function [x,iter,err] = gauss_seidel(A,b,tol,nmax)
% by Shelvean Kapita
% Gauss-Seidel
% A must be strictly diagonally dominant
% nmax maximum number of iterations
% tol tolerance
i = 1;
res = 1;
n = size(A,1);
x_old = zeros(n,1);
x = x_old;
invD = 1./diag(A);
err = zeros(nmax,1);
U = triu(A,1);
L = tril(A,-1);
while (res>tol)&&(i < nmax)
    for j=1:n
        x(j)= invD(j)*(b(j)-U(j,:)*x_old-L(j,1:j-1)*x(1:j-1));
    end
    res = norm(x-x_old);
    x_old = x;
    err(i) = res;
    i = i+1;
end
iter = i;
err = err(1:i);