class_docstr: Graph attention layer with edge features from `SCENE
  <https://arxiv.org/pdf/2301.03512.pdf>`__
  
  .. math::
  
      \mathbf{v}_i^\prime = \mathbf{\Theta}_\mathrm{s} \cdot \mathbf{v}_i +
      \sum\limits_{j \in \mathcal{N}(v_i)} \alpha_{j, i} \left( \mathbf{\Theta}_\mathrm{n}
      \cdot \mathbf{v}_j + \mathbf{\Theta}_\mathrm{e} \cdot \mathbf{e}_{j,i} \right)
  
  where :math:`\mathbf{\Theta}` is used to denote learnable weight matrices
  for the transformation of features of the node to update (s=self),
  neighboring nodes (n=neighbor) and edge features (e=edge).
  Attention weights are obtained by
  
  .. math::
  
      \alpha_{j, i} = \mathrm{softmax}_i \Big( \mathrm{LeakyReLU} \big( \mathbf{a}^T
      [ \mathbf{\Theta}_\mathrm{n} \cdot \mathbf{v}_i || \mathbf{\Theta}_\mathrm{n}
      \cdot \mathbf{v}_j || \mathbf{\Theta}_\mathrm{e} \cdot \mathbf{e}_{j,i} ] \big) \Big)
  
  with :math:`\mathbf{a}` corresponding to a learnable vector.
  :math:`\mathrm{softmax_i}` stands for the normalization by all incoming edges of node :math:`i`.
  
  Parameters
  ----------
  in_feats : int, or pair of ints
      Input feature size; i.e, the number of dimensions of :math:`\mathbf{v}_i`.
      GATConv can be applied on homogeneous graph and unidirectional
      `bipartite graph <https://docs.dgl.ai/generated/dgl.bipartite.html?highlight=bipartite>`__.
      If the layer is to be applied to a unidirectional bipartite graph, ``in_feats``
      specifies the input feature size on both the source and destination nodes.  If
      a scalar is given, the source and destination node feature size would take the
      same value.
  edge_feats: int
      Edge feature size; i.e., the number of dimensions of :math:\mathbf{e}_{j,i}`.
  out_feats : int
      Output feature size; i.e, the number of dimensions of :math:`\mathbf{v}_i^\prime`.
  num_heads : int
      Number of heads in Multi-Head Attention.
  feat_drop : float, optional
      Dropout rate on feature. Defaults: ``0``.
  attn_drop : float, optional
      Dropout rate on attention weight. Defaults: ``0``.
  negative_slope : float, optional
      LeakyReLU angle of negative slope. Defaults: ``0.2``.
  residual : bool, optional
      If True, use residual connection. Defaults: ``False``.
  activation : callable activation function/layer or None, optional.
      If not None, applies an activation function to the updated node features.
      Default: ``None``.
  allow_zero_in_degree : bool, optional
      If there are 0-in-degree nodes in the graph, output for those nodes will be invalid
      since no message will be passed to those nodes. This is harmful for some applications
      causing silent performance regression. This module will raise a DGLError if it detects
      0-in-degree nodes in input graph. By setting ``True``, it will suppress the check
      and let the users handle it by themselves. Defaults: ``False``.
  bias : bool, optional
      If True, learns a bias term. Defaults: ``True``.
  
  Note
  ----
  Zero in-degree nodes will lead to invalid output value. This is because no message
  will be passed to those nodes, the aggregation function will be appied on empty input.
  A common practice to avoid this is to add a self-loop for each node in the graph if
  it is homogeneous, which can be achieved by:
  
  >>> g = ... # a DGLGraph
  >>> g = dgl.add_self_loop(g)
  
  Calling ``add_self_loop`` will not work for some graphs, for example, heterogeneous graph
  since the edge type can not be decided for self_loop edges. Set ``allow_zero_in_degree``
  to ``True`` for those cases to unblock the code and handle zero-in-degree nodes manually.
  A common practise to handle this is to filter out the nodes with zero-in-degree when use
  after conv.
  
