158 lines
4.5 KiB
Matlab
158 lines
4.5 KiB
Matlab
function [xparam1, hh, gg, fval] = newrat(func0,x,hh,gg,flag,varargin)
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%
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% [xparam1, hh, gg, fval] = newrat(func0,x,hh,gg,flag,varargin)
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%
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% Standard Newton search
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%
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% flag = 0, to begin with a pure gradient search (the program shifts to
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% pure Newton when improvement of pure gradient is below ftol)
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%
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% flag = 1, to start with the compelte Newton search
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icount=0;
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nx=length(x);
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xparam1=x;
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lamtol=1.e-7;
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ftol=1.e-5;
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options=optimset('fminunc');
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options.MaxFunEvals=200;
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options.TolFun= 1.0000e-005;
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options.MaxIter=1;
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options.LargeScale='off';
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optim_options=optimset('fminsearch');
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optim_options.display='iter';
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optim_options.MaxFunEvals=1000;
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optim_options.TolFun= 1.0000e-003;
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optim_options.TolX= 1.0000e-006;
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func = str2func(func0);
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fval0=feval(func,x,varargin{:});
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if isempty(hh)
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[dum, gg]=mr_hessian(func0,x,flag,varargin{:});
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hh = reshape(dum,nx,nx);
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end
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disp(['Gradient norm ',num2str(norm(gg))])
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disp(['Minimum Hessian eigenvalue ',num2str(min(eig(hh)))])
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disp(['Maximum Hessian eigenvalue ',num2str(max(eig(hh)))])
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g=gg;
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h{1}=hh;
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check=0;
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if max(eig(hh))<0, disp('Negative definite Hessian! Local maximum!'), pause, end,
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while norm(gg)>1.e-3 & check==0,
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icount=icount+1;
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disp([' '])
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disp(['Iteration ',num2str(icount)])
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x0=xparam1-inv(hh)*gg;
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c=mr_nlincon(x0,varargin{:},1);
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lam=1;
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while c
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lam=lam*0.9;
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x0=xparam1-inv(hh)*gg.*lam;
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c=mr_nlincon(x0,varargin{:},1);
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end
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fval=feval(func,x0,varargin{:});
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% if (fval0(icount)-fval)<ftol & flag==0,
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% fvala=fval;
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% x0a=x0;
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% disp('Try to modify Hessian')
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% x0=xparam1-inv(gg*gg')*gg;
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% c=mr_nlincon(x0,varargin{:},1);
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% lam=1;
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% while c
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% lam=lam*0.9;
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% x0=xparam1-inv(gg*gg')*gg.*lam;
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% c=mr_nlincon(x0,varargin{:},1);
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% end
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% fval=feval(func,x0,varargin{:});
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% if fvala<=fval,
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% x0=x0a;
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% fval=fvala;
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% end
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% end
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if (fval0(icount)-fval)<ftol,
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disp('Try line search')
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[lam,fval,EXITFLAG,OUTPUT,GRAD,HESSIAN]=fminunc(@lsearch, 0, options, func, xparam1, inv(hh)*gg , varargin{:});
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x0=xparam1-inv(hh)*gg.*lam;
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end
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if (fval0(icount)-fval)<ftol & flag==1,
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fvala=fval;
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x0a=x0;
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disp('Try gradient direction')
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[lam,fval,EXITFLAG,OUTPUT,GRAD,HESSIAN]=fminunc(@lsearch, 0, options, func, xparam1, gg , varargin{:});
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if fvala<=fval,
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x0=x0a;
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fval=fvala;
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else
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x0=xparam1-gg*lam;
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if (fval0(icount)-fval)>ftol,
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flag=0;
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end
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end
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end
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if (fval0(icount)-fval)<ftol,
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fvala=fval;
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x0a=x0;
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disp('Try some simplex iterations')
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[x0,fval,EXITFLAG,OUTPUT] = fminsearch(func, xparam1, optim_options, varargin{:});
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if fvala<fval,
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x0=x0a;
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fval=fvala;
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else
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lam = NaN;
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end
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end
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if (fval0(icount)-fval)<ftol*ftol & flag==1;,
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% if fvala<fval,
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% fval=fvala;
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% x0=x0a;
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% end
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disp('No further improvement is possible!')
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check=1;
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else
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if (fval0(icount)-fval)<ftol & flag==0,
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flag=1;
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end
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xparam1=x0;
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x(:,icount+1)=xparam1;
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fval0(icount+1)=fval;
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disp(['LAMBDA ',num2str(lam)])
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%disp(['DX norm ',num2str(norm(inv(hh)*gg.*lam))])
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disp(['DX norm ',num2str(norm(x(:,end)-x(:,end-1)))])
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disp(['FVAL ',num2str(fval)])
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disp(['Improvement ',num2str(fval0(icount)-fval)])
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if norm(x(:,icount)-xparam1)>1.e-12,
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%[dum, gg]=hessian('mj_optmumlik',xparam1,gend,data,1);
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[dum, gg]=mr_hessian(func0,xparam1,flag,varargin{:});
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hh = reshape(dum,nx,nx);
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end
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disp(['Gradient norm ',num2str(norm(gg))])
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disp(['Minimum Hessian eigenvalue ',num2str(min(eig(hh)))])
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disp(['Maximum Hessian eigenvalue ',num2str(max(eig(hh)))])
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if max(eig(hh))<0, disp('Negative definite Hessian! Local maximum!'), pause, end,
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h{icount+1}=hh;
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g(:,icount+1)=gg;
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save m1 x h g fval0
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end
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end
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return
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%
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function f00 = lsearch(lam,func,x,dx,varargin)
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x0=x-dx*lam;
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f00=feval(func,x0,varargin{:});
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