code: def log_det(
      F, batch_D: Tensor, batch_capacitance_tril: Tensor
  ) -> Tensor:
      r"""
      Uses the matrix determinant lemma.
  
      .. math::
          \log|D + W W^T| = \log|C| + \log|D|,
  
      where :math:`C` is the capacitance matrix :math:`I + W^T D^{-1} W`, to
      compute the log determinant.
  
      Parameters
      ----------
      F
      batch_D
      batch_capacitance_tril
  
      Returns
      -------
  
      """
      log_D = batch_D.log().sum(axis=-1)
      log_C = 2 * F.linalg.sumlogdiag(batch_capacitance_tril)
      return log_C + log_D
  
imports: import math
  from typing import Optional, Tuple
  import numpy
  from mxnet import gluon
  from gluonts.core.component import validated
  from gluonts.mx import Tensor
  from .distribution import Distribution, _sample_multiple, getF
  from .distribution_output import ArgProj, DistributionOutput, AffineTransformedDistribution
label_desc: Use image node_id 2 for calling a global function with example usage: log_det(F, batch_D, batch_capacitance_tril) and returns: unknown