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function [freq] = ft_spiketriggeredspectrum_stat(cfg, spike)
% FT_SPIKETRIGGEREDSPECTRUM_STAT computes phase-locking statistics for spike-LFP
% phases. These contain the PPC statistics according to Vinck et al. 2010 (Neuroimage)
% and Vinck et al. 2011 (Journal of Computational Neuroscience).
%
% Use as:
% [stat] = ft_spiketriggeredspectrum_stat(cfg, spike)
%
% The input SPIKE should be a structure as obtained from the FT_SPIKETRIGGEREDSPECTRUM function.
%
% Configurations (cfg)
%
% cfg.method = string, indicating which statistic to compute. Can be:
% -'plv' : phase-locking value, computes the resultant length over spike
% phases. More spikes -> lower value (bias).
% -'ang' : computes the angular mean of the spike phases.
% -'ral' : computes the rayleigh p-value.
% -'ppc0': computes the pairwise-phase consistency across all available
% spike pairs (Vinck et al., 2010).
% -'ppc1': computes the pairwise-phase consistency across all available
% spike pairs with exclusion of spike pairs in the same trial.
% This avoids history effects within spike-trains to influence
% phase lock statistics.
% -'ppc2': computes the PPC across all spike pairs with exclusion of
% spike pairs in the same trial, but applies a normalization
% for every set of trials. This estimator has more variance but
% is more robust against dependencies between spike phase and
% spike count.
%
% cfg.timwin = double or 'all' (default)
% - double: indicates we compute statistic with a
% sliding window of cfg.timwin, i.e. time-resolved analysis.
% - 'all': we compute statistic over all time-points,
% i.e. in non-time resolved fashion.
%
% cfg.winstepsize = double, stepsize of sliding window in seconds. For
% example if cfg.winstepsize = 0.1, we compute stat every other 100 ms.
%
% cfg.channel = Nx1 cell-array or numerical array with selection of
% channels (default = 'all'),See CHANNELSELECTION for details
%
% cfg.spikechannel = label of ONE unit, according to FT_CHANNELSELECTION
%
% cfg.spikesel = 'all' (default) or numerical or logical selection of spikes.
%
% cfg.foi = 'all' or numerical vector that specifies a subset of
% frequencies in Hz, e.g. cfg.foi = spike.freq(1:10);
%
% cfg.latency = [beg end] in sec, or 'maxperiod', 'poststim' or
% 'prestim'. This determines the start and end of analysis window.
%
% cfg.avgoverchan = 'weighted', 'unweighted' (default) or 'no'.
% This regulates averaging of fourierspectra prior to
% computing the statistic.
% - 'weighted' : we average across channels by weighting by the LFP power.
% This is identical to adding the raw LFP signals in time
% and then taking their FFT.
% - 'unweighted': we average across channels after normalizing for LFP power.
% This is identical to normalizing LFP signals for
% their power, averaging them, and then taking their FFT.
% - 'no' : no weighting is performed, statistic is computed for
% every LFP channel.
% cfg.trials = vector of indices (e.g., 1:2:10),
% logical selection of trials (e.g., [1010101010]), or
% 'all' (default)
%
% Main outputs:
% stat.nspikes = nChancmb-by-nFreqs-nTimepoints number
% of spikes used to compute stat
% stat.dimord = 'chan_freq_time'
% stat.labelcmb = nChancmbs cell-array with spike vs
% LFP labels
% stat.(cfg.method) = nChancmb-by-nFreqs-nTimepoints statistic
% stat.freq = 1xnFreqs array of frequencies
% stat.nspikes = number of spikes used to compute
%
% The output stat structure can be plotted using ft_singleplotTFR or ft_multiplotTFR.
% Copyright (C) 2012, 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/>.
