Question

I have some difficulties in converting a pseudocode into a MatLab algorithm. Specifically, there is one part I don’t quite know how to do. I will write the pseudocode up to the point where I am uncertain:

 input n, (a_{ij}), (b_i), (x_i), M
    for k = 1 to M do
       for i = 1 to n do

           u_i = (b_i - sum[(from j = 1, (j ≠ i), to n) a_{ij} * x_j]) / a_{ii}
       end do

The difficulty I have is when I have to write the sum-part. What I can’t figure out is how to write the algorithm so that terms where j ≠ i are not included. So far I have written:

function [k,x] = jacobimethod(A,b,M)
n = length(A);
u = zeros(1,n);
x = zeros(1,n);
for k = 1:M
    for i = 1:n
        u(i) = (b(i) - (A(i

And this is where I get stuck. So far, all my algorithms have involved sums where all terms should be included, even those where j = i. In this case, the sum term will simply be:

A(i,1:n)*x(1:n)'

But how can I modify this so that A(i,i) is not included?

Any help will be greatly appreciated!

Answer 1

You could make an explicit index array and remove the index you don’t need

% inside of the loop
idx = 1:n;
idx(i) = [];
u(i) = (b(i)-sum(A(i,idx).*x(idx)))/A(i,i);