[人工智能]解析torch.norm函数

官方文档：https://pytorch.org/docs/stable/generated/torch.norm.html?highlight=norm#torch.norm

函数：

norm(input, p='fro', dim=None, keepdim=False, out=None, dtype=None)
    Returns the matrix norm or vector norm of a given tensor.

参数:

• input (Tensor) – 输入张量
• p (int, float, inf, -inf, ‘fro’, ‘nuc’, optional) – 范数顺序.
  Default: 'fro'，此时p为Frobenius范数计算中的幂指数值

 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 (int, 2-tuple of ints, 2-list of ints, optional):进行范数计算的维度

Example：

import torch
from torch import tensor

a = tensor([[[1, 2, 3, 4], [1, 2, 3, 4]],
            [[0, 2, 3, 4], [0, 2, 3, 4]]], dtype=torch.float32)
print(a.shape)
a0 = torch.norm(a, p=2, dim=0)       # 对0 dim求vector 2-norm
a1 = torch.norm(a, p=2, dim=1)       # 对1 dim求vector 2-norm
a2 = torch.norm(a, p=2, dim=2)       # 对2 dim求vector 2-norm
a3 = torch.norm(a, p=2, dim=(0, 1))  # 对0,1 dim求matrix 2-norm
a4 = torch.norm(a, p=2, dim=None)    # input是超过二维的tensor，vector norm将被应用到最后的dim
print(a0)
print(a1)
print(a2)
print(a3)
print(a4)

Out：

torch.Size([2, 2, 4])
tensor([[1.0000, 2.8284, 4.2426, 5.6569],
        [1.0000, 2.8284, 4.2426, 5.6569]])
tensor([[1.4142, 2.8284, 4.2426, 5.6569],
        [0.0000, 2.8284, 4.2426, 5.6569]])
tensor([[5.4772, 5.4772],
        [5.3852, 5.3852]])
tensor([1.4142, 4.0000, 6.0000, 8.0000])
tensor(10.8628)

• keepdim（bool, optional）– 是否保持输入时的维度. Default: False

b0 = torch.norm(a, p=2, dim=0, keepdim=True)
b1 = torch.norm(a, p=2, dim=0, keepdim=False)   # 就是刚才的a0
print(b0.shape)
print(b1.shape)

Out：

torch.Size([1, 2, 4])
torch.Size([2, 4])

• out (Tensor, optional) – 结果张量.
• dtype (:class:torch.dtype, optional): 返回的tensor的数据类型. Default: None.