function [grandavg] = ft_timelockgrandaverage(cfg, varargin)

% FT_TIMELOCKGRANDAVERAGE computes ERF/ERP average and variance

% over multiple subjects or over blocks within one subject

%

% Use as

% [grandavg] = ft_timelockgrandaverage(cfg, avg1, avg2, avg3, ...)

%

% where

% avg1..N are the ERF/ERP averages as obtained from FT_TIMELOCKANALYSIS

%

% and cfg is a configuration structure with

% cfg.method = string, 'across' or 'within' (default = 'across'), see below for details

% cfg.parameter = string, which parameter to average (default = 'avg')

% cfg.channel = Nx1 cell-array with selection of channels (default = 'all'), see FT_CHANNELSELECTION for details

% cfg.latency = [begin end] in seconds or 'all' (default = 'all')

% cfg.keepindividual = string, 'yes' or 'no' (default = 'no')

% cfg.nanmean = string, can be 'yes' or 'no' (default = 'yes')

% cfg.normalizevar = string, 'N' or 'N-1' (default = 'N-1')

%

% If cfg.method = 'across', a plain average is performed, i.e. the requested

% parameter in each input argument is weighted equally in the average. This is useful

% when averaging across subjects. The variance-field will contain the variance across

% the parameter of interest, and the output dof-field will contain the number of

% input arguments.

%

% If cfg.method = 'within', a weighted average is performed, i.e. the requested

% parameter in each input argument is weighted according to the degrees of freedom in

% the dof-field. This is useful when averaging within subjects across blocks, e.g.

% when each block was recorded in a separate file. The variance-field will contain

% the variance across all input observations, and the output dof-field will contain

% the total number of observations.

%

% 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. For this particular function, the input should be

% structured as a cell-array.

%

% See also FT_TIMELOCKANALYSIS, FT_TIMELOCKSTATISTICS, FT_TIMELOCKBASELINE

% Copyright (C) 2003-2006, Jens Schwarzbach

% Copyright (C) 2013, Burkhard Maess

%

% 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 debug

ft_preamble loadvar varargin

ft_preamble provenance varargin

% the ft_abort variable is set to true or false in ft_preamble_init

if ft_abort

return

end

% return immediately after distributed execution

if ~isempty(ft_getopt(cfg, 'distribute'))

return

end

% check if the input data is valid for this function

for i=1:length(varargin)

if isfield(varargin{i}, 'trial') && isfield(varargin{i}, 'avg') % see bug2372 (dieloz)

varargin{i} = rmfield(varargin{i}, 'trial');

varargin{i}.dimord = 'chan_time';

ft_warning('not using the trials, using the single-subject average to compute the grand average');

end

varargin{i} = ft_checkdata(varargin{i}, 'datatype', 'timelock', 'feedback', 'no');

% ensure that it contains an average

if ~isfield(varargin{i}, 'avg')

ft_error('input structure %d does not contain an average, use FT_TIMELOCKANALYSIS first', i);

end

end

% check if the input cfg is valid for this function

cfg = ft_checkconfig(cfg, 'forbidden', {'channels'}); % prevent accidental typos, see issue 1729

% set the defaults

cfg.method = ft_getopt(cfg, 'method' , 'across');

cfg.parameter = ft_getopt(cfg, 'parameter' , 'avg');

cfg.channel = ft_getopt(cfg, 'channel' , 'all');

cfg.latency = ft_getopt(cfg, 'latency' , 'all');

cfg.keepindividual = ft_getopt(cfg, 'keepindividual', 'no');

cfg.nanmean = ft_getopt(cfg, 'nanmean' , 'yes');

cfg.normalizevar = ft_getopt(cfg, 'normalizevar' , 'N-1');

if iscell(cfg.parameter)

if numel(cfg.parameter)>1

ft_error('only a single parameter can be specified to be averaged');

else

cfg.parameter = cfg.parameter{1};

end

end

if strcmp(cfg.parameter, 'trial')

ft_error('not supporting averaging over the repetition dimension, please use FT_TIMELOCKANALYSIS');

end

% select trials and channels of interest

orgcfg = cfg;

tmpcfg = keepfields(cfg, {'parameter', 'channel', 'tolerance', 'latency', 'showcallinfo', 'trackcallinfo', 'trackusage', 'trackdatainfo', 'trackmeminfo', 'tracktimeinfo', 'checksize'});

[varargin{:}] = ft_selectdata(tmpcfg, varargin{:});

% restore the provenance information

[cfg, varargin{:}] = rollback_provenance(cfg, varargin{:});

% do not use the default option returned by FT_SELECTDATA, but the original one for this function

cfg.nanmean = orgcfg.nanmean;

% determine the size of the data to be averaged

datsiz = size(varargin{1}.(cfg.parameter));

dimord = getdimord(varargin{1}, cfg.parameter);

nsubj = length(varargin);

