def zeta_a(eN,cL,w):
  """
  EnKF-N inflation estimation via w.
  Returns zeta_a = (N-1)/pre-inflation^2.

  Using this inside an iterative minimization as in the iEnKS
  effectively blends the distinction between the primal and dual EnKF-N.
  """
  N  = len(w)
  N1 = N-1
  za = N1*cL/(eN + w@w)
  return za