code: def test_gen_one_shot_hvkg_initial_conditions(self):
      num_fantasies = 8
      num_restarts = 4
      raw_samples = 16
      tkwargs = {"device": self.device}
      for dtype in (torch.float, torch.double):
          tkwargs["dtype"] = dtype
          X = torch.rand(4, 2, **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)
          for acqf_class in (
              qHypervolumeKnowledgeGradient,
              qMultiFidelityHypervolumeKnowledgeGradient,
          ):
              is_mf_kg = (
                  acqf_class
                  is qMultiFidelityHypervolumeKnowledgeGradient
              )
              mf_kwargs = (
                  {"target_fidelities": {1: 1.0}} if is_mf_kg else {}
              )
              hvkg = acqf_class(
                  model=model,
                  ref_point=torch.zeros(2, **tkwargs),
                  num_fantasies=num_fantasies,
                  **mf_kwargs,
              )
              bounds = torch.tensor(
                  [[0, 0], [1, 1]], device=self.device, dtype=dtype
              )
              # test option error
              with self.assertRaises(ValueError):
                  gen_one_shot_hvkg_initial_conditions(
                      acq_function=hvkg,
                      bounds=bounds,
                      q=1,
                      num_restarts=num_restarts,
                      raw_samples=raw_samples,
                      options={"frac_random": 2.0},
                  )
              # test generation logic
              q = 2
              mock_fantasy_cands = torch.ones(20, 10, 2)
              mock_fantasy_vals = torch.randn(20)
  
              def mock_gen_ics(*args, **kwargs):
                  fixed_X_fantasies = kwargs.get("fixed_X_fantasies")
                  if fixed_X_fantasies is None:
                      return torch.rand(
                          kwargs["num_restarts"],
                          q + hvkg.num_pseudo_points,
                          2,
                      )
                  rand_candidates = torch.rand(
                      1,
                      q,
                      2,
                      dtype=fixed_X_fantasies.dtype,
                      device=fixed_X_fantasies.device,
                  )
                  return torch.cat(
                      [
                          rand_candidates,
                          fixed_X_fantasies.unsqueeze(0),
                      ],
                      dim=-2,
                  )
  
              for frac_random in (0.1, 0.5, 0.99):
                  with ExitStack() as es:
                      mock_gbics = es.enter_context(
                          mock.patch(
                              (
                                  "botorch.optim.initializers."
                                  "gen_batch_initial_conditions"
                              ),
                              wraps=mock_gen_ics,
                          )
                      )
                      mock_optacqf = es.enter_context(
                          mock.patch(
                              "botorch.optim.optimize.optimize_acqf",
                              return_value=(
                                  mock_fantasy_cands[..., :1]
                                  if is_mf_kg
                                  else mock_fantasy_cands,
                                  mock_fantasy_vals,
                              ),
                          )
                      )
                      ics = gen_one_shot_hvkg_initial_conditions(
                          acq_function=hvkg,
                          bounds=bounds,
                          q=q,
                          num_restarts=num_restarts,
                          raw_samples=raw_samples,
                          options={"frac_random": frac_random},
                      )
                      if frac_random == 0.5:
                          expected_call_count = 3
                      elif frac_random == 0.99:
                          expected_call_count = 1
                      else:
                          expected_call_count = 4
                      self.assertEqual(
                          mock_gbics.call_count, expected_call_count
                      )
                      mock_optacqf.assert_called_once()
                      n_value = int(
                          round((1 - frac_random) * num_restarts)
                      )
                      # check that there are the expected number of optimized points
                      self.assertTrue(
                          (ics == 1).all(dim=-1).sum()
                          == n_value * hvkg.num_pseudo_points
                      )
  
imports: import warnings
  from contextlib import ExitStack
  from itertools import product
  from random import random
  from typing import Optional
  from unittest import mock
  import torch
  from botorch import settings
  from botorch.acquisition.analytic import PosteriorMean
  from botorch.acquisition.fixed_feature import FixedFeatureAcquisitionFunction
  from botorch.acquisition.knowledge_gradient import qKnowledgeGradient
  from botorch.acquisition.monte_carlo import qExpectedImprovement, qNoisyExpectedImprovement
  from botorch.acquisition.multi_objective.hypervolume_knowledge_gradient import qHypervolumeKnowledgeGradient, qMultiFidelityHypervolumeKnowledgeGradient
  from botorch.acquisition.multi_objective.monte_carlo import qNoisyExpectedHypervolumeImprovement
  from botorch.exceptions import BadInitialCandidatesWarning, SamplingWarning
  from botorch.exceptions.errors import BotorchTensorDimensionError, UnsupportedError
  from botorch.exceptions.warnings import BotorchWarning
  from botorch.models import SingleTaskGP
  from botorch.models.model_list_gp_regression import ModelListGP
  from botorch.optim import initialize_q_batch, initialize_q_batch_nonneg
  from botorch.optim.initializers import gen_batch_initial_conditions, gen_one_shot_hvkg_initial_conditions, gen_one_shot_kg_initial_conditions, gen_value_function_initial_conditions, sample_perturbed_subset_dims, sample_points_around_best, sample_q_batches_from_polytope, sample_truncated_normal_perturbations, transform_constraints, transform_inter_point_constraint, transform_intra_point_constraint
  from botorch.sampling.normal import IIDNormalSampler
  from botorch.utils.sampling import draw_sobol_samples, manual_seed
  from botorch.utils.testing import _get_max_violation_of_bounds, _get_max_violation_of_constraints, BotorchTestCase, MockAcquisitionFunction, MockModel, MockPosterior
label_desc: Use image node_id 1 for calling the TestGenOneShotHVKGInitialConditions obj's underlying member method code with example usage: obj.test_gen_one_shot_hvkg_initial_conditions() and returns: torch, torch