function [nodes,weights,nnodes] = setup_integration_nodes(EpOptions,pfm) if EpOptions.stochastic.order % Compute weights and nodes for the stochastic version of the extended path. switch EpOptions.stochastic.IntegrationAlgorithm case 'Tensor-Gaussian-Quadrature' % Get the nodes and weights from a univariate Gauss-Hermite quadrature. [nodes0,weights0] = gauss_hermite_weights_and_nodes(EpOptions.stochastic.quadrature.nodes); % Replicate the univariate nodes for each innovation and dates, and, if needed, correlate them. nodes0 = repmat(nodes0,1,pfm.number_of_shocks*pfm.stochastic_order)*kron(eye(pfm.stochastic_order),pfm.Omega); % Put the nodes and weights in cells for i=1:pfm.number_of_shocks 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(pfm.number_of_shocks*pfm.stochastic_order,3,'Stroud') nodes = kron(eye(pfm.stochastic_order),transpose(pfm.Omega))*nodes; weights = weights; nnodes = length(weights); case 'Stroud-Cubature-5' [nodes,weights] = cubature_with_gaussian_weight(pfm.number_of_shocks*pfm.stochastic_order,5,'Stroud') nodes = kron(eye(pfm.stochastic_order),transpose(pfm.Omega))*nodes; weights = weights; nnodes = length(weights); case 'Unscented' p = pfm.number_of_shocks; k = 3;%EpOptions.ut.k; C = sqrt(pfm.number_of_shocks + k)*pfm.Omega'; nodes = [zeros(1,p); -C; C]; weights = [k/(p+k); (1/(2*(p+k)))*ones(2*p,1)]; nnodes = 2*p+1; otherwise error('Stochastic extended path:: Unknown integration algorithm!') end end