code: def repanel_cov(groups, sigmas):
      """calculate error covariance matrix for random effects model
  
      Parameters
      ----------
      groups : ndarray, (nobs, nre) or (nobs,)
          array of group/category observations
      sigma : ndarray, (nre+1,)
          array of standard deviations of random effects,
          last element is the standard deviation of the
          idiosyncratic error
  
      Returns
      -------
      omega : ndarray, (nobs, nobs)
          covariance matrix of error
      omegainv : ndarray, (nobs, nobs)
          inverse covariance matrix of error
      omegainvsqrt : ndarray, (nobs, nobs)
          squareroot inverse covariance matrix of error
          such that omega = omegainvsqrt * omegainvsqrt.T
  
      Notes
      -----
      This does not use sparse matrices and constructs nobs by nobs
      matrices. Also, omegainvsqrt is not sparse, i.e. elements are non-zero
      """
  
      if groups.ndim == 1:
          groups = groups[:, None]
      nobs, nre = groups.shape
      omega = sigmas[-1] * np.eye(nobs)
      for igr in range(nre):
          group = groups[:, igr : igr + 1]
          groupuniq = np.unique(group)
          dummygr = sigmas[igr] * (group == groupuniq).astype(float)
          omega += np.dot(dummygr, dummygr.T)
      ev, evec = np.linalg.eigh(omega)  # eig does not work
      omegainv = np.dot(evec, (1 / ev * evec).T)
      omegainvhalf = evec / np.sqrt(ev)
      return omega, omegainv, omegainvhalf
  
imports: from functools import reduce
  import numpy
  from statsmodels.regression.linear_model import GLS
  from pandas import Panel
label_desc: Use image node_id 2 for calling a global function with example usage: repanel_cov(groups, sigmas) and returns: omega,  omegainv,  omegainvhalf