function [x,fx,ea,iter]=goldmin(f,xl,xu,es,maxit,varargin)
% goldmin: minimization golden section search
% [x,fx,ea,iter]=goldmin(f,xl,xu,es,maxit,p1,p2,...):
% uses golden section search to find the minimum of f
% input:
% f = name of function
% xl, xu = lower and upper guesses
% es = desired relative error (default = 0.0001%)
% maxit = maximum allowable iterations (default = 50)
% p1,p2,... = additional parameters used by f
% output:
% x = location of minimum
% fx = minimum function value
% ea = approximate relative error (%)
% iter = number of iterations
if nargin<3,error('at least 3 input arguments required'),end
if nargin<4|isempty(es), es=0.0001;end
if nargin<5|isempty(maxit), maxit=50;end
phi=(1+sqrt(5))/2;
iter=0;
while(1)
d = (phi-1)*(xu - xl);
x1 = xl + d;
x2 = xu - d;
if f(x1,varargin{:}) < f(x2,varargin{:})
xopt = x1;
xl = x2;
else
xopt = x2;
xu = x1;
end
iter=iter+1;
if xopt~=0, ea = (2 - phi) * abs((xu - xl) / xopt) * 100;end
if ea <= es | iter >= maxit,break,end
end
x=xopt;fx=f(xopt,varargin{:});
end