code: def autocorrelation(input, dim=0):
      """
      Computes the autocorrelation of samples at dimension ``dim``.
  
      Reference: https://en.wikipedia.org/wiki/Autocorrelation#Efficient_computation
  
      Implementation copied form `pyro <https://github.com/pyro-ppl/pyro/blob/dev/pyro/ops/stats.py>`_.
  
      :param torch.Tensor input: the input tensor.
      :param int dim: the dimension to calculate autocorrelation.
      :returns torch.Tensor: autocorrelation of ``input``.
      """
      # Adapted from Stan implementation
      # https://github.com/stan-dev/math/blob/develop/stan/math/prim/mat/fun/autocorrelation.hpp
      N = input.size(dim)
      M = next_fast_len(N)
      M2 = 2 * M
  
      # transpose dim with -1 for Fourier transform
      input = input.transpose(dim, -1)
  
      # centering and padding x
      centered_signal = input - input.mean(dim=-1, keepdim=True)
  
      # Fourier transform
      freqvec = torch.view_as_real(rfft(centered_signal, n=M2))
      # take square of magnitude of freqvec (or freqvec x freqvec*)
      freqvec_gram = freqvec.pow(2).sum(-1)
      # inverse Fourier transform
      autocorr = irfft(freqvec_gram, n=M2)
  
      # truncate and normalize the result, then transpose back to original shape
      autocorr = autocorr[..., :N]
      autocorr = autocorr / torch.tensor(
          range(N, 0, -1), dtype=input.dtype, device=input.device
      )
      autocorr = autocorr / autocorr[..., :1]
      return autocorr.transpose(dim, -1)
  
imports: from collections import namedtuple
  from contextlib import redirect_stdout
  import inspect
  import os
  from typing import Any, Callable, Dict, List, Tuple, Union
  import lightning.pytorch
  import torch
  from torch import nn
  from torch.fft import irfft, rfft
  import torch.nn.functional
  from torch.nn.utils import rnn
label_desc: Use image node_id 7 for calling a global function with example usage: autocorrelation(input, dim) and returns: autocorr