code: def testMTGPPosteriorPredictive(self):
      amplitude = np.float64(0.5)
      length_scale = np.float64(2.0)
      observation_noise_variance = np.float64(3e-3)
      kernel = exponentiated_quadratic.ExponentiatedQuadratic(
          amplitude, length_scale
      )
      # Ensure Symmetric + Strictly Diagonally Dominant -> Positive Definite.
      task_kernel_matrix = np.array(
          [[6.0, 2.0, 3.0], [2.0, 7.0, 4.0], [3.0, 4.0, 8.0]],
          dtype=np.float64,
      )
      task_kernel_matrix_linop = tf.linalg.LinearOperatorFullMatrix(
          task_kernel_matrix
      )
      multi_task_kernel = multitask_kernel.Separable(
          num_tasks=3,
          task_kernel_matrix_linop=task_kernel_matrix_linop,
          base_kernel=kernel,
      )
  
      index_points = np.random.uniform(-1.0, 1.0, 10)[..., np.newaxis]
  
      mtgp = multitask_gaussian_process.MultiTaskGaussianProcess(
          multi_task_kernel,
          index_points,
          observation_noise_variance=observation_noise_variance,
          validate_args=True,
      )
  
      predictive_index_points = np.random.uniform(1.0, 2.0, 10)[
          ..., np.newaxis
      ]
      observations = np.linspace(1.0, 10.0, 30).reshape(10, 3)
  
      expected_mtgprm = mtgprm.MultiTaskGaussianProcessRegressionModel(
          kernel=multi_task_kernel,
          observation_index_points=index_points,
          observations=observations,
          observation_noise_variance=observation_noise_variance,
          index_points=predictive_index_points,
          validate_args=True,
      )
  
      actual_mtgprm = mtgp.posterior_predictive(
          predictive_index_points=predictive_index_points,
          observations=observations,
      )
  
      samples = self.evaluate(
          actual_mtgprm.sample(10, seed=test_util.test_seed())
      )
  
      self.assertAllClose(
          self.evaluate(expected_mtgprm.mean()),
          self.evaluate(actual_mtgprm.mean()),
      )
  
      self.assertAllClose(
          self.evaluate(expected_mtgprm.log_prob(samples)),
          self.evaluate(actual_mtgprm.log_prob(samples)),
      )
  
imports: from absl.testing import parameterized
  import numpy
  import tensorflow.compat.v2
  from tensorflow_probability.python.distributions import gaussian_process
  from tensorflow_probability.python.experimental.distributions import multitask_gaussian_process
  from tensorflow_probability.python.experimental.distributions import multitask_gaussian_process_regression_model
  from tensorflow_probability.python.experimental.psd_kernels import multitask_kernel
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import parameter_properties
  from tensorflow_probability.python.internal import tensor_util
  from tensorflow_probability.python.internal import test_util
  from tensorflow_probability.python.math.psd_kernels import exponentiated_quadratic
  from tensorflow_probability.python.math.psd_kernels.internal import test_util
label_desc: Use image node_id 9 for calling the MultiTaskGaussianProcessTest obj's underlying member method code with example usage: obj.testMTGPPosteriorPredictive() without return types