code: def aggregate_dir_dx(h, vector_field, h_in, eig_idx=1):
      eig_w = (
          (vector_field[:, :, eig_idx])
          / (
              torch.sum(
                  torch.abs(vector_field[:, :, eig_idx]),
                  keepdim=True,
                  dim=1,
              )
              + 1e-8
          )
      ).unsqueeze(-1)
      h_mod = torch.mul(h, eig_w)
      return torch.abs(
          torch.sum(h_mod, dim=1) - torch.sum(eig_w, dim=1) * h_in
      )
  
imports: import argparse
  import random
  import dgl
  import numpy
  import torch
  import torch.nn
  import torch.nn.functional
  import torch.optim
  from dgl.dataloading import GraphDataLoader
  from ogb.graphproppred import Evaluator
  from ogb.graphproppred.mol_encoder import AtomEncoder
  from preprocessing import prepare_dataset
  from torch.utils.data import Dataset
  from tqdm import tqdm
label_desc: Use image node_id 4 for calling a global function with example usage: aggregate_dir_dx(h, vector_field, h_in, eig_idx) and returns: torch