code: def multivariate_prior_KL(
      meanA: AnyNDArray,
      covA: AnyNDArray,
      meanB: AnyNDArray,
      covB: AnyNDArray,
  ) -> AnyNDArray:
      # KL[ qA | qB ] = E_{qA} \log [qA / qB] where qA and aB are
      # K dimensional multivariate normal distributions.
      # Analytically tractable and equal to...
      # 0.5 * (Tr(covB^{-1} covA) + (meanB - meanA)^T covB^{-1} (meanB - meanA)
      #        - K + log(det(covB)) - log (det(covA)))
      K = covA.shape[0]
      traceTerm = 0.5 * np.trace(np.linalg.solve(covB, covA))
      delta: AnyNDArray = meanB - meanA
      mahalanobisTerm = 0.5 * np.dot(
          delta.T, np.linalg.solve(covB, delta)
      )
      constantTerm = -0.5 * K
      priorLogDeterminantTerm = 0.5 * np.linalg.slogdet(covB)[1]
      variationalLogDeterminantTerm = -0.5 * np.linalg.slogdet(covA)[1]
      return cast(
          AnyNDArray,
          (
              traceTerm
              + mahalanobisTerm
              + constantTerm
              + priorLogDeterminantTerm
              + variationalLogDeterminantTerm
          ),
      )
  
imports: from typing import Tuple, cast
  import numpy
  import pytest
  from check_shapes import check_shapes
  from numpy.testing import assert_allclose
  import gpflow
  from gpflow.base import AnyNDArray
  from gpflow.kernels import SquaredExponential
  from gpflow.likelihoods import Gaussian
  from tests.gpflow.kernels.reference import ref_rbf_kernel
label_desc: Use image node_id 4 for calling a global function with example usage: multivariate_prior_KL(meanA, covA, meanB, covB) and returns: cast