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function mse = ft_entropyanalysis(cfg, data)
% FT_ENTROPYANALYSIS performs entropy and time-entropy analysis
% on time series data over multiple trials
%
% Use as
% mse = ft_entropyanalysis(cfg, data)
%
% The input data should be organised in a structure as obtained from
% the FT_PREPROCESSING function. The configuration
% depends on the type of computation that you want to perform.
%
% cfg is a configuration structure that should contain
%
% cfg.toi = vector 1 x numtoi, the times on which the analysis
% windows should be centered (in seconds).
% cfg.timwin = vector 1 x numfoi, length of time window (in seconds)
% cfg.timescales = vector 1 x numtimescales, the time scales to compute MSE for.
% Scale 1 is the fastest scale, i.e. sample entropy at the native
% sampling rate of the signal. Slower scales are achieved
% by coarse graining the data. The highest scales achievable
% is determined by pattern length m and the time window timwin: at
% least m+1 samples need to be present in the time window
% for MSE computation at this scale.
% cfg.coarsegrainmethod = string, method used for coarse% graining:'filt_skip'
% (default) (filter, then skip points) or 'pointavg'
% (average groups of timepoints)
% cfg.filtmethod = string, method used for filtering: {lp, hp, bp, no}
% cfg.m = pattern length for MSE computation, default is 2
% cfg.r = similarity criterion, set as a fraction of the time
% series SD. Default is 0.5.
% cfg.recompute_r = recompute r parameter. 'perscale' or 'perscale_toi_sp'
% (default)
% cfg.polyremoval = number (default = 0), specifying the order of the
% polynome which is fitted and subtracted from the time
% domain data prior to the spectral analysis. For
% example, a value of 1 corresponds to a linear trend.
% The default is a mean subtraction, thus a value of 0.
% If no removal is requested, specify -1.
% see FT_PREPROC_POLYREMOVAL for details
% cfg.mem_available = Memory available to perform computations (default
% 8e9 bytes).
% cfg.allowgpu = 1 to use gpu if available, 0 to force
% cpu computation (default 1). if a gpu is found,
% available memory on that gpu is used.
%
%
% The configuration can optionally contain
% cfg.option3 = value, explain it here (default is automatic)
%
% To facilitate data-handling and distributed computing you can use
% cfg.inputfile = ...
% cfg.outputfile = ...
% If you specify one of these (or both) the input data will be read from a *.mat
% file on disk and/or the output data will be written to a *.mat file. These mat
% files should contain only a single variable, corresponding with the
% input/output structure.
%
% See also <<give a list of function names, all in capitals>>
% Copyright (C) 2018, MPIB Berlin, Niels Kloosterman
%
% Here comes the Revision tag, which is auto-updated by the version control system
% $Id$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% the initial part deals with parsing the input options and data
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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
% the ft_preamble function works by calling a number of scripts from
% fieldtrip/utility/private that are able to modify the local workspace
ft_defaults % this ensures that the path is correct and that the ft_defaults global variable is available
ft_preamble init % this will reset ft_warning and show the function help if nargin==0 and return an error
ft_preamble debug % this allows for displaying or saving the function name and input arguments upon an error
ft_preamble loadvar data % this reads the input data in case the user specified the cfg.inputfile option
ft_preamble provenance data % this records the time and memory usage at the beginning of the function
ft_preamble trackconfig % this converts the cfg structure in a config object, which tracks the cfg options that are being used
