SOLE :: Jacobian function

function [x] = jacobian(A, b, x_1, max_error, max_iter)

    [rows, cols] = size(A);

    if rows ~= cols
        return;
    end

    x = x_1;
    for counter = 1: max_iter
        for i = 1:rows
            sum = 0;
            for j = 1:cols
                if i ~= j
                    sum = sum + x_1(j)*A(i, j);
                end
            end
            x(i) = (b(i) - sum)/A(i, i);
        end

        if abs(x-x_1) < max_error
            break
        end

        x_1 = x;
    end
end