class_docstr: Apply dot product version of self attention in `Graph Attention Network
  <https://arxiv.org/pdf/1710.10903.pdf>`__
  
      .. math::
          h_i^{(l+1)} = \sum_{j\in \mathcal{N}(i)} \alpha_{i, j} h_j^{(l)}
  
      where :math:`\alpha_{ij}` is the attention score bewteen node :math:`i` and node :math:`j`:
  
      .. math::
          \alpha_{i, j} &= \mathrm{softmax_i}(e_{ij}^{l})
  
          e_{ij}^{l} &= ({W_i^{(l)} h_i^{(l)}})^T \cdot {W_j^{(l)} h_j^{(l)}}
  
      where :math:`W_i` and :math:`W_j` transform node :math:`i`'s and node :math:`j`'s
      features into the same dimension, so that when compute note features' similarity,
      it can use dot-product.
  
  Parameters
  ----------
  in_feats : int, or pair of ints
      Input feature size; i.e, the number of dimensions of :math:`h_i^{(l)}`.
      DotGatConv 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.
  out_feats : int
      Output feature size; i.e, the number of dimensions of :math:`h_i^{(l+1)}`.
  num_heads : int
      Number of head in Multi-Head Attention
  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. Default: ``False``.
  
  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 DotGatConv
  
  >>> # Case 1: Homogeneous graph
  >>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
  >>> g = dgl.add_self_loop(g)
  >>> feat = th.ones(6, 10)
  >>> dotgatconv = DotGatConv(10, 2, num_heads=3)
  >>> res = dotgatconv(g, feat)
  >>> res
  tensor([[[ 3.4570,  1.8634],
          [ 1.3805, -0.0762],
          [ 1.0390, -1.1479]],
          [[ 3.4570,  1.8634],
          [ 1.3805, -0.0762],
          [ 1.0390, -1.1479]],
          [[ 3.4570,  1.8634],
          [ 1.3805, -0.0762],
          [ 1.0390, -1.1479]],
          [[ 3.4570,  1.8634],
          [ 1.3805, -0.0762],
          [ 1.0390, -1.1479]],
          [[ 3.4570,  1.8634],
          [ 1.3805, -0.0762],
          [ 1.0390, -1.1479]],
          [[ 3.4570,  1.8634],
          [ 1.3805, -0.0762],
          [ 1.0390, -1.1479]]], grad_fn=<BinaryReduceBackward>)
  
  >>> # Case 2: Unidirectional bipartite graph
  >>> u = [0, 1, 0, 0, 1]
  >>> v = [0, 1, 2, 3, 2]
  >>> g = dgl.heterograph({('_N', '_E', '_N'):(u, v)})
  >>> u_feat = th.tensor(np.random.rand(2, 5).astype(np.float32))
  >>> v_feat = th.tensor(np.random.rand(4, 10).astype(np.float32))
  >>> dotgatconv = DotGatConv((5,10), 2, 3)
  >>> res = dotgatconv(g, (u_feat, v_feat))
  >>> res
  tensor([[[-0.6066,  1.0268],
          [-0.5945, -0.4801],
          [ 0.1594,  0.3825]],
          [[ 0.0268,  1.0783],
          [ 0.5041, -1.3025],
          [ 0.6568,  0.7048]],
          [[-0.2688,  1.0543],
          [-0.0315, -0.9016],
          [ 0.3943,  0.5347]],
          [[-0.6066,  1.0268],
          [-0.5945, -0.4801],
          [ 0.1594,  0.3825]]], grad_fn=<BinaryReduceBackward>)
docstr: Description
  -----------
  Apply dot product version of self attention in GCN.
  
  Parameters
  ----------
  graph: DGLGraph or bi_partities graph
      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}})`.
  get_attention : bool, optional
      Whether to return the attention values. Default to False.
  
  Returns
  -------
  torch.Tensor
      The output feature of shape :math:`(N, D_{out})` where :math:`D_{out}` is size
      of output feature.
  torch.Tensor, optional
      The attention values of shape :math:`(E, 1)`, where :math:`E` is the number of
      edges. 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``.
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code: def forward(self, graph, feat, get_attention=False):
      r"""
  
      Description
      -----------
      Apply dot product version of self attention in GCN.
  
      Parameters
      ----------
      graph: DGLGraph or bi_partities graph
          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}})`.
      get_attention : bool, optional
          Whether to return the attention values. Default to False.
  
      Returns
      -------
      torch.Tensor
          The output feature of shape :math:`(N, D_{out})` where :math:`D_{out}` is size
          of output feature.
      torch.Tensor, optional
          The attention values of shape :math:`(E, 1)`, where :math:`E` is the number of
          edges. 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``.
      """
  
      graph = graph.local_var()
  
      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."
              )
  
      # check if feat is a tuple
      if isinstance(feat, tuple):
          h_src = feat[0]
          h_dst = feat[1]
          feat_src = self.fc_src(h_src).view(
              -1, self._num_heads, self._out_feats
          )
          feat_dst = self.fc_dst(h_dst).view(
              -1, self._num_heads, self._out_feats
          )
      else:
          h_src = feat
          feat_src = feat_dst = self.fc(h_src).view(
              -1, self._num_heads, self._out_feats
          )
          if graph.is_block:
              feat_dst = feat_src[: graph.number_of_dst_nodes()]
  
      # Assign features to nodes
      graph.srcdata.update({"ft": feat_src})
      graph.dstdata.update({"ft": feat_dst})
  
      # Step 1. dot product
      graph.apply_edges(fn.u_dot_v("ft", "ft", "a"))
  
      # Step 2. edge softmax to compute attention scores
      graph.edata["sa"] = edge_softmax(
          graph, graph.edata["a"] / self._out_feats**0.5
      )
  
      # Step 3. Broadcast softmax value to each edge, and aggregate dst node
      graph.update_all(
          fn.u_mul_e("ft", "sa", "attn"), fn.sum("attn", "agg_u")
      )
  
      # output results to the destination nodes
      rst = graph.dstdata["agg_u"]
  
      if get_attention:
          return rst, graph.edata["sa"]
      else:
          return rst
  
file_path: dgl/python/dgl/nn/pytorch/conv/dotgatconv.py
imports: 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 2 for calling the DotGatConv obj's underlying member method code with example usage: obj.forward(graph, feat, get_attention) and returns: rst,  graph, rst