%GAUSS_PDF Multivariate Gaussian PDF
%
% Syntax:
% [P,E] = GAUSS_PDF(X,M,S)
%
% In:
% X - Dx1 value or N values as DxN matrix
% M - Dx1 mean of distibution or N values as DxN matrix.
% S - DxD covariance matrix
%
% Out:
% P - Probability of X.
% E - Negative logarithm of P
%
% Description:
% Calculate values of PDF (Probability Density
% Function) of multivariate Gaussian distribution
%
% N(X | M, S)
%
% Function returns probability of X in PDF. If multiple
% X's or M's are given (as multiple columns), function
% returns probabilities for each of them. X's and M's are
% repeated to match each other, S must be the same for all.
%
% See also:
% GAUSS_RND
% Copyright (C) 2002 Simo Särkkä
%
% $Id: gauss_pdf.m 111 2007-09-04 12:09:23Z ssarkka $
%
% This software is distributed under the GNU General Public
% Licence (version 2 or later); please refer to the file
% Licence.txt, included with the software, for details.
function [P,E] = gauss_pdf(X,M,S)
if size(M,2) == 1
DX = X-repmat(M,1,size(X,2));
E = 0.5*sum(DX.*(S\DX),1);
d = size(M,1);
E = E + 0.5 * d * log(2*pi) + 0.5 * log(det(S));
P = exp(-E);
elseif size(X,2) == 1
DX = repmat(X,1,size(M,2))-M;
E = 0.5*sum(DX.*(S\DX),1);
d = size(M,1);
E = E + 0.5 * d * log(2*pi) + 0.5 * log(det(S));
P = exp(-E);
else
DX = X-M;
E = 0.5*DX'*(S\DX);
d = size(M,1);
E = E + 0.5 * d * log(2*pi) + 0.5 * log(det(S));
P = exp(-E);
end