code: def test_get_default_partitioning_alpha(self):
      for m in range(2, 7):
          expected_val = 0.0 if m < 5 else 10 ** (-8 + m)
          self.assertEqual(
              expected_val,
              get_default_partitioning_alpha(num_objectives=m),
          )
      # In `BotorchTestCase.setUp` warnings are filtered, so here we
      # remove the filter to ensure a warning is issued as expected.
      warnings.resetwarnings()
      with warnings.catch_warnings(record=True) as ws:
          self.assertEqual(
              0.1, get_default_partitioning_alpha(num_objectives=7)
          )
      self.assertEqual(len(ws), 1)
  
imports: import warnings
  from itertools import product
  from unittest import mock
  import torch
  from botorch.acquisition.multi_objective.objective import MCMultiOutputObjective, UnstandardizeMCMultiOutputObjective
  from botorch.acquisition.multi_objective.utils import compute_sample_box_decomposition, get_default_partitioning_alpha, prune_inferior_points_multi_objective, random_search_optimizer, sample_optimal_points
  from botorch.exceptions.errors import UnsupportedError
  from botorch.models.gp_regression import SingleTaskGP
  from botorch.models.model_list_gp_regression import ModelListGP
  from botorch.models.transforms.outcome import Standardize
  from botorch.utils.gp_sampling import get_gp_samples
  from botorch.utils.multi_objective import is_non_dominated
  from botorch.utils.testing import BotorchTestCase, MockModel, MockPosterior
  from torch import Tensor
label_desc: Use image node_id 1 for calling the TestUtils obj's underlying member method code with example usage: obj.test_get_default_partitioning_alpha() without return types