function d = mahal_symetric(X1, X2, E1, E2)
% function d = mahal_symetric(X1, X2, E1, E2)
% Symetric Mahalanobis distance
% 
% mahal_symetric(X1, X2) : where X1 and X2 are the data of the first and 
% second group of data to be compared, in the columns 
% 
% mahal_symetric(u1, u2, E1, E2) : where u1 and u2 are the centroids of the
% two groups of data; and E1 and E2 are the covariance matrix of each
% group of data
% 
% Work protected by the Attribution-NonCommercial-ShareAlike 3.0 Unported
% Creative Commons license
% http://creativecommons.org/licenses/by-nc-sa/3.0/

if nargin==2,
    u1 = mean(X1)'; %mean of each collumn
    E1 = cov(X1); %each collumn is a variable

    u2 = mean(X2)'; %mean of each collumn
    E2 = cov(X2); %each collumn is a variable
elseif nargin==4,
    u1 = X1;
    u2 = X2;
else
    display('Wrong number of input arguments, please use mahal_symetric(X1, X2) or mahal_symetric( u1, u2, E1, E2)'),
    return,
end

d = ((u1-u2)'*pinv(E2)*(u1-u2) + (u2-u1)'*pinv(E1)*(u2-u1))/2;