% file name: goldmin.m
%minimization golden section serch
%Prof. Reyolando Brasil abril 2021
%
% xL, xU = lower and upper bounds
xL=0; xU=4;
% es = desired relative error (%)
es=0.0001;
% ea = present relative error (%)
% maxit = maximum number of iterations
maxit=100;
% x = location of minimum
%fx = minimum value
phi=(1+sqrt(5))/2;
iter=0;
while(1)
    d=(phi-1)*(xU-xL);
    x1=xL+d;
    x2=xU-d;
    if ftest(x1)<ftest(x2)
        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, break,end
    if iter>=maxit, break,end
end
disp('Location of minimum')
xopt
disp('Minimum value of function')
fx=ftest(xopt)
disp('Number of iterations')
iter