class_docstr: MC-based batch Multi-Step Look-Ahead (one-shot optimization).
docstr: Fantasy model induced by X.
  
  Args:
      X: A `batch_shape x q' x d`-dim Tensor with `q'` design points for each
          batch, where `q' = q_0 + f_1 q_1 + f_2 f_1 q_2 + ...`. Here `q_i`
          is the number of candidates jointly considered in look-ahead step
          `i`, and `f_i` is respective number of fantasies.
  
  Returns:
      The fantasy model induced by X.
code: def get_induced_fantasy_model(self, X: Tensor) -> Model:
      r"""Fantasy model induced by X.
  
      Args:
          X: A `batch_shape x q' x d`-dim Tensor with `q'` design points for each
              batch, where `q' = q_0 + f_1 q_1 + f_2 f_1 q_2 + ...`. Here `q_i`
              is the number of candidates jointly considered in look-ahead step
              `i`, and `f_i` is respective number of fantasies.
  
      Returns:
          The fantasy model induced by X.
      """
      Xs = self.get_multi_step_tree_input_representation(X)
  
      # set batch_range on samplers if not collapsing on fantasy dims
      if not self._collapse_fantasy_base_samples:
          self._set_samplers_batch_range(batch_shape=X.shape[:-2])
  
      return _get_induced_fantasy_model(
          model=self.model, Xs=Xs, samplers=self.samplers
      )
  
imports: from __future__ import annotations
  import math
  import warnings
  from typing import Any, Callable, Dict, List, Optional, Tuple, Type
  import numpy
  import torch
  from botorch.acquisition import AcquisitionFunction, OneShotAcquisitionFunction
  from botorch.acquisition.analytic import AnalyticAcquisitionFunction, PosteriorMean
  from botorch.acquisition.monte_carlo import MCAcquisitionFunction
  from botorch.acquisition.objective import MCAcquisitionObjective, PosteriorTransform
  from botorch.exceptions.errors import UnsupportedError
  from botorch.exceptions.warnings import BotorchWarning
  from botorch.models.model import Model
  from botorch.optim.initializers import initialize_q_batch
  from botorch.sampling.base import MCSampler
  from botorch.sampling.normal import SobolQMCNormalSampler
  from botorch.utils.transforms import match_batch_shape, t_batch_mode_transform, unnormalize
  from torch import Size, Tensor
  from torch.distributions import Beta
  from torch.nn import ModuleList
label_desc: Use image node_id 9 for calling the qMultiStepLookahead obj's underlying member method code with example usage: obj.get_induced_fantasy_model(X) and returns: _get_induced_fantasy_model