadata = all(
name not in metadata.columns for name in [
'annot_onset', 'annot_duration', 'annot_description'])
if hasattr(data, 'annotations') and not annots_in_metadata:
data.add_annotations_to_metadata(overwrite=True)
metadata = data.metadata
data = data.get_data()
else:
data = np.asarray(data)
n_epochs, n_signals, n_times = data.shape
names = np.arange(0, n_signals)
metadata = None
if sfreq is None:
raise ValueError('Sampling frequency (sfreq) is required with '
'array input.')
# check that method is a list
if isinstance(method, str):
method = [method]
# defaults for fmin and fmax
if fmin is None:
fmin = np.min(freqs)
logger.info('Fmin was not specified. Using fmin=min(freqs)')
if fmax is None:
fmax = np.max(freqs)
logger.info('Fmax was not specified. Using fmax=max(freqs).')
fmin = np.array((fmin,), dtype=float).ravel()
fmax = np.array((fmax,), dtype=float).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')
# convert kernel width in time to samples
if isinstance(sm_times, (int, float)):
sm_times = int(np.round(sm_times * sfreq))
# convert frequency smoothing from hz to samples
if isinstance(sm_freqs, (int, float)):
sm_freqs = int(np.round(max(sm_freqs, 1)))
# temporal decimation
if isinstance(decim, int):
sm_times = int(np.round(sm_times / decim))
sm_times = max(sm_times, 1)
# Create smoothing kernel
kernel = _create_kernel(sm_times, sm_freqs, kernel=sm_kernel)
# get indices of pairs of (group) regions
if indices is None:
indices_use = np.tril_indices(n_signals, k=-1)
else:
indices_use = check_indices(indices)
source_idx = indices_use[0]
target_idx = indices_use[1]
n_pairs = len(source_idx)
# check freqs
if isinstance(freqs, (int, float)):
freqs = [freqs]
# array conversion
freqs = np.asarray(freqs)
# check order for multiple frequencies
if len(freqs) >= 2:
delta_f = np.diff(freqs)
increase = np.all(delta_f > 0)
assert increase, "Frequencies should be in increasing order"
# check that freqs corresponds to at least n_cycles cycles
dur = float(n_times) / sfreq
cycle_freq = n_cycles / dur
if np.any(freqs < cycle_freq):
raise ValueError('At least one value in n_cycles corresponds to a'
'wavelet longer than the signal. Use less cycles, '
'higher frequencies, or longer epochs.')
# check for Nyquist
if np.any(freqs > sfreq / 2):
raise ValueError(f'Frequencies {freqs[freqs > sfreq / 2]} Hz are '
f'larger than Nyquist = {sfreq / 2:.2f} Hz')
# compute frequency mask based on specified min/max and decimation factor
freq_mask = _compute_freq_mask(freqs, fmin, fmax, fskip)
# the frequency points where we compute connectivity
freqs = freqs[freq_mask]
# compute central frequencies
_f = xr.DataArray(np.arange(len(freqs)), dims=('freqs',),
coords=(freqs,))
foi_s = _f.sel(freqs=fmin, method='nearest').data
foi_e = _f.sel(freqs=fmax, method='nearest').data
foi_idx = np.c_[foi_s, foi_e]
f_vec = freqs[foi_idx].mean(1)
if faverage:
n_freqs = len(fmin)
out_freqs = f_vec
else:
n_freqs = len(freqs)
out_freqs = freqs
conn = dict()
for m in method:
conn[m] = np.zeros((n_epochs, n_pairs, n_freqs))
logger.info('Connectivity computation...')
