code: def test_lkj_covariance_prior_batch_log_prob(self, cuda=False):
      device = torch.device("cuda") if cuda else torch.device("cpu")
      v = torch.ones(2, 1, device=device)
      sd_prior = SmoothedBoxPrior(exp(-1) * v, exp(1) * v)
      prior = LKJCovariancePrior(
          2, torch.tensor([0.5, 1.5], device=device), sd_prior
      )
      corr_dist = LKJCholesky(
          2, torch.tensor([0.5, 1.5], 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)
      )
      self.assertLessEqual(
          (prior.log_prob(S) - dist_log_prob).abs().sum(), 1e-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.assertLessEqual(
          (prior.log_prob(S) - dist_log_prob).abs().sum(), 1e-4
      )
  
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 7 for calling the TestLKJCovariancePrior obj's underlying member method code with example usage: obj.test_lkj_covariance_prior_batch_log_prob(cuda) without return types