28 lines
1.8 KiB
Matlab
28 lines
1.8 KiB
Matlab
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% function hessian_mat = hessian_sparse(func,x,varargin)
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% Computes second order partial derivatives
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% used the 7 points formula
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%
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% INPUTS
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% func: name of the function
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% x: vector of variables around which the Hessian is calculated
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% varargin: list of arguments following x
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%
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% OUTPUTS
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% hessian_matrix: 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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%
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% part of DYNARE, copyright Dynare Team (2001-2007)
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% Gnu Public License.
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%% computes second order partial derivatives
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% uses Abramowitz and Stegun (1965) formulas 25.3.24 and 25.3.27 p. 884
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function hessian_mat = hessian_sparse(func,x,varargin)
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global options_func = str2func(func);n=size(x,1);
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%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 |