# parameters to pass to the connectivity function
call_params = dict(
method=method, kernel=kernel, foi_idx=foi_idx,
source_idx=source_idx, target_idx=target_idx,
mode=mode, sfreq=sfreq, freqs=freqs, faverage=faverage,
n_cycles=n_cycles, mt_bandwidth=mt_bandwidth,
decim=decim, padding=padding, kw_cwt={}, kw_mt={}, n_jobs=n_jobs,
verbose=verbose)
for epoch_idx in np.arange(n_epochs):
logger.info(f' Processing epoch {epoch_idx+1} / {n_epochs} ...')
conn_tr = _spectral_connectivity(data[epoch_idx], **call_params)
for m in method:
conn[m][epoch_idx] = np.stack(conn_tr[m], axis=0)
if indices is None:
conn_flat = conn
conn = dict()
for m in method:
this_conn = np.zeros((n_epochs, n_signals, n_signals) +
conn_flat[m].shape[2:],
dtype=conn_flat[m].dtype)
this_conn[:, source_idx, target_idx] = conn_flat[m]
this_conn = this_conn.reshape((n_epochs, n_signals ** 2,) +
conn_flat[m].shape[2:])
conn[m] = this_conn
# create a Connectivity container
if average:
out = [SpectralConnectivity(
conn[m].mean(axis=0), freqs=out_freqs, n_nodes=n_signals,
names=names, indices=indices, method=method, spec_method=mode,
events=events, event_id=event_id, metadata=metadata)
for m in method]
else:
out = [EpochSpectralConnectivity(
conn[m], freqs=out_freqs, n_nodes=n_signals, names=names,
indices=indices, method=method, spec_method=mode, events=events,
event_id=event_id, metadata=metadata) for m in method]
logger.info('[Connectivity computation done]')
# return the object instead of list of length one
if len(out) == 1:
return out[0]
else:
return out
def _spectral_connectivity(data, method, kernel, foi_idx,
source_idx, target_idx,
mode, sfreq, freqs, faverage, n_cycles,
mt_bandwidth, decim, padding, kw_cwt, kw_mt,
n_jobs, verbose):
"""Estimate time-resolved connectivity for one epoch.
Parameters
----------
data : array_like, shape (n_channels, n_times)
Time-series data.
method : list of str
List of connectivity metrics to compute.
kernel : array_like, shape (n_sm_fres, n_sm_times)
Smoothing kernel.
foi_idx : array_like, shape (n_foi, 2)
Upper and lower bound indices of frequency bands.
source_idx : array_like, shape (n_pairs,)
Defines the signal pairs of interest together with ``target_idx``.
target_idx : array_like, shape (n_pairs,)
Defines the signal pairs of interest together with ``source_idx``.
mode : str
Time-frequency transformation method.
sfreq : float
Sampling frequency.
freqs : array_like
Array of frequencies of interest for time-frequency decomposition.
Only the frequencies within the range specified by ``fmin`` and
``fmax`` are used.
faverage : bool
Average over frequency bands.
n_cycles : float | array_like of float
Number of cycles in the wavelet, either a fixed number or one per
frequency.
mt_bandwidth : float | None
Multitaper time-bandwidth.
decim : int
Decimation factor after time-frequency
decomposition.
padding : float
Amount of time to consider as padding at the beginning and end of each
epoch in seconds.
Returns
-------
this_conn : list of array
List of connectivity estimates corresponding to the metrics in
``method``. Each element is an array of shape (n_pairs, n_freqs) or
(n_pairs, n_fbands) if ``faverage`` is `True`.
"""
n_pairs = len(source_idx)
data = np.expand_dims(data, axis=0)
if mode == 'cwt_morlet':
out = tfr_array_morlet(
data, sfreq, freqs, n_cycles=n_cycles, output='complex',
decim=decim, n_jobs=n_jobs, **kw_cwt)
out = np.expand_dims(out, axis=2) # same dims with multitaper
weights = None
elif mode == 'multitaper':
out = tfr_array_multitaper(
data, sfreq, freqs, n_cycles=n_cycles,
time_bandwidth=mt_bandwidth, output='complex', decim=decim,
n_jobs=n_jobs, **kw_mt)
if isinstance(n_cycles, (int, float)):
n_cycles = [n_cycles] * len(freqs)
mt_bandwidth = mt_bandwidth if mt_bandwidth else 4
n_tapers = int(np.floor(mt_bandwidth - 1))
weights = np.zeros((n_tapers, len(freqs), out.shape[-1]))
for i, (f, n_c) in enumerate(zip(freqs, n_cycles)):
window_length = np.arange(0., n_c / float(f), 1.0 / sfreq).shape[0]
half_nbw = mt_bandwidth / 2.
