82 lines
2.3 KiB
Matlab
82 lines
2.3 KiB
Matlab
function hessian_mat = hessian(func,x,gstep,varargin)
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% function hessian_mat = hessian(func,x,gstep,varargin)
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% Computes second order partial derivatives
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%
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% INPUTS
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% func [string] name of the function
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% x [double] vector, the Hessian of "func" is evaluated at x.
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% gstep [double] scalar, size of epsilon.
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% varargin [void] list of additional arguments for "func".
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%
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% OUTPUTS
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% hessian_mat [double] Hessian matrix
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%
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% ALGORITHM
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% Uses Abramowitz and Stegun (1965) formulas 25.3.24 and 25.3.27 p. 884
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%
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% SPECIAL REQUIREMENTS
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% none
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%
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% Copyright (C) 2001-2009 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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if ~isa(func, 'function_handle')
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func = str2func(func);
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end
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n=size(x,1);
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h1=max(abs(x),sqrt(gstep)*ones(n,1))*eps^(1/6);
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h_1=h1;
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xh1=x+h1;
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h1=xh1-x;
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xh1=x-h_1;
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h_1=x-xh1;
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xh1=x;
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f0=feval(func,x,varargin{:});
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f1=zeros(size(f0,1),n);
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f_1=f1;
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for i=1:n
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xh1(i)=x(i)+h1(i);
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f1(:,i)=feval(func,xh1,varargin{:});
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xh1(i)=x(i)-h_1(i);
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f_1(:,i)=feval(func,xh1,varargin{:});
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xh1(i)=x(i);
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i=i+1;
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end
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xh_1=xh1;
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hessian_mat = zeros(size(f0,1),n*n);
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for i=1:n
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if i > 1
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k=[i:n:n*(i-1)];
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hessian_mat(:,(i-1)*n+1:(i-1)*n+i-1)=hessian_mat(:,k);
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end
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hessian_mat(:,(i-1)*n+i)=(f1(:,i)+f_1(:,i)-2*f0)./(h1(i)*h_1(i));
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temp=f1+f_1-f0*ones(1,n);
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for j=i+1:n
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xh1(i)=x(i)+h1(i);
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xh1(j)=x(j)+h_1(j);
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xh_1(i)=x(i)-h1(i);
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xh_1(j)=x(j)-h_1(j);
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hessian_mat(:,(i-1)*n+j)=-(-feval(func,xh1,varargin{:})-feval(func,xh_1,varargin{:})+temp(:,i)+temp(:,j))./(2*h1(i)*h_1(j));
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xh1(i)=x(i);
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xh1(j)=x(j);
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xh_1(i)=x(i);
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xh_1(j)=x(j);
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j=j+1;
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end
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i=i+1;
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end |