wehub-resource-sync
240 lines
7.6 KiB
Python
240 lines
7.6 KiB
Python
"""Utilities for pytorch NN package"""
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# pylint: disable=no-member, invalid-name
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import numpy as np
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from mxnet import gluon, nd
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from ... import DGLGraph
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def matmul_maybe_select(A, B):
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"""Perform Matrix multiplication C = A * B but A could be an integer id vector.
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If A is an integer vector, we treat it as multiplying a one-hot encoded tensor.
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In this case, the expensive dense matrix multiply can be replaced by a much
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cheaper index lookup.
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For example,
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::
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A = [2, 0, 1],
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B = [[0.1, 0.2],
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[0.3, 0.4],
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[0.5, 0.6]]
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then matmul_maybe_select(A, B) is equivalent to
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::
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[[0, 0, 1], [[0.1, 0.2],
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[1, 0, 0], * [0.3, 0.4],
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[0, 1, 0]] [0.5, 0.6]]
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In all other cases, perform a normal matmul.
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Parameters
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----------
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A : mxnet.NDArray
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lhs tensor
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B : mxnet.NDArray
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rhs tensor
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Returns
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-------
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C : mxnet.NDArray
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result tensor
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"""
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if A.dtype in (np.int32, np.int64) and len(A.shape) == 1:
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return nd.take(B, A, axis=0)
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else:
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return nd.dot(A, B)
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def bmm_maybe_select(A, B, index):
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"""Slice submatrices of A by the given index and perform bmm.
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B is a 3D tensor of shape (N, D1, D2), which can be viewed as a stack of
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N matrices of shape (D1, D2). The input index is an integer vector of length M.
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A could be either:
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(1) a dense tensor of shape (M, D1),
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(2) an integer vector of length M.
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The result C is a 2D matrix of shape (M, D2)
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For case (1), C is computed by bmm:
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::
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C[i, :] = matmul(A[i, :], B[index[i], :, :])
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For case (2), C is computed by index select:
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::
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C[i, :] = B[index[i], A[i], :]
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Parameters
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----------
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A : mxnet.NDArray
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lhs tensor
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B : mxnet.NDArray
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rhs tensor
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index : mxnet.NDArray
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index tensor
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Returns
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-------
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C : mxnet.NDArray
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return tensor
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"""
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if A.dtype in (np.int32, np.int64) and len(A.shape) == 1:
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return B[index, A, :]
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else:
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BB = nd.take(B, index, axis=0)
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return nd.batch_dot(A.expand_dims(1), BB).squeeze(1)
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def normalize(x, p=2, axis=1, eps=1e-12):
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r"""Performs :math:`L_p` normalization of inputs over specified dimension.
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For a tensor :attr:`input` of sizes :math:`(n_0, ..., n_{dim}, ..., n_k)`, each
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:math:`n_{dim}` -element vector :math:`v` along dimension :attr:`dim` is transformed as
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.. math::
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v = \frac{v}{\max(\lVert v \rVert_p, \epsilon)}.
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With the default arguments it uses the Euclidean norm over vectors along dimension
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:math:`1` for normalization.
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Args:
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x: input ndarray of any shape
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ord (float): the exponent value in the norm formulation. Default: 2
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dim (int): the dimension to reduce. Default: 1
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eps (float): small value to avoid division by zero. Default: 1e-12
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"""
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denom = nd.clip(
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nd.norm(x, ord=p, axis=axis, keepdims=True), eps, float("inf")
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)
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return x / denom
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class Sequential(gluon.nn.Sequential):
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r"""A squential container for stacking graph neural network blocks
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We support two modes: sequentially apply GNN blocks on the same graph or
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a list of given graphs. In the second case, the number of graphs equals the
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number of blocks inside this container.
