function prob = gaussPDF(Data, Mu, Sigma)
%
% This function computes the Probability Density Function (PDF) of a
% multivariate Gaussian represented by means and covariance matrix.
%
% Inputs -----------------------------------------------------------------
%   o Data:  D x N array representing N datapoints of D dimensions.
%   o Mu:    D x K array representing the centers of the K GMM components.
%   o Sigma: D x D x K array representing the covariance matrices of the 
%            K GMM components.
% Outputs ----------------------------------------------------------------
%   o prob:  1 x N array representing the probabilities for the 
%            N datapoints.     
%
% Copyright (c) 2006 Sylvain Calinon, LASA Lab, EPFL, CH-1015 Lausanne,
%               Switzerland, http://lasa.epfl.ch

[nbVar,nbData] = size(Data);

Data = Data' - repmat(Mu',nbData,1);
prob = sum( (Data*inv(Sigma)).*Data, 2 );
prob = exp(-0.5*prob) / sqrt((2*pi)^nbVar * (abs(det(Sigma))+realmin));