% TTEST_CELL - compute paired t-test. Allow fast computation of 
%                multiple t-test using matrix manipulation.
%
% Usage:
%    >> [F df] = ttest_cell( { a b } );
%    >> [F df] = ttest_cell(a, b);
%
% Inputs:
%   a,b       = data consisting of PAIRED arrays to be compared. The last 
%               dimension of the data array is used to compute the t-test.
% Outputs:
%   T   - T-value
%   df  - degree of freedom (array)
%
% Example:
%   a = { rand(1,10) rand(1,10)+0.5 }
%   [T df] = ttest_cell(a)
%   signif = 1-tcdf(T, df(1))
%
%   % for comparison, the same using the Matlab t-test function
%   [h p ci stats] = ttest(a{1}', b{1}');
%   [ stats.tstat' p] 
%
%   % fast computation (fMRI scanner volume 100x100x100 and 10 subjects in
%   % two conditions). The computation itself takes 0.5 seconds instead of 
%   % half an hour using the standard approach (1000000 loops and Matlab 
%   % t-test function)
%   a = rand(100,100,100,10); b = rand(100,100,100,10);
%   [F df] = ttest_cell({ a b });
%
% Author: Arnaud Delorme, SCCN/INC/UCSD, La Jolla, 2005
%
% Reference:
%   Schaum's outlines in statistics (3rd edition). 1999. Mc Graw-Hill.

% Copyright (C) Arnaud Delorme
%
% This file is part of EEGLAB, see http://www.eeglab.org
% for the documentation and details.
%
% Redistribution and use in source and binary forms, with or without
% modification, are permitted provided that the following conditions are met:
%
% 1. Redistributions of source code must retain the above copyright notice,
% this list of conditions and the following disclaimer.
%
% 2. Redistributions in binary form must reproduce the above copyright notice,
% this list of conditions and the following disclaimer in the documentation
% and/or other materials provided with the distribution.
%
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
% THE POSSIBILITY OF SUCH DAMAGE.

function [tval, df] = ttest_cell(a,b)
    
    if nargin < 1
        help ttest_cell;
        return;
    end
    
    if iscell(a), b = a{2}; a = a{1}; end
    tmpdiff = a-b;
    diff = mymean(tmpdiff,    myndims(a));
    sd   = mystd( tmpdiff,[], myndims(a));
    tval = diff./sd*sqrt(size(a, myndims(a)));
    df   = size(a, myndims(a))-1;
    
    % check values againg Matlab statistics toolbox
    %[h p ci stats] = ttest(a', b');
    % [ tval stats.tstat' ]  
    
function val = myndims(a)
    if ndims(a) > 2
        val = ndims(a);
    else
        if size(a,1) == 1,
            val = 2;
        elseif size(a,2) == 1,
            val = 1;
        else
            val = 2;
        end
    end; 
  
function res = mymean( data, varargin) % deal with complex numbers
    res = mean( data, varargin{:});
    if ~isreal(data)
        res = abs( res );
    end

function res = mystd( data, varargin) % deal with complex numbers
    if ~isreal(data)
        res = std( abs(data), varargin{:});
    else
        res = sqrt(sum( bsxfun(@minus, data, mean( data, varargin{2})).^2, varargin{2})/(size(data,varargin{2})-1)); % 8 percent speedup
        %res = std( data, varargin{:});
    end