code: def crps_empirical(pred, truth):
      """
      Computes negative Continuous Ranked Probability Score CRPS* [1] between a
      set of samples ``pred`` and true data ``truth``. This uses an ``n log(n)``
      time algorithm to compute a quantity equal that would naively have
      complexity quadratic in the number of samples ``n``::
  
          CRPS* = E|pred - truth| - 1/2 E|pred - pred'|
                = (pred - truth).abs().mean(0)
                - (pred - pred.unsqueeze(1)).abs().mean([0, 1]) / 2
  
      Note that for a single sample this reduces to absolute error.
  
      **References**
  
      [1] Tilmann Gneiting, Adrian E. Raftery (2007)
          `Strictly Proper Scoring Rules, Prediction, and Estimation`
          https://www.stat.washington.edu/raftery/Research/PDF/Gneiting2007jasa.pdf
  
      :param torch.Tensor pred: A set of sample predictions batched on rightmost dim.
          This should have shape ``(num_samples,) + truth.shape``.
      :param torch.Tensor truth: A tensor of true observations.
      :return: A tensor of shape ``truth.shape``.
      :rtype: torch.Tensor
      """
      if (
          pred.shape[1:]
          != (1,) * (pred.dim() - truth.dim() - 1) + truth.shape
      ):
          raise ValueError(
              "Expected pred to have one extra sample dim on left. "
              "Actual shapes: {} versus {}".format(
                  pred.shape, truth.shape
              )
          )
      opts = dict(device=pred.device, dtype=pred.dtype)
      num_samples = pred.size(0)
      if num_samples == 1:
          return (pred[0] - truth).abs()
  
      pred = pred.sort(dim=0).values
      diff = pred[1:] - pred[:-1]
      weight = torch.arange(1, num_samples, **opts) * torch.arange(
          num_samples - 1, 0, -1, **opts
      )
      weight = weight.reshape(weight.shape + (1,) * (diff.dim() - 1))
  
      return (pred - truth).abs().mean(0) - (diff * weight).sum(
          0
      ) / num_samples**2
  
imports: import math
  import numbers
  import torch
  from torch.fft import irfft, rfft
  from .tensor_utils import next_fast_len
label_desc: Use image node_id 16 for calling a global function with example usage: crps_empirical(pred, truth) and returns: unknown, unknown