code: def test_multivariate_normal_lazy(self, cuda=False):
      device = torch.device("cuda") if cuda else torch.device("cpu")
      for dtype in (torch.float, torch.double):
          mean = torch.tensor([0, 1, 2], device=device, dtype=dtype)
          covmat = torch.diag(
              torch.tensor([1, 0.75, 1.5], device=device, dtype=dtype)
          )
          covmat_chol = torch.linalg.cholesky(covmat)
          mvn = MultivariateNormal(
              mean=mean, covariance_matrix=DenseLinearOperator(covmat)
          )
          self.assertTrue(torch.is_tensor(mvn.covariance_matrix))
          self.assertIsInstance(
              mvn.lazy_covariance_matrix, LinearOperator
          )
          self.assertAllClose(mvn.variance, torch.diag(covmat))
          self.assertAllClose(mvn.covariance_matrix, covmat)
          self.assertAllClose(
              mvn._unbroadcasted_scale_tril, covmat_chol
          )
          mvn_plus1 = mvn + 1
          self.assertAllClose(mvn_plus1.mean, mvn.mean + 1)
          self.assertAllClose(
              mvn_plus1.covariance_matrix, mvn.covariance_matrix
          )
          self.assertAllClose(
              mvn_plus1._unbroadcasted_scale_tril, covmat_chol
          )
          mvn_times2 = mvn * 2
          self.assertAllClose(mvn_times2.mean, mvn.mean * 2)
          self.assertAllClose(
              mvn_times2.covariance_matrix, mvn.covariance_matrix * 4
          )
          self.assertAllClose(
              mvn_times2._unbroadcasted_scale_tril, covmat_chol * 2
          )
          mvn_divby2 = mvn / 2
          self.assertAllClose(mvn_divby2.mean, mvn.mean / 2)
          self.assertAllClose(
              mvn_divby2.covariance_matrix, mvn.covariance_matrix / 4
          )
          self.assertAllClose(
              mvn_divby2._unbroadcasted_scale_tril, covmat_chol / 2
          )
          # TODO: Add tests for entropy, log_prob, etc. - this an issue b/c it
          # uses using root_decomposition which is not very reliable
          # self.assertAlmostEqual(mvn.entropy().item(), 4.3157, places=4)
          # self.assertAlmostEqual(mvn.log_prob(torch.zeros(3)).item(), -4.8157, places=4)
          # self.assertTrue(
          #     torch.allclose(
          #         mvn.log_prob(torch.zeros(2, 3)), -4.8157 * torch.ones(2))
          #     )
          # )
          conf_lower, conf_upper = mvn.confidence_region()
          self.assertAllClose(conf_lower, mvn.mean - 2 * mvn.stddev)
          self.assertAllClose(conf_upper, mvn.mean + 2 * mvn.stddev)
          self.assertTrue(mvn.sample().shape == torch.Size([3]))
          self.assertTrue(
              mvn.sample(torch.Size([2])).shape == torch.Size([2, 3])
          )
          self.assertTrue(
              mvn.sample(torch.Size([2, 4])).shape
              == torch.Size([2, 4, 3])
          )
  
imports: import math
  import unittest
  import torch
  from linear_operator import to_linear_operator
  from linear_operator.operators import DenseLinearOperator, DiagLinearOperator, LinearOperator, RootLinearOperator
  from torch.distributions import MultivariateNormal
  from gpytorch.distributions import MultivariateNormal
  from gpytorch.test.base_test_case import BaseTestCase
  from gpytorch.test.utils import least_used_cuda_device
label_desc: Use image node_id 5 for calling the TestMultivariateNormal obj's underlying member method code with example usage: obj.test_multivariate_normal_lazy(cuda) without return types