code: def test_dtype_compatibility_with_PairwiseGP(self) -> None:
      og_sample_shape = 3
      batch_size = 2
      n = 8
  
      test_X = torch.rand(
          torch.Size((og_sample_shape, batch_size, n, self.x_dim)),
      )
  
      for pref_model_dtype, test_x_dtype, expected_output_dtype in [
          (torch.float64, torch.float64, torch.float64),
          (torch.float32, torch.float32, torch.float32),
          (torch.float64, torch.float32, torch.float64),
      ]:
          with self.subTest(
              "numerical behavior",
              pref_model_dtype=pref_model_dtype,
              test_x_dtype=test_x_dtype,
              expected_output_dtype=expected_output_dtype,
          ):
              # Ignore a single-precision warning in PairwiseGP
              # and mixed-precision warning tested below
              with warnings.catch_warnings():
                  warnings.filterwarnings(
                      "ignore",
                      category=InputDataWarning,
                      message=_get_single_precision_warning(
                          str(torch.float32)
                      ),
                  )
                  pref_model = self._get_pref_model(
                      dtype=pref_model_dtype,
                      input_transform=Normalize(d=2),
                  )
              pref_obj = LearnedObjective(pref_model=pref_model)
              with warnings.catch_warnings():
                  warnings.filterwarnings(
                      "ignore",
                      category=InputDataWarning,
                      message=LEARNED_OBJECTIVE_PREF_MODEL_MIXED_DTYPE_WARN,
                  )
                  first_call_output = pref_obj(
                      test_X.to(dtype=test_x_dtype)
                  )
                  second_call_output = pref_obj(
                      test_X.to(dtype=test_x_dtype)
                  )
  
              self.assertEqual(
                  first_call_output.dtype, expected_output_dtype
              )
              self.assertTrue(
                  torch.equal(first_call_output, second_call_output)
              )
  
      with self.subTest("mixed precision warning"):
          # should warn and test should pass
          with warnings.catch_warnings():
              warnings.simplefilter("ignore", category=InputDataWarning)
              pref_model = self._get_pref_model(
                  dtype=torch.float64, input_transform=Normalize(d=2)
              )
          pref_obj = LearnedObjective(pref_model=pref_model)
          with self.assertWarnsRegex(
              InputDataWarning,
              LEARNED_OBJECTIVE_PREF_MODEL_MIXED_DTYPE_WARN,
          ):
              first_call_output = pref_obj(test_X)
  
imports: import itertools
  import warnings
  from typing import Optional
  import torch
  from botorch import settings
  from botorch.acquisition import LearnedObjective
  from botorch.acquisition.objective import ConstrainedMCObjective, DEFAULT_NUM_PREF_SAMPLES, ExpectationPosteriorTransform, GenericMCObjective, IdentityMCObjective, LEARNED_OBJECTIVE_PREF_MODEL_MIXED_DTYPE_WARN, LinearMCObjective, MCAcquisitionObjective, PosteriorTransform, ScalarizedPosteriorTransform
  from botorch.exceptions.errors import UnsupportedError
  from botorch.exceptions.warnings import _get_single_precision_warning, InputDataWarning
  from botorch.models.deterministic import PosteriorMeanModel
  from botorch.models.pairwise_gp import PairwiseGP
  from botorch.models.transforms.input import Normalize
  from botorch.posteriors import GPyTorchPosterior
  from botorch.utils import apply_constraints
  from botorch.utils.testing import _get_test_posterior, BotorchTestCase
  from gpytorch.distributions import MultitaskMultivariateNormal, MultivariateNormal
  from linear_operator.operators.dense_linear_operator import to_linear_operator
  from torch import Tensor
label_desc: Use image node_id 4 for calling the TestLearnedObjective obj's underlying member method code with example usage: obj.test_dtype_compatibility_with_PairwiseGP() without return types