code: def _hpsd_logdet_bwd(aux, g):
      """Reverse mode impl for hpsd_logdet."""
      (cholesky_matrix,) = aux
      dmatrix = g
      chol_linop = tf.linalg.LinearOperatorLowerTriangular(
          cholesky_matrix
      )
      chol_inverse = chol_linop.solve(
          tf.linalg.eye(
              num_rows=chol_linop.domain_dimension_tensor(),
              dtype=chol_linop.dtype,
          )
      )
      inverse_matrix = tf.linalg.matmul(
          chol_inverse, chol_inverse, transpose_a=True
      )
  
      return dmatrix[..., tf.newaxis, tf.newaxis] * inverse_matrix, None
  
imports: import numpy
  import tensorflow.compat.v1
  import tensorflow.compat.v2
  from tensorflow_probability.python.internal import assert_util
  from tensorflow_probability.python.internal import custom_gradient
  from tensorflow_probability.python.internal import distribution_util
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import prefer_static
  from tensorflow_probability.python.internal import tensorshape_util
  from tensorflow_probability.python.math import generic
label_desc: Use image node_id 21 for calling a global function with example usage: _hpsd_logdet_bwd(aux, g) and returns: unknown,  None