function c=cosmo_corr(x,y,corr_type)
% Computes correlation - faster than than matlab's "corr" for Pearson.
%
% c=comso_corr(x[,y[,corr_type]])
%
% Inputs:
% x PxM matrix.
% y PxN matrix (optional). If omitted then y=x.
% corr_type 'Pearson' or 'Spearman' or 'Kendall' (optional). If omitted
% then corrtype='Pearson' and the computation time is
% significantly reduced for small matrices x and y (with
% /tiny/ numerical imprecisions) by the use of a custom
% implementation.
% Using 'Kendall' required the matlab stats
% toolbox and is currently not supported in Octave.
% Output:
% c MxN matrix with c(i,j)=corr(x(:,i),y(:,j),'type',corr_type).
%
% Notes:
% - this function does not compute probability values.
% - Using 'Kendall' for corr_type requires the matlab stats toolbox.
%
% Example:
% % generate some pseudo-random data.
% x=reshape(mod(2:7:100,41),5,[]);
% y=reshape(mod(1:7:100,37),5,[]);
% % compute builtin corr with cosmo_corr
% % call the function first to avoid lookup delays; then measure time
% c=corr(x,y);
% cc=cosmo_corr(x,y);
% % compute differences in output
% delta=c-cc;
% max_delta=max(abs(delta(:)));
% fprintf('difference not greater than eps: %d\n',max_delta<=eps);
% > difference not greater than eps: 1
%
% See also: corr
%
% # For CoSMoMVPA's copyright information and license terms, #
% # see the COPYING file distributed with CoSMoMVPA. #
