code: def test_lkj_cholesky_factor_prior_batch_log_prob(self, cuda=False):
      device = torch.device("cuda") if cuda else torch.device("cpu")
      prior = LKJCholeskyFactorPrior(
          2, torch.tensor([0.5, 1.5], device=device)
      )
      dist = LKJCholesky(2, torch.tensor([0.5, 1.5], device=device))
  
      S = torch.eye(2, device=device)
      S_chol = torch.linalg.cholesky(S)
      self.assertTrue(
          approx_equal(prior.log_prob(S_chol), dist.log_prob(S_chol))
      )
      S = torch.stack(
          [S, torch.tensor([[1.0, 0.5], [0.5, 1]], device=S.device)]
      )
      S_chol = torch.stack([torch.linalg.cholesky(Si) for Si in S])
      self.assertTrue(
          approx_equal(prior.log_prob(S_chol), dist.log_prob(S_chol))
      )
  
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 TestLKJCholeskyFactorPrior obj's underlying member method code with example usage: obj.test_lkj_cholesky_factor_prior_batch_log_prob(cuda) without return types