function [xopt,fval,k,err]=mgoldensection(f,a,b,delta,max1)


% Purpose: golden section algorithm for linear search 
% Programmer: LU Dagang
% Date: 25/05/2003
% Revised: 25/05/2003
% Version 1.0
% Copyright (C) 2003, LU Dagang, HIT
%
% Modified by Peng Xiaobo (Institute of Engineering Mechanics)
% Data :27/05/2006
%
% Input  - f is the objective function input as a string 'f'
%        - a and b are the lower and upper bound of the optimized variable
%        - delta is the prescibed precision
%        - max1 is the maximum number interations
% 
% Output - xopt is the optimal value of the variable
%        - fval is the optimal value of the objective function

% This program is free software; you can redistribute it and/or modify it
% under the permission of LU Dagang
% 
% This program is distributed in the hope that it will be useful in studying
% the graduate course "Structural Optimum Design", but WITHOUT ANY WARRANTY.

a1 = b-0.618*(b-a);
f1 = feval(f,a1);
b1 = a+0.618*(b-a);
f2 = feval(f,b1);
for k=1:max1
   if abs(b-a) > delta 
      if f1 < f2
        b = b1;
        b1 = a1;
        f2 = f1;
        a1 = b-0.618*(b-a);
        f1 = feval(f,a1);
      else
        a = a1;
        a1 = b1;
        f1 = f2;
        b1 = a+0.618*(b-a);
        f2 = feval(f,b1);
      end
  else break,end
end
xopt = (b+a)/2;
fval = feval(f,xopt);