# Copyright 2022 Huawei Technologies Co., Ltd
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
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# ============================================================================
"""normalization"""
import mindspore as ms
from mindspore import ops
from mindspore_gl.graph import get_laplacian
[文档]def norm(edge_index, num_nodes, edge_weight=None, normalization='sym',
lambda_max=None, batch=None):
r"""
graph laplacian normalization.
Args:
edge_index (Tensor): Edge index. The shape is :math:`(2, N\_e)`
where :math:`N\_e` is the number of edges.
num_nodes (int): Number of nodes.
edge_weight (Tensor): Edge weights. The shape is :math:`(N\_e)`
where :math:`N\_e` is the number of edges. Default: ``None``.
normalization (str): Normalization method. Default: ``'sym'``.
:math:`(L)` is normalized matrix, :math:`(D)` is degree matrix, :math:`(A)` is adjaceny matrix,
:math:`(I)` is unit matrix.
1. ``None``: No normalization
:math:`\mathbf{L} = \mathbf{D} - \mathbf{A}`
2. ``'sym'``: Symmetric normalization
:math:`\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1/2} \mathbf{A}
\mathbf{D}^{-1/2}`
3. ``'rw'``: Random-walk normalization
:math:`\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1} \mathbf{A}`
lambda_max (int, float): Lambda value of graph. Default: ``None``.
batch (Tensor): Batch vector. Default: ``None``.
Returns:
- **edge_index** (Tensor) - normalized edge_index.
- **edge_weight** (Tensor) - normalized edge_weight
Raises:
ValueError: if `normalization` not is ``None`` or ``'sym'`` or ``'rw'``.
Supported Platforms:
``Ascend`` ``GPU``
Examples:
>>> import mindspore as ms
>>> from mindspore_gl.graph import norm
>>> edge_index = [[1, 1, 2, 2], [0, 2, 0, 1]]
>>> edge_index = ms.Tensor(edge_index, ms.int32)
>>> num_nodes = 3
>>> edge_index, edge_weight = norm(edge_index, num_nodes)
>>> print(edge_index)
[[1 1 2 2 0 1 2]
[0 2 0 1 0 1 2]]
>>> print(edge_weight)
[-0. -0.4999999 -0. -0.4999999 1. 1.
1. ]
"""
if normalization not in [None, 'sym', 'rw']:
raise ValueError('Invalid normalization')
edge_index, edge_weight = get_laplacian(edge_index, num_nodes, edge_weight,
normalization)
if lambda_max is None:
lambda_max = 2.0 * edge_weight.max()
elif not isinstance(lambda_max, ms.Tensor):
lambda_max = ms.tensor(lambda_max, ms.float32)
if lambda_max is None:
raise ValueError("lambda_max is None")
if batch is not None and lambda_max.size > 1:
lambda_max = lambda_max[batch[edge_index[0]]]
edge_weight = (2.0 * edge_weight) / lambda_max
mask = ops.isfinite(edge_weight)
mask = ops.logical_not(mask)
edge_weight = ops.MaskedFill()(edge_weight, mask, 0.0)
return edge_index, edge_weight