code: def test_split_hvkg_fantasy_points(self):
      d = 4
      for dtype, batch_shape, n_f, num_pareto, q in product(
          (torch.float, torch.double),
          ([], [2], [3, 2]),
          (1, 4),
          (1, 3),
          (1, 2),
      ):
          X = torch.rand(
              *batch_shape,
              q + num_pareto * n_f,
              d,
              dtype=dtype,
              device=self.device,
          )
          X_actual, X_fant = _split_hvkg_fantasy_points(
              X=X, n_f=n_f, num_pareto=num_pareto
          )
          self.assertTrue(torch.equal(X_actual, X[..., :q, :]))
          self.assertTrue(
              torch.equal(
                  X_fant,
                  X[..., q:, :].reshape(
                      n_f, *batch_shape, num_pareto, d
                  ),
              )
          )
      # test two many fantasies
      X = torch.rand(10, d, device=self.device)
      n_f = 100
      num_pareto = 3
      msg = (
          rf".*\({n_f*num_pareto}\) must be less than"
          rf" the `q`-batch dimension of `X` \({X.size(-2)}\)\."
      )
      with self.assertRaisesRegex(ValueError, msg):
          _split_hvkg_fantasy_points(
              X=X, n_f=n_f, num_pareto=num_pareto
          )
  
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 3 for calling the TestHypervolumeKnowledgeGradient obj's underlying member method code with example usage: obj.test_split_hvkg_fantasy_points() without return types