code: def test_kl_divergence(self, cuda=False):
      device = torch.device("cuda") if cuda else torch.device("cpu")
      for dtype in (torch.float, torch.double):
          mean0 = torch.randn(4, device=device, dtype=dtype)
          mean1 = mean0 + 1
          var0 = torch.randn(4, device=device, dtype=dtype).abs_()
          var1 = var0 * math.exp(2)
  
          dist_a = MultivariateNormal(mean0, DiagLinearOperator(var0))
          dist_b = MultivariateNormal(mean1, DiagLinearOperator(var0))
          dist_c = MultivariateNormal(mean0, DiagLinearOperator(var1))
  
          res = torch.distributions.kl.kl_divergence(dist_a, dist_a)
          actual = 0.0
          self.assertLess((res - actual).abs().item(), 1e-2)
  
          res = torch.distributions.kl.kl_divergence(dist_b, dist_a)
          actual = var0.reciprocal().sum().div(2.0)
          self.assertLess((res - actual).div(res).abs().item(), 1e-2)
  
          res = torch.distributions.kl.kl_divergence(dist_a, dist_c)
          actual = 0.5 * (8 - 4 + 4 * math.exp(-2))
          self.assertLess((res - actual).div(res).abs().item(), 1e-2)
  
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 15 for calling the TestMultivariateNormal obj's underlying member method code with example usage: obj.test_kl_divergence(cuda) without return types