code: def test_safe_omega_update(self):
      tkwargs = {"device": self.device}
      # test exception when EP fails because the jitter is too small and omega
      # update skips. This naturally depends on the precision.
      for dtype in (torch.float, torch.double):
          tkwargs["dtype"] = dtype
          N = 1
          P = 3
          M = 2
          mean_f = torch.zeros(2, M, N + P, **tkwargs)
          cov_f = torch.ones(2, M, N + P, N + P, **tkwargs)
          omega_f_nat_mean = torch.zeros(2, M, N + P, P, 2, **tkwargs)
          omega_f_nat_cov = torch.zeros(2, M, N + P, P, 2, 2, **tkwargs)
          maximize = True
          jitter = 0.0
  
          # The inversion of a factor of `cov_f` will fail spit out a
          # `torch._C._LinAlgError` error.
          (
              omega_f_nat_mean_new,
              omega_f_nat_cov_new,
          ) = _safe_update_omega(
              mean_f=mean_f,
              cov_f=cov_f,
              omega_f_nat_mean=omega_f_nat_mean,
              omega_f_nat_cov=omega_f_nat_cov,
              N=N,
              P=P,
              M=M,
              maximize=maximize,
              jitter=jitter,
          )
  
          self.assertTrue(
              torch.equal(omega_f_nat_mean, omega_f_nat_mean_new)
          )
          self.assertTrue(
              torch.equal(omega_f_nat_cov, omega_f_nat_cov_new)
          )
  
file_path: botorch/test/acquisition/multi_objective/test_predictive_entropy_search.py
imports: from itertools import product
  import torch
  from botorch.acquisition.multi_objective.predictive_entropy_search import _safe_update_omega, _update_damping, qMultiObjectivePredictiveEntropySearch
  from botorch.exceptions 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.testing import BotorchTestCase
label_desc: Use image node_id 7 for calling the TestQMultiObjectivePredictiveEntropySearch obj's underlying member method code with example usage: obj.test_safe_omega_update() without return types