lnsrch1

 Copyright (C) 2001 Michel Juillard

0001 % Copyright (C) 2001 Michel Juillard
0002 %
0003 function [x,f,fvec,check]=lnsrch(xold,fold,g,p,stpmax,func,j1,j2,varargin)
0004 
0005   alf = 1e-4 ;
0006   tolx = 3.7e-11 ;
0007   alam = 1;
0008   
0009   x = xold;
0010   nn = length(j2);
0011   summ = sqrt(sum(p.*p)) ;
0012   if ~isfinite(summ)
0013     error(['Some element of Newton direction isn''t finite. Jacobian maybe' ...
0014        ' singular or there is a problem with initial values'])
0015   end
0016   
0017   if summ > stpmax
0018     p=p.*stpmax/summ ;
0019   end
0020 
0021   slope = g'*p ;
0022   
0023   test = max(abs(p)'./max([abs(xold(j2))';ones(1,nn)])) ;
0024   alamin = tolx/test ;
0025 
0026   if alamin > 0.1
0027     alamin = 0.1;
0028   end
0029   
0030   while 1
0031     if alam < alamin
0032       check = 1 ;
0033       return
0034     end
0035     
0036     x(j2) = xold(j2) + (alam*p) ;
0037     fvec = feval(func,x,varargin{:}) ;
0038     fvec = fvec(j1);
0039     f = 0.5*fvec'*fvec ;
0040 
0041     if any(isnan(fvec))
0042       alam = alam/2 ;
0043       alam2 = alam ;
0044       f2 = f ;
0045       fold2 = fold ;
0046     else
0047 
0048       if f <= fold+alf*alam*slope
0049     check = 0;
0050     break ;
0051       else
0052     if alam == 1
0053       tmplam = -slope/(2*(f-fold-slope)) ;
0054     else
0055       rhs1 = f-fold-alam*slope ;
0056       rhs2 = f2-fold2-alam2*slope ;
0057       a = (rhs1/(alam^2)-rhs2/(alam2^2))/(alam-alam2) ;
0058       b = (-alam2*rhs1/(alam^2)+alam*rhs2/(alam2^2))/(alam-alam2) ;
0059       if a == 0
0060         tmplam = -slope/(2*b) ;
0061       else
0062         disc = (b^2)-3*a*slope ;
0063 
0064         if disc < 0
0065           error ('Roundoff problem in nlsearch') ;
0066         else
0067           tmplam = (-b+sqrt(disc))/(3*a) ;
0068         end
0069 
0070       end
0071 
0072       if tmplam > 0.5*alam
0073         tmplam = 0.5*alam;
0074       end
0075 
0076     end
0077 
0078     alam2 = alam ;
0079     f2 = f ;
0080     fold2 = fold ;
0081     alam = max([tmplam;(0.1*alam)]) ;
0082       end
0083     end
0084   end
0085 
0086 % 01/14/01 MJ lnsearch is now a separate function
0087 % 01/12/03 MJ check for finite summ to avoid infinite loop when Jacobian
0088 %             is singular or model is denormalized