code: def combine_filter_elements(fi, fj):
      """Binary operation used to combine partial Kalman filter results."""
      with tf.name_scope("combine_filter_elements"):
          m1t = tf.linalg.solve(
              _add_identity_to_diagonal(
                  tf.linalg.matmul(
                      fi.posterior_cov, fj.marginal_likelihood_prec
                  )
              ),
              # TODO(b/168836494): `solve` should support an implicit transpose.
              tf.linalg.matrix_transpose(fj.posterior_link_matrix),
              adjoint=True,
          )
          m2t = tf.linalg.solve(
              _add_identity_to_diagonal(
                  tf.linalg.matmul(
                      fj.marginal_likelihood_prec, fi.posterior_cov
                  )
              ),
              fi.posterior_link_matrix,
              adjoint=True,
          )
  
          return FilterElements(
              posterior_link_matrix=tf.linalg.matmul(
                  m1t, fi.posterior_link_matrix, transpose_a=True
              ),
              posterior_mean=tf.linalg.matvec(
                  m1t,
                  fi.posterior_mean
                  + tf.linalg.matvec(
                      fi.posterior_cov, fj.marginal_likelihood_meanprec
                  ),
                  transpose_a=True,
              )
              + fj.posterior_mean,
              posterior_cov=(
                  tf.linalg.matmul(
                      tf.linalg.matmul(
                          m1t, fi.posterior_cov, transpose_a=True
                      ),
                      fj.posterior_link_matrix,
                      transpose_b=True,
                  )
                  + fj.posterior_cov
              ),
              marginal_likelihood_meanprec=(
                  tf.linalg.matvec(
                      m2t,
                      (
                          fj.marginal_likelihood_meanprec
                          - tf.linalg.matvec(
                              fj.marginal_likelihood_prec,
                              fi.posterior_mean,
                          )
                      ),
                      transpose_a=True,
                  )
                  + fi.marginal_likelihood_meanprec
              ),
              marginal_likelihood_prec=(
                  tf.linalg.matmul(
                      tf.linalg.matmul(
                          m2t,
                          fj.marginal_likelihood_prec,
                          transpose_a=True,
                      ),
                      fi.posterior_link_matrix,
                  )
                  + fi.marginal_likelihood_prec
              ),
          )
  
imports: import collections
  import functools
  import numpy
  import tensorflow.compat.v2
  from tensorflow_probability.python.distributions import mvn_tril
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import prefer_static
  from tensorflow_probability.python.internal import samplers
  from tensorflow_probability.python.math import linalg
  from tensorflow_probability.python.math.scan_associative import scan_associative
label_desc: Use image node_id 4 for calling a global function with example usage: combine_filter_elements(fi, fj) and returns: FilterElements