code: def mahalanobis_distance(
      F, W: Tensor, D: Tensor, capacitance_tril: Tensor, x: Tensor
  ) -> Tensor:
      r"""
      Uses the Woodbury matrix identity
  
      .. math::
          (W W^T + D)^{-1} = D^{-1} - D^{-1} W C^{-1} W^T D^{-1},
  
      where :math:`C` is the capacitance matrix :math:`I + W^T D^{-1} W`, to
      compute the squared Mahalanobis distance :math:`x^T (W W^T + D)^{-1} x`.
  
      Parameters
      ----------
      F
      W
          (..., dim, rank)
      D
          (..., dim)
      capacitance_tril
          (..., rank, rank)
      x
          (..., dim)
  
      Returns
      -------
  
      """
      xx = x.expand_dims(axis=-1)
  
      # (..., rank, 1)
      Wt_Dinv_x = F.linalg_gemm2(
          F.broadcast_div(W, D.expand_dims(axis=-1)),
          xx,
          transpose_a=True,
      )
  
      # compute x^T D^-1 x, (...,)
      maholanobis_D_inv = F.broadcast_div(x.square(), D).sum(axis=-1)
  
      # (..., rank)
      L_inv_Wt_Dinv_x = F.linalg_trsm(
          capacitance_tril, Wt_Dinv_x
      ).squeeze(axis=-1)
  
      maholanobis_L = L_inv_Wt_Dinv_x.square().sum(axis=-1).squeeze()
  
      return F.broadcast_minus(maholanobis_D_inv, maholanobis_L)
  
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 3 for calling a global function with example usage: mahalanobis_distance(F, W, D, capacitance_tril, x) and returns: F