n_tapers = int(np.floor(mt_bandwidth - 1))
_, eigvals = dpss_windows(window_length, half_nbw, n_tapers,
sym=False)
weights[:, i, :] = np.sqrt(eigvals[:, np.newaxis])
# weights have shape (n_tapers, n_freqs, n_times)
else:
raise ValueError("Mode must be 'cwt_morlet' or 'multitaper'.")
out = np.squeeze(out, axis=0)
if padding:
if padding < 0:
raise ValueError(f'Padding cannot be negative, got {padding}.')
if padding >= data.shape[-1] / sfreq / 2:
raise ValueError(f'Padding cannot be larger than half of data '
f'length, got {padding}.')
pad_idx = int(np.floor(padding * sfreq / decim))
out = out[..., pad_idx:-pad_idx]
weights = weights[..., pad_idx:-pad_idx] if weights is not None \
else None
# compute for each connectivity method
this_conn = {}
conn = _parallel_con(out, method, kernel, foi_idx, source_idx, target_idx,
n_jobs, verbose, n_pairs, faverage, weights)
for i, m in enumerate(method):
this_conn[m] = [out[i] for out in conn]
return this_conn
###############################################################################
###############################################################################
# TIME-RESOLVED CORE FUNCTIONS
###############################################################################
###############################################################################
def _parallel_con(w, method, kernel, foi_idx, source_idx, target_idx, n_jobs,
verbose, total, faverage, weights):
"""Compute spectral connectivity in parallel.
Parameters
----------
w : array_like, shape (n_chans, n_tapers, n_freqs, n_times)
Time-frequency data (complex signal).
method : list of str
List of connectivity metrics to compute.
kernel : array_like, shape (n_sm_fres, n_sm_times)
Smoothing kernel.
foi_idx : array_like, shape (n_foi, 2)
Upper and lower bound indices of frequency bands.
source_idx : array_like, shape (n_pairs,)
Defines the signal pairs of interest together with ``target_idx``.
target_idx : array_like, shape (n_pairs,)
Defines the signal pairs of interest together with ``source_idx``.
n_jobs : int
Number of parallel jobs.
total : int
Number of pairs of signals.
faverage : bool
Average over frequency bands.
weights : array_like, shape (n_tapers, n_freqs, n_times)
Multitaper weights.
Returns
-------
out : array_like, shape (n_pairs, n_methods, n_freqs_out)
Connectivity estimates for each signal pair, method, and frequency or
frequency band.
"""
if 'coh' in method:
# psd
if weights is not None:
psd = weights * w
psd = psd * np.conj(psd)
psd = psd.real.sum(axis=1)
psd = psd * 2 / (weights * weights.conj()).real.sum(axis=0)
else:
psd = w.real ** 2 + w.imag ** 2
psd = np.squeeze(psd, axis=1)
# smooth
psd = _smooth_spectra(psd, kernel)
else:
psd = None
# only show progress if verbosity level is DEBUG
if verbose != 'DEBUG' and verbose != 'debug' and verbose != 10:
total = None
# define the function to compute in parallel
parallel, my_pairwise_con, n_jobs = parallel_func(
_pairwise_con, n_jobs=n_jobs, verbose=verbose, total=total)
return parallel(
my_pairwise_con(w, psd, s, t, method, kernel,
foi_idx, faverage, weights)
for s, t in zip(source_idx, target_idx))
def _pairwise_con(w, psd, x, y, method, kernel, foi_idx,
faverage, weights):
"""Compute spectral connectivity metrics between two signals.
Parameters
----------
w : array_like, shape (n_chans, n_tapers, n_freqs, n_times)
Time-frequency data.
psd : array_like, shape (n_chans, n_freqs, n_times)
Power spectrum between signals ``x`` and ``y``.
x : int
Channel index.
y : int
Channel index.
method : str
Connectivity method.
kernel : array_like, shape (n_sm_fres, n_sm_times)
Smoothing kernel.
foi_idx : array_like, shape (n_foi, 2)
Upper and lower bound indices of frequency bands.
faverage : bool
Average over frequency bands.
weights : array_like, shape (n_tapers, n_freqs, n_times) | None
Multitaper weights.
