Nan Mihai - Eliminare gaussiana

function x = eliminareGaussiana(A, b)

n = size(A, 1);
r = zeros(n, 1);
for i = 1 : 1 : n
   r(i) = i;
endfor

x = zeros(n, 1);
for k = 1:n
    max = abs(A(r(k), r(k)));
    max_pos = k;
    for l = k : 1 : n
        if abs(A(r(l), r(k))) > max
            max = abs(A(r(l), r(k)));
            max_pos = l;
        endif
    endfor

    temp_r = r;
    r(k) = temp_r(max_pos);
    r(max_pos) = temp_r(k);

    for i = 1:n
        if i ~= k
            zeta = A(r(i), k) / A(r(k), k);
            for j = k : 1 : n
                A(r(i), j) = A(r(i), j) - A(r(k), j) * zeta;
            endfor
            b(r(i)) = b(r(i)) - b(r(k)) * zeta;
        endif
    endfor
endfor

for i = 1:n
    x(i) = b(r(i)) / A(r(i), i);
endfor

endfunction