code: def _fractional_power_superdiag_entry(l1, l2, t12, p):
      """
      Compute a superdiagonal entry of a fractional matrix power.
  
      This is Eq. (5.6) in [1]_.
  
      Parameters
      ----------
      l1 : complex
          A diagonal entry of the matrix.
      l2 : complex
          A diagonal entry of the matrix.
      t12 : complex
          A superdiagonal entry of the matrix.
      p : float
          A fractional power.
  
      Returns
      -------
      f12 : complex
          A superdiagonal entry of the fractional matrix power.
  
      Notes
      -----
      Care has been taken to return a real number if possible when
      all of the inputs are real numbers.
  
      References
      ----------
      .. [1] Nicholas J. Higham and Lijing lin (2011)
             "A Schur-Pade Algorithm for Fractional Powers of a Matrix."
             SIAM Journal on Matrix Analysis and Applications,
             32 (3). pp. 1056-1078. ISSN 0895-4798
  
      """
      if l1 == l2:
          f12 = t12 * p * l1 ** (p - 1)
      elif abs(l2 - l1) > abs(l1 + l2) / 2:
          f12 = t12 * ((l2**p) - (l1**p)) / (l2 - l1)
      else:
          # This is Eq. (5.5) in [1].
          z = (l2 - l1) / (l2 + l1)
          log_l1 = np.log(l1)
          log_l2 = np.log(l2)
          arctanh_z = np.arctanh(z)
          tmp_a = t12 * np.exp((p / 2) * (log_l2 + log_l1))
          tmp_u = _unwindk(log_l2 - log_l1)
          if tmp_u:
              tmp_b = p * (arctanh_z + np.pi * 1j * tmp_u)
          else:
              tmp_b = p * arctanh_z
          tmp_c = 2 * np.sinh(tmp_b) / (l2 - l1)
          f12 = tmp_a * tmp_c
      return f12
  
imports: from __future__ import division, print_function, absolute_import
  import warnings
  import numpy
  from scipy.linalg._matfuncs_sqrtm import SqrtmError, _sqrtm_triu
  from scipy.linalg.decomp_schur import schur, rsf2csf
  from scipy.linalg.matfuncs import funm
  from scipy.linalg import svdvals, solve_triangular
  from scipy.sparse.linalg.interface import LinearOperator
  from scipy.sparse.linalg import onenormest
  import scipy.special
label_desc: Use image node_id 4 for calling a global function with example usage: _fractional_power_superdiag_entry(l1, l2, t12, p) and returns: f12