# LapPEο

Bases: `BaseTransform`

Laplacian Positional Encoding, as introduced in Benchmarking Graph Neural Networks

This module only works for homogeneous bidirected graphs.

Parameters:
• k (int) β Number of smallest non-trivial eigenvectors to use for positional encoding.

• feat_name (str, optional) β Name to store the computed positional encodings in ndata.

• eigval_name (str, optional) β If None, store laplacian eigenvectors only. Otherwise, itβs the name to store corresponding laplacian eigenvalues in ndata. Default: None.

• padding (bool, optional) β If False, raise an exception when k>=n. Otherwise, add zero paddings in the end of eigenvectors and βnanβ paddings in the end of eigenvalues when k>=n. Default: False. n is the number of nodes in the given graph.

Example

```>>> import dgl
>>> from dgl import LapPE
>>> transform1 = LapPE(k=3)
>>> transform3 = LapPE(k=5, feat_name='eigvec', eigval_name='eigval', padding=True)
>>> g = dgl.graph(([0,1,2,3,4,2,3,1,4,0], [2,3,1,4,0,0,1,2,3,4]))
>>> g1 = transform1(g)
>>> print(g1.ndata['PE'])
tensor([[ 0.6325,  0.1039,  0.3489],
[-0.5117,  0.2826,  0.6095],
[ 0.1954,  0.6254, -0.5923],
[-0.5117, -0.4508, -0.3938],
[ 0.1954, -0.5612,  0.0278]])
>>> g2 = transform2(g)
>>> print(g2.ndata['PE'])
tensor([[-0.6325, -0.1039,  0.3489, -0.2530,  0.0000],
[ 0.5117, -0.2826,  0.6095,  0.4731,  0.0000],
[-0.1954, -0.6254, -0.5923, -0.1361,  0.0000],
[ 0.5117,  0.4508, -0.3938, -0.6295,  0.0000],
[-0.1954,  0.5612,  0.0278,  0.5454,  0.0000]])
>>> g3 = transform3(g)
>>> print(g3.ndata['eigval'])
tensor([[0.6910, 0.6910, 1.8090, 1.8090,    nan],
[0.6910, 0.6910, 1.8090, 1.8090,    nan],
[0.6910, 0.6910, 1.8090, 1.8090,    nan],
[0.6910, 0.6910, 1.8090, 1.8090,    nan],
[0.6910, 0.6910, 1.8090, 1.8090,    nan]])
>>> print(g3.ndata['eigvec'])
tensor([[ 0.6325, -0.1039,  0.3489,  0.2530,  0.0000],
[-0.5117, -0.2826,  0.6095, -0.4731,  0.0000],
[ 0.1954, -0.6254, -0.5923,  0.1361,  0.0000],
[-0.5117,  0.4508, -0.3938,  0.6295,  0.0000],
[ 0.1954,  0.5612,  0.0278, -0.5454,  0.0000]])
```