Returns
-------
out : list
List of connectivity estimates between signals ``x`` and ``y``
corresponding to the methods in ``method``. Each element is an array
with shape (n_freqs,) or (n_fbands) depending on ``faverage``.
"""
w_x, w_y = w[x], w[y]
if weights is not None:
s_xy = np.sum(weights * w_x * np.conj(weights * w_y), axis=0)
s_xy = s_xy * 2 / (weights * np.conj(weights)).real.sum(axis=0)
else:
s_xy = w_x * np.conj(w_y)
s_xy = np.squeeze(s_xy, axis=0)
s_xy = _smooth_spectra(s_xy, kernel)
out = []
conn_func = {'plv': _plv, 'ciplv': _ciplv, 'pli': _pli, 'wpli': _wpli,
'coh': _coh}
for m in method:
if m == 'coh':
s_xx = psd[x]
s_yy = psd[y]
out.append(conn_func[m](s_xx, s_yy, s_xy))
else:
out.append(conn_func[m](s_xy))
for i, _ in enumerate(out):
# mean inside frequency sliding window (if needed)
if isinstance(foi_idx, np.ndarray) and faverage:
out[i] = _foi_average(out[i], foi_idx)
# squeeze time dimension
out[i] = out[i].squeeze(axis=-1)
return out
def _plv(s_xy):
s_xy = s_xy / np.abs(s_xy)
plv = np.abs(s_xy.mean(axis=-1, keepdims=True))
return plv
def _ciplv(s_xy):
s_xy = s_xy / np.abs(s_xy)
rplv = np.abs(np.mean(np.real(s_xy), axis=-1, keepdims=True))
iplv = np.abs(np.mean(np.imag(s_xy), axis=-1, keepdims=True))
ciplv = iplv / (np.sqrt(1 - rplv ** 2))
return ciplv
def _pli(s_xy):
pli = np.abs(np.mean(np.sign(np.imag(s_xy)),
axis=-1, keepdims=True))
return pli
def _wpli(s_xy):
con_num = np.abs(s_xy.imag.mean(axis=-1, keepdims=True))
con_den = np.mean(np.abs(s_xy.imag), axis=-1, keepdims=True)
wpli = con_num / con_den
return wpli
def _coh(s_xx, s_yy, s_xy):
con_num = np.abs(s_xy.mean(axis=-1, keepdims=True))
con_den = np.sqrt(s_xx.mean(axis=-1, keepdims=True) *
s_yy.mean(axis=-1, keepdims=True))
coh = con_num / con_den
return coh
def _compute_csd(x, y, weights):
"""Compute cross spectral density between signals x and y."""
if weights is not None:
s_xy = np.sum(weights * x * np.conj(weights * y), axis=-3)
s_xy = s_xy * 2 / (weights * np.conj(weights)).real.sum(axis=-3)
else:
s_xy = x * np.conj(y)
s_xy = np.squeeze(s_xy, axis=-3)
return s_xy
def _foi_average(conn, foi_idx):
"""Average inside frequency bands.
The frequency dimension should be located at -2.
Parameters
----------
conn : array_like, shape (..., n_freqs, n_times)
Connectivity estimate array.
foi_idx : array_like, shape (n_foi, 2)
Upper and lower frequency bounds of each frequency band.
Returns
-------
conn_f : np.ndarray, shape (..., n_fbands, n_times)
Connectivity estimate array, averaged within frequency bands.
"""
# get the number of foi
n_foi = foi_idx.shape[0]
# get input shape and replace n_freqs with the number of foi
sh = list(conn.shape)
sh[-2] = n_foi
# compute average
conn_f = np.zeros(sh, dtype=conn.dtype)
for n_f, (f_s, f_e) in enumerate(foi_idx):
f_e += 1 if f_s == f_e else f_e
conn_f[..., n_f, :] = conn[..., f_s:f_e, :].mean(-2)
return conn_f