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function [nodes,W_m,W_c] = unscented_sigma_points(n,DynareOptions)
%
% Computes nodes and weigths for a scaled unscented transform cubature
% INPUTS
% n [integer] scalar, number of variables.
%
% OUTPUTS
% nodes [double] nodes of the cubature
% weigths [double] associated weigths
%
% REFERENCES
%
%
%
% NOTES
%
% Copyright (C) 2009-2012 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 <http://www.gnu.org/licenses/>.
lambda = (DynareOptions.particle.unscented.alpha^2)*(n+DynareOptions.particle.unscented.kappa) - n ;
nodes = [ zeros(n,1) ( sqrt(n+lambda).*([ eye(n) -eye(n)]) ) ]' ;
W_m = lambda/(n+lambda) ;
W_c = W_m + (1-DynareOptions.particle.unscented.alpha^2+DynareOptions.particle.unscented.beta) ;
temp = ones(2*n,1)/(2*(n+lambda)) ;
W_m = [W_m ; temp] ;
W_c = [W_c ; temp] ;
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