code: def test_warn_independent_sampling(
      capsys: _pytest.capture.CaptureFixture,
  ) -> None:
      def objective(trial: Trial) -> float:
          x = trial.suggest_categorical("x", ["a", "b"])
          if x == "a":
              return trial.suggest_float("y", 0, 1)
          else:
              return trial.suggest_float("z", 0, 1)
  
      # We need to reconstruct our default handler to properly capture stderr.
      optuna.logging._reset_library_root_logger()
      optuna.logging.enable_default_handler()
      optuna.logging.set_verbosity(optuna.logging.WARNING)
  
      sampler = optuna.integration.PyCmaSampler(
          warn_independent_sampling=True, n_startup_trials=0
      )
      study = optuna.create_study(sampler=sampler)
      study.optimize(objective, n_trials=10)
  
      _, err = capsys.readouterr()
      assert err
  
imports: import math
  from typing import Any
  from typing import Dict
  from unittest.mock import call
  from unittest.mock import patch
  import warnings
  import _pytest.capture
  import pytest
  import optuna
  from optuna._imports import try_import
  from optuna.distributions import BaseDistribution
  from optuna.distributions import CategoricalDistribution
  from optuna.distributions import FloatDistribution
  from optuna.distributions import IntDistribution
  from optuna.integration.cma import _Optimizer
  from optuna.study._study_direction import StudyDirection
  from optuna.testing.distributions import UnsupportedDistribution
  from optuna.testing.trials import _create_frozen_trial
  from optuna.trial import Trial
  from optuna.trial import TrialState
label_desc: Use image node_id 3 for calling the TestPyCmaSampler obj's underlying member method code with example usage: obj.test_warn_independent_sampling(capsys) and returns: trial, trial