code: def _split_hvkg_fantasy_points(
      X: Tensor, n_f: int, num_pareto: int
  ) -> Tuple[Tensor, Tensor]:
      r"""Split a one-shot HV-KGoptimization input into actual and fantasy points
  
      Args:
          X: A `batch_shape x (q + n_f*num_pareto) x d`-dim tensor of actual
              and fantasy points
  
      Returns:
          2-element tuple containing
  
          - A `batch_shape x q x d`-dim tensor `X_actual` of input candidates.
          - A `n_f x batch_shape x num_pareto x d`-dim tensor `X_fantasies` of
              fantasy points, where `X_fantasies[i, batch_idx]` is the i-th
              fantasy point associated with the batch indexed by `batch_idx`.
      """
      if n_f * num_pareto > X.size(-2):
          raise ValueError(
              f"`n_f*num_pareto` ({n_f*num_pareto}) must be less than"
              f" the `q`-batch dimension of `X` ({X.size(-2)})."
          )
      split_sizes = [X.size(-2) - n_f * num_pareto, n_f * num_pareto]
      X_actual, X_fantasies = torch.split(X, split_sizes, dim=-2)
      # X_fantasies is b x n_f * num_pareto x d, needs to be n_f x b x num_pareto x d
      # reshape into num_fantasies x b x num_pareto x d
      new_shape = torch.Size(
          [
              n_f,
              *X_fantasies.shape[:-2],
              num_pareto,
              X_fantasies.shape[-1],
          ]
      )
      X_fantasies = X_fantasies.reshape(new_shape)
      # n_f x b x num_pareto x d
      return X_actual, X_fantasies
  
imports: from copy import deepcopy
  from typing import Any, Callable, Dict, List, Optional, Tuple, Type
  import torch
  from botorch import settings
  from botorch.acquisition.acquisition import AcquisitionFunction, OneShotAcquisitionFunction
  from botorch.acquisition.cost_aware import CostAwareUtility
  from botorch.acquisition.decoupled import DecoupledAcquisitionFunction
  from botorch.acquisition.knowledge_gradient import ProjectedAcquisitionFunction
  from botorch.acquisition.multi_objective.monte_carlo import MultiObjectiveMCAcquisitionFunction, qExpectedHypervolumeImprovement
  from botorch.acquisition.multi_objective.objective import MCMultiOutputObjective
  from botorch.exceptions.errors import UnsupportedError
  from botorch.models.deterministic import PosteriorMeanModel
  from botorch.models.model import Model
  from botorch.sampling.base import MCSampler
  from botorch.sampling.list_sampler import ListSampler
  from botorch.sampling.normal import SobolQMCNormalSampler
  from botorch.sampling.stochastic_samplers import StochasticSampler
  from botorch.utils.multi_objective.box_decompositions.non_dominated import FastNondominatedPartitioning
  from botorch.utils.transforms import match_batch_shape, t_batch_mode_transform
  from torch import Tensor
label_desc: Use image node_id 2 for calling a global function with example usage: _split_hvkg_fantasy_points(X, n_f, num_pareto) and returns: X_actual,  X_fantasies