% whether to normalize the variance with N or N-1, see VAR

normalizewithN = strcmpi(cfg.normalizevar, 'N');

% whether nans should persist in the output or be treated as missing values

if istrue(cfg.nanmean)

mymean = @nanmean;

myvar = @nanvar;

mysum = @nansum;

else

mymean = @mean;

myvar = @var;

mysum = @sum;

end

if istrue(cfg.keepindividual)

fprintf('not computing average, but keeping individual %s for %d subjects\n', cfg.parameter, nsubj);

% allocate memory to hold the data and collect it

dat = zeros([nsubj, datsiz]);

for s=1:nsubj

dat(s, :, :, :) = varargin{s}.(cfg.parameter);

end

grandavg.individual = dat; % Nsubj x Nchan x Nsamples

else

dat = nan([nsubj, datsiz]);

dof = nan([nsubj, datsiz]);

switch cfg.method

case 'across'

fprintf('computing average of %s across %d subjects\n', cfg.parameter, nsubj);

for s=1:nsubj

dat(s, :, :, :) = varargin{s}.(cfg.parameter);

end

% compute the mean and variance across subjects

grandavg.avg = reshape(mymean(dat, 1), datsiz);

grandavg.var = reshape(myvar(dat, normalizewithN, 1), datsiz);

grandavg.dof = reshape(sum(isfinite(dat), 1), datsiz);

if normalizewithN

% just to be sure

grandavg.var(grandavg.dof<=0) = NaN;

else

% see https://stats.stackexchange.com/questions/4068/how-should-one-define-the-sample-variance-for-scalar-input

% the fieldtrip/external/stats/nanvar implementation behaves differently here than Mathworks VAR and NANVAR implementations

grandavg.var(grandavg.dof<=1) = NaN;

end

case 'within'

fprintf('computing average of %s within subjects over %d blocks\n', cfg.parameter, nsubj);

for s=1:nsubj

dat(s, :, :, :) = varargin{s}.(cfg.parameter);

dof(s, :, :, :) = varargin{s}.dof;

end % for nsub

% compute the weighted mean across input arguments

grandavg.avg = mysum(dat .* dof, 1) ./ sum(dof, 1);

grandavg.avg = reshape(grandavg.avg, datsiz);

grandavg.dof = sum(dof, 1);

grandavg.dof = reshape(grandavg.dof, datsiz);

% this follows https://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Weighted_sample_variance with frequency weights

if normalizewithN

grandavg.var = mysum(dof .* (dat - repmat(reshape(grandavg.avg, [1 datsiz]), [nsubj 1 1])).^2, 1) ./ sum(dof, 1);

grandavg.var = reshape(grandavg.var, datsiz);

else

grandavg.var = mysum(dof .* (dat - repmat(reshape(grandavg.avg, [1 datsiz]), [nsubj 1 1])).^2, 1) ./ (sum(dof, 1) - 1);

grandavg.var = reshape(grandavg.var, datsiz);

end

otherwise

ft_error('unsupported value for cfg.method')

end % switch

end % if keepindividual

% collect the output data

grandavg = copyfields(varargin{1}, grandavg, {'time', 'freq', 'label', 'labelcmb'});

% sensor positions should only be present in the output when they are identical in all inputs

hasgrad = cellfun(@(x) isfield(x, 'grad'), varargin(:));

if all(hasgrad) % check if positions are different between subjects

samegrad = cellfun(@(x) isequal(varargin{1}.grad, x.grad), varargin(2:end));

if all(samegrad)

grandavg.grad = varargin{1}.grad;

else

ft_warning('discarding gradiometer information because it is not identical in all inputs');

end

end

haselec = cellfun(@(x) isfield(x, 'elec'), varargin(:));

if all(haselec) % check if positions are different between subjects

sameelec = cellfun(@(x) isequal(varargin{1}.elec, x.elec), varargin(2:end));

if all(sameelec)

grandavg.elec = varargin{1}.elec;

else

ft_warning('discarding electrode information because it is not identical in all inputs');

end

end

hasopto = cellfun(@(x) isfield(x, 'opto'), varargin(:));

if all(hasopto) % check if positions are different between subjects

sameopto = cellfun(@(x) isequal(varargin{1}.opto, x.opto), varargin(2:end));

if all(sameopto)

grandavg.opto = varargin{1}.opto;

else

ft_warning('discarding optode information because it is not identical in all inputs');

end

end

% set dimord

if strcmp(cfg.keepindividual, 'yes')

grandavg.dimord = ['subj_', dimord];

elseif strcmp(cfg.keepindividual, 'no')

grandavg.dimord = dimord;

end

% do the general cleanup and bookkeeping at the end of the function

ft_postamble debug

ft_postamble previous varargin

ft_postamble provenance grandavg

ft_postamble history grandavg

ft_postamble savevar grandavg