code: def testMultiTaskBlockSeparable(self):
      # Check that the naive implementation matches any optimizations for a
      # Separable Kernel.
  
      # 5x5 grid of index points in R^2 and flatten to 25x2
      index_points = np.linspace(-10.0, 10.0, 5, dtype=np.float64)
      index_points = np.stack(
          np.meshgrid(index_points, index_points), axis=-1
      )
      index_points = np.reshape(index_points, [-1, 2])
      # ==> shape = [25, 2]
  
      # Kernel with batch_shape [2, 4, 3, 1]
      amplitude = np.array([1.0, 2.0], np.float64).reshape([2, 1, 1, 1])
      length_scale = np.array([1.0, 2.0, 3.0, 4.0], np.float64).reshape(
          [1, 4, 1, 1]
      )
      observation_noise_variance = np.array(
          [1e-3, 1e-2, 1e-1], np.float64
      ).reshape([1, 1, 3, 1])
      batched_index_points = np.stack([index_points] * 6)
      # ==> shape = [6, 25, 2]
      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,
      )
      multitask_gp = (
          multitask_gaussian_process.MultiTaskGaussianProcess(
              multi_task_kernel,
              batched_index_points,
              observation_noise_variance=observation_noise_variance,
              validate_args=True,
          )
      )
      naive_multi_task_kernel = InefficientSeparable(
          num_tasks=3,
          task_kernel_matrix_linop=task_kernel_matrix_linop,
          base_kernel=kernel,
      )
      actual_multitask_gp = (
          multitask_gaussian_process.MultiTaskGaussianProcess(
              naive_multi_task_kernel,
              batched_index_points,
              observation_noise_variance=observation_noise_variance,
              validate_args=False,
          )
      )
  
      observations = (
          np.linspace(-20.0, 20.0, 75).reshape(25, 3).astype(np.float64)
      )
      multitask_log_prob = multitask_gp.log_prob(observations)
      actual_multitask_log_prob = actual_multitask_gp.log_prob(
          observations
      )
      self.assertAllClose(
          self.evaluate(actual_multitask_log_prob),
          self.evaluate(multitask_log_prob),
          rtol=4e-3,
      )
  
      multitask_mean = multitask_gp.mean()
      actual_multitask_mean = actual_multitask_gp.mean()
      self.assertAllClose(
          self.evaluate(actual_multitask_mean),
          self.evaluate(multitask_mean),
          rtol=4e-3,
      )
  
      multitask_var = multitask_gp.variance()
      actual_multitask_var = actual_multitask_gp.variance()
      self.assertAllClose(
          self.evaluate(actual_multitask_var),
          self.evaluate(multitask_var),
          rtol=4e-3,
      )
  
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 6 for calling the MultiTaskGaussianProcessTest obj's underlying member method code with example usage: obj.testMultiTaskBlockSeparable() without return types