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Examples
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--------
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Mode 1: sequentially apply GNN modules on the same graph
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>>> import dgl
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>>> from mxnet import nd
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>>> from mxnet.gluon import nn
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>>> import dgl.function as fn
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>>> from dgl.nn.mxnet import Sequential
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>>> class ExampleLayer(nn.Block):
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>>> def __init__(self, **kwargs):
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>>> super().__init__(**kwargs)
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>>> def forward(self, graph, n_feat, e_feat):
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>>> with graph.local_scope():
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>>> graph.ndata['h'] = n_feat
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>>> graph.update_all(fn.copy_u('h', 'm'), fn.sum('m', 'h'))
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>>> n_feat += graph.ndata['h']
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>>> graph.apply_edges(fn.u_add_v('h', 'h', 'e'))
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>>> e_feat += graph.edata['e']
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>>> return n_feat, e_feat
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>>>
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>>> g = dgl.DGLGraph()
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>>> g.add_nodes(3)
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>>> g.add_edges([0, 1, 2, 0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1, 2, 2, 2])
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>>> net = Sequential()
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>>> net.add(ExampleLayer())
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>>> net.add(ExampleLayer())
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>>> net.add(ExampleLayer())
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>>> net.initialize()
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>>> n_feat = nd.random.randn(3, 4)
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>>> e_feat = nd.random.randn(9, 4)
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>>> net(g, n_feat, e_feat)
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(
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[[ 12.412863 99.61184 21.472883 -57.625923 ]
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[ 10.08097 100.68611 20.627377 -60.13458 ]
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[ 11.7912245 101.80654 22.427956 -58.32772 ]]
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<NDArray 3x4 @cpu(0)>,
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[[ 21.818504 198.12076 42.72387 -115.147736]
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[ 23.070837 195.49811 43.42292 -116.17203 ]
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[ 24.330334 197.10927 42.40048 -118.06538 ]
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[ 21.907919 199.11469 42.1187 -115.35658 ]
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[ 22.849625 198.79213 43.866085 -113.65381 ]
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[ 20.926125 198.116 42.64334 -114.246704]
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[ 23.003159 197.06662 41.796425 -117.14977 ]
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[ 21.391375 198.3348 41.428078 -116.30361 ]
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[ 21.291483 200.0701 40.8239 -118.07314 ]]
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<NDArray 9x4 @cpu(0)>)
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Mode 2: sequentially apply GNN modules on different graphs
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>>> import dgl
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>>> from mxnet import nd
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>>> from mxnet.gluon import nn
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>>> import dgl.function as fn
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>>> import networkx as nx
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>>> from dgl.nn.mxnet import Sequential
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>>> class ExampleLayer(nn.Block):
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>>> def __init__(self, **kwargs):
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>>> super().__init__(**kwargs)
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>>> def forward(self, graph, n_feat):
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>>> with graph.local_scope():
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>>> graph.ndata['h'] = n_feat
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>>> graph.update_all(fn.copy_u('h', 'm'), fn.sum('m', 'h'))
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>>> n_feat += graph.ndata['h']
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>>> return n_feat.reshape(graph.num_nodes() // 2, 2, -1).sum(1)
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>>>
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>>> g1 = dgl.DGLGraph(nx.erdos_renyi_graph(32, 0.05))
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>>> g2 = dgl.DGLGraph(nx.erdos_renyi_graph(16, 0.2))
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>>> g3 = dgl.DGLGraph(nx.erdos_renyi_graph(8, 0.8))
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>>> net = Sequential()
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>>> net.add(ExampleLayer())
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>>> net.add(ExampleLayer())
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>>> net.add(ExampleLayer())
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>>> net.initialize()
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>>> n_feat = nd.random.randn(32, 4)
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>>> net([g1, g2, g3], n_feat)
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[[-101.289566 -22.584694 -89.25348 -151.6447 ]
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[-130.74239 -49.494812 -120.250854 -199.81546 ]
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[-112.32089 -50.036713 -116.13266 -190.38638 ]
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[-119.23065 -26.78553 -111.11185 -166.08322 ]]
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<NDArray 4x4 @cpu(0)>
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"""
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def __init__(self, prefix=None, params=None):
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super(Sequential, self).__init__(prefix=prefix, params=params)
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def forward(self, graph, *feats):
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r"""Sequentially apply modules to the input.
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Parameters
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----------
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graph : DGLGraph or list of DGLGraphs
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The graph(s) to apply modules on.
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*feats :
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Input features.
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The output of :math:`i`-th block should match that of the input
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of :math:`(i+1)`-th block.
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"""
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if isinstance(graph, list):
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for graph_i, module in zip(graph, self):
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if not isinstance(feats, tuple):
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feats = (feats,)
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feats = module(graph_i, *feats)
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elif isinstance(graph, DGLGraph):
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for module in self:
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if not isinstance(feats, tuple):
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feats = (feats,)
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feats = module(graph, *feats)
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else:
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raise TypeError(
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"The first argument of forward must be a DGLGraph"
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" or a list of DGLGraph s"
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)
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return feats
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