% the ft_abort variable is set to true or false in ft_preamble_init
if ft_abort
% do not continue function execution in case the outputfile is present and the user indicated to keep it
return
end
% ensure that the input data is valid for this function, this will also do
% backward-compatibility conversions of old data that for example was
% read from an old *.mat file
data = ft_checkdata(data, 'datatype', {'raw+comp', 'raw'}, 'feedback', 'yes', 'hassampleinfo', 'yes');
% % TODO check if the input cfg is valid for this function
% cfg = ft_checkconfig(cfg, 'renamed', {'blc', 'demean'});
% cfg = ft_checkconfig(cfg, 'renamed', {'blcwindow', 'baselinewindow'});
% ensure that the required options are present
cfg = ft_checkconfig(cfg, 'required', {'toi', 'timescales' 'filtmethod'});
% ensure that the options are valid
cfg = ft_checkopt(cfg, 'recompute_r', 'char', {'perscale_toi_sp', 'per_scale', 'per_toi'});
cfg = ft_checkopt(cfg, 'coarsegrainmethod', 'char', {'filtskip', 'pointavg'});
cfg = ft_checkopt(cfg, 'filtmethod', 'char', {'lp', 'hp', 'bp', 'no'});
% get the options
cfg.trials = ft_getopt(cfg, 'trials', 'all', 1);
cfg.channel = ft_getopt(cfg, 'channel', 'all');
toi = ft_getopt(cfg, 'toi'); % time points for mse, e.g. cfg.toi = -0.75:0.05:1.5;
timescales = ft_getopt(cfg, 'timescales'); % time scales, depends on sample rate and winsize
timwin = ft_getopt(cfg, 'timwin', 0.5); % e.g. 0.5 s
m = ft_getopt(cfg, 'm', 2); % pattern length, e.g. 2
r = ft_getopt(cfg, 'r', 0.5); % similarity criterion, 0.5
polyremoval = ft_getopt(cfg, 'polyremoval', 0);
recompute_r = ft_getopt(cfg, 'recompute_r', 'perscale_toi_sp'); % recompute r for each scale (1)
coarsegrainmethod = ft_getopt(cfg, 'coarsegrainmethod', 'filtskip'); % coarsening_filt_skip or coarsening_avg
filtmethod = ft_getopt(cfg, 'filtmethod', 'lp');
mem_available = ft_getopt(cfg, 'mem_available', 8e9); % 8 GB
allowgpu = ft_getopt(cfg, 'allowgpu', 1); % 8 GB
if strcmp(cfg.coarsegrainmethod, 'pointavg')
filtmethod = 'no'; % no filtering for point averaging
end
gpuavailable = gpuDeviceCount;
if allowgpu && gpuavailable
fprintf('GPU device found. Running things there\n')
gpu = gpuDevice;
mem_available = gpu.AvailableMemory * 0.6; % only use % of available mem, other vars also required there
end
% select channels and trials of interest, by default this will select all channels and trials
tmpcfg = keepfields(cfg, {'trials', 'channel', 'showcallinfo'});
data = ft_selectdata(tmpcfg, data);
% restore the provenance information
%[cfg, data] = rollback_provenance(cfg, data);
% make sure there are no nans in raw data (e.g. if coming from timelock with var trl lengths)
ntrials = length(data.trial);
cfgtmp = [];
cfgtmp.begsample = nan(ntrials,1);
cfgtmp.endsample = nan(ntrials,1);
for itrial = 1:ntrials
nonnans = find(~isnan(data.trial{itrial}(1,:)));
cfgtmp.begsample(itrial,:) = nonnans(1);
cfgtmp.endsample(itrial,:) = nonnans(end);
end
data = ft_redefinetrial(cfgtmp, data);
clear cfgtmp nonnans
% demean the trials
if polyremoval >= 0
for itrial = 1:ntrials
ndatsample = size(data.trial{itrial}, 2);
data.trial{itrial} = ft_preproc_polyremoval(data.trial{itrial}, polyremoval, 1, ndatsample);
end
end
% preallocate matrices
nchan = length(data.label);
nscales = length(timescales);
ntoi = size(toi,2);
sampen = nan(nchan, nscales, ntoi);
r_estimate = nan(nchan, nscales, ntoi, nscales); % dimord chan nsc ntoi nstartingpts
for s = 1:numel(timescales) % loop through timescales
sc = timescales(s);
% apply filtering here
switch filtmethod
case 'lp'
if sc == 1
data_filt = data;
else
fs = data.fsample;
nyquist = (fs/2);
fcLowPass = (1/sc)*nyquist;
if fcLowPass == nyquist
fcLowPass = fcLowPass-1;
end
[B,A] = butter(6,fcLowPass/nyquist);
cfg.freq(1,s) = fcLowPass;
padlength = ceil(size(data.trial{1},2)./2); % use half the length of trial 1 as padding (JQK)
