code: def test_optimize_acqf_homotopy(self):
      tkwargs = {"device": self.device, "dtype": torch.double}
      p = Parameter(-2 * torch.ones(1, **tkwargs))
      hp = HomotopyParameter(
          parameter=p,
          schedule=LinearHomotopySchedule(start=4, end=0, num_steps=5),
      )
      model = GenericDeterministicModel(f=lambda x: 5 - (x - p) ** 2)
      acqf = PosteriorMean(model=model)
      candidate, acqf_val = optimize_acqf_homotopy(
          q=1,
          acq_function=acqf,
          bounds=torch.tensor([[-10], [5]]).to(**tkwargs),
          homotopy=Homotopy(homotopy_parameters=[hp]),
          num_restarts=2,
          raw_samples=16,
          post_processing_func=lambda x: x.round(),
      )
      self.assertEqual(candidate, torch.zeros(1, **tkwargs))
      self.assertEqual(acqf_val, 5 * torch.ones(1, **tkwargs))
  
      # test fixed feature
      fixed_features = {0: 1.0}
      model = GenericDeterministicModel(
          f=lambda x: 5 - (x - p).sum(dim=-1, keepdims=True) ** 2
      )
      acqf = PosteriorMean(model=model)
      candidate, acqf_val = optimize_acqf_homotopy(
          q=1,
          acq_function=acqf,
          bounds=torch.tensor([[-10, -10], [5, 5]]).to(**tkwargs),
          homotopy=Homotopy(homotopy_parameters=[hp]),
          num_restarts=2,
          raw_samples=16,
          fixed_features=fixed_features,
      )
      self.assertEqual(candidate[0, 0], torch.tensor(1, **tkwargs))
  
      # With q > 1.
      acqf = qExpectedImprovement(model=model, best_f=0.0)
      candidate, acqf_val = optimize_acqf_homotopy(
          q=3,
          acq_function=acqf,
          bounds=torch.tensor([[-10, -10], [5, 5]]).to(**tkwargs),
          homotopy=Homotopy(homotopy_parameters=[hp]),
          num_restarts=2,
          raw_samples=16,
          fixed_features=fixed_features,
      )
      self.assertEqual(candidate.shape, torch.Size([3, 2]))
      self.assertEqual(acqf_val.shape, torch.Size([3]))
  
file_path: botorch/test/optim/test_homotopy.py
imports: import unittest.mock
  import torch
  from botorch.acquisition import PosteriorMean
  from botorch.acquisition.monte_carlo import qExpectedImprovement
  from botorch.models import GenericDeterministicModel
  from botorch.optim.homotopy import FixedHomotopySchedule, Homotopy, HomotopyParameter, LinearHomotopySchedule, LogLinearHomotopySchedule
  from botorch.optim.optimize_homotopy import optimize_acqf_homotopy, prune_candidates
  from botorch.utils.testing import BotorchTestCase
  from torch.nn import Parameter
label_desc: Use image node_id 6 for calling the TestHomotopy obj's underlying member method code with example usage: obj.test_optimize_acqf_homotopy() without return types