Given a n-by-n matrix $\mathbf{\phi}$ and a vector $\mathbf{X}$, solve for the two vectors $\mathbf{\Phi}$ and $\mathbf{\Omega}$ that satisfy:

$$
\Phi_i = \sum_{l} \frac{\phi_{il}X_l}{\Omega_l}
$$

$$
\Omega_j = \sum_{l} \frac{\phi_{lj}X_l}{\Phi_l}
$$