132 lines
3.6 KiB
Matlab
132 lines
3.6 KiB
Matlab
% Copyright (C) 2001 Michel Juillard
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%
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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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%
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% Adapted by M. Ratto from original M. Juillard routine
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%
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function [hessian_mat, gg] = mr_hessian(func,x,hflag,varargin)
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global gstep_
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persistent h1
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func = str2func(func);
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f0=feval(func,x,varargin{:});
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n=size(x,1);
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%h1=max(abs(x),gstep_*ones(n,1))*eps^(1/3);
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%h1=max(abs(x),sqrt(gstep_)*ones(n,1))*eps^(1/6);
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if isempty(h1),
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h1=max(abs(x),sqrt(gstep_)*ones(n,1))*eps^(1/4);
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end
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htol = 1.e-4;
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xh1=x;
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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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fx=feval(func,xh1,varargin{:});
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if abs(fx-f0)<htol | abs(fx-f0)>(5*htol),
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c=mr_nlincon(xh1,varargin{:});
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ic=0;
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while c
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h1(i)=h1(i)*0.9;
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xh1(i)=x(i)+h1(i);
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c=mr_nlincon(xh1,varargin{:});
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ic=1;
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end
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if ic,
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fx=feval(func,xh1,varargin{:});
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end
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icount = 0;
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while abs(fx-f0)<htol & icount< 10,
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icount=icount+1;
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h1(i)=min(0.3*abs(x(i)), 1.e-3/(abs(fx-f0)/h1(i)));
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xh1(i)=x(i)+h1(i);
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c=mr_nlincon(xh1,varargin{:});
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while c
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h1(i)=h1(i)*0.9;
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xh1(i)=x(i)+h1(i);
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c=mr_nlincon(xh1,varargin{:});
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end
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fx=feval(func,xh1,varargin{:});
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end
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while abs(fx-f0)>(5*htol),
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h1(i)=h1(i)*0.5;
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xh1(i)=x(i)+h1(i);
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fx=feval(func,xh1,varargin{:});
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end
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end
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f1(:,i)=fx;
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xh1(i)=x(i)-h1(i);
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c=mr_nlincon(xh1,varargin{:});
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ic=0;
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while c
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h1(i)=h1(i)*0.9;
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xh1(i)=x(i)-h1(i);
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c=mr_nlincon(xh1,varargin{:});
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ic = 1;
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end
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fx=feval(func,xh1,varargin{:});
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f_1(:,i)=fx;
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if ic,
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xh1(i)=x(i)+h1(i);
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f1(:,i)=feval(func,xh1,varargin{:});
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end
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xh1(i)=x(i);
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end
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h_1=h1;
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xh1=x;
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xh_1=xh1;
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gg=(f1'-f_1')./(2.*h1);
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if hflag,
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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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temp1 = feval(func,xh1,varargin{:});
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%c=mr_nlincon(xh1,varargin{:});
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%if c, disp( ['hessian warning cross ', num2str(c) ]), end
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temp2 = feval(func,xh_1,varargin{:});
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%c=mr_nlincon(xh_1,varargin{:});
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%if c, disp( ['hessian warning cross ', num2str(c) ]), end
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hessian_mat(:,(i-1)*n+j)=-(-temp1 -temp2+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
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else
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hessian_mat = zeros(size(f0,1),n*n);
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for i=1:n,
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dum = (f1(:,i)+f_1(:,i)-2*f0)./(h1(i)*h_1(i));
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if dum>0,
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hessian_mat(:,(i-1)*n+i)=dum;
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else
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hessian_mat(:,(i-1)*n+i)=gg(i)^2;
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end
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end
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end
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hh1=h1;
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save hess
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% 11/25/03 SA Created from Hessian_sparse (removed sparse)
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