FreeMat - NORM Norm Calculation

NORM Norm Calculation

Section: Array Generation and Manipulations

Usage

Calculates the norm of a matrix. There are two ways to use the norm function. The general syntax is

   y = norm(A,p)

where A is the matrix to analyze, and p is the type norm to compute. The following choices of p are supported

p = 1 returns the 1-norm, or the max column sum of A
p = 2 returns the 2-norm (largest singular value of A)
p = inf returns the infinity norm, or the max row sum of A
p = 'fro' returns the Frobenius-norm (vector Euclidean norm, or RMS value)

For a vector, the regular norm calculations are performed:

1 <= p < inf returns sum(abs(A).^p)^(1/p)
p unspecified returns norm(A,2)
p = inf returns max(abs(A))
p = -inf returns min(abs(A))

Examples

Here are the various norms calculated for a sample matrix

--> A = float(rand(3,4))

A = 

    0.2751    0.5250    0.0532    0.8315 
    0.9886    0.7171    0.6396    0.5145 
    0.5634    0.9679    0.7133    0.0706 

--> norm(A,1)

ans = 

    2.2099 

--> norm(A,2)

ans = 

    2.0674 

--> norm(A,inf)

ans = 

    2.8597 

--> norm(A,'fro')

ans = 

    2.2313 

--> 
quit

Next, we calculate some vector norms.

--> A = float(rand(4,1))

A = 

    0.0288 
    0.6311 
    0.4853 
    0.6145 

--> norm(A,1)

ans = 

    1.7596 

--> norm(A,2)

ans = 

    1.0061 

--> norm(A,7)

ans = 

    0.6962 

--> norm(A,inf)

ans = 

    0.6311 

--> norm(A,-inf)

ans = 

 2.8751e-02 

--> 
quit

FreeMat v3.6 - Online Documentation

NORM Norm Calculation

Usage

Examples