code: def test_helper_functions(self) -> None:
      for batch_shape in (torch.Size(), torch.Size([2])):
          tkwargs = {"device": self.device, "dtype": self.dtype}
          # M is borderline PSD
          M = torch.ones((*batch_shape, 2, 2), **tkwargs)
          with self.assertRaises(torch._C._LinAlgError):
              torch.linalg.cholesky(M)
          # This should work fine
          _ensure_psd_with_jitter(M)
  
          bad_M = torch.tensor(
              [[1.0, 2.0], [2.0, 1.0]], **tkwargs
          ).expand((*batch_shape, 2, 2))
          with self.assertRaises(NotPSDError):
              _ensure_psd_with_jitter(bad_M)
  
imports: import itertools
  import random
  import warnings
  from typing import Dict, Tuple, Union
  import torch
  from botorch.acquisition.objective import ScalarizedPosteriorTransform
  from botorch.exceptions import OptimizationWarning, UnsupportedError
  from botorch.exceptions.warnings import _get_single_precision_warning, InputDataWarning
  from botorch.fit import fit_gpytorch_mll
  from botorch.models.likelihoods.pairwise import PairwiseLikelihood, PairwiseLogitLikelihood, PairwiseProbitLikelihood
  from botorch.models.model import Model
  from botorch.models.pairwise_gp import _ensure_psd_with_jitter, PairwiseGP, PairwiseLaplaceMarginalLogLikelihood
  from botorch.models.transforms.input import Normalize
  from botorch.posteriors import GPyTorchPosterior
  from botorch.sampling.pairwise_samplers import PairwiseSobolQMCNormalSampler
  from botorch.utils.testing import BotorchTestCase
  from gpytorch.kernels import RBFKernel, ScaleKernel
  from gpytorch.kernels.linear_kernel import LinearKernel
  from gpytorch.means import ConstantMean
  from gpytorch.priors import GammaPrior, SmoothedBoxPrior
  from linear_operator.utils.errors import NotPSDError
  from torch import Tensor
label_desc: Use image node_id 9 for calling the TestPairwiseGP obj's underlying member method code with example usage: obj.test_helper_functions() without return types