%
% $Id$
% these are used by the ft_preamble/ft_postamble function and scripts
ft_revision = '$Id$';
ft_nargin = nargin;
ft_nargout = nargout;
% do the general setup of the function
ft_defaults
ft_preamble init
ft_preamble provenance spike
% check if the data is of spike format, and convert from old format if required
spike = ft_checkdata(spike,'datatype', 'spike', 'feedback', 'yes');
% get the options
cfg.method = ft_getopt(cfg, 'method', 'ppc1');
cfg.channel = ft_getopt(cfg, 'channel', 'all');
cfg.spikechannel = ft_getopt(cfg, 'spikechannel', spike.label{1});
cfg.latency = ft_getopt(cfg, 'latency', 'maxperiod');
cfg.spikesel = ft_getopt(cfg, 'spikesel', 'all');
cfg.avgoverchan = ft_getopt(cfg, 'avgoverchan', 'no');
cfg.foi = ft_getopt(cfg, 'foi', 'all');
cfg.trials = ft_getopt(cfg, 'trials', 'all');
cfg.timwin = ft_getopt(cfg, 'timwin', 'all');
cfg.winstepsize = ft_getopt(cfg, 'winstepsize', 0.01);
% ensure that the options are valid
cfg = ft_checkopt(cfg, 'method', 'char', {'ppc0', 'ppc1', 'ppc2', 'ang', 'ral', 'plv'});
cfg = ft_checkopt(cfg, 'foi',{'char', 'double'});
cfg = ft_checkopt(cfg, 'spikechannel',{'cell', 'char', 'double'});
cfg = ft_checkopt(cfg, 'channel', {'cell', 'char', 'double'});
cfg = ft_checkopt(cfg, 'spikesel', {'char', 'logical', 'double'});
cfg = ft_checkopt(cfg, 'avgoverchan', 'char', {'weighted', 'unweighted', 'no'});
cfg = ft_checkopt(cfg, 'latency', {'char', 'doublevector'});
cfg = ft_checkopt(cfg, 'trials', {'char', 'double', 'logical'});
cfg = ft_checkopt(cfg, 'timwin', {'double', 'char'});
cfg = ft_checkopt(cfg, 'winstepsize', {'double'});
cfg = ft_checkconfig(cfg, 'allowed', {'method', 'channel', 'spikechannel', 'latency', 'spikesel', 'avgoverchan', 'foi', 'trials', 'timwin', 'winstepsize'});
% collect channel information
cfg.channel = ft_channelselection(cfg.channel, spike.lfplabel);
chansel = match_str(spike.lfplabel, cfg.channel);
% get the spikechannels
spikelabel = spike.label;
cfg.spikechannel = ft_channelselection(cfg.spikechannel, spikelabel);
unitsel = match_str(spikelabel, cfg.spikechannel);
nspikesel = length(unitsel); % number of spike channels
if nspikesel>1, error('only one unit should be selected for now'); end
if nspikesel==0, error('no unit was selected'); end
% collect frequency information
if strcmp(cfg.foi, 'all'),
cfg.foi = spike.freq(:)';
freqindx = 1:length(spike.freq);
else
freqindx = zeros(1,length(foi));
for iFreq = 1:length(cfg.foi)
freqindx(iFreq) = nearest(spike.freq,cfg.foi(iFreq));
end
end
if length(freqindx)~=length(unique(freqindx))
error('Please select every frequency only once, are you sure you selected in Hz?')
end
nFreqs = length(freqindx);
cfg.foi = spike.freq(freqindx); % update the information again
% create the spike selection
nSpikes = length(spike.trial{unitsel});
if strcmp(cfg.spikesel,'all'),
cfg.spikesel = 1:length(spike.trial{unitsel});
elseif islogical(cfg.spikesel)
cfg.spikesel = find(cfg.spikesel);
end
if ~isempty(cfg.spikesel)
if max(cfg.spikesel)>nSpikes || length(cfg.spikesel)>nSpikes
error('cfg.spikesel must not exceed number of spikes and select every spike just once')
end
end
% select on basis of latency
if strcmp(cfg.latency, 'maxperiod'),
cfg.latency = [min(spike.trialtime(:)) max(spike.trialtime(:))];
elseif strcmp(cfg.latency,'prestim')
cfg.latency = [min(spike.trialtime(:)) 0];
elseif strcmp(cfg.latency,'poststim')
cfg.latency = [0 max(spike.trialtime(:))];
elseif ~isrealvec(cfg.latency) && length(cfg.latency)~=2
error('cfg.latency should be "maxperiod", "prestim", "poststim" or 1-by-2 numerical vector');
end
if cfg.latency(1)>=cfg.latency(2),
error('cfg.latency should be a vector in ascending order, i.e., cfg.latency(2)>cfg.latency(1)');
end
inWindow = find(spike.time{unitsel}>=cfg.latency(1) & cfg.latency(2)>=spike.time{unitsel});
