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Added two routines for evaluating multivariate integrals with gaussian quadratures.

time-shift
Stéphane Adjemian (Charybdis) 2011-12-12 19:05:25 +01:00
parent 8fa4bfc160
commit f7b6e917ac
2 changed files with 115 additions and 0 deletions
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56
matlab/cartesian_product_of_sets.m Normal file
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function cprod = cartesian_product_of_sets(varargin)
% Computes the cartesian product.
%@info:
%! @deftypefn {Function File} {@var{cprod} =} cartesian_product_of_sets (@var{a},@var{b}, ...)
%! @anchor{cartesian_product_of_sets}
%! @sp 1
%! Computes A_1 * A_2 * .... * A_n with a generic set A_i = {e_1,e_2,e_3,...} where e_i is a string
%! or a number. It is assumed that each element e_i is unique in set A_i.
%! @sp 2
%! @strong{Inputs}
%! @sp 1
%! @table @ @var
%! @item a
%! n*1 vector of doubles.
%! @item a
%! m*1 vector of doubles.
%! @end table
%! @sp 1
%! @strong{Outputs}
%! @sp 1
%! @table @ @var
%! @item cprod
%! nm*2 matrix of doubles, the nodes cartesian product of sets @var{a} and @var{b}.
%! @end table
%! @sp 2
%! @strong{This function is called by:}
%! @sp 2
%! @strong{This function calls:}
%! @sp 2
%! @end deftypefn
%@eod:
% Copyright (C) 2011 Dynare Team
% stephane DOT adjemian AT univ DASH lemans DOT fr
%
% 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/>.
[ F{1:nargin} ] = ndgrid( varargin{:} );
for i=1:nargin
cprod(:,i) = F{i}(:);
end

59
matlab/gauss_hermite_weights_and_nodes.m Normal file
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function [nodes,weights] = gauss_hermite_weights_and_nodes(n)
% Computes the weights and nodes for an Hermite Gaussian quadrature rule.
%@info:
%! @deftypefn {Function File} {@var{nodes}, @var{weights} =} gauss_hermite_weights_and_nodes (@var{n})
%! @anchor{gauss_hermite_weights_and_nodes}
%! @sp 1
%! Computes the weights and nodes for an Hermite Gaussian quadrature rule. designed to approximate integrals
%! on the infinite interval (-\infty,\infty) of an unweighted smooth function.
%! @sp 2
%! @strong{Inputs}
%! @sp 1
%! @table @ @var
%! @item n
%! Positive integer scalar, number of nodes (order of approximation).
%! @end table
%! @sp 1
%! @strong{Outputs}
%! @sp 1
%! @table @ @var
%! @item nodes
%! n*1 vector of doubles, the nodes (roots of an order n Hermite polynomial)
%! @item weights
%! n*1 vector of doubles, the associated weights.
%! @end table
%! @sp 2
%! @strong{This function is called by:}
%! @sp 2
%! @strong{This function calls:}
%! @sp 2
%! @end deftypefn
%@eod:
% Copyright (C) 2011 Dynare Team
% stephane DOT adjemian AT univ DASH lemans DOT fr
%
% 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/>.
b = sqrt([1:n-1]/2);
JacobiMatrix = diag(b,1)+diag(b,-1);
[JacobiEigenVectors,JacobiEigenValues] = eig(JacobiMatrix);
[nodes,idx] = sort(diag(JacobiEigenValues));
JacobiEigenVector = JacobiEigenVectors(1,:);
JacobiEigenVector = transpose(JacobiEigenVector(idx));
weights = JacobiEigenVector.^2;
nodes = sqrt(2)*nodes;