class_docstr: MC-based batch Multi-Step Look-Ahead (one-shot optimization).
docstr: Get the multi-step tree representation of 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:
      A list `[X_j, ..., X_k]` of tensors, where `X_i` has shape
      `f_i x .... x f_1 x batch_shape x q_i x d`.
code: def get_multi_step_tree_input_representation(
      self, X: Tensor
  ) -> List[Tensor]:
      r"""Get the multi-step tree representation of 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:
          A list `[X_j, ..., X_k]` of tensors, where `X_i` has shape
          `f_i x .... x f_1 x batch_shape x q_i x d`.
  
      """
      batch_shape, shapes, sizes = self.get_split_shapes(X=X)
      # Each X_i in Xsplit has shape batch_shape x qtilde x d with
      # qtilde = f_i * ... * f_1 * q_i
      Xsplit = torch.split(X, sizes, dim=-2)
      # now reshape (need to permute batch_shape and qtilde dimensions for i > 0)
      perm = [-2] + list(range(len(batch_shape))) + [-1]
      X0 = Xsplit[0].reshape(shapes[0])
      Xother = [
          X.permute(*perm).reshape(shape)
          for X, shape in zip(Xsplit[1:], shapes[1:])
      ]
      # concatenate in pending points
      if self.X_pending is not None:
          X0 = torch.cat(
              [X0, match_batch_shape(self.X_pending, X0)], dim=-2
          )
  
      return [X0] + Xother
  
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 7 for calling the qMultiStepLookahead obj's underlying member method code with example usage: obj.get_multi_step_tree_input_representation(X) and returns: unknown