% selection of the trials
cfg = trialselection(cfg,spike);
% do the final selection, and select on spike structure
isintrial = ismember(spike.trial{unitsel}, cfg.trials);
spikesel = intersect(cfg.spikesel(:),inWindow(:));
spikesel = intersect(spikesel,find(isintrial));
cfg.spikesel = spikesel;
spikenum = length(cfg.spikesel); % number of spikes that were finally selected
if isempty(spikenum), warning('No spikes were selected after applying cfg.latency, cfg.spikesel and cfg.trials'); end
spike.fourierspctrm = spike.fourierspctrm{unitsel}(cfg.spikesel,chansel,freqindx);
spike.time = spike.time{unitsel}(cfg.spikesel);
spike.trial = spike.trial{unitsel}(cfg.spikesel);
% average the lfp channels (weighted, unweighted, or not)
if strcmp(cfg.avgoverchan,'unweighted')
spike.fourierspctrm = spike.fourierspctrm ./ abs(spike.fourierspctrm); % normalize the angles before averaging
spike.fourierspctrm = nanmean(spike.fourierspctrm,2); % now rep x 1 x freq
nChans = 1;
outlabels = {'avgLFP'};
elseif strcmp(cfg.avgoverchan,'no')
nChans = length(chansel);
outlabels = cfg.channel;
elseif strcmp(cfg.avgoverchan,'weighted')
spike.fourierspctrm = nanmean(spike.fourierspctrm,2); % now rep x 1 x freq
outlabels = {'avgLFP'};
nChans = 1;
end
% normalize the spectrum first
spike.fourierspctrm = spike.fourierspctrm ./ abs(spike.fourierspctrm); % normalize the angles before averaging
ft_progress('init', 'text', 'Please wait...');
if strcmp(cfg.timwin,'all')
freq.time = 'all';
switch cfg.method
case 'ang'
out = angularmean(spike.fourierspctrm);
case 'plv'
out = resultantlength(spike.fourierspctrm);
case 'ral'
out = rayleightest(spike.fourierspctrm); % the rayleigh test
case 'ppc0'
out = ppc(spike.fourierspctrm);
case {'ppc1', 'ppc2'}
% check the final set of trials present in the spikes
trials = unique(spike.trial);
% loop init for PPC 2.0
[S,SS,dof,dofSS] = deal(zeros(1,nChans,nFreqs));
nTrials = length(trials);
if nTrials==1
warning('computing ppc1 or ppc2 can only be performed with more than 1 trial');
end
for iTrial = 1:nTrials % compute the firing rate
trialNum = trials(iTrial);
spikesInTrial = find(spike.trial == trialNum);
spc = spike.fourierspctrm(spikesInTrial,:,:);
ft_progress(iTrial/nTrials, 'Processing trial %d from %d', iTrial, nTrials);
% compute PPC 1.0 and 2.0 according to Vinck et al. (2011) using summation per trial
if strcmp(cfg.method,'ppc2')
if ~isempty(spc)
m = nanmean(spc,1); % no problem with NaN
hasNum = ~isnan(m);
S(hasNum) = S(hasNum) + m(hasNum); % add the imaginary and real components
SS(hasNum) = SS(hasNum) + m(hasNum).*conj(m(hasNum));
dof(hasNum) = dof(hasNum) + 1; % dof needs to be kept per frequency
end
elseif strcmp(cfg.method,'ppc1')
if ~isempty(spc)
n = sum(~isnan(spc),1);
m = nansum(spc,1);
hasNum = ~isnan(m);
S(hasNum) = S(hasNum) + m(hasNum); % add the imaginary and real components
SS(hasNum) = SS(hasNum) + m(hasNum).*conj(m(hasNum));
dof(hasNum) = dof(hasNum) + n(hasNum);
dofSS(hasNum) = dofSS(hasNum) + n(hasNum).^2;
end
end
end
[out] = deal(NaN(1,nChans,nFreqs));
hasTrl = dof>1;
if strcmp(cfg.method,'ppc1')
out(hasTrl) = (S(hasTrl).*conj(S(hasTrl)) - SS(hasTrl))./(dof(hasTrl).^2 - dofSS(hasTrl));
elseif strcmp(cfg.method, 'ppc2')
out(hasTrl) = (S(hasTrl).*conj(S(hasTrl)) - SS(hasTrl))./(dof(hasTrl).*(dof(hasTrl)-1));
end
end
nSpikes = sum(~isnan(spike.fourierspctrm));
else % compute time-resolved spectra of statistic
% make the sampling axis for the window
bins = cfg.latency(1):cfg.winstepsize:cfg.latency(2);
N = length(bins)-1; % number of bins
wintime = 0:cfg.winstepsize:cfg.timwin;
win = ones(1,length(wintime));
freq.time = (bins(2:end)+bins(1:end-1))/2;
if ~mod(length(win),2), win = [win 1]; end % make sure the number of samples is uneven.
