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