code: def get_default_partitioning_alpha(num_objectives: int) -> float:
      r"""Determines an approximation level based on the number of objectives.
  
      If `alpha` is 0, FastNondominatedPartitioning should be used. Otherwise,
      an approximate NondominatedPartitioning should be used with approximation
      level `alpha`.
  
      Args:
          num_objectives: the number of objectives.
  
      Returns:
          The approximation level `alpha`.
      """
      if num_objectives <= 4:
          return 0.0
      elif num_objectives > 6:
          warnings.warn(
              "EHVI works best for less than 7 objectives.",
              BotorchWarning,
          )
      return 10 ** (-8 + num_objectives)
  
imports: from __future__ import annotations
  import math
  import warnings
  from math import ceil
  from typing import Any, Callable, Dict, List, Optional, Tuple
  import torch
  from botorch.acquisition import monte_carlo
  from botorch.acquisition.multi_objective.objective import IdentityMCMultiOutputObjective, MCMultiOutputObjective
  from botorch.exceptions.errors import UnsupportedError
  from botorch.exceptions.warnings import BotorchWarning
  from botorch.models.deterministic import GenericDeterministicModel
  from botorch.models.fully_bayesian import MCMC_DIM
  from botorch.models.model import Model
  from botorch.sampling.get_sampler import get_sampler
  from botorch.utils.gp_sampling import get_gp_samples
  from botorch.utils.multi_objective.box_decompositions.box_decomposition import BoxDecomposition
  from botorch.utils.multi_objective.box_decompositions.box_decomposition_list import BoxDecompositionList
  from botorch.utils.multi_objective.box_decompositions.dominated import DominatedPartitioning
  from botorch.utils.multi_objective.pareto import is_non_dominated
  from botorch.utils.objective import compute_feasibility_indicator
  from botorch.utils.sampling import draw_sobol_samples
  from botorch.utils.transforms import is_ensemble
  from torch import Tensor
label_desc: Use image node_id 1 for calling a global function with example usage: get_default_partitioning_alpha(num_objectives) and returns: unknown, int