code: def _get_omega_f_contribution(
      mean: Tensor, cov: Tensor, N: int, P: int, M: int
  ) -> Tuple[Tensor, Tensor]:
      r"""Extract the mean vector and covariance matrix corresponding to the `2 x 2`
      multivariate normal blocks in the objective model between the points in `X` and
      the Pareto optimal set.
  
      [There is likely a more efficient way to do this.]
  
      Args:
          mean: A `batch_shape x M x (N + P)`-dim Tensor containing the natural
              mean matrix for the objectives.
          cov: A `batch_shape x M x (N + P) x (N + P)`-dim Tensor containing
              the natural mean matrix for the objectives.
          N: The number of design points.
          P: The number of Pareto optimal points.
          M: The number of objectives.
  
      Return:
          A two-element tuple containing
  
          - mean_fX_fS: A `batch_shape x M x (N + P) x P x 2`-dim Tensor containing the
              means of the inputs and Pareto optimal points.
          - cov_fX_fS: A `batch_shape x M x (N + P) x P x 2 x 2`-dim Tensor containing
              the covariances between the inputs and Pareto optimal points.
      """
      tkwargs = {"dtype": mean.dtype, "device": mean.device}
      batch_shape = mean.shape[:-2]
      # `batch_shape x M x (N + P) x P x 2 x 2`
      cov_fX_fS = torch.zeros(
          batch_shape + torch.Size([M, N + P, P, 2, 2]), **tkwargs
      )
      # `batch_shape x M x (N + P) x P x 2`
      mean_fX_fS = torch.zeros(
          batch_shape + torch.Size([M, N + P, P, 2]), **tkwargs
      )
  
      # `batch_shape x M x (N + P) x P`
      mean_fX_fS[..., 0] = mean.unsqueeze(-1).expand(
          mean.shape + torch.Size([P])
      )
      # `batch_shape x M x (N + P) x P`
      mean_fX_fS[..., 1] = (
          mean[..., N:]
          .unsqueeze(-2)
          .expand(mean.shape + torch.Size([P]))
      )
      # `batch_shape x M x (N + P) x P`
      cov_fX_fS[..., 0, 0] = (
          cov[..., range(N + P), range(N + P)]
          .unsqueeze(-1)
          .expand(batch_shape + torch.Size([M, N + P, P]))
      )
      # `batch_shape x M x (N + P) x P`
      cov_fX_fS[..., 1, 1] = (
          cov[..., range(N, N + P), range(N, N + P)]
          .unsqueeze(-2)
          .expand(batch_shape + torch.Size([M, N + P, P]))
      )
  
      for p in range(P):
          # `batch_shape x M x (N + P)`
          cov_p = cov[..., range(N + P), N + p]
          cov_fX_fS[..., p, 0, 1] = cov_p
          cov_fX_fS[..., p, 1, 0] = cov_p
  
      return mean_fX_fS, cov_fX_fS
  
imports: from __future__ import annotations
  from typing import Any, Optional, Tuple
  import torch
  from botorch.acquisition.acquisition import AcquisitionFunction
  from botorch.exceptions import InputDataError
  from botorch.exceptions.errors import UnsupportedError
  from botorch.models.model import Model
  from botorch.models.model_list_gp_regression import ModelListGP
  from botorch.models.utils import check_no_nans
  from botorch.utils.transforms import concatenate_pending_points, t_batch_mode_transform
  from torch import Tensor
  from torch.distributions import Normal
label_desc: Use image node_id 3 for calling a global function with example usage: _get_omega_f_contribution(mean, cov, N, P, M) and returns: mean_fX_fS,  cov_fX_fS