code: def test_initialization(self):
      tkwargs = {"device": self.device}
      for dtype, acqf_class in product(
          (torch.float, torch.double),
          (
              qHypervolumeKnowledgeGradient,
              qMultiFidelityHypervolumeKnowledgeGradient,
          ),
      ):
          tkwargs["dtype"] = dtype
          X = torch.rand(4, 3, **tkwargs)
          Y1 = torch.rand(4, 1, **tkwargs)
          Y2 = torch.rand(4, 1, **tkwargs)
          m1 = SingleTaskGP(X, Y1)
          m2 = SingleTaskGP(X, Y2)
          model = ModelListGP(m1, m2)
          ref_point = torch.zeros(2, **tkwargs)
          # test sampler is None
          if acqf_class == qMultiFidelityHypervolumeKnowledgeGradient:
              mf_kwargs = {"target_fidelities": {-1: 1.0}}
          else:
              mf_kwargs = {}
          acqf = acqf_class(
              model=model, ref_point=ref_point, **mf_kwargs
          )
  
          self.assertIsInstance(acqf.sampler, ListSampler)
          self.assertEqual(
              acqf.sampler.samplers[0].sample_shape, torch.Size([8])
          )
          # test ref point
          self.assertTrue(torch.equal(acqf.ref_point, ref_point))
          # test sampler is not None
          sampler = ListSampler(
              SobolQMCNormalSampler(sample_shape=torch.Size([4])),
              SobolQMCNormalSampler(sample_shape=torch.Size([4])),
          )
          with self.assertRaisesRegex(
              ValueError,
              "The sampler shape must match num_fantasies=8.",
          ):
              acqf_class(
                  model=model,
                  ref_point=ref_point,
                  sampler=sampler,
                  **mf_kwargs,
              )
          acqf = acqf_class(
              model=model,
              ref_point=ref_point,
              num_fantasies=4,
              num_pareto=8,
              sampler=sampler,
              use_posterior_mean=False,
              **mf_kwargs,
          )
          self.assertEqual(acqf.num_fantasies, 4)
          self.assertEqual(acqf.num_pareto, 8)
          self.assertEqual(acqf.num_pseudo_points, 32)
          self.assertFalse(acqf.use_posterior_mean)
          self.assertIsInstance(
              acqf.inner_sampler, SobolQMCNormalSampler
          )
          self.assertEqual(
              acqf.inner_sampler.sample_shape, torch.Size([32])
          )
          self.assertIsNone(acqf._cost_sampler)
          # test objective
          mc_objective = GenericMCMultiOutputObjective(
              lambda Y, X: 2 * Y
          )
          acqf = acqf_class(
              model=model,
              ref_point=ref_point,
              objective=mc_objective,
              **mf_kwargs,
          )
          self.assertIs(acqf.objective, mc_objective)
          # test X_pending
          X_pending = torch.rand(2, 3, **tkwargs)
          acqf = acqf_class(
              model=model,
              ref_point=ref_point,
              X_pending=X_pending,
              **mf_kwargs,
          )
          self.assertTrue(torch.equal(acqf.X_pending, X_pending))
          # test X_pending_evaluation_mask
          X_pending_evaluation_mask = torch.eye(
              2, device=self.device
          ).bool()
          acqf = acqf_class(
              model=model,
              ref_point=ref_point,
              X_pending=X_pending,
              X_pending_evaluation_mask=X_pending_evaluation_mask,
              **mf_kwargs,
          )
          self.assertTrue(
              torch.equal(
                  acqf.X_pending_evaluation_mask,
                  X_pending_evaluation_mask,
              )
          )
          # test cost aware utility
          cost_model = GenericDeterministicModel(
              lambda X: torch.ones(X.shape[:-1], 2, **tkwargs)
          )
          for use_mean in (True, False):
              cost_aware_utility = InverseCostWeightedUtility(
                  cost_model=cost_model, use_mean=use_mean
              )
              with self.assertRaisesRegex(
                  UnsupportedError,
                  "Cost-aware HVKG requires current_value to be specified.",
              ):
                  acqf_class(
                      model=model,
                      ref_point=ref_point,
                      cost_aware_utility=cost_aware_utility,
                      **mf_kwargs,
                  )
              acqf = acqf_class(
                  model=model,
                  ref_point=ref_point,
                  cost_aware_utility=cost_aware_utility,
                  current_value=0.0,
                  **mf_kwargs,
              )
              self.assertEqual(acqf.current_value, 0.0)
              self.assertIs(acqf.cost_aware_utility, cost_aware_utility)
  
          # test get_aug_q_batch_size
          self.assertEqual(acqf.get_augmented_q_batch_size(q=3), 83)
  
          if acqf_class is qMultiFidelityHypervolumeKnowledgeGradient:
              # test default
              x = torch.rand(5, 3, **tkwargs)
              self.assertTrue(torch.equal(acqf.project(x), x))
              # test expand raises exception
              with self.assertRaisesRegex(
                  NotImplementedError,
                  "Trace observations are not currently supported.",
              ):
                  acqf_class(
                      model=model,
                      ref_point=ref_point,
                      expand=lambda X: X,
                      **mf_kwargs,
                  )
  
imports: from itertools import product
  from unittest import mock
  import numpy
  import torch
  from botorch.acquisition.cost_aware import InverseCostWeightedUtility
  from botorch.acquisition.multi_objective.hypervolume_knowledge_gradient import _get_hv_value_function, _split_hvkg_fantasy_points, qHypervolumeKnowledgeGradient, qMultiFidelityHypervolumeKnowledgeGradient
  from botorch.acquisition.multi_objective.objective import GenericMCMultiOutputObjective, IdentityMCMultiOutputObjective
  from botorch.exceptions.errors import UnsupportedError
  from botorch.models.deterministic import GenericDeterministicModel
  from botorch.models.gp_regression import SingleTaskGP
  from botorch.models.model_list_gp_regression import ModelListGP
  from botorch.sampling.list_sampler import ListSampler
  from botorch.sampling.normal import SobolQMCNormalSampler
  from botorch.utils.multi_objective.box_decompositions.dominated import DominatedPartitioning
  from botorch.utils.testing import BotorchTestCase, MockModel, MockPosterior
label_desc: Use image node_id 1 for calling the TestHypervolumeKnowledgeGradient obj's underlying member method code with example usage: obj.test_initialization() without return types