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function [nodes, weights, nnodes] = setup_integration_nodes(opt, pfm)
% INPUTS:
% - opt [struct] EP options
% - pfm [struct] perfect foresight model description
%
% OUTPUTS:
% - nodes [double] vector of integration nodes
% - weights [double] vector of weights
% - nnodes [integer] number of nodes
% Copyright © 2012-2026 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/>.
nodes=[];
weights=[];
nnodes=[];
if opt.stochastic.order
% Compute weights and nodes for the stochastic version of the extended path.
% Use only shocks with positive variance (effective shocks).
n = pfm.effective_number_of_shocks;
switch opt.stochastic.IntegrationAlgorithm
case 'Tensor-Gaussian-Quadrature'
% Get the nodes and weights from a univariate Gauss-Hermite quadrature.
[nodes0, weights0] = gauss_hermite_weights_and_nodes(opt.stochastic.quadrature.nodes);
% Replicate the univariate nodes for each innovation and, if needed, correlate them.
nodes0 = repmat(nodes0, 1, n)*pfm.Omega;
% Put the nodes and weights in cells
for i=1:n
rr(i) = {nodes0(:,i)};
ww(i) = {weights0};
end
% Build the tensorial grid
nodes = cartesian_product_of_sets(rr{:});
weights = prod(cartesian_product_of_sets(ww{:}),2);
nnodes = length(weights);
case 'Stroud-Cubature-3'
[nodes,weights] = cubature_with_gaussian_weight(n, 3, 'Stroud');
nodes = transpose(pfm.Omega'*nodes);
weights = weights/sum(weights);
nnodes = length(weights);
case 'Stroud-Cubature-5'
if n==1
info = warning('query', 'backtrace');
if strcmp(info.state, 'on')
warning('off', 'backtrace');
end
warning('Stroud-Cubature-5 is not defined for a single shock, falling back to Gaussian quadrature with 3 nodes.')
skipline()
warning(info.state, 'backtrace');
[nodes, weights] = gauss_hermite_weights_and_nodes(3);
nodes = nodes*pfm.Omega;
nnodes = length(weights);
else
[nodes,weights] = cubature_with_gaussian_weight(n,5,'Stroud');
nodes = transpose(pfm.Omega'*nodes);
weights = weights/sum(weights);
nnodes = length(weights);
end
case 'Unscented'
k = 3;
C = sqrt(n + k)*pfm.Omega';
nodes = [zeros(1,n); -C; C];
weights = [k/(n+k); (1/(2*(n+k)))*ones(2*n,1)];
nnodes = 2*n+1;
otherwise
error('Stochastic extended path:: Unknown integration algorithm %s!',opt.stochastic.IntegrationAlgorithm)
end
end
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