code: def test_natgrad(self, D=5):
      mu = torch.randn(D)
      cov = torch.randn(D, D)
      cov = cov @ cov.t()
      dist = MultivariateNormal(
          mu,
          CholLinearOperator(
              TriangularLinearOperator(torch.linalg.cholesky(cov))
          ),
      )
      sample = dist.sample()
  
      v_dist = TrilNaturalVariationalDistribution(D, mean_init_std=0.0)
      v_dist.initialize_variational_distribution(dist)
      v_dist().log_prob(sample).squeeze().backward()
      dout_dnat1 = v_dist.natural_vec.grad
      dout_dnat2 = v_dist.natural_tril_mat.grad
  
      # mean_init_std=0. because we need to ensure both have the same distribution
      v_dist_ref = NaturalVariationalDistribution(D, mean_init_std=0.0)
      v_dist_ref.initialize_variational_distribution(dist)
      v_dist_ref().log_prob(sample).squeeze().backward()
      dout_dnat1_noforward_ref = v_dist_ref.natural_vec.grad
      dout_dnat2_noforward_ref = v_dist_ref.natural_mat.grad
  
      def f(natural_vec, natural_tril_mat):
          "Transform natural_tril_mat to L"
          Sigma = torch.inverse(-2 * natural_tril_mat)
          mu = natural_vec
          return mu, torch.linalg.cholesky(Sigma).inverse().tril()
  
      (mu_ref, natural_tril_mat_ref), (
          dout_dmu_ref,
          dout_dnat2_ref,
      ) = jvp(
          f,
          (
              v_dist_ref.natural_vec.detach(),
              v_dist_ref.natural_mat.detach(),
          ),
          (dout_dnat1_noforward_ref, dout_dnat2_noforward_ref),
      )
  
      assert torch.allclose(
          natural_tril_mat_ref, v_dist.natural_tril_mat
      ), "Sigma transformation"
      assert torch.allclose(
          dout_dnat2_ref, dout_dnat2
      ), "Sigma gradient"
  
      assert torch.allclose(
          mu_ref, v_dist.natural_vec
      ), "mu transformation"
      assert torch.allclose(dout_dmu_ref, dout_dnat1), "mu gradient"
  
imports: import unittest
  import torch
  from linear_operator.operators import CholLinearOperator, TriangularLinearOperator
  import gpytorch
  from gpytorch.constraints import GreaterThan
  from gpytorch.distributions import MultivariateNormal
  from gpytorch.variational import NaturalVariationalDistribution, TrilNaturalVariationalDistribution
label_desc: Use image node_id 2 for calling the TestTrilNatVariational obj's underlying member method code with example usage: obj.test_natgrad(D) and returns: mu,  torch