code: def test_lkj_covariance_prior_log_prob_hetsd(self, cuda=False):
      device = torch.device("cuda") if cuda else torch.device("cpu")
      a = torch.tensor([exp(-1), exp(-2)], device=device)
      b = torch.tensor([exp(1), exp(2)], device=device)
      sd_prior = SmoothedBoxPrior(a, b)
      prior = LKJCovariancePrior(
          2, torch.tensor(0.5, device=device), sd_prior
      )
      corr_dist = LKJCholesky(2, torch.tensor(0.5, device=device))
  
      S = torch.eye(2, device=device)
      dist_log_prob = (
          corr_dist.log_prob(S)
          + sd_prior.log_prob(S.diagonal(dim1=-1, dim2=-2)).sum()
      )
      self.assertAlmostEqual(prior.log_prob(S), dist_log_prob, places=4)
  
      S = torch.stack(
          [S, torch.tensor([[1.0, 0.5], [0.5, 1]], device=S.device)]
      )
      S_chol = torch.linalg.cholesky(S)
      dist_log_prob = corr_dist.log_prob(S_chol) + sd_prior.log_prob(
          torch.diagonal(S, dim1=-2, dim2=-1)
      )
      self.assertTrue(approx_equal(prior.log_prob(S), dist_log_prob))
  
imports: import unittest
  from math import exp
  import torch
  from torch.distributions import LKJCholesky
  from gpytorch.priors import LKJCholeskyFactorPrior, LKJCovariancePrior, LKJPrior, SmoothedBoxPrior
  from gpytorch.priors.lkj_prior import _is_valid_correlation_matrix, _is_valid_correlation_matrix_cholesky_factor
  from gpytorch.test.utils import approx_equal, least_used_cuda_device
label_desc: Use image node_id 5 for calling the TestLKJCovariancePrior obj's underlying member method code with example usage: obj.test_lkj_covariance_prior_log_prob_hetsd(cuda) without return types