code: def _update_dPrxy(self):
          
          super(ExpCM_empirical_phi, self)._update_dPrxy()
          if 'beta' in self.freeparams:
              self.dQxy_dbeta = scipy.zeros((N_CODON, N_CODON), dtype='float')
              for w in range(N_NT):
                  scipy.copyto(self.dQxy_dbeta, self.dphi_dbeta[w],
                          where=CODON_NT_MUT[w])
              self.dQxy_dbeta[CODON_TRANSITION] *= self.kappa
              self.dPrxy['beta'] += self.Frxy * self.dQxy_dbeta
              _fill_diagonals(self.dPrxy['beta'], self._diag_indices)
docs: Update `dPrxy`, accounting for dependence of `phi` on `beta`.