Matlab code for creating matrix

Question

I have a problem, I am working with numerical approximations.

Now I have $-1=x_0<x_1 <...<x_n=1$ with $x_i=x_{i-1}+h$ and $h=2/n$. Now given a function $f$, I want to find $f(x_i)$ for $i=1:n-1$ and store it in a column matrix $F$.

How will I code it in matlab? Here is my code but it does not working. Any help is appreciated.

function F =  matrix(f , n)

    h=2/n;

    for i=1:n-1;

        x(0)=-1;

        x(n)=1

        x(i)=h+x(i-1)

    end

endfunction

Answer 1

The function header specifies the output as F, but you don't assign any value to F in your code. Nor do you ever use f. All you are doing is producing the array x (and that in an inefficient way, but that's beside the point).

Answer 2

In the version of Matlab that I use, the index starts at 1, instead of 0. So
x(1) = -1;
x(n+1) = 1;

and so on.

Another way to set up the matrix is

x = -1:(2/n):1;

Answer 3

You could try

function F = f_matrix (f, n)
  x = transpose(linspace(-1, 1, n+1));
  F = f(x);
endfunction

Answer 4

try this which returns not only F but also the x values

function [F,x] = Fmatrix(f, n)

    h = 2/n;

    x = zeros(n+1,1);  %initialize array with size n+1
    F = zeros(n+1,1);  
    for i=1:n+1
        x(i) = -1 + h*( i-1 );
        F(i) = f(x(i));
    end
    % vector 'x' contains '[x_0,x_1,x_2,..x_n]`
    % vector 'F' contains '[f(x_0),f(x_1),.. f(x_n)]`
end