function [density] = probability2(mu,S,X)
%
% Multivariate gaussian density
%
% INPUTS
%    n                  [integer]   scalar, number of variables.
%
% OUTPUTS
%    nodes          [double]    nodes of the cubature
%    weigths        [double]    associated weigths
%
% REFERENCES
%
%
% NOTES
%
% Copyright © 2009-2017 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare.  If not, see <https://www.gnu.org/licenses/>.

dim = size(X,1) ;
normfact = bsxfun(@power,(2*pi),(dim/2)) ;
foo = S\(bsxfun(@minus,X,mu)) ;
density = exp(-0.5*sum(foo.*foo)')./abs((normfact*prod(diag(S)))) + 1e-99 ;