1function [nodes,weights,nnodes] = setup_integration_nodes(EpOptions,pfm) 2if EpOptions.stochastic.order 3 % Compute weights and nodes for the stochastic version of the extended path. 4 switch EpOptions.stochastic.IntegrationAlgorithm 5 case 'Tensor-Gaussian-Quadrature' 6 % Get the nodes and weights from a univariate Gauss-Hermite quadrature. 7 [nodes0,weights0] = gauss_hermite_weights_and_nodes(EpOptions.stochastic.quadrature.nodes); 8 % Replicate the univariate nodes for each innovation and dates, and, if needed, correlate them. 9 nodes0 = repmat(nodes0,1,pfm.number_of_shocks*pfm.stochastic_order)*kron(eye(pfm.stochastic_order),pfm.Omega); 10 % Put the nodes and weights in cells 11 for i=1:pfm.number_of_shocks 12 rr(i) = {nodes0(:,i)}; 13 ww(i) = {weights0}; 14 end 15 % Build the tensorial grid 16 nodes = cartesian_product_of_sets(rr{:}); 17 weights = prod(cartesian_product_of_sets(ww{:}),2); 18 nnodes = length(weights); 19 case 'Stroud-Cubature-3' 20 [nodes,weights] = cubature_with_gaussian_weight(pfm.number_of_shocks*pfm.stochastic_order,3,'Stroud') 21 nodes = kron(eye(pfm.stochastic_order),transpose(pfm.Omega))*nodes; 22 weights = weights; 23 nnodes = length(weights); 24 case 'Stroud-Cubature-5' 25 [nodes,weights] = cubature_with_gaussian_weight(pfm.number_of_shocks*pfm.stochastic_order,5,'Stroud') 26 nodes = kron(eye(pfm.stochastic_order),transpose(pfm.Omega))*nodes; 27 weights = weights; 28 nnodes = length(weights); 29 case 'Unscented' 30 p = pfm.number_of_shocks; 31 k = 3;%EpOptions.ut.k; 32 C = sqrt(pfm.number_of_shocks + k)*pfm.Omega'; 33 nodes = [zeros(1,p); -C; C]; 34 weights = [k/(p+k); (1/(2*(p+k)))*ones(2*p,1)]; 35 nnodes = 2*p+1; 36 otherwise 37 error('Stochastic extended path:: Unknown integration algorithm!') 38 end 39end 40