Golden Section algorithm only iterating once?

Hi, I'm new to matlab and I'm having trouble with my code which uses the golden section method to calculate a maximum. I'm pretty sure it has something to do with the for loop, because the algorithm only seems to iterate once, but I'm not sure. Any help would be appreciated. Thanks!

function [xopt] = gss(xl,xu,N)
r=(-1+sqrt(5))/2;
d=r*(xu-xl);
x1=xl+d;
x2=xu-d;
f1=f(x1);
f2=f(x2);

for i=1:N
  if f1>f2
      xl=x2;
      x2=x1;
      x1=xl+d;
      f2=f1;
      f1=f(x1);
  else 
      xu=x1;
      x1=x2;
      x2=xu-d;
      f1=f2;
      f2=f(x2);
  end

    if f1>f2
        xopt=x1;
    end

    if f1<f2
        xopt=x2;
    end

end
end

function fout = f(x)

fout=-0.1*(x^2)-exp(-x);

end

Answer 1

[Jan]

Use the debugger to see, what is going on: Set a breakpoint in the first line and step through the code line by line.

You will find out, that the loop runs N times as expected. But d does not change its value. Then you can expect that the calculated points are hopping back and forth.

Note: Using x1 and xl is a confusing idea. Hard to read...

[Image Analyst]

I agree. Call them xLeft and xRight, or leftX and rightX, or xLower and xUpper, or something that is readable.