function X = gauss(A, f)
    n = length(f);
    X = zeros(n, 1);
    buffer = zeros(n, 1);
    for i=1:n
        main_el = A(i, i);
        row = i;
        col = i;
        %find main element
        for k=i:n
            for l=1:n
                if abs(A(row, col)) < abs(A(k, l))
                    row = k;
                    col = l;
                end;
            end;
        end;
        buffer(i) = col;
        for j=i:n
            if (j == row)
                continue;
            end;
            d = A(j, col)/A(row, col);
            A(j, 1:n) =  A(j, 1:n) - d*A(row, 1:n);
            f(j) = f(j) - d*f(row);
        end;
        %swap lines
        B = A(row, 1:n);
        A(row, 1:n) = A(i, 1:n);
        A(i, 1:n) = B;
    end;
    for i=n:-1:1
        s = f(i);
        for j=i+1:n
            s = s - A(i, buffer(j))*X(buffer(j));
        end;
        X(buffer(i)) = s/A(i, buffer(i));
    end;
    A*X - f
endfunction