code: def test_optimization_optimal_error(
      self, num_inducing=16, num_data=32, D=2
  ):
      inducing_points = torch.randn(num_inducing, D)
  
      class SVGP(gpytorch.models.ApproximateGP):
          def __init__(self):
              v_dist = NaturalVariationalDistribution(num_inducing)
              v_strat = (
                  gpytorch.variational.UnwhitenedVariationalStrategy(
                      self, inducing_points, v_dist
                  )
              )
              super().__init__(v_strat)
              self.mean_module = gpytorch.means.ZeroMean()
              self.covar_module = gpytorch.kernels.RBFKernel()
  
          def forward(self, x):
              return MultivariateNormal(
                  self.mean_module(x), self.covar_module(x)
              )
  
      model = SVGP().train()
      likelihood = gpytorch.likelihoods.GaussianLikelihood().train()
      mll = gpytorch.mlls.VariationalELBO(likelihood, model, num_data)
      X = torch.randn((num_data, D))
      y = torch.randn(num_data)
  
      def loss():
          return -mll(model(X), y)
  
      optimizer = torch.optim.SGD(
          model.variational_strategy._variational_distribution.parameters(),
          lr=float(num_data),
      )
  
      optimizer.zero_grad()
      loss().backward()
      optimizer.step()  # Now we should be at the optimum
  
      optimizer.zero_grad()
      loss().backward()
      natgrad_natural_vec2, natgrad_natural_mat2 = (
          model.variational_strategy._variational_distribution.natural_vec.grad.clone(),
          model.variational_strategy._variational_distribution.natural_mat.grad.clone(),
      )
      # At the optimum, the (natural) gradients are zero:
      assert torch.allclose(natgrad_natural_vec2, torch.zeros(()))
      assert torch.allclose(natgrad_natural_mat2, torch.zeros(()))
  
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 4 for calling the TestNatVariational obj's underlying member method code with example usage: obj.test_optimization_optimal_error(num_inducing, num_data, D) and returns: unknown, MultivariateNormal