class_docstr: DGCF is a disentangled representation enhanced matrix factorization model.
  The interaction matrix of :math:`n_{users} \times n_{items}` is decomposed to :math:`n_{factors}` intent graph,
  we carefully design the data interface and use sparse tensor to train and test efficiently.
  We implement the model following the original author with a pairwise training mode.
code: def forward(self):
      ego_embeddings = self._get_ego_embeddings()
      all_embeddings = [ego_embeddings.unsqueeze(1)]
      # initialize with every factor value as 1
      A_values = torch.ones((self.num_edge, self.n_factors)).to(
          self.device
      )
      A_values = Variable(A_values, requires_grad=True)
      for k in range(self.n_layers):
          layer_embeddings = []
  
          # split the input embedding table
          # .... ego_layer_embeddings is a (n_factors)-length list of embeddings
          # [n_users+n_items, embed_size/n_factors]
          ego_layer_embeddings = torch.chunk(
              ego_embeddings, self.n_factors, 1
          )
          for t in range(0, self.n_iterations):
              iter_embeddings = []
              A_iter_values = []
              factor_edge_weight = self.build_matrix(A_values=A_values)
              for i in range(0, self.n_factors):
                  # update the embeddings via simplified graph convolution layer
                  edge_weight = factor_edge_weight[i]
                  # (num_edge, 1)
                  edge_val = torch.sparse.mm(
                      self.tail2edge_mat, ego_layer_embeddings[i]
                  )
                  # (num_edge, dim / n_factors)
                  edge_val = edge_val * edge_weight
                  # (num_edge, dim / n_factors)
                  factor_embeddings = torch.sparse.mm(
                      self.edge2head_mat, edge_val
                  )
                  # (num_node, num_edge) (num_edge, dim) -> (num_node, dim)
  
                  iter_embeddings.append(factor_embeddings)
  
                  if t == self.n_iterations - 1:
                      layer_embeddings = iter_embeddings
  
                  # get the factor-wise embeddings
                  # .... head_factor_embeddings is a dense tensor with the size of [all_h_list, embed_size/n_factors]
                  # .... analogous to tail_factor_embeddings
                  head_factor_embeddings = torch.index_select(
                      factor_embeddings, dim=0, index=self.all_h_list
                  )
                  tail_factor_embeddings = torch.index_select(
                      ego_layer_embeddings[i],
                      dim=0,
                      index=self.all_t_list,
                  )
  
                  # .... constrain the vector length
                  # .... make the following attentive weights within the range of (0,1)
                  # to adapt to torch version
                  head_factor_embeddings = F.normalize(
                      head_factor_embeddings, p=2, dim=1
                  )
                  tail_factor_embeddings = F.normalize(
                      tail_factor_embeddings, p=2, dim=1
                  )
  
                  # get the attentive weights
                  # .... A_factor_values is a dense tensor with the size of [num_edge, 1]
                  A_factor_values = torch.sum(
                      head_factor_embeddings
                      * torch.tanh(tail_factor_embeddings),
                      dim=1,
                      keepdim=True,
                  )
  
                  # update the attentive weights
                  A_iter_values.append(A_factor_values)
              A_iter_values = torch.cat(A_iter_values, dim=1)
              # (num_edge, n_factors)
              # add all layer-wise attentive weights up.
              A_values = A_values + A_iter_values
  
          # sum messages of neighbors, [n_users+n_items, embed_size]
          side_embeddings = torch.cat(layer_embeddings, dim=1)
  
          ego_embeddings = side_embeddings
          # concatenate outputs of all layers
          all_embeddings += [ego_embeddings.unsqueeze(1)]
  
      all_embeddings = torch.cat(all_embeddings, dim=1)
      # (num_node, n_layer + 1, embedding_size)
      all_embeddings = torch.mean(all_embeddings, dim=1, keepdim=False)
      # (num_node, embedding_size)
  
      u_g_embeddings = all_embeddings[: self.n_users, :]
      i_g_embeddings = all_embeddings[self.n_users :, :]
  
      return u_g_embeddings, i_g_embeddings
  
imports: import random
  import numpy
  import torch
  import torch.nn
  import torch.nn.functional
  from torch.autograd import Variable
  from recbole.model.abstract_recommender import GeneralRecommender
  from recbole.model.init import xavier_normal_initialization
  from recbole.model.loss import BPRLoss, EmbLoss
  from recbole.utils import InputType
label_desc: Use image node_id 5 for calling the DGCF obj's underlying member method code with example usage: obj.forward() and returns: u_g_embeddings,  i_g_embeddings