目录
一、函数定义
公式：
意思就是inputs的一共N维的话对这N个数据求p范数，当然这个还是太抽象了，接下来还是看具体的代码~
p指的是求p范数的p值，函数默认p=2，那么就是求2范数
def norm(self, input, p=2): # real signature unknown; restored from __doc__
"""
.. function:: norm(input, p=2) -> Tensor
Returns the p-norm of the :attr:`input` tensor.
.. math::
||x||_{p} = \sqrt[p]{x_{1}^{p} + x_{2}^{p} + \ldots + x_{N}^{p}}
Args:
input (Tensor): the input tensor
p (float, optional): the exponent value in the norm formulation
Example::
>>> a = torch.randn(1, 3)
>>> a
tensor([[-0.5192, -1.0782, -1.0448]])
>>> torch.norm(a, 3)
tensor(1.3633)
.. function:: norm(input, p, dim, keepdim=False, out=None) -> Tensor
Returns the p-norm of each row of the :attr:`input` tensor in the given
dimension :attr:`dim`.
If :attr:`keepdim` is ``True``, the output tensor is of the same size as
:attr:`input` except in the dimension :attr:`dim` where it is of size 1.
Otherwise, :attr:`dim` is squeezed (see :func:`torch.squeeze`), resulting
in the output tensor having 1 fewer dimension than :attr:`input`.
Args:
input (Tensor): the input tensor
p (float): the exponent value in the norm formulation
dim (int): the dimension to reduce
keepdim (bool): whether the output tensor has :attr:`dim` retained or not
out (Tensor, optional): the output tensor
Example::
>>> a = torch.randn(4, 2)
>>> a
tensor([[ 2.1983, 0.4141],
[ 0.8734, 1.9710],
[-0.7778, 0.7938],
[-0.1342, 0.7347]])
>>> torch.norm(a, 2, 1)
tensor([ 2.2369, 2.1558, 1.1113, 0.7469])
>>> torch.norm(a, 0, 1, True)
tensor([[ 2.],
[ 2.],
[ 2.],
[ 2.]])
"""
pass二、代码示例
输入代码
import torch
rectangle_height = 3
rectangle_width = 4
inputs = torch.randn(rectangle_height, rectangle_width)
for i in range(rectangle_height):
for j in range(rectangle_width):
inputs[i][j] = (i + 1) * (j + 1)
print(inputs)得到一个3×4矩阵，如下
tensor([[ 1., 2., 3., 4.],
[ 2., 4., 6., 8.],
[ 3., 6., 9., 12.]])接着我们分别对其行和列分别求2范数
inputs1 = torch.norm(inputs, p=2, dim=1, keepdim=True)
print(inputs1)
inputs2 = torch.norm(inputs, p=2, dim=0, keepdim=True)
print(inputs2)结果分别为
tensor([[ 5.4772],
[10.9545],
[16.4317]])
tensor([[ 3.7417, 7.4833, 11.2250, 14.9666]])怎么来的？
inputs1：（p = 2，dim = 1）每行的每一列数据进行2范数运算
inputs2：（p = 2，dim = 0）每列的每一行数据进行2范数运算
关注keepdim = False这个参数
inputs3 = inputs.norm(p=2, dim=1, keepdim=False)
print(inputs3)inputs3为
tensor([ 5.4772, 10.9545, 16.4317])输出inputs1和inputs3的shape
print(inputs1.shape)
print(inputs3.shape)
torch.Size([3, 1])
torch.Size([3])可以看到inputs3少了一维，其实就是dim=1（求范数）那一维(列)少了，因为从4列变成1列，就是3行中求每一行的2范数，就剩1列了，不保持这一维不会对数据产生影响。
或者也可以这么理解，就是数据每个数据有没有用[]扩起来。
keepdim = True，用[]扩起来；
keepdim = False，不用[]括起来~；
不写keepdim，则默认不保留dim的那个维度
inputs4 = torch.norm(inputs, p=2, dim=1)
print(inputs4)tensor([ 5.4772, 10.9545, 16.4317])不写dim，则计算Tensor中所有元素的2范数
inputs5 = torch.norm(inputs, p=2)
print(inputs5)tensor(20.4939)等价于这句话
inputs6 = inputs.pow(2).sum().sqrt()
print(inputs6)tensor(20.4939)总之，norm操作后dim这一维变为1或者消失。
三、整体代码
"""
@author:nickhuang1996
"""
import torch
rectangle_height = 3
rectangle_width = 4
inputs = torch.randn(rectangle_height, rectangle_width)
for i in range(rectangle_height):
for j in range(rectangle_width):
inputs[i][j] = (i + 1) * (j + 1)
print(inputs)
inputs1 = torch.norm(inputs, p=2, dim=1, keepdim=True)
print(inputs1)
inputs2 = torch.norm(inputs, p=2, dim=0, keepdim=True)
print(inputs2)
inputs3 = inputs.norm(p=2, dim=1, keepdim=False)
print(inputs3)
print(inputs1.shape)
print(inputs3.shape)
inputs4 = torch.norm(inputs, p=2, dim=1)
print(inputs4)
inputs5 = torch.norm(inputs, p=2)
print(inputs5)
inputs6 = inputs.pow(2).sum().sqrt()
print(inputs6)