class_docstr: Standardize outcomes (zero mean, unit variance).
  
  This module is stateful: If in train mode, calling forward updates the
  module state (i.e. the mean/std normalizing constants). If in eval mode,
  calling forward simply applies the standardization using the current module
  state.
docstr: Un-standardize outcomes.
  
  Args:
      Y: A `batch_shape x n x m`-dim tensor of standardized targets.
      Yvar: A `batch_shape x n x m`-dim tensor of standardized observation
          noises associated with the targets (if applicable).
  
  Returns:
      A two-tuple with the un-standardized outcomes:
  
      - The un-standardized outcome observations.
      - The un-standardized observation noise (if applicable).
docstr_tok: ["Un-standardize","outcomes",".","Args",":","Y",":","A","`","batch_shape","x","n","x","m","`","-dim","tensor","of","standardized","targets",".","Yvar",":","A","`","batch_shape","x","n","x","m","`","-dim","tensor","of","standardized","observation","noises","associated","with","the","targets","(","if","applicable",")",".","Returns",":","A","two-tuple","with","the","un-standardized","outcomes",":","-","The","un-standardized","outcome","observations",".","-","The","un-standardized","observation","noise","(","if","applicable",")","."]
code: def untransform(
      self, Y: Tensor, Yvar: Optional[Tensor] = None
  ) -> Tuple[Tensor, Optional[Tensor]]:
      r"""Un-standardize outcomes.
  
      Args:
          Y: A `batch_shape x n x m`-dim tensor of standardized targets.
          Yvar: A `batch_shape x n x m`-dim tensor of standardized observation
              noises associated with the targets (if applicable).
  
      Returns:
          A two-tuple with the un-standardized outcomes:
  
          - The un-standardized outcome observations.
          - The un-standardized observation noise (if applicable).
      """
      if not self._is_trained:
          raise RuntimeError(
              "`Standardize` transforms must be called on outcome data "
              "(e.g. `transform(Y)`) before calling `untransform`, since "
              "means and standard deviations need to be computed."
          )
  
      Y_utf = self.means + self.stdvs * Y
      Yvar_utf = self._stdvs_sq * Yvar if Yvar is not None else None
      return Y_utf, Yvar_utf
  
imports: from __future__ import annotations
  import warnings
  from abc import ABC, abstractmethod
  from collections import OrderedDict
  from typing import Any, List, Mapping, Optional, Tuple, Union
  import torch
  from botorch.models.transforms.utils import norm_to_lognorm_mean, norm_to_lognorm_variance
  from botorch.posteriors import GPyTorchPosterior, Posterior, TransformedPosterior
  from botorch.utils.transforms import normalize_indices
  from linear_operator.operators import CholLinearOperator, DiagLinearOperator
  from torch import Tensor
  from torch.nn import Module, ModuleDict
label_desc: Use image node_id 5 for calling the Standardize obj's underlying member method code with example usage: obj.untransform(Y, Yvar) and returns: Y_utf,  Yvar_utf