x_pad = cellfun(@(a) ft_preproc_padding(a, 'mean', padlength), data.trial, 'UniformOutput', false ); % add padding
x_pad = cellfun(@transpose, x_pad, 'UniformOutput', false); % transpose for filtfilt: time x chan
resamp_x_pad = cellfun(@(x_pad) filtfilt(B,A,x_pad), x_pad, 'UniformOutput', false ); % filter data
resamp_x_pad = cellfun(@transpose, resamp_x_pad, 'UniformOutput', false); % transpose back : chan x time again
resamp_x = cellfun(@(resamp_x_pad) ft_preproc_padding(resamp_x_pad, 'remove', padlength), resamp_x_pad, 'UniformOutput', false ); % remove padding
% create data_filt structure
data_filt = data;
data_filt.trial = resamp_x;
clear resamp_* x_pad;
end
case 'bp'
fs = data.fsample;
nyquist = fs/2;
fcLowPass = (1/sc)*nyquist;
if fcLowPass == nyquist
fcLowPass = fcLowPass-1;
end
if s == numel(timescales)
fcHighPass = 0.5;
else
fcHighPass = (1/(timescales(s+1)))*nyquist;
end
[B,A] = butter(6,fcLowPass/nyquist); % define low-pass filter: https://de.mathworks.com/help/signal/ref/butter.html
[D,C] = butter(6,fcHighPass/nyquist, 'high'); % define high-pass filter
cfg.freq(1,s) = fcLowPass;
cfg.freq(2,s) = fcHighPass;
padlength = ceil(size(data.trial{1},2)./2); % use half the length of trial 1 as padding (JQK)
x_pad = cellfun(@(a) ft_preproc_padding(a, 'mean', padlength), data.trial, 'UniformOutput', false ); % add padding
x_pad = cellfun(@transpose, x_pad, 'UniformOutput', false); % transpose for filtfilt: time x chan
if sc == 1 % only HPF
resamp_x_pad = cellfun(@(x_pad) filtfilt(D,C,x_pad), x_pad, 'UniformOutput', false ); % high-pass filter data
else
resamp_x_pad = cellfun(@(x_pad) filtfilt(B,A,x_pad), x_pad, 'UniformOutput', false ); % low-pass filter data
resamp_x_pad = cellfun(@(resamp_x_pad) filtfilt(D,C,resamp_x_pad), resamp_x_pad, 'UniformOutput', false ); % high-pass filter data
end
resamp_x_pad = cellfun(@transpose, resamp_x_pad, 'UniformOutput', false); % transpose back : chan x time again
resamp_x = cellfun(@(resamp_x_pad) ft_preproc_padding(resamp_x_pad, 'remove', padlength), ... % remove padding
resamp_x_pad, 'UniformOutput', false );
%figure; hold on; plot(resamp_x{1}(1,:)); plot(data.trial{1}(1,:))
% create data_filt structure
data_filt = data;
data_filt.trial = resamp_x;
clear resamp_* x_pad;
case 'hp'
fs = data.fsample;
nyquist = (fs/2);
fcHighPass = (1/(sc+1))*nyquist;
[D,C] = butter(6,fcHighPass/nyquist, 'high'); % define high-pass filter
cfg.freq(1,s) = fcHighPass;
padlength = ceil(size(data.trial{1},2)./2); % use half the length of trial 1 as padding (JQK)
x_pad = cellfun(@(a) ft_preproc_padding(a, 'mean', padlength), data.trial, 'UniformOutput', false ); % add padding
x_pad = cellfun(@transpose, x_pad, 'UniformOutput', false); % transpose for filtfilt: time x chan
resamp_x_pad = cellfun(@(x_pad) filtfilt(D,C,x_pad), x_pad, 'UniformOutput', false ); % low-pass filter data
resamp_x_pad = cellfun(@transpose, resamp_x_pad, 'UniformOutput', false); % transpose back : chan x time again
resamp_x = cellfun(@(resamp_x_pad) ft_preproc_padding(resamp_x_pad, 'remove', padlength), ... % remove padding
resamp_x_pad, 'UniformOutput', false );
%figure; hold on; plot(resamp_x{1}(1,:)); plot(data_sel.trial{1}(1,:))
% create data_filt structure
data_filt = data;
data_filt.trial = resamp_x;
clear resamp_* x_pad;
case 'no'
data_filt = data;
end
if strcmp(recompute_r, 'per_scale') % recompute r for each scale or: sc toi sp
% per_scale
% per_toi
% pertoi_sp (fixed per scale)
% perscale_toi_sp (run til now)
% perscale_toi
r_new = r * std(cell2mat(data_filt.trial),1,2);
end
for itoi = 1:ntoi
fprintf('Scale %d of %d; Time %d of %d\n', s, length(timescales),itoi, ntoi)
% select time window of interest from each trial
tmpcfg=[];
tmpcfg.toilim = [toi(itoi)-timwin*0.5 toi(itoi)+timwin*0.5];
tmpcfg.showcallinfo = 'no';
data_sel = ft_redefinetrial(tmpcfg, data_filt);
