Incorrect answer - Incorrect looping?

I have a code:

function [ I, h ] = Simpson( f, a, b, tol )
n=2;
h=(b-a)/n;
x=h/3;
I=x*(f(a)+4*f((a+b)/2)+f(b));
Iold=I;
while abs((I-Iold)/Iold)>=tol
  n=n+2;
  h=(b-a)/n;
  j=1:((n/2)-1);
  term1=sum(f(a+2*j*h));
  term1=2*term1;
  i=1:(n/2);
  term2=sum(f(a+(2*i-1)*h));
  term2=term2*4;
  x=h/3;
  I=x*(f(a)+term1+term2+f(b));
  if abs((I-Iold)/Iold)<tol
      break
  end
end
end

But when I test the code with this input:

[t_simp, h]=Simpson(@(x) cos(x),0,pi/2,10^-3)

I get

t_simp=
1.0023
h=
0.7854

When the answer should be

t_simp=
1.0000
h=
0.1963

From what I can tell, the code should loop 3 times before stopping. Right now, the code doesn't loop. What am I doing wrong?

Answer 1

[Walter Roberson]

You do

Iold=I;
while abs((I-Iold)/Iold)>=tol

but when you execute that second line, you have just set Iold to I so I-Iold is going to be 0, which is not going to be greater than the tol