Commit 9b4537cf authored by assia's avatar assia
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git-svn-id: https://www.dynare.org/svn/dynare/dynare_v4@1669 ac1d8469-bf42-47a9-8791-bf33cf982152
parent 8e5cfdcf
% Copyright (C) 2001 Michel Juillard%% computes second order partial derivatives% uses Abramowitz and Stegun (1965) formulas 25.3.24 and 25.3.27 p. 884function hessian_mat = hessian_sparse(func,x,varargin)global options_func = str2func(func);n=size(x,1);%h1=max(abs(x),options_.gstep*ones(n,1))*eps^(1/3);h1=max(abs(x),sqrt(options_.gstep)*ones(n,1))*eps^(1/6);h_1=h1;xh1=x+h1;h1=xh1-x;xh1=x-h_1;h_1=x-xh1;xh1=x;f0=feval(func,x,varargin{:});nf = size(f0,1);f1=zeros(nf,n);f_1=f1;for i=1:n xh1(i)=x(i)+h1(i); f1(:,i)=feval(func,xh1,varargin{:}); xh1(i)=x(i)-h_1(i); f_1(:,i)=feval(func,xh1,varargin{:}); xh1(i)=x(i); i=i+1;endxh_1=xh1;hessian_mat = spalloc(nf,n*n,3*nf*n);for i=1:n if i > 1 k=[i:n:n*(i-1)]; hessian_mat(:,(i-1)*n+1:(i-1)*n+i-1)=hessian_mat(:,k); end hessian_mat(:,(i-1)*n+i)=sparse((f1(:,i)+f_1(:,i)-2*f0)./(h1(i)*h_1(i))); temp=f1+f_1-f0*ones(1,n); for j=i+1:n xh1(i)=x(i)+h1(i); xh1(j)=x(j)+h_1(j); xh_1(i)=x(i)-h1(i); xh_1(j)=x(j)-h_1(j); hessian_mat(:,(i-1)*n+j)=sparse(-(-feval(func,xh1,varargin{:})-feval(func,xh_1,varargin{:})+temp(:,i)+temp(:,j))./(2*h1(i)*h_1(j))); xh1(i)=x(i); xh1(j)=x(j); xh_1(i)=x(i); xh_1(j)=x(j); j=j+1; end i=i+1;end% 10/03/02 MJ used the 7 points formula
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% function hessian_mat = hessian_sparse(func,x,varargin)
% Computes second order partial derivatives
% used the 7 points formula
%
% INPUTS
% func: name of the function
% x: vector of variables around which the Hessian is calculated
% varargin: list of arguments following x
%
% OUTPUTS
% hessian_matrix: Hessian matrix
%
% ALGORITHM
% Uses Abramowitz and Stegun (1965) formulas 25.3.24 and 25.3.27 p. 884
%
% SPECIAL REQUIREMENTS
% none
%
%
% part of DYNARE, copyright Dynare Team (2001-2007)
% Gnu Public License.
%% computes second order partial derivatives
% uses Abramowitz and Stegun (1965) formulas 25.3.24 and 25.3.27 p. 884
function hessian_mat = hessian_sparse(func,x,varargin)
global options_func = str2func(func);n=size(x,1);
%h1=max(abs(x),options_.gstep*ones(n,1))*eps^(1/3);h1=max(abs(x),sqrt(options_.gstep)*ones(n,1))*eps^(1/6);h_1=h1;xh1=x+h1;h1=xh1-x;xh1=x-h_1;h_1=x-xh1;xh1=x;f0=feval(func,x,varargin{:});nf = size(f0,1);f1=zeros(nf,n);f_1=f1;for i=1:n xh1(i)=x(i)+h1(i); f1(:,i)=feval(func,xh1,varargin{:}); xh1(i)=x(i)-h_1(i); f_1(:,i)=feval(func,xh1,varargin{:}); xh1(i)=x(i); i=i+1;endxh_1=xh1;hessian_mat = spalloc(nf,n*n,3*nf*n);for i=1:n if i > 1 k=[i:n:n*(i-1)]; hessian_mat(:,(i-1)*n+1:(i-1)*n+i-1)=hessian_mat(:,k); end hessian_mat(:,(i-1)*n+i)=sparse((f1(:,i)+f_1(:,i)-2*f0)./(h1(i)*h_1(i))); temp=f1+f_1-f0*ones(1,n); for j=i+1:n xh1(i)=x(i)+h1(i); xh1(j)=x(j)+h_1(j); xh_1(i)=x(i)-h1(i); xh_1(j)=x(j)-h_1(j); hessian_mat(:,(i-1)*n+j)=sparse(-(-feval(func,xh1,varargin{:})-feval(func,xh_1,varargin{:})+temp(:,i)+temp(:,j))./(2*h1(i)*h_1(j))); xh1(i)=x(i); xh1(j)=x(j); xh_1(i)=x(i); xh_1(j)=x(j); j=j+1; end i=i+1;end% 10/03/02 MJ used the 7 points formula
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