golden.m

这是在网上下的一个东东

%%%%%%%%%% start of function golden.m %%%%%%%%%%
%
% Function to perform a Golden section search to calculate 
%           optimal step length
%
% Written by: Roseanna M. Neupauer
% Modification Date: April 24, 1999
% Modification Date: June 25, 1999 (added option to use additive noise,
%		multiplicative noise, or a combination of the two)
%
% alpha=golden(funfcn,lambda,dellame,tolls,g,beta,upper,...
%          csample,noise,nearzero,large)
% Inputs
%     funfcn       name of matlab function that calculates the 
%                    F vector (Equation 2.28) funfcn='getfk'
%     lambda       array containing the Lagrange multipliers
%     dellame      step direction
%     tolls        tolerance for golden section search
%     g            matrix of scaled kernel functions
%     beta         array of Lagrange multipliers, beta
%     upper        array containing upper limit of prior 
%                    distributions
%     csample      array containing sampled concentrations
%     noise        vector of noise levels:
%			1. standard deviation of normally-distributed 
%                    	additive random noise in measurements;
%			2. standard deviation of normally-distributed 
%                    	multiplicative random noise in measurements;
%     nearzero     value below which the asymptotic 
%                    approximation to zero is used
%     large        value above which the asymptotic 
%                    approximation to infinity is used
%
% Outputs
%     alpha        optimal step length
%
% Functions called
%     getfk        calculates the F vector

function alpha=golden(funfcn,lambda,dellame,tolls,g,beta,...
          upper,csample,noise,nearzero,large)

% bracket the step length to within a .1-length interval
normdel=ones(11,1);
for brack=1:11
     del=0.1*(brack-1);
     [newfe,dummy,dummy1]=feval(funfcn,lambda+del*dellame,...
          g,beta,upper,csample,noise,nearzero,large);
     normdel(brack)=norm(newfe);
end
minbrack=find(normdel==min(normdel));
minbrack=minbrack(1);
if (minbrack >=  10)
     aa=0.9;
     bb=1.0;
elseif (minbrack <= 2)
     aa=0.;
     bb=0.1;
          
else
     aa=0.1*(minbrack-1);
     bb=0.1*(minbrack+1);
end

% Using the 0.1-length interval as a starting interval, 
%     perform a Golden section search in the step direction

[newfe,dummy,dummy1]=feval(funfcn,lambda+aa*dellame,g,beta,...
     upper,csample,noise,nearzero,large);
fa=norm(newfe);
[newfe,dummy,dummy1]=feval(funfcn,lambda+bb*dellame,g,beta,...
     upper,csample,noise,nearzero,large);
fb=norm(newfe);

tau=2/(1+sqrt(5));
F1=aa+(1-tau)*(bb-aa);
F2=aa+tau*(bb-aa);
[newfe,dummy,dummy1]=feval(funfcn,lambda+F1*dellame,g,beta,...
     upper,csample,noise,nearzero,large);
fF1=norm(newfe);
[newfe,dummy,dummy1]=feval(funfcn,lambda+F2*dellame,g,beta,...
     upper,csample,noise,nearzero,large);
fF2=norm(newfe);
while abs(F1-F2) > tolls
     if (fF1 > fF2 & fa > fF1)
          aa=F1;
          temp=F2;
          F1=F2;
          fF1=fF2;
          F2=temp+tau*(bb-temp);
          [newfe,dummy,dummy1]=feval(funfcn,...
               lambda+F2*dellame,g,beta,upper,...
               csample,noise,nearzero,large);
          fF2=norm(newfe);
     else
          bb=F2;
          temp=F1;
          F2=F1;
          fF2=fF1;
          F1=aa+(1-tau)*(temp-aa);
          [newfe,dummy,dummy1]=feval(funfcn,...
               lambda+F1*dellame,g,beta,upper,...
               csample,noise,nearzero,large);
          fF1=norm(newfe);
     end
end
alpha=(F1+F2)/2;
return
%%%%%%%%%%  end of function golden.m  %%%%%%%%%%