searchq.m

function [pcnt, matl,matx,stepsize,fnew,how]=searchq(pcnt,fnew,oldx,matl,matx,sd,gdold,stepsize,how)
%SEARCHQ Line search routine for FMINU and LEASTSQ functions.
%	Performs line search procedure for unconstrained and least squares
% 	optimization. Uses Quadratic Interpolation.
%	When finished pcnt returns 0.

%	Copyright (c) 1990 by the MathWorks, Inc.
%	Andy Grace 7-9-90.
if pcnt==1
% Case 1: Next point less than initial point. 
%	  Increase step-length based on last gradient evaluation
	if fnew<matl(1)
% Quadratic Extrapolation using gradient of first point and 
% values of two other points.
		matl(2)=fnew;
		matx(2)=stepsize;
		newstep=-0.5*gdold*stepsize*stepsize/(fnew-gdold*stepsize-matl(1)+eps);
		if newstep<stepsize,how=[how,'QEF ']; newstep=1.2*stepsize; end
		stepsize=1.2*newstep;
		pcnt=2;
	else
% Case 2: New point greater than initial point. Decrease step-length.
		matl(3)=fnew;
		matx(3)=stepsize;
%Interpolate to get stepsize
		stepsize=max([1e-8*stepsize,-gdold*0.5*stepsize^2/(fnew-gdold*stepsize-matl(1)+eps)]);
		how=[how,'r'];
		pcnt=3;
	end
% Case 3: Last run was Case 1 (pcnt=2) and new point less than 
%	  both of other 2. Replace. 
elseif pcnt==2  & fnew< matl(2)
	newstep=cubici2(gdold,[matl(1);matl(2);fnew],[matx(1);matx(2);stepsize]);
	if newstep<stepsize,how=[how, 'CEF ']; end
		matl(1)=matl(2);
		matx(1)=matx(2);
		matl(2)=fnew;
		matx(2)=stepsize;
		stepsize=min([newstep,1])+1.5*stepsize;
		stepsize=max([1.2*newstep,1.2*stepsize]);
		how=[how,'i'];
% Case 4: Last run was Case 2: (pcnt=3) and new function still 
%	  greater than initial value.
elseif pcnt==3 & fnew>=matl(1)
	matl(2)=fnew;
	matx(2)=stepsize;
 	if stepsize<1e-6
		newstep=-stepsize/2;
%		if abs(newstep)<eps, newstep=rand(1)-0.5; how=[how,'RAND']; end
	else
		newstep=cubici2(gdold,[matl(1);matl(3);fnew],[matx(1);matx(3);stepsize]);
	end
	matx(3)=stepsize;
	if isnan(newstep), stepsize=stepsize/2; else stepsize=newstep; end
	matl(3)=fnew;
	how=[how,'R'];
% Otherwise must have Bracketed Minimum so do quadratic interpolation.
%  ... having just increased step.
elseif pcnt==2 & fnew>matl(2)
	matx(3)=stepsize;
	matl(3)=fnew;
	[stepsize]=cubici2(gdold,matl,matx);
	pcnt=4;
% ...  having just reduced step.
elseif  pcnt==3  & fnew<matl(1)
	matx(2)=stepsize;
	matl(2)=fnew;
	[stepsize]=cubici2(gdold,matl,matx);
	pcnt=4;
% Have just interpolated - Check to see whether function is any better 
% - if not replace.
elseif pcnt==4 
	pcnt=0;
	stepsize=abs(stepsize);
% If interpolation failed use old point.
 	if fnew>matl(2),
		fnew=matl(2);
		how='f';
 		stepsize=matx(2);		
	end
end %if pcnt==1