81 lines
2.4 KiB
Matlab
81 lines
2.4 KiB
Matlab
function hessian_mat = hessian_sparse(func,x,gstep,varargin)
|
|
% function hessian_mat = hessian_sparse(func,x,gstep,varargin)
|
|
% Computes second order partial derivatives
|
|
%
|
|
% INPUTS
|
|
% func [string] name of the function
|
|
% x [double] vector, the Hessian of "func" is evaluated at x.
|
|
% gstep [double] scalar, size of epsilon.
|
|
% varargin [void] list of additional arguments for "func".
|
|
%
|
|
% OUTPUTS
|
|
% hessian_mat [double, sparse] Hessian matrix
|
|
%
|
|
% ALGORITHM
|
|
% Uses Abramowitz and Stegun (1965) formulas 25.3.24 and 25.3.27 p. 884
|
|
%
|
|
% SPECIAL REQUIREMENTS
|
|
% none
|
|
%
|
|
|
|
% Copyright © 2001-2017 Dynare Team
|
|
%
|
|
% 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 <https://www.gnu.org/licenses/>.
|
|
|
|
if ~isa(func, 'function_handle')
|
|
func = str2func(func);
|
|
end
|
|
n=size(x,1);
|
|
h1=max(abs(x),sqrt(gstep(1))*ones(n,1))*eps^(1/6)*gstep(2);
|
|
h_1=h1;
|
|
xh1=x+h1;
|
|
h1=xh1-x;
|
|
xh1=x-h_1;
|
|
h_1=x-xh1;
|
|
xh1=x;
|
|
f0=feval(func,x,varargin{:});
|
|
f1=zeros(size(f0,1),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);
|
|
end
|
|
xh_1=xh1;
|
|
hessian_mat = sparse(size(f0,1),n*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);
|
|
% hessian_mat(:,k)=0;
|
|
% end
|
|
hessian_mat(:,(i-1)*n+i)=(f1(:,i)+f_1(:,i)-2*f0)./(h1(i)*h_1(i));
|
|
temp=f1+f_1-f0*ones(1,n);
|
|
for j=1:i-1
|
|
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)=-(-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);
|
|
end
|
|
end |