code: def concat(
      self, other: PivotedCholesky, dim: int = 0
  ) -> PivotedCholesky:
      if self.step != other.step:
          raise ValueError(
              "Cannot conncatenate decompositions at different steps."
          )
  
      fields = {}
      for name in ("tril", "perm", "diag"):
          a = getattr(self, name)
          b = getattr(other, name)
          if type(a) is not type(b):
              raise NotImplementedError(
                  f"Types of field {name} do not match."
              )
  
          if a is not None:
              fields[name] = torch.concat((a, b), dim=dim)
  
      return type(self)(step=self.step, **fields)
  
file_path: botorch/botorch/utils/probability/linalg.py
imports: from __future__ import annotations
  from dataclasses import dataclass, InitVar
  from itertools import chain
  from typing import Any, Optional, Sequence
  import torch
  from botorch.utils.probability.utils import swap_along_dim_
  from linear_operator.utils.errors import NotPSDError
  from torch import LongTensor, Tensor
  from torch.nn.functional import pad
label_desc: Use image node_id 6 for calling the PivotedCholesky obj's underlying member method code with example usage: obj.concat(other, dim) and returns: type