%{
  Gauss-Seidel, using sparse coefficient matrix
%}
clear all;
close all;
clc;

N = 150;
% Sparse, tridiagonal matrix
SA = spdiags([[-0.5*ones(N-1,1);0],2*ones(N,1),[0.;-0.5*ones(N-1,1)]],[-1,0,1],N,N);
b = rand(N,1);

% Tentative solution
x = zeros(N,1);

% Tollerance
toll = 1e-12;

% Max admissible number of iterations
itMax = 1000;

% Using explicit loops and working an all elements of A, including zeros
hf = figure; 
nit = 0;
while 1
    nit = nit+1;

    % Works only on non-zero elements of "SA"
    x = tril(SA,0)\(b-triu(SA,1)*x);

    res = b-SA*x;
    err = norm(res)/norm(b);
    figure(hf); h=loglog(nit,err,'ro'); hold on; if (nit==1) grid on; end
    if (err<toll)||(nit>itMax)
        break;
    end
end