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function [ldens,Dldens,D2ldens] = lpdfnorm(x,a,b)
% Evaluates the logged UNIVARIATE GAUSSIAN PDF at x.
%
% INPUTS
% x [double] m*n matrix of locations,
% a [double] m*n matrix or scalar, First GAUSSIAN distribution parameters (expectation)
% b [double] m*n matrix or scalar, Second GAUSSIAN distribution parameters (standard deviation).
%
% OUTPUTS
% ldens [double] m*n matrix of logged GAUSSIAN densities evaluated at x.
% Dldens [double] m*n matrix of first derivatives of logged GAUSSIAN densities.
% D2ldens [double] m*n matrix of second derivatives of logged matrix of GAUSSIAN densities.
%
% SPECIAL REQUIREMENTS
% none
% Copyright © 2003-2021 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/>.
if nargin<3, b=1; end
if nargin<2, a=0; end
ldens = -log(b) -.5*log(2*pi) - .5*((x-a)./b).*((x-a)./b) ;
if nargout >1
Dldens = - (1./b).*((x-a)./b) ;
end
if nargout == 3
D2ldens = - (1./b).^2 ;
end
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