Pytorch torch.norm函数详解用法

向右看齐 2024-02-06 06:18 64阅读 0赞

## **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。**  
![在这里插入图片描述][b00114ba466e458f86bd15f47f50cdd8.png]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  
![在这里插入图片描述][36665602bec941bfaa6c45cfa1343551.png]  
![在这里插入图片描述][4ac3e084eee342e1be641887250b5c60.png]  
例子来源：[机器学习 | Schatten范数 - 知乎][_ Schatten_ -]

p=`other`时,当作vec norm计算，p为int的形式,则是如下形式：  
![在这里插入图片描述][12f147302aed478ca9cb96698d82d03b.png]  
详细解释：[torch.norm()函数的用法 - 知乎][torch.norm_ -]

##### 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：![,][43ec1d7556de4c408409819cfcc9577b.png]

#### 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)

[b00114ba466e458f86bd15f47f50cdd8.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/02/06/37976be0637445e2bfb7d94f35abdfd2.png
[36665602bec941bfaa6c45cfa1343551.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/02/06/c176ce55020b44e69b68ddefe60b6482.png
[4ac3e084eee342e1be641887250b5c60.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/02/06/254e67a836b14221b8fbea7f296803cf.png
[_ Schatten_ -]: https://zhuanlan.zhihu.com/p/104402273
[12f147302aed478ca9cb96698d82d03b.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/02/06/a2e12a2693294a19889dc7a6b84be91d.png
[torch.norm_ -]: https://zhuanlan.zhihu.com/p/260162240
[43ec1d7556de4c408409819cfcc9577b.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/02/06/0c08ec7e237b4cacbea49dcbb665deca.png