norm

Vector and matrix norms

Syntax

n = norm(v)

n = norm(v,p)

n = norm(X)

n = norm(X,p)

n = norm(X,'fro')

Description

n = norm（v）返回向量v的欧几里德范数。该范数也称为2范数，向量幅度或欧几里德长度。

n = norm（v，p）返回广义向量p范数。

n = norm（X）返回矩阵X的2范数或最大奇异值，其近似为max（svd（X））。

n = norm（X，p）返回矩阵X的p范数，其中p为1,2或Inf：

• 如果p = 1，则n是矩阵的最大绝对列和。

• 如果p = 2，则n近似为max（svd（X））。 这相当于norm（X）。

• 如果p = Inf，那么n是矩阵的最大绝对行和。

n = norm（X，'fro'）返回矩阵X的Frobenius范数。

有关范数的基础知识，见博文：【 MATLAB 】范数的必备基础知识

下面举例说明：

Vector Magnitude（向量幅度）

  

   

    

     

    
    

     

      %Create a vector and calculate the magnitude.
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      v = [1 -2 3];
     
    
   

    

     

    
    

     

      n = norm(v)
     
    
   

    

     

    
    

     

      % n = 3.7417
     
    
  
 

1-Norm of Vector

  

   

    

     

    
    

     

      clc
     
    
   

    

     

    
    

     

      clear
     
    
   

    

     

    
    

     

      close all
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      % Calculate the 1-norm of a vector, which is the sum of the element magnitudes.
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      X = [-2 3 -1];
     
    
   

    

     

    
    

     

      n = norm(X,1)
     
    
   

    

     

    
    

     

      % n = 6
     
    
  
 

Euclidean Distance Between Two Points

  

   

    

     

    
    

     

      clc
     
    
   

    

     

    
    

     

      clear
     
    
   

    

     

    
    

     

      close all
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      % Calculate the distance between two points as the norm of the difference between the vector elements.
     
    
   

    

     

    
    

     

      % 
     
    
   

    

     

    
    

     

      % Create two vectors representing the (x,y) coordinates for two points on the Euclidean plane.
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      a = [0 3];
     
    
   

    

     

    
    

     

      b = [-2 1];
     
    
   

    

     

    
    

     

      % Use norm to calculate the distance between the points.
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      d = norm(b-a)
     
    
  
 

d =

    2.8284
几何上，两点之间的距离：

2-Norm of Matrix

  

   

    

     

    
    

     

      clc
     
    
   

    

     

    
    

     

      clear
     
    
   

    

     

    
    

     

      close all
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      % Calculate the 2-norm of a matrix, which is the largest singular value.
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      X = [2 0 1;-1 1 0;-3 3 0];
     
    
   

    

     

    
    

     

      n = norm(X)
     
    
   

    

     

    
    

     

      % n = 4.7234
     
    
  
 

Frobenius Norm of Sparse Matrix

  

   

    

     

    
    

     

      clc
     
    
   

    

     

    
    

     

      clear
     
    
   

    

     

    
    

     

      close all
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      % 使用'fro'计算稀疏矩阵的Frobenius范数，该范数计算列向量的2范数S（:)。
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      S = sparse(1:25,1:25,1);
     
    
   

    

     

    
    

     

      n = norm(S,'fro')
     
    
   

    

     

    
    

     

      % n = 5
     
    
  
 

文章来源: reborn.blog.csdn.net，作者：李锐博恩，版权归原作者所有，如需转载，请联系作者。

原文链接：reborn.blog.csdn.net/article/details/83119363