www.pudn.com > calibr8.zip > apprgrdn.m

function g = apprgrdn(x,f,fun,deltax,obj) 
% Usage: 
% g = apprgrdn(x,f,fun,deltax,obj) 
% Function apprgrdn.m performs the finite difference approximation  
% of the gradient  at a point . 
%  is the calculated function value at a point , 
%  is the name of the Matlab function, which calculates function values 
%  is a vector of the relative stepsizes, 
%  is the flag indicating whether the gradient of the objective 
%        function (1) or the constraint function (0) is to be calculated.  
% 
      n=max(size(x)); ee=ones(size(x)); 
        di=abs(x); idx=find(di<5e-15); di(idx)=5e-15*ee(idx);  
        di=deltax.*di;  
        if obj, idx=find(abs(di)<2e-10); di(idx)=2e-10*sign(di(idx)); 
        else,   idx=find(abs(di)<5e-15); di(idx)=5e-15*sign(di(idx)); 
        end 
        y=x;  
        for i=1:n 
          y(i)=x(i)+di(i); 
          fi=feval(fun,y); 
          if obj, if fi==f,  
             for j=1:3 
                di(i)=di(i)*10;  y(i)=x(i)+di(i);  
                fi=feval(fun,y); if fi~=f, break, end 
             end    
          end, end 
          g(i)=(fi-f)/di(i); 
          if obj, if any(idx==i) 
            y(i)=x(i)-di(i); 
            fi=feval(fun,y); 
            g(i)=.5*(g(i)+(f-fi)/di(i)); 
          end, end             
          y(i)=x(i); 
        end