class_docstr: EdgeConv layer from `Dynamic Graph CNN for Learning on Point Clouds
  <https://arxiv.org/pdf/1801.07829>`__
  
  It can be described as follows:
  
  .. math::
     h_i^{(l+1)} = \max_{j \in \mathcal{N}(i)} (
     \Theta \cdot (h_j^{(l)} - h_i^{(l)}) + \Phi \cdot h_i^{(l)})
  
  where :math:`\mathcal{N}(i)` is the neighbor of :math:`i`.
  :math:`\Theta` and :math:`\Phi` are linear layers.
  
  .. note::
  
     The original formulation includes a ReLU inside the maximum operator.
     This is equivalent to first applying a maximum operator then applying
     the ReLU.
  
  Parameters
  ----------
  in_feat : int
      Input feature size; i.e, the number of dimensions of :math:`h_j^{(l)}`.
  out_feat : int
      Output feature size; i.e., the number of dimensions of :math:`h_i^{(l+1)}`.
  batch_norm : bool
      Whether to include batch normalization on messages. Default: ``False``.
  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 EdgeConv
  
  >>> # 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)
  >>> conv = EdgeConv(10, 2)
  >>> res = conv(g, feat)
  >>> res
  tensor([[-0.2347,  0.5849],
          [-0.2347,  0.5849],
          [-0.2347,  0.5849],
          [-0.2347,  0.5849],
          [-0.2347,  0.5849],
          [-0.2347,  0.5849]], grad_fn=<CopyReduceBackward>)
  
  >>> # 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_fea = th.rand(2, 5)
  >>> v_fea = th.rand(4, 5)
  >>> conv = EdgeConv(5, 2, 3)
  >>> res = conv(g, (u_fea, v_fea))
  >>> res
  tensor([[ 1.6375,  0.2085],
          [-1.1925, -1.2852],
          [ 0.2101,  1.3466],
          [ 0.2342, -0.9868]], grad_fn=<CopyReduceBackward>)
docstr: Description
  -----------
  Forward computation
  
  Parameters
  ----------
  g : DGLGraph
      The graph.
  feat : Tensor or pair of tensors
      :math:`(N, D)` where :math:`N` is the number of nodes and
      :math:`D` is the number of feature dimensions.
  
      If a pair of tensors is given, the graph must be a uni-bipartite graph
      with only one edge type, and the two tensors must have the same
      dimensionality on all except the first axis.
  
  Returns
  -------
  torch.Tensor
      New node features.
  
  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, g, feat):
      """
  
      Description
      -----------
      Forward computation
  
      Parameters
      ----------
      g : DGLGraph
          The graph.
      feat : Tensor or pair of tensors
          :math:`(N, D)` where :math:`N` is the number of nodes and
          :math:`D` is the number of feature dimensions.
  
          If a pair of tensors is given, the graph must be a uni-bipartite graph
          with only one edge type, and the two tensors must have the same
          dimensionality on all except the first axis.
  
      Returns
      -------
      torch.Tensor
          New node features.
  
      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 g.local_scope():
          if not self._allow_zero_in_degree:
              if (g.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."
                  )
  
          h_src, h_dst = expand_as_pair(feat, g)
          g.srcdata["x"] = h_src
          g.dstdata["x"] = h_dst
          g.apply_edges(fn.v_sub_u("x", "x", "theta"))
          g.edata["theta"] = self.theta(g.edata["theta"])
          g.dstdata["phi"] = self.phi(g.dstdata["x"])
          if not self.batch_norm:
              g.update_all(
                  fn.e_add_v("theta", "phi", "e"), fn.max("e", "x")
              )
          else:
              g.apply_edges(fn.e_add_v("theta", "phi", "e"))
              # Although the official implementation includes a per-edge
              # batch norm within EdgeConv, I choose to replace it with a
              # global batch norm for a number of reasons:
              #
              # (1) When the point clouds within each batch do not have the
              #     same number of points, batch norm would not work.
              #
              # (2) Even if the point clouds always have the same number of
              #     points, the points may as well be shuffled even with the
              #     same (type of) object (and the official implementation
              #     *does* shuffle the points of the same example for each
              #     epoch).
              #
              #     For example, the first point of a point cloud of an
              #     airplane does not always necessarily reside at its nose.
              #
              #     In this case, the learned statistics of each position
              #     by batch norm is not as meaningful as those learned from
              #     images.
              g.edata["e"] = self.bn(g.edata["e"])
              g.update_all(fn.copy_e("e", "e"), fn.max("e", "x"))
          return g.dstdata["x"]
  
file_path: dgl/python/dgl/nn/pytorch/conv/edgeconv.py
imports: from torch import nn
  from ....None import function
  from ....base import DGLError
  from ....utils import expand_as_pair
label_desc: Use image node_id 3 for calling the EdgeConv obj's underlying member method code with example usage: obj.forward(g, feat) and returns: g