code: def test_pairwise_gp(self) -> None:
      torch.manual_seed(random.randint(0, 10))
      for batch_shape, likelihood_cls in itertools.product(
          (torch.Size(), torch.Size([2])),
          (PairwiseLogitLikelihood, PairwiseProbitLikelihood),
      ):
          tkwargs = {"device": self.device, "dtype": self.dtype}
          X_dim = 2
  
          model, model_kwargs = self._get_model_and_data(
              batch_shape=batch_shape,
              X_dim=X_dim,
              likelihood_cls=likelihood_cls,
          )
          train_X = model_kwargs["datapoints"]
          train_comp = model_kwargs["comparisons"]
  
          # test training
          # regular training
          mll = PairwiseLaplaceMarginalLogLikelihood(
              model.likelihood, model
          ).to(**tkwargs)
          with warnings.catch_warnings():
              warnings.filterwarnings(
                  "ignore", category=OptimizationWarning
              )
              fit_gpytorch_mll(
                  mll,
                  optimizer_kwargs={"options": {"maxiter": 2}},
                  max_attempts=1,
              )
          with self.subTest("prior training"):
              # prior training
              prior_m = PairwiseGP(None, None).to(**tkwargs)
              with self.assertRaises(RuntimeError):
                  prior_m(train_X)
  
          with self.subTest(
              "forward in training mode with non-training data"
          ):
              custom_m = PairwiseGP(**model_kwargs)
              other_X = torch.rand(
                  batch_shape + torch.Size([3, X_dim]), **tkwargs
              )
              other_comp = train_comp.clone()
              with self.assertRaises(RuntimeError):
                  custom_m(other_X)
              custom_mll = PairwiseLaplaceMarginalLogLikelihood(
                  custom_m.likelihood, custom_m
              ).to(**tkwargs)
              post = custom_m(train_X)
              with self.assertRaises(RuntimeError):
                  custom_mll(post, other_comp)
  
          with self.subTest("init"):
              self.assertIsInstance(model.mean_module, ConstantMean)
              self.assertIsInstance(model.covar_module, ScaleKernel)
              self.assertIsInstance(
                  model.covar_module.base_kernel, RBFKernel
              )
              self.assertIsInstance(
                  model.covar_module.base_kernel.lengthscale_prior,
                  GammaPrior,
              )
              self.assertIsInstance(
                  model.covar_module.outputscale_prior, SmoothedBoxPrior
              )
              self.assertEqual(model.num_outputs, 1)
              self.assertEqual(model.batch_shape, batch_shape)
  
          # test not using a ScaleKernel
          with self.assertRaisesRegex(
              UnsupportedError, "used with a ScaleKernel"
          ):
              PairwiseGP(**model_kwargs, covar_module=LinearKernel())
  
          # test custom models
          custom_m = PairwiseGP(
              **model_kwargs, covar_module=ScaleKernel(LinearKernel())
          )
          self.assertIsInstance(custom_m.covar_module, ScaleKernel)
          self.assertIsInstance(
              custom_m.covar_module.base_kernel, LinearKernel
          )
  
          # prior prediction
          prior_m = PairwiseGP(None, None).to(**tkwargs)
          prior_m.eval()
          post = prior_m.posterior(train_X)
          self.assertIsInstance(post, GPyTorchPosterior)
  
          # test initial utility val
          util_comp = torch.topk(
              model.utility, k=2, dim=-1
          ).indices.unsqueeze(-2)
          self.assertTrue(torch.all(util_comp == train_comp))
  
          # test posterior
          # test non batch evaluation
          X = torch.rand(
              batch_shape + torch.Size([3, X_dim]), **tkwargs
          )
          expected_shape = batch_shape + torch.Size([3, 1])
          posterior = model.posterior(X)
          self.assertIsInstance(posterior, GPyTorchPosterior)
          self.assertEqual(posterior.mean.shape, expected_shape)
          self.assertEqual(posterior.variance.shape, expected_shape)
  
          # test posterior transform
          post_tf = ScalarizedPosteriorTransform(weights=torch.ones(1))
          posterior_tf = model.posterior(X, posterior_transform=post_tf)
          self.assertTrue(
              torch.equal(posterior.mean, posterior_tf.mean)
          )
  
          # expect to raise error when output_indices is not None
          with self.assertRaises(RuntimeError):
              model.posterior(X, output_indices=[0])
  
          # test re-evaluating utility when it's None
          model.utility = None
          posterior = model.posterior(X)
          self.assertIsInstance(posterior, GPyTorchPosterior)
  
          # test batch evaluation
          X = torch.rand(2, *batch_shape, 3, X_dim, **tkwargs)
          expected_shape = (
              torch.Size([2]) + batch_shape + torch.Size([3, 1])
          )
  
          posterior = model.posterior(X)
          self.assertIsInstance(posterior, GPyTorchPosterior)
          self.assertEqual(posterior.mean.shape, expected_shape)
  
          # test input_transform
          # the untransfomed one should be stored
          normalize_tf = Normalize(
              d=2, bounds=torch.tensor([[0, 0], [0.5, 1.5]])
          )
          model = PairwiseGP(
              **model_kwargs, input_transform=normalize_tf
          )
          self.assertTrue(torch.equal(model.datapoints, train_X))
  
          # test set_train_data strict mode
          model = PairwiseGP(**model_kwargs)
          changed_train_X = train_X.unsqueeze(0)
          changed_train_comp = train_comp.unsqueeze(0)
          # expect to raise error when set data to something different
          with self.assertRaises(RuntimeError):
              model.set_train_data(
                  changed_train_X, changed_train_comp, strict=True
              )
  
          # the same datapoints but changed comparison will also raise error
          with self.assertRaises(RuntimeError):
              model.set_train_data(
                  train_X, changed_train_comp, strict=True
              )
  
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 4 for calling the TestPairwiseGP obj's underlying member method code with example usage: obj.test_pairwise_gp() without return types