out = NaN(N,nChans,nFreqs);
nSpikes = zeros(N,nChans,nFreqs);
for iChan = 1:nChans
for iFreq = 1:nFreqs
spctra = spike.fourierspctrm(:,iChan,iFreq); % values to accumulate
tm = spike.time;
hasnan = isnan(spctra);
tm(hasnan) = [];
spctra(hasnan) = [];
% compute the degree of freedom per time bin and the index for every spike
[dof, indx] = histc(tm, bins); % get the index per spike, and number per bin
if isempty(dof), continue,end
toDel = indx==length(bins) | indx==0; % delete those points that are equal to last output histc or don't fall in
spctra(toDel) = [];
indx(toDel) = [];
dof(end) = []; % the last bin is a single point in time, so we delete it
% compute the sum of spikes per window at every time point
dof = dof(:); % force it to be row
dof = conv2(dof(:),win(:),'same'); % get the total number of spikes across all trials
nSpikes(:,iChan,iFreq) = dof;
switch cfg.method
case {'ang', 'plv', 'ppc0', 'ral'}
% first create a vector with the phases at the samples
x = accumarray(indx(:),spctra,[N 1]); % simply the sum of the complex numbers
% then compute the sum of the spectra for every timepoint
y = conv2(x(:),win(:),'same');
% now compute the output statistic
hasnum = dof>1;
hasnum0 = dof>0;
if strcmp(cfg.method,'plv')
out(hasnum,iChan,iFreq) = abs(y(hasnum)./dof(hasnum));
elseif strcmp(cfg.method,'ral')
Z = abs(y).^2./dof;
P = exp(-Z) .* (1 + (2*Z - Z.^2)./(4*dof) -(24.*Z - 123*(Z.^2) + 76*(Z.^3) - 9*(Z.^4))./(288*dof.^2)); %Mardia 1972
out(hasnum,iChan,iFreq) = P(hasnum);
elseif strcmp(cfg.method,'ang')
out(hasnum0,iChan,iFreq) = angle(y(hasnum0)); %
elseif strcmp(cfg.method,'ppc0')
out(hasnum,iChan,iFreq) = (y(hasnum).*conj(y(hasnum)) - dof(hasnum))./(dof(hasnum).*(dof(hasnum)-1)); % simplest form of ppc
end
case {'ppc1', 'ppc2'}
trials = unique(spike.trial);
nTrials = length(trials);
[S,SS,dofS,dofSS] = deal(zeros(length(bins)-1,1));
if nTrials==1
warning('computing ppc1 or ppc2 can only be performed with more than 1 trial');
end
% compute the new ppc versions
for iTrial = 1:nTrials
ft_progress(iTrial/nTrials, 'Processing trial %d from %d for freq %d and chan %d', iTrial, nTrials, iFreq, iChan);
% select the spectra, time points, and trial numbers again
trialNum = trials(iTrial);
spikesInTrial = find(spike.trial == trialNum);
if isempty(spikesInTrial), continue,end
spctraTrial = spike.fourierspctrm(spikesInTrial,iChan,iFreq);
tm = spike.time;
hasnan = isnan(spctraTrial);
tm(hasnan) = [];
spctraTrial(hasnan) = [];
% bin the spikes and delete spikes out of the selected time
[dof, indx] = histc(tm(spikesInTrial), bins); % get the index per spike, and number per bin
dof(end) = [];
toDel = indx==length(bins) | indx==0; % delete those points that are equal to last output histc
spctraTrial(toDel,:,:) = []; % delete those spikes from fourierspctrm as well
indx(toDel) = []; % make sure index doesn't contain them
% first create a vector that sums the spctra
x = accumarray(indx(:),spctraTrial,[N 1]);
% then compute the moving average sum of this vector
