vecnorm

矢量规范

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Syntax

N = vecnorm(A)

n = vecnorm（a，p）

N = vecnorm(A,p,dim)

Description

example

N = vecnorm(A)returns the 2-norm or欧几里得规范的A:

IfAis a vector, thenvecnorm返回向量的规范。
IfA是矩阵，然后vecnorm返回每列的标准。
IfA是一个多维数组，然后vecnorm沿着大小不等于1的第一个数组维度返回标准。

example

N = vecnorm(A,p)calculates thegeneralized vector p-norm.

example

N = vecnorm(A,p,dim)operates along dimensiondim. The size of this dimension reduces to 1 while the sizes of all other dimensions remain the same.

Examples

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1-Norm and 2-Norm of Vector

打开实时脚本

Calculate the 2-norm of a vector corresponding to the point (2,2,2) in 3-D space. The 2-norm is equal to the Euclidean length of the vector, $\sqrt{12}$ .

x = [2 2 2]; n = vecnorm(x)

n = 3.4641

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

n = vecnorm(x,1)

n = 6

矩阵列的2个norm

打开实时脚本

计算矩阵的列的2个词。

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

A =3×32 0 1 -1 1 0 -3 3 0

n = vecnorm(A)

n =1×33.7417 3.1623 1.0000

As an alternative, you can use the规范function to calculate the 2-norm of the entire matrix.

Input Arguments

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`A`—Input array
vector|matrix|multidimensional array

Input array, specified as a vector, matrix, or multidimensional array. By convention,vecnormreturnsNaNvalues if the vector being operated on contains aNaNvalue.

Data Types:single|double
Complex Number Support:Yes

`p`—Norm type
2(default) |positive scalar|`inf`

Norm type, specified as2（默认），一个正标量或inf.

`dim`—Dimension to operate along
正整数标量

Dimension to operate along, specified as a positive integer scalar. If you do not specify a value, then the default is the first array dimension whose size does not equal 1.

Dimensiondimindicates the dimension whose length reduces to 1. In other words,size(N,dim)is1, while the sizes of all other dimensions remain the same.

考虑二维输入阵列，A:

vecnorm(A,p,1)calculates the norm of each column.
vecnorm(A,p,2)计算每一行的标准。

vecnormreturnsabs(A)whendim大于ndims(A)or whensize(A,dim)is1.

More About

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欧几里得规范

矢量的欧几里得规范（也称为矢量幅度，欧几里得长度或2个norm）vwithNelements is defined by

$‖ v ‖ = \sqrt{\sum_{k = 1}^{N} {| v_{k} |}^{2}} .$

General Vector Norm

The general definition for the p-norm of a vectorvthat hasNelements is

${‖ v ‖}_{p} = {[\sum_{k = 1}^{N} {| v_{k} |}^{p}]}^{1 / p},$

wherepis any positive real value orinf. Some interesting values ofpare:

Ifp = 1，然后由此产生的1个总体是向量元素的绝对值之和。
Ifp = 2, then the resulting 2-norm gives the vector magnitude or Euclidean length of the vector.
Ifp = Inf, then ${‖ v ‖}_{\infty} = \max_{i} (| v (i) |)$ .

Extended Capabilities

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, seeTall Arrays.

C/C++ Code Generation
使用MATLAB®CODER™生成C和C ++代码。

Usage notes and limitations:

If you supplydim, then it must be constant.
有关与可变大小输入相关的限制，请参见Variable-Sizing Restrictions for Code Generation of Toolbox Functions(MATLAB Coder).
代码生成不支持此功能的稀疏矩阵输入。万博1manbetx

Thread-Based Environment
Run code in the background using MATLAB®`backgroundPool`or accelerate code with Parallel Computing Toolbox™`ThreadPool`.

This function fully supports thread-based environments. For more information, seeRun MATLAB Functions in Thread-Based Environment.

GPU Arrays
使用并行计算工具箱™在图形处理单元（GPU）上运行加速代码。

此功能完全支持GPU数组。万博1manbetx有关更多信息，请参阅Run MATLAB Functions on a GPU(Parallel Computing Toolbox).

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

此功能完全支持分布式数组。万博1manbetx有关更多信息，请参阅运行具有分布式数组的MATLAB功能(Parallel Computing Toolbox).

版本历史

Introduced in R2017b

vecnorm

Syntax

Description

Examples

1-Norm and 2-Norm of Vector

矩阵列的2个norm

Input Arguments

A—Input arrayvector|matrix|multidimensional array

p—Norm type2(default) |positive scalar|inf

dim—Dimension to operate along正整数标量

More About

欧几里得规范

General Vector Norm

Extended Capabilities

Tall ArraysCalculate with arrays that have more rows than fit in memory.

C/C++ Code Generation使用MATLAB®CODER™生成C和C ++代码。

Thread-Based EnvironmentRun code in the background using MATLAB®backgroundPoolor accelerate code with Parallel Computing Toolbox™ThreadPool.

GPU Arrays使用并行计算工具箱™在图形处理单元（GPU）上运行加速代码。

Distributed ArraysPartition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

版本历史

See Also

`A`—Input array
vector|matrix|multidimensional array

`p`—Norm type
2(default) |positive scalar|`inf`

`dim`—Dimension to operate along
正整数标量

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

C/C++ Code Generation
使用MATLAB®CODER™生成C和C ++代码。

Thread-Based Environment
Run code in the background using MATLAB®`backgroundPool`or accelerate code with Parallel Computing Toolbox™`ThreadPool`.

GPU Arrays
使用并行计算工具箱™在图形处理单元（GPU）上运行加速代码。

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.