code: def distance_logdet(A, B, squared=False):
      r"""Log-det distance between SPD/HPD matrices.
  
      The log-det distance between two SPD/HPD matrices :math:`\mathbf{A}` and
      :math:`\mathbf{B}` is [1]_:
  
      .. math::
          d(\mathbf{A},\mathbf{B}) =
          \sqrt{\log(\det \left( \frac{\mathbf{A}+\mathbf{B}}{2} \right))
          - \frac{1}{2} \log(\det(\mathbf{A} \mathbf{B}))}
  
      Parameters
      ----------
      A : ndarray, shape (..., n, n)
          First SPD/HPD matrices, at least 2D ndarray.
      B : ndarray, shape (..., n, n)
          Second SPD/HPD matrices, same dimensions as A.
      squared : bool, default False
          Return squared distance.
  
          .. versionadded:: 0.5
  
      Returns
      -------
      d : float or ndarray, shape (...,)
          Log-det distance between A and B.
  
      See Also
      --------
      distance
  
      References
      ----------
      .. [1] `Matrix nearness problems with Bregman divergences
          <https://epubs.siam.org/doi/abs/10.1137/060649021>`_
          I.S. Dhillon, J.A. Tropp.
          SIAM J Matrix Anal Appl, 2007, 29 (4), pp. 1120-1146
      """
      _check_inputs(A, B)
      logdet_ApB = np.linalg.slogdet((A + B) / 2.0)[1]
      logdet_AxB = np.linalg.slogdet(A @ B)[1]
      d2 = logdet_ApB - 0.5 * logdet_AxB
      d2 = np.maximum(0, d2)
      return d2 if squared else np.sqrt(d2)
  
imports: import numpy
  from scipy.linalg import eigvalsh, solve
  from sklearn.metrics import euclidean_distances
  from .base import logm, sqrtm, invsqrtm
label_desc: Use image node_id 8 for calling a global function with example usage: distance_logdet(A, B, squared) and returns: unknown