code: def test_homotopy(self):
      tkwargs = {"device": self.device, "dtype": torch.double}
      p1 = Parameter(-2 * torch.ones(1, **tkwargs))
      v1 = [1, 2, 3, 4, 5]
      p2 = -3 * torch.ones(1, **tkwargs)
      v2 = [0.01, 0.1, 1, 10, 100]
      callback = mock.Mock()
      homotopy_parameters = [
          HomotopyParameter(
              parameter=p1,
              schedule=LinearHomotopySchedule(
                  start=1, end=5, num_steps=5
              ),
          ),
          HomotopyParameter(
              parameter=p2,
              schedule=LogLinearHomotopySchedule(
                  start=0.01, end=100, num_steps=5
              ),
          ),
      ]
      homotopy = Homotopy(
          homotopy_parameters=homotopy_parameters, callbacks=[callback]
      )
      self.assertEqual(homotopy._original_values, [-2, -3])
      self.assertEqual(
          homotopy._homotopy_parameters, homotopy_parameters
      )
      self.assertEqual(homotopy._callbacks, [callback])
      self.assertEqual(
          [h.parameter.item() for h in homotopy._homotopy_parameters],
          [v1[0], v2[0]],
      )
      for i in range(4):
          homotopy.step()
          self.assertEqual(
              [
                  h.parameter.item()
                  for h in homotopy._homotopy_parameters
              ],
              [v1[i + 1], v2[i + 1]],
          )
          self.assertFalse(homotopy.should_stop)
      homotopy.step()
      self.assertTrue(homotopy.should_stop)
      # Restart the schedules
      homotopy.restart()
      self.assertEqual(
          [h.parameter.item() for h in homotopy._homotopy_parameters],
          [v1[0], v2[0]],
      )
      # Reset the parameters to their original values
      homotopy.reset()
      self.assertEqual(
          [h.parameter.item() for h in homotopy._homotopy_parameters],
          [-2, -3],
      )
      # Expect the call count to be 8: init (1), step (5), restart (1), reset (1).
      self.assertEqual(callback.call_count, 8)
  
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 5 for calling the TestHomotopy obj's underlying member method code with example usage: obj.test_homotopy() without return types