text: import torch
  from torch.nn import Parameter
  import torch.nn.functional as F
  from torch_geometric.nn.conv import MessagePassing
  from torch_geometric.utils import remove_self_loops, add_self_loops, softmax
  
  from ..inits import glorot, zeros
  
  
  class GATConv(MessagePassing):
      r"""The graph attentional operator from the `"Graph Attention Networks"
      <https://arxiv.org/abs/1710.10903>`_ paper
  
      .. math::
          \mathbf{x}^{\prime}_i = \alpha_{i,i}\mathbf{\Theta}\mathbf{x}_{i} +
          \sum_{j \in \mathcal{N}(i)} \alpha_{i,j}\mathbf{\Theta}\mathbf{x}_{j},
  
      where the attention coefficients :math:`\alpha_{i,j}` are computed as
  
      .. math::
          \alpha_{i,j} =
          \frac{
          \exp\left(\mathrm{LeakyReLU}\left(\mathbf{a}^{\top}
          [\mathbf{\Theta}\mathbf{x}_i \, \Vert \, \mathbf{\Theta}\mathbf{x}_j]
          \right)\right)}
          {\sum_{k \in \mathcal{N}(i) \cup \{ i \}}
          \exp\left(\mathrm{LeakyReLU}\left(\mathbf{a}^{\top}
          [\mathbf{\Theta}\mathbf{x}_i \, \Vert \, \mathbf{\Theta}\mathbf{x}_k]
          \right)\right)}.
  
      Args:
          in_channels (int): Size of each input sample.
          out_channels (int): Size of each output sample.
          heads (int, optional): Number of multi-head-attentions.
              (default: :obj:`1`)
          concat (bool, optional): If set to :obj:`False`, the multi-head
              attentions are averaged instead of concatenated.
              (default: :obj:`True`)
          negative_slope (float, optional): LeakyReLU angle of the negative
              slope. (default: :obj:`0.2`)
          dropout (float, optional): Dropout probability of the normalized
              attention coefficients which exposes each node to a stochastically
              sampled neighborhood during training. (default: :obj:`0`)
          bias (bool, optional): If set to :obj:`False`, the layer will not learn
              an additive bias. (default: :obj:`True`)
          **kwargs (optional): Additional arguments of
              :class:`torch_geometric.nn.conv.MessagePassing`.
      """
      def __init__(self, in_channels, out_channels, heads=1, concat=True,
                   negative_slope=0.2, dropout=0, bias=True, **kwargs):
          super(GATConv, self).__init__(aggr='add', **kwargs)
  
          self.in_channels = in_channels
          self.out_channels = out_channels
          self.heads = heads
          self.concat = concat
          self.negative_slope = negative_slope
          self.dropout = dropout
  
          self.__alpha__ = None
  
          self.weight = Parameter(torch.Tensor(in_channels,
                                               heads * out_channels))
          self.att = Parameter(torch.Tensor(1, heads, 2 * out_channels))
  
          if bias and concat:
              self.bias = Parameter(torch.Tensor(heads * out_channels))
          elif bias and not concat:
              self.bias = Parameter(torch.Tensor(out_channels))
          else:
              self.register_parameter('bias', None)
  
          self.reset_parameters()
  
      def reset_parameters(self):
          glorot(self.weight)
          glorot(self.att)
          zeros(self.bias)
  
      def forward(self, x, edge_index, size=None,
                  return_attention_weights=False):
          """"""
          if size is None and torch.is_tensor(x):
              edge_index, _ = remove_self_loops(edge_index)
              edge_index, _ = add_self_loops(edge_index,
                                             num_nodes=x.size(self.node_dim))
  
          if torch.is_tensor(x):
              x = torch.matmul(x, self.weight)
          else:
              x = (None if x[0] is None else torch.matmul(x[0], self.weight),
                   None if x[1] is None else torch.matmul(x[1], self.weight))
  
          out = self.propagate(edge_index, size=size, x=x,
                               return_attention_weights=return_attention_weights)
  
          if return_attention_weights:
              alpha, self.__alpha__ = self.__alpha__, None
              return out, (edge_index, alpha)
          else:
              return out
  
      def message(self, edge_index_i, x_i, x_j, size_i,
                  return_attention_weights):
          # Compute attention coefficients.
          x_j = x_j.view(-1, self.heads, self.out_channels)
          if x_i is None:
              alpha = (x_j * self.att[:, :, self.out_channels:]).sum(dim=-1)
          else:
              x_i = x_i.view(-1, self.heads, self.out_channels)
              alpha = (torch.cat([x_i, x_j], dim=-1) * self.att).sum(dim=-1)
  
          alpha = F.leaky_relu(alpha, self.negative_slope)
          alpha = softmax(alpha, edge_index_i, size_i)
  
          if return_attention_weights:
              self.__alpha__ = alpha
  
          # Sample attention coefficients stochastically.
          alpha = F.dropout(alpha, p=self.dropout, training=self.training)
  
          return x_j * alpha.view(-1, self.heads, 1)
  
      def update(self, aggr_out):
          if self.concat is True:
              aggr_out = aggr_out.view(-1, self.heads * self.out_channels)
          else:
              aggr_out = aggr_out.mean(dim=1)
  
          if self.bias is not None:
              aggr_out = aggr_out + self.bias
          return aggr_out
  
      def __repr__(self):
          return '{}({}, {}, heads={})'.format(self.__class__.__name__,
                                               self.in_channels,
                                               self.out_channels, self.heads)
  