class_docstr: Linear Elliptical Slice Sampler.
  
  Ideas:
  - Add batch support, broadcasting over parallel chains.
  - Optimize computations if possible, potentially with torch.compile.
  - Extend fixed features constraint to general linear equality constraints.
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docstr: _transform helper standardizing the input `x`, which is assumed to be a
  `d x 1`-dim Tensor, or a `len(self._not_fixed) x 1`-dim if there are fixed
  indices.
docstr_tok: ["_transform","helper","standardizing","the","input","`","x","`",",","which","is","assumed","to","be","a","`","d","x","1","`","-dim","Tensor",",","or","a","`","len","(","self._not_fixed",")","x","1","`","-dim","if","there","are","fixed","indices","."]
code: def _standardize(self, x: Tensor) -> Tensor:
      """_transform helper standardizing the input `x`, which is assumed to be a
      `d x 1`-dim Tensor, or a `len(self._not_fixed) x 1`-dim if there are fixed
      indices.
      """
      z = x
      if self._mean is not None:
          z = z - self._mean
      if self._covariance_root is not None:
          z = torch.linalg.solve_triangular(
              self._covariance_root, z, upper=False
          )
      return z
  
imports: from __future__ import annotations
  import math
  from typing import List, Optional, Tuple, Union
  import torch
  from botorch.utils.sampling import PolytopeSampler
  from torch import Tensor
label_desc: Use image node_id 16 for calling the LinearEllipticalSliceSampler obj's underlying member method code with example usage: obj._standardize(x) and returns: z