IDL Reference Guide: Procedures and Functions

NORM

The NORM function computes the norm of a vector or a two-dimensional array.

By default, NORM computes the L₂ (Euclidean) norm for vectors, and the L_¥ norm for arrays. You may use the LNORM keyword to specify different norms.

This routine is written in the IDL language. Its source code can be found in the file norm.pro in the lib subdirectory of the IDL distribution.

Syntax

Result = NORM( A [, /DOUBLE] [, LNORM={0 | 1 | 2 | n