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