% only take trials that have the whole interval
tmpcfg = [];
tmpcfg.minlength = timwin;
tmpcfg.showcallinfo = 'no';
data_sel = ft_redefinetrial(tmpcfg, data_sel);
% need 40 samples for mse calc, 3 smp per trial for scale 42: 40/3 = 13.3 trials, make 15
ntrials = size(data_sel.trial,2);
if ntrials < 1
warning('Time point %g: Not enough trials remain', toi(itoi))
break % subsequent time points will also not work
end
if strcmp(recompute_r, 'per_toi') % not per scale
% select time window of interest from each trial
tmpcfg=[];
tmpcfg.toilim = [toi(itoi)-timwin*0.5 toi(itoi)+timwin*0.5];
data_sel_unfilt = ft_redefinetrial(tmpcfg, data);
% only take trials that have the whole interval
tmpcfg = [];
tmpcfg.minlength = timwin;
data_sel_unfilt = ft_redefinetrial(tmpcfg, data_sel_unfilt);
% need 40 samples for mse calc, 3 smp per trial for scale 42: 40/3 = 13.3 trials, make 15
ntrials = size(data_sel_unfilt.trial,2);
if ntrials < 1
warning('Time point %g: Not enough trials remain', toi(itoi))
break % subsequent time points will also not work
end
% calculate similarity criterion
r_new = r * std(cell2mat(data_sel_unfilt.trial),1,2);
nchan = size(data_sel_unfilt.trial{1},1);
elseif strcmp(recompute_r, 'perscale_toi')
% calculate similarity criterion
r_new = r * std(cell2mat(data_sel.trial),1,2);
nchan = size(data_sel.trial{1},1);
end
% do point skipping for scales > 1, non-HP option
cg_data = {};
switch coarsegrainmethod
case 'filtskip'
if strcmp(filtmethod, 'hp')
nloops = 1; % keep original sampling rate
stepSize = 1;
else
nloops = sc;
stepSize = sc;
end
cg_data = cell(nloops,1); % make cell: cg_data{istart}{trials}(chan-by-time)
resamp_x = data_sel.trial;
for is = 1:nloops % loop over starting points here!
cg_data{is} = cellfun(@(resamp_x) resamp_x(:, is:(sc-1+1):end), resamp_x, 'UniformOutput', false ); % add padding% Filter
end
clear resamp_x;
case 'pointavg' % original point averaging coarse graining, no loop over starting points
nloops = 1; % no starting points loop for point avg
if sc == 1 || strcmp(filtmethod, 'hp') % no coarse graining for native sampling rate or high-pass entropy
cg_data{1} = data_sel.trial; %only keep trial data
else % coarse-grain time series at this time scale
nchan = size(data_sel.trial{1},1);
for itrial = 1:length(data_sel.trial)
num_cg_tpts = floor(length(data_sel.trial{itrial})/sc); % number of coarse-grained time points
cg_data{1}{itrial} = zeros(nchan, num_cg_tpts); % preallocate cg_data matrix
for t = 1:num_cg_tpts % calculate coarse_grained time series
cg_data{1}{itrial}(:,t) = mean( data_sel.trial{itrial}(:, (t-1)*sc + [1:sc]) ,2);
end
end
end
end
% after coarsegraining, loop mse computation across starting points
allcont = zeros(sc, nchan, m+1); % start_chan_m
for istart = 1:nloops
if max(cellfun(@(x) size(x,2), cg_data{istart})) == m % TODO check this at start
fprintf('Coarse grained trials below %d + 1 samples, skipping remaining starting points\n', m)
break
end
% concatenate trials and convert to single
y = single(cell2mat(cg_data{istart}));
% collect trial bounds and create mask with valid time points for pats
trl_bounds = cumsum(cellfun(@(x) size(x,2), cg_data{istart}))';
trl_mask = true(size(y,2),1);
if allowgpu && gpuavailable
trl_mask = gpuArray(trl_mask);
end
trl_mask([trl_bounds-1; trl_bounds]) = false;
% break if n data points < 100 (See Grandy et al., 2016)
ndatapoints = length(trl_mask); % TODO check this at start
if ndatapoints < 100
fprintf('N data points < 100, breaking\n')
break
end
% Calculate sample entropy of coarse grained time series
if strcmp(recompute_r, 'perscale_toi_sp')
r_new = r * std(y,1,2);
end
% keep the estimated r parameter
r_estimate(:, s, itoi, istart) = r_new; % dimord chan nsc ntoi nstartingpts
% chunk y to keep memory usage in check
num_avail_netto = mem_available * 1/4 - numel(y) - numel(r_new) - numel(trl_mask); % save space for y itself, cont?
