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iCAPs/packages/spm12/external/fieldtrip/connectivity/ft_connectivity_wpli.m
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ft_connectivity_wpli.m
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function [wpli, v, n] = ft_connectivity_wpli(input, varargin)
% FT_CONNECTIVITY_WPLI computes the weighted phase lag index from a
% data-matrix containing a cross-spectral density. It implements the method
% described in: Vinck M, Oostenveld R, van Wingerden M, Battaglia F,
% Pennartz CM. An improved index of phase-synchronization for
% electrophysiological data in the presence of volume-conduction, noise and
% sample-size bias. Neuroimage. 2011 Apr 15;55(4):1548-65.
%
% Use as
% [wpi, v, n] = ft_connectivity_wpli(input, varargin)
%
% The input data input should be organized as:
%
% Repetitions x Channel x Channel (x Frequency) (x Time)
%
% or
%
% Repetitions x Channelcombination (x Frequency) (x Time)
%
% The first dimension should contain repetitions and should not contain an
% average already. Also, it should not consist of leave one out averages.
%
% Additional input arguments come as key-value pairs:
%
% dojack 1 or 0, compute a variance estimate, based on leave-one-out
% feedback 'none', 'text', 'textbar' type of feedback showing progress of
% computation
% debias 1 (or true) or 0 (or false), compute debiased wpli or not
%
% The output wpli contains the wpli, v is a leave-one-out variance estimate
% which is only computed if dojack = 1,and n is the number of repetitions
% in the input data.
%
% See also FT_CONNECTIVITYANALYSIS
% Copyright (C) 2011, Martin Vinck
%
% This file is part of FieldTrip, see http://www.fieldtriptoolbox.org
% for the documentation and details.
%
% FieldTrip is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% FieldTrip is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with FieldTrip. If not, see <http://www.gnu.org/licenses/>.
%
% $Id$
feedback = ft_getopt(varargin, 'feedback', 'none');
debias = ft_getopt(varargin, 'debias');
dojack = ft_getopt(varargin, 'dojack');
siz = size(input);
n = siz(1);
ft_progress('init', feedback, 'computing metric...');
if n>1
input = imag(input); % make everything imaginary
outsum = nansum(input,1); % compute the sum; this is 1 x size(2:end)
outsumW = nansum(abs(input),1); % normalization of the WPLI
if debias
outssq = nansum(input.^2,1);
wpli = (outsum.^2 - outssq)./(outsumW.^2 - outssq); % do the pairwise thing in a handy way
else
wpli = outsum./outsumW; % estimator of E(Im(X))/E(|Im(X)|)
end
wpli = reshape(wpli,siz(2:end)); % remove the first singular dimension
else
wpli = NaN(siz(2:end)); % for one observation, we should return NaNs
ft_warning('ft_connectivity_wpli:nTrials', 'computation wpli requires >1 trial, returning NaNs');
end
[leave1outsum, leave1outssq] = deal(zeros([1 siz(2:end)]));
if dojack && n>2 % n needs to be larger than 2 to get a meaningful variance
for k = 1:n
s = outsum - input(k,:,:,:,:,:,:); % works for any array up to 7-D
sw = outsumW - abs(input(k,:,:,:,:,:,:));
if debias
sq = outssq - input(k,:,:,:,:,:,:).^2;
num = s.^2 - sq;
denom = sw.^2 - sq;
else
num = s; % this is estimator of E(Im(X))
denom = sw; % estimator of E(|Im(X)|)
end
tmp = num./denom; % avoids doing the division twice
tmp(isnan(tmp)) = 0; % added for nan support
leave1outsum = leave1outsum + tmp;% added this for nan support
leave1outssq = leave1outssq + tmp.^2; % added this for nan support
end
% compute the sem here
n = sum(~isnan(input),1); % this is the actual df when nans are found in the input matrix
v = (n-1).^2.*(leave1outssq - (leave1outsum.^2)./n)./(n - 1); % 11.5 efron, sqrt and 1/n done in ft_connectivityanalysis
v = reshape(v,siz(2:end)); % remove the first singular dimension
n = reshape(n,siz(2:end));
elseif dojack && n<=2
v = NaN(siz(2:end));
else
v = [];
end
ft_progress('close');
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