code: def logmeanexp(
      X: Tensor, dim: Union[int, Tuple[int, ...]], keepdim: bool = False
  ) -> Tensor:
      """Computes `log(mean(exp(X), dim=dim, keepdim=keepdim))`.
  
      Args:
          X: Values of which to compute the logmeanexp.
          dim: The dimension(s) over which to compute the mean.
          keepdim: If True, keeps the reduced dimensions.
  
      Returns:
          A Tensor of values corresponding to `log(mean(exp(X), dim=dim))`.
      """
      n = (
          X.shape[dim]
          if isinstance(dim, int)
          else math.prod(X.shape[i] for i in dim)
      )
      return logsumexp(X, dim=dim, keepdim=keepdim) - math.log(n)
  
imports: from __future__ import annotations
  import math
  from typing import Callable, Tuple, Union
  import torch
  from botorch.exceptions import UnsupportedError
  from botorch.utils.constants import get_constants_like
  from torch import finfo, Tensor
  from torch.nn.functional import softplus
label_desc: Use image node_id 15 for calling a global function with example usage: logmeanexp(X, dim, keepdim) and returns: unknown