% max_numel = num_avail_netto/4; % single = 4 bytes
if num_avail_netto > intmax('int32') && allowgpu && gpuavailable % max numel allowed on gpu
num_avail_netto = double(intmax('int32') - numel(y) - numel(r_new));
end
chunk_size = floor(num_avail_netto / numel(y));
n_chunks = ceil(size(y,2)/chunk_size);
n_chunks = ceil((size(y,2)+n_chunks)/chunk_size); % account for needed overlap
temp = 1;
chunk_borders = zeros(n_chunks,2);
for ic = 1:n_chunks
chunk_borders(ic,:) = [temp temp+chunk_size];
temp = temp+chunk_size-1; % chunks need to overlap to avoid missing pats at chunk borders
end
chunk_borders(end) = size(y,2);
clear temp
%fprintf('starting point %d\n', istart)
cont = zeros(m+1, n_chunks, nchan);
y_chunk1 = shiftdim(y', -1 ); % insert singleton dim
r_new2 = shiftdim(r_new, -2);
if allowgpu && gpuavailable
cont = gpuArray(cont);
y_chunk1 = gpuArray(y_chunk1);
r_new2 = gpuArray(r_new2);
end
fprintf('%d chunks: ', n_chunks)
for ic = 1:n_chunks
fprintf('%d ', ic)
y_inds = transpose(chunk_borders(ic,1):chunk_borders(ic,2));
y_chunk2 = permute(y_chunk1(1,y_inds,:), [2 1 3]); % insert singleton dim
if allowgpu && gpuavailable
y_chunk2 = gpuArray(y_chunk2);
end
ymat = bsxfun(@le, abs(bsxfun(@minus, y_chunk1, y_chunk2 )), r_new2 );
for ichan=1:nchan % loop since triu only supports 2D
ymat(:,:,ichan) = triu(ymat(:,:,ichan), chunk_borders(ic,1));
end
for k = 1:m+1
if k >= m % TODO try for m > 2
cont(k,ic,:) = sum(reshape(ymat(trl_mask(y_inds(1:end-2)), trl_mask, :), [], nchan));
end
if k < m+1
ymat = ymat & circshift(ymat, [-1 -1 0]);
end
end
clear ymat y_inds y_chunk2
end
allcont(istart, :, :) = gather(squeeze(sum(cont,2))'); % sum over chunks. dimord: start_chan_m
%fprintf('\n')
end % cg starting points
allcont = sum(allcont,1); % sum counts over starting points
if ndatapoints < 100
fprintf('N data points < 100, breaking\n')
break
end
% calculate sample entropy
for ichan=1:nchan
if allcont(1,ichan,m+1) == 0 || allcont(1,ichan,m) == 0
fprintf('zero patterns found!\n')
% nlin_sc = size(pnts,1); % ori THG code
% mse(s) = -log(1/((nlin_sc)*(nlin_sc -1)));
npossiblepats = length(find(trl_mask));
sampen(ichan,s,itoi) = -log(1/(npossiblepats*(npossiblepats-1)));
else
sampen(ichan,s,itoi) = -log(allcont(1,ichan,m+1)./allcont(1,ichan,m)); % same as log(cont(m)/cont(m+1))
end
end
end % for toi
end % for timescales
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% deal with the output
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
mse = [];
mse.label = data.label;
mse.fsample = bsxfun(@rdivide, data.fsample, timescales); % sample rates after coarse graining
mse.timescales = 1000 ./ mse.fsample; % by convention
mse.time = toi;
mse.dimord = 'chan_timescales_time';
mse.sampen = sampen;
mse.r = squeeze(nanmean(r_estimate,4)); % average across starting points
if isfield(data, 'trialinfo')
mse.trialinfo = data.trialinfo;
end
% do the general cleanup and bookkeeping at the end of the function
ft_postamble debug % this clears the onCleanup function used for debugging in case of an error
ft_postamble trackconfig % this converts the config object back into a struct and can report on the unused fields
ft_postamble previous data % this copies the data.cfg structure into the cfg.previous field. You can also use it for multiple inputs, or for "varargin"
ft_postamble provenance mse % this records the time and memory at the end of the function, prints them on screen and adds this information together with the function name and MATLAB version etc. to the output cfg
ft_postamble history mse % this adds the local cfg structure to the output data structure, i.e. dataout.cfg = cfg
ft_postamble savevar mse % this saves the output data structure to disk in case the user specified the cfg.outputfile option
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