code: def multioutput_to_batch_mode_transform(
      train_X: Tensor,
      train_Y: Tensor,
      num_outputs: int,
      train_Yvar: Optional[Tensor] = None,
  ) -> Tuple[Tensor, Tensor, Optional[Tensor]]:
      r"""Transforms training inputs for a multi-output model.
  
      Used for multi-output models that internally are represented by a
      batched single output model, where each output is modeled as an
      independent batch.
  
      Args:
          train_X: A `n x d` or `input_batch_shape x n x d` (batch mode) tensor of
              training features.
          train_Y: A `n x m` or `target_batch_shape x n x m` (batch mode) tensor of
              training observations.
          num_outputs: number of outputs
          train_Yvar: A `n x m` or `target_batch_shape x n x m` tensor of observed
              measurement noise.
  
      Returns:
          3-element tuple containing
  
          - A `input_batch_shape x m x n x d` tensor of training features.
          - A `target_batch_shape x m x n` tensor of training observations.
          - A `target_batch_shape x m x n` tensor observed measurement noise.
      """
      # make train_Y `batch_shape x m x n`
      train_Y = train_Y.transpose(-1, -2)
      # expand train_X to `batch_shape x m x n x d`
      train_X = train_X.unsqueeze(-3).expand(
          train_X.shape[:-2]
          + torch.Size([num_outputs])
          + train_X.shape[-2:]
      )
      if train_Yvar is not None:
          # make train_Yvar `batch_shape x m x n`
          train_Yvar = train_Yvar.transpose(-1, -2)
      return train_X, train_Y, train_Yvar
  
imports: from __future__ import annotations
  import warnings
  from contextlib import contextmanager, ExitStack
  from typing import Iterator, List, Optional, Tuple
  import torch
  from botorch import settings
  from botorch.exceptions import InputDataError, InputDataWarning
  from botorch.settings import _Flag
  from gpytorch import settings
  from gpytorch.module import Module
  from torch import Tensor
label_desc: Use image node_id 2 for calling a global function with example usage: multioutput_to_batch_mode_transform(train_X, train_Y, num_outputs, train_Yvar) and returns: train_X,  train_Y,  train_Yvar