def normalize(tensor, ord="euclidean", axis=None, name=None):
"""Normalizes tensor along dimension axis using specified norm.
This uses tf.linalg.norm to compute the norm along axis.
This function can compute several different vector norms (the 1-norm, the
Euclidean or 2-norm, the inf-norm, and in general the p-norm for p > 0) and
matrix norms (Frobenius, 1-norm, 2-norm and inf-norm).
Args:
tensor: Tensor of types float32, float64, complex64, complex128
ord: Order of the norm. Supported values are 'fro', 'euclidean', 1,
2, np.inf and any positive real number yielding the corresponding
p-norm. Default is 'euclidean' which is equivalent to Frobenius norm if
tensor is a matrix and equivalent to 2-norm for vectors.
Some restrictions apply: a) The Frobenius norm 'fro' is not defined for
vectors, b) If axis is a 2-tuple (matrix norm), only 'euclidean',
'fro', 1, 2, np.inf are supported. See the description of axis
on how to compute norms for a batch of vectors or matrices stored in a
tensor.
axis: If axis is None (the default), the input is considered a vector
and a single vector norm is computed over the entire set of values in the
tensor, i.e. norm(tensor, ord=ord) is equivalent to
norm(reshape(tensor, [-1]), ord=ord). If axis is a Python integer, the
input is considered a batch of vectors, and axis determines the axis in
tensor over which to compute vector norms. If axis is a 2-tuple of
Python integers it is considered a batch of matrices and axis determines
the axes in tensor over which to compute a matrix norm.
Negative indices are supported. Example: If you are passing a tensor that
can be either a matrix or a batch of matrices at runtime, pass
axis=[-2,-1] instead of axis=None to make sure that matrix norms are
computed.
args:
tensor 输入
ord 标准化方法，有l1/l2，常用的是l2，euclidean是欧式距离，我个人理解和l2是一样的
此处默认是euclidean
axis 沿哪一个轴/维度标准化，tensorflow此处的函数可以指定元组的轴
示例：
data = np.array([[[ 1., -1., 2.],
[ 2., 0., 0.],
[ 0., 1., -1.]],
[[ 1., 1., 1.],
[ 2., 2., 2.],
[ 1., 1., -1.]],
[[ 1., 0., 0.],
[ 2., 0., 0.],
[ 0., 0., -1.]]])
data_tensor = tf.convert_to_tensor(data,dtype=tf.float32)
默认 ord=l2 , axis = None , 此处将tensor展平，27个元素的平方和加起来 = 36 ，norm=6
result,__ = tf.linalg.normalize(data_tensor)
print(result)
tf.Tensor(
[[[ 0.16666667 -0.16666667 0.33333334]
[ 0.33333334 0. 0. ]
[ 0. 0.16666667 -0.16666667]]
[[ 0.16666667 0.16666667 0.16666667]
[ 0.33333334 0.33333334 0.33333334]
[ 0.16666667 0.16666667 -0.16666667]]
[[ 0.16666667 0. 0. ]
[ 0.33333334 0. 0. ]
[ 0. 0. -0.16666667]]], shape=(3, 3, 3), dtype=float32)
axis = 0，沿batch维度
result,__ = tf.linalg.normalize(data_tensor,axis=0)
print(result)
tf.Tensor(
[[[ 0.57735026 -0.70710677 0.8944272 ]
[ 0.57735026 0. 0. ]
[ 0. 0.70710677 -0.57735026]]
[[ 0.57735026 0.70710677 0.4472136 ]
[ 0.57735026 1. 1. ]
[ 1. 0.70710677 -0.57735026]]
[[ 0.57735026 0. 0. ]
[ 0.57735026 0. 0. ]
[ 0. 0. -0.57735026]]], shape=(3, 3, 3), dtype=float32)
axis = 1 ,沿每一列维度
result,__ = tf.linalg.normalize(data_tensor,axis=1)
print(result)
tf.Tensor(
[[[ 0.4472136 -0.70710677 0.8944272 ]
[ 0.8944272 0. 0. ]
[ 0. 0.70710677 -0.4472136 ]]
[[ 0.40824828 0.40824828 0.40824828]
[ 0.81649655 0.81649655 0.81649655]
[ 0.40824828 0.40824828 -0.40824828]]
[[ 0.4472136 nan 0. ]
[ 0.8944272 nan 0. ]
[ 0. nan -1. ]]], shape=(3, 3, 3), dtype=float32)
axis = 2,沿每一行维度
result,__ = tf.linalg.normalize(data_tensor,axis=2)
print(result)
tf.Tensor(
[[[ 0.40824828 -0.40824828 0.81649655]
[ 1. 0. 0. ]
[ 0. 0.70710677 -0.70710677]]
[[ 0.57735026 0.57735026 0.57735026]
[ 0.57735026 0.57735026 0.57735026]
[ 0.57735026 0.57735026 -0.57735026]]
[[ 1. 0. 0. ]
[ 1. 0. 0. ]
[ 0. 0. -1. ]]], shape=(3, 3, 3), dtype=float32)
axis = (1,2) 第0维的batch标准化
result,__ = tf.linalg.normalize(data_tensor,axis=(1,2))
print(result)
tf.Tensor(
[[[ 0.28867513 -0.28867513 0.57735026]
[ 0.57735026 0. 0. ]
[ 0. 0.28867513 -0.28867513]]
[[ 0.23570228 0.23570228 0.23570228]
[ 0.47140455 0.47140455 0.47140455]
[ 0.23570228 0.23570228 -0.23570228]]
[[ 0.40824828 0. 0. ]
[ 0.81649655 0. 0. ]
[ 0. 0. -0.40824828]]], shape=(3, 3, 3), dtype=float32)
def normalize(input: Tensor, p: float = 2, dim: int = 1, eps: float = 1e-12, out: Optional[Tensor] = None) -> Tensor:
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:
input: input tensor of any shape
p (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
out (Tensor, optional): the output tensor. If :attr:out is used, this
operation won't be differentiable.
"""
args
input 输入
p normalize的方法，l1,l2，p=2默认为l2标准化
dim 沿哪一个维度标准化，默认为1
data = np.array([[[ 1., -1., 2.],
[ 2., 0., 0.],
[ 0., 1., -1.]],
[[ 1., 1., 1.],
[ 2., 2., 2.],
[ 1., 1., -1.]],
[[ 1., 0., 0.],
[ 2., 0., 0.],
[ 0., 0., -1.]]])
data_tensor = torch.tensor(data,dtype=torch.float32)
dim=0，结果与tf的axis=0是相同的
result = F.normalize(data_tensor,dim=0)
print(result)
tensor([[[ 0.5774, -0.7071, 0.8944],
[ 0.5774, 0.0000, 0.0000],
[ 0.0000, 0.7071, -0.5774]],
[[ 0.5774, 0.7071, 0.4472],
[ 0.5774, 1.0000, 1.0000],
[ 1.0000, 0.7071, -0.5774]],
[[ 0.5774, 0.0000, 0.0000],
[ 0.5774, 0.0000, 0.0000],
[ 0.0000, 0.0000, -0.5774]]])
Original: https://blog.csdn.net/henry_xiong030/article/details/123865308
Author: henry_xiong030
Title: tensorflow,pytorch中normalize方法
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