  Examples
  ----------
  >>> import dgl
  >>> import numpy as np
  >>> import torch as th
  >>> from dgl.nn import EdgeGATConv
  
  >>> # Case 1: Homogeneous graph.
  >>> num_nodes, num_edges = 8, 30
  >>> # Generate a graph.
  >>> graph = dgl.rand_graph(num_nodes,num_edges)
  >>> node_feats = th.rand((num_nodes, 20))
  >>> edge_feats = th.rand((num_edges, 12))
  >>> edge_gat = EdgeGATConv(
  ...     in_feats=20,
  ...     edge_feats=12,
  ...     out_feats=15,
  ...     num_heads=3,
  ... )
  >>> # Forward pass.
  >>> new_node_feats = edge_gat(graph, node_feats, edge_feats)
  >>> new_node_feats.shape
  torch.Size([8, 3, 15]) torch.Size([30, 3, 10])
  
  >>> # Case 2: Unidirectional bipartite graph.
  >>> u = [0, 1, 0, 0, 1]
  >>> v = [0, 1, 2, 3, 2]
  >>> g = dgl.heterograph({('A', 'r', 'B'): (u, v)})
  >>> u_feat = th.tensor(np.random.rand(2, 25).astype(np.float32))
  >>> v_feat = th.tensor(np.random.rand(4, 30).astype(np.float32))
  >>> nfeats = (u_feat,v_feat)
  >>> efeats = th.tensor(np.random.rand(5, 15).astype(np.float32))
  >>> in_feats = (25,30)
  >>> edge_feats = 15
  >>> out_feats = 10
  >>> num_heads = 3
  >>> egat_model =  EdgeGATConv(
  ...     in_feats,
  ...     edge_feats,
  ...     out_feats,
  ...     num_heads,
  ... )
  >>> # Forward pass.
  >>> new_node_feats, attention_weights = egat_model(g, nfeats, efeats, get_attention=True)
  >>> new_node_feats.shape, attention_weights.shape
  (torch.Size([4, 3, 10]), torch.Size([5, 3, 1]))
docstr: Description
  -----------
  Compute graph attention network layer.
  
  Parameters
  ----------
  graph : DGLGraph
      The graph.
  feat : torch.Tensor or pair of torch.Tensor
      If a torch.Tensor is given, the input feature of shape :math:`(N, *, D_{in})` where
      :math:`D_{in}` is size of input feature, :math:`N` is the number of nodes.
      If a pair of torch.Tensor is given, the pair must contain two tensors of shape
      :math:`(N_{in}, *, D_{in_{src}})` and :math:`(N_{out}, *, D_{in_{dst}})`.
  edge_feat : torch.Tensor
      The input edge feature of shape :math:`(E, D_{in_{edge}})`,
      where :math:`E` is the number of edges and :math:`D_{in_{edge}}`
      the size of the edge features.
  get_attention : bool, optional
      Whether to return the attention values. Default to False.
  
  Returns
  -------
  torch.Tensor
      The output feature of shape :math:`(N, *, H, D_{out})` where :math:`H`
      is the number of heads, and :math:`D_{out}` is size of output feature.
  torch.Tensor, optional
      The attention values of shape :math:`(E, *, H, 1)`. This is returned only
      when :attr:`get_attention` is ``True``.
  
  Raises
  ------
  DGLError
      If there are 0-in-degree nodes in the input graph, it will raise DGLError
      since no message will be passed to those nodes. This will cause invalid output.
      The error can be ignored by setting ``allow_zero_in_degree`` parameter to ``True``.
code: def forward(self, graph, feat, edge_feat, get_attention=False):
      r"""
  
      Description
      -----------
      Compute graph attention network layer.
  
      Parameters
      ----------
      graph : DGLGraph
          The graph.
      feat : torch.Tensor or pair of torch.Tensor
          If a torch.Tensor is given, the input feature of shape :math:`(N, *, D_{in})` where
          :math:`D_{in}` is size of input feature, :math:`N` is the number of nodes.
          If a pair of torch.Tensor is given, the pair must contain two tensors of shape
          :math:`(N_{in}, *, D_{in_{src}})` and :math:`(N_{out}, *, D_{in_{dst}})`.
      edge_feat : torch.Tensor
          The input edge feature of shape :math:`(E, D_{in_{edge}})`,
          where :math:`E` is the number of edges and :math:`D_{in_{edge}}`
          the size of the edge features.
      get_attention : bool, optional
          Whether to return the attention values. Default to False.
  
      Returns
      -------
      torch.Tensor
          The output feature of shape :math:`(N, *, H, D_{out})` where :math:`H`
          is the number of heads, and :math:`D_{out}` is size of output feature.
      torch.Tensor, optional
          The attention values of shape :math:`(E, *, H, 1)`. This is returned only
          when :attr:`get_attention` is ``True``.
  
