SOLE :: Gauss partial pivoting

function [x] = gauss_partial_pivoting(A, b)
    [m, n] = size(A);

    if (m ~= n)
        x = -0;
        return
    end

    for k = 1:m-1
        % Nalazi indeks reda pivot elementa
        max_index = k;
        for counter = k+1:n
            if abs(A(counter, k)) > abs(A(max_index, k))
                max_index = counter;
            end
        end

        % Mijenja redove pivot elementa i trenutnog elementa
        A([k max_index], :) = A([max_index k], :);
        % Mijenjamo redove i vektora kolone b
        b([k max_index], 1) = b([max_index k], 1);

        for i = k+1:m
            coefficient = (-1) * A(i,k)/A(k,k);
            for j = k:n
                A(i, j) = A(i, j) + A(k, j)*coefficient;
            end
            b(i) = b(i) + b(k)*coefficient;
        end
    end

    % Izracunamo posljednje x i vracamo u sve prethodne
    x(n) = b(n)/A(n,n);
    for i = n-1:-1:1
        sum = 0;
        for j = n:-1:i+1
            sum = sum + A(i, j)*x(j);
        end
        x(i) = (b(i) - sum)/A(i,i);
    end

end