I have a having a a matrix index bounds in matlab

Question

I keep getting the error( this is in Matlab) Attempted to access r(0,0); index must be a positive integer or logical.

Error in ==> Romberg at 15

I ran it with Romberg(1.3, 2.19,8)

I think the problem is the statment is not logical because I made it positive and still got the same error. anyone got some ideas of what i could do?

function Romberg(a, b, n)

h = b - a;

r = zeros(n,n);

for i = 1:n

    h = h/2;

    sum1 = 0;

    for k = 1:2:2^(i)

        sum1 = sum1 + f(a + k*h);

    end

    r(i,0) = (1/2)*r(i-1,0) + (sum1)*h;

    for j = 1:i

        r(i,j) = r(i,j-1) + (r(i,j-1) - r(i-1,j-1))/((4^j) - 1);

    end

end

disp(r);

end

function f_of_x = f(x)

f_of_x = sin(x)/x;

end

Answer 1

In MATLAB, vectors and matrices are indexed starting from 1. Therefore, the very first line of your code is invalid because the index on r is 0.

Answer 2

You have zero subscripts in

r(i,0) = (1/2)*r(i-1,0) + (sum1)*h;

This is impossible in MATLAB -- all indices start form 1.

Answer 3

There are two lines where you're using 0 to index, which you can't in Matlab:

r(i,0) = (1/2)*r(i-1,0) + (sum1)*h;

and

r(i,j) = r(i,j-1) + (r(i,j-1) - r(i-1,j-1))/((4^j) - 1);

when j==1 or i==1.

I suggest that you run your loops starting from 2, and replace the exponents i and j with (i-1) and (j-1), respectively.

As an aside: You could write the loop

for k = 1:2:2^(i)

   sum1 = sum1 + f(a + k*h);

end

as

k = 1:2:2^i;
tmp = f(a + k*h);
sum1 = sum(tmp);

if you write f_of_x as

sin(x)./x