      Raises
      ------
      DGLError
          If there are 0-in-degree nodes in the input graph, it will raise DGLError
          since no message will be passed to those nodes. This will cause invalid output.
          The error can be ignored by setting ``allow_zero_in_degree`` parameter to ``True``.
      """
      with graph.local_scope():
          if not self._allow_zero_in_degree:
              if (graph.in_degrees() == 0).any():
                  raise DGLError(
                      "There are 0-in-degree nodes in the graph, "
                      "output for those nodes will be invalid. "
                      "This is harmful for some applications, "
                      "causing silent performance regression. "
                      "Adding self-loop on the input graph by "
                      "calling `g = dgl.add_self_loop(g)` will resolve "
                      "the issue. Setting ``allow_zero_in_degree`` "
                      "to be `True` when constructing this module will "
                      "suppress the check and let the code run."
                  )
  
          if isinstance(feat, tuple):
              src_prefix_shape = feat[0].shape[:-1]
              dst_prefix_shape = feat[1].shape[:-1]
              h_src = self.feat_drop(feat[0])
              h_dst = self.feat_drop(feat[1])
              if not hasattr(self, "fc_src"):
                  feat_src = self.fc(h_src).view(
                      *src_prefix_shape,
                      self._num_heads,
                      self._out_feats,
                  )
                  feat_dst = self.fc(h_dst).view(
                      *dst_prefix_shape,
                      self._num_heads,
                      self._out_feats,
                  )
              else:
                  feat_src = self.fc_src(h_src).view(
                      *src_prefix_shape,
                      self._num_heads,
                      self._out_feats,
                  )
                  feat_dst = self.fc_dst(h_dst).view(
                      *dst_prefix_shape,
                      self._num_heads,
                      self._out_feats,
                  )
          else:
              src_prefix_shape = dst_prefix_shape = feat.shape[:-1]
              h_src = h_dst = self.feat_drop(feat)
              feat_src = feat_dst = self.fc(h_src).view(
                  *src_prefix_shape, self._num_heads, self._out_feats
              )
              if graph.is_block:
                  feat_dst = feat_src[: graph.number_of_dst_nodes()]
                  h_dst = h_dst[: graph.number_of_dst_nodes()]
                  dst_prefix_shape = (
                      graph.number_of_dst_nodes(),
                  ) + dst_prefix_shape[1:]
  
          # Linearly tranform the edge features.
          n_edges = edge_feat.shape[:-1]
          feat_edge = self.fc_edge(edge_feat).view(
              *n_edges, self._num_heads, self._out_feats
          )
  
          # Add edge features to graph.
          graph.edata["ft_edge"] = feat_edge
  
          el = (feat_src * self.attn_l).sum(dim=-1).unsqueeze(-1)
          er = (feat_dst * self.attn_r).sum(dim=-1).unsqueeze(-1)
  
          # Calculate scalar for each edge.
          ee = (feat_edge * self.attn_edge).sum(dim=-1).unsqueeze(-1)
          graph.edata["ee"] = ee
  
          graph.srcdata.update({"ft": feat_src, "el": el})
          graph.dstdata.update({"er": er})
          # Compute edge attention, el and er are a_l Wh_i and a_r Wh_j respectively.
          graph.apply_edges(fn.u_add_v("el", "er", "e_tmp"))
  
          # e_tmp combines attention weights of source and destination node.
          # Add the attention weight of the edge.
          graph.edata["e"] = graph.edata["e_tmp"] + graph.edata["ee"]
  
          # Create new edges features that combine the
          # features of the source node and the edge features.
          graph.apply_edges(fn.u_add_e("ft", "ft_edge", "ft_combined"))
  
          e = self.leaky_relu(graph.edata.pop("e"))
          # Compute softmax.
          graph.edata["a"] = self.attn_drop(edge_softmax(graph, e))
  
          # For each edge, element-wise multiply the combined features with
          # the attention coefficient.
          graph.edata["m_combined"] = (
              graph.edata["ft_combined"] * graph.edata["a"]
          )
  
          # First copy the edge features and then sum them up.
          graph.update_all(
              fn.copy_e("m_combined", "m"), fn.sum("m", "ft")
          )
  
          rst = graph.dstdata["ft"]
          # Residual.
          if self.res_fc is not None:
              # Use -1 rather than self._num_heads to handle broadcasting.
              resval = self.res_fc(h_dst).view(
                  *dst_prefix_shape, -1, self._out_feats
              )
              rst = rst + resval
          # Bias.
          if self.bias is not None:
              rst = rst + self.bias.view(
                  *((1,) * len(dst_prefix_shape)),
                  self._num_heads,
                  self._out_feats,
              )
          # Activation.
          if self.activation:
              rst = self.activation(rst)
  
          if get_attention:
              return rst, graph.edata["a"]
          else:
              return rst
  
file_path: dgl/python/dgl/nn/pytorch/conv/edgegatconv.py
imports: import torch
  from torch import nn
  from ....None import function
  from ....base import DGLError
  from ....utils import expand_as_pair
  from ...functional import edge_softmax
label_desc: Use image node_id 4 for calling the EdgeGATConv obj's underlying member method code with example usage: obj.forward(graph, feat, edge_feat, get_attention) and returns: rst,  graph, rst