normalize

paddle.nn.functional. normalize ( x, p=2, axis=1, epsilon=1e-12, name=None ) [source]

This op normalizes x along dimension axis using \(L_p\) norm. This layer computes

\[\begin{split}y = \\frac{x}{ \\max\\left( \\lvert \\lvert x \\rvert \\rvert_p, epsilon\\right) }\end{split}\]
\[\begin{split}\\lvert \\lvert x \\rvert \\rvert_p = \\left( \\sum_i {\\lvert x_i \\rvert^p} \\right)^{1/p}\end{split}\]

where, \(\\sum_i{\\lvert x_i \\rvert^p}\) is calculated along the axis dimension.

Parameters
  • x (Tensor) – The input tensor could be N-D tensor, and the input data type could be float32 or float64.

  • p (float|int, optional) – The exponent value in the norm formulation. Default: 2

  • axis (int, optional) – The axis on which to apply normalization. If axis < 0, the dimension to normalization is x.ndim + axis. -1 is the last dimension.

  • epsilon (float, optional) – Small float added to denominator to avoid dividing by zero. Default is 1e-12.

  • name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, the output has the same shape and data type with x.

Examples

import numpy as np
import paddle
import paddle.nn.functional as F

paddle.disable_static()
x = np.arange(6, dtype=np.float32).reshape(2,3)
x = paddle.to_tensor(x)
y = F.normalize(x)
print(y.numpy())
# [[0.         0.4472136  0.8944272 ]
# [0.42426404 0.5656854  0.7071067 ]]

y = F.normalize(x, p=1.5)
print(y.numpy())
# [[0.         0.40862012 0.81724024]
# [0.35684016 0.4757869  0.5947336 ]]

y = F.normalize(x, axis=0)
print(y.numpy())
# [[0.         0.24253564 0.37139067]
# [1.         0.97014254 0.9284767 ]]