y = conv2(x(:),win(:),'same'); % convolution again just means a sum
d = conv2(dof(:),win(:),'same'); % get the dof of spikes per trial
if strcmp(cfg.method,'ppc1')
S = S + y; % add the imaginary and real components
SS = SS + y.*conj(y);
dofS = dofS + d(:);
dofSS = dofSS + d(:).^2;
else
sl = d(:)>0;
m = y./d(:);
S(sl) = S(sl) + m(sl); % add the imaginary and real components
SS(sl) = SS(sl) + m(sl).*conj(m(sl));
dofS(sl) = dofS(sl) + 1;
end
end
% we need at least two trials
hasNum = dofS>1;
if strcmp(cfg.method,'ppc1')
out(hasNum,iChan,iFreq) = (S(hasNum).*conj(S(hasNum)) - SS(hasNum))./(dofS(hasNum).^2 - dofSS(hasNum));
else
out(hasNum,iChan,iFreq) = (S(hasNum).*conj(S(hasNum)) - SS(hasNum))./(dofS(hasNum).*(dofS(hasNum)-1));
end
end
end
end
end
ft_progress('close');
% collect the outputs: in labelcmb representation
outparam = cfg.method;
freq.(outparam) = permute(out,[2 3 1]);
freq.nspikes = permute(nSpikes,[2 3 1]); % also cross-unit purposes
freq.labelcmb = cell(nChans,2);
freq.labelcmb(1:nChans,1) = cfg.spikechannel;
for iCmb = 1:nChans
freq.labelcmb{iCmb,2} = outlabels{iCmb};
end
freq.freq = spike.freq(freqindx);
freq.dimord = 'chancmb_freq_time';
% do the general cleanup and bookkeeping at the end of the function
ft_postamble previous spike
ft_postamble provenance freq
ft_postamble history freq
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% SUBFUNCTION
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [P] = rayleightest(x)
n = sum(~isnan(x),1);
R = resultantlength(x);
Z = n.*R.^2;
P = exp(-Z).*...
(1 + (2*Z - Z.^2)./(4*n) -(24.*Z - 123*(Z.^2) + 76*(Z.^3) - 9*(Z.^4))./(288*n.^2)); %Mardia 1972
function [resLen] = resultantlength(angles)
n = sum(~isnan(angles),1);
resLen = abs(nansum(angles,1))./n; %calculate the circular variance
function [y] = ppc(crss)
dim = 1;
dof = sum(~isnan(crss),dim);
sinSum = abs(nansum(imag(crss),dim));
cosSum = nansum(real(crss),dim);
y = (cosSum.^2+sinSum.^2 - dof)./(dof.*(dof-1));
function [angMean] = angularmean(angles)
angMean = angle(nanmean(angles,1)); %get the mean angle
function [cfg] = trialselection(cfg,spike)
% get the number of trials or change DATA according to cfg.trials
nTrials = size(spike.trialtime,1);
if strcmp(cfg.trials, 'all')
cfg.trials = 1:nTrials;
elseif islogical(cfg.trials) || all(cfg.trials==0 | cfg.trials==1)
cfg.trials = find(cfg.trials);
end
cfg.trials = sort(cfg.trials(:));
if max(cfg.trials)>nTrials, warning('maximum trial number in cfg.trials should not exceed length of DATA.trial')
end
if isempty(cfg.trials), error('No trials were selected');
end
function m = nansum(x,dim)
% Find NaNs and set them to zero
nans = isnan(x);
x(nans) = 0;
if nargin == 1 % let sum deal with figuring out which dimension to use
% Count up non-NaNs.
n = sum(~nans);
n(n==0) = NaN; % prevent divideByZero warnings
% Sum up non-NaNs, and divide by the number of non-NaNs.
m = sum(x);
else
% Count up non-NaNs.
n = sum(~nans,dim);
n(n==0) = NaN; % prevent divideByZero warnings
% Sum up non-NaNs, and divide by the number of non-NaNs.
m = sum(x,dim);
end