【深度学习框架-torch】torch.norm函数详解用法

目录

torch.norm参数定义

torch版本1.6

def norm(input, p="fro", dim=None, keepdim=False, out=None, dtype=None)

input

input (Tensor): the input tensor 输入为tensor

p

 p (int, float, inf, -inf, 'fro', 'nuc', optional): the order of norm. Default: ``'fro'``
            The following norms can be calculated:

            =====  ============================  ==========================
            ord    matrix norm                   vector norm
            =====  ============================  ==========================
            None   Frobenius norm                2-norm
            'fro'  Frobenius norm                --
            'nuc'  nuclear norm                  --
            Other  as vec norm when dim is None  sum(abs(x)**ord)**(1./ord)
            =====  ============================  ==========================

dim是matrix norm

如果input是

matrix norm

,也就是维度大于等于2维，则
P值默认为

fro

,

Frobenius norm

可认为是与计算向量的欧氏距离类似
有时候为了比较真实的矩阵和估计的矩阵值之间的误差
或者说比较真实矩阵和估计矩阵之间的相似性，我们可以采用 Frobenius 范数。
计算矩阵的Frobenius norm (Frobenius 范数)，就是矩阵A各项元素的绝对值平方的总和再开根号

p=

'nuc’

时，是求核范数，核范数是矩阵奇异值的和。核范数的具体定义为


例子来源：https://zhuanlan.zhihu.com/p/104402273

p=

other

时,当作vec norm计算，p为int的形式,则是如下形式：

详细解释：https://zhuanlan.zhihu.com/p/260162240

dim是vector norm

p=

none

时,为L2 Norm，也是属于P范数一种，

pytorch

调用的函数是

F.normalize

,

pytorch

官网定义如下：

dim

dim (int, 2-tuple of ints, 2-list of ints, optional): If it is an int,
            vector norm will be calculated, if it is 2-tuple of ints, matrix norm
            will be calculated. If the value is None, matrix norm will be calculated
            when the input tensor only has two dimensions, vector norm will be
            calculated when the input tensor only has one dimension. If the input
            tensor has more than two dimensions, the vector norm will be applied to
            last dimension.

如果

dim

为

None

, 当input的维度只有2维时使用

matrix norm

，当input的维度只有1维时使用

vector norm

，当input的维度超过2维时，只在最后一维上使用

vector norm

。
如果

dim

不为

None

,1.

dim

是int类型，则使用

vector norm

,如果

dim

是2-tuple int类型，则使用

matrix norm

.

Keepdim

keepdim (bool, optional): whether the output tensors have :attr:`dim`
            retained or not. Ignored if :attr:`dim` = ``None`` and
            :attr:`out` = ``None``. Default: ``False``

keepdim

为True，则保留dim指定的维度，如果为False，则不保留。默认为False

out

out (Tensor, optional): the output tensor. Ignored if
            :attr:`dim` = ``None`` and :attr:`out` = ``None``.

输出为tensor，如果

dim

=

None

and

out

=

None

.则不输出

dtype

dtype (:class:`torch.dtype`, optional): the desired data type of
            returned tensor. If specified, the input tensor is casted to
            :attr:'dtype' while performing the operation. Default: None.

指定输出的数据类型

示例

>>> import torch
>>> a = torch.arange(9, dtype= torch.float) - 4
>>> a
tensor([-4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])
>>> b = a.reshape((3, 3))
>>> b
tensor([[-4., -3., -2.],
        [-1.,  0.,  1.],
        [ 2.,  3.,  4.]])
>>> torch.norm(a)
>tensor(7.7460)
>>>计算流程: math.sqrt((4*4 + 3*3 + 2*2 + 1*1 +  -4*-4 + -3*-3 + -2*-2 + -1*-1))
7.7460
>>> torch.norm(b) # 默认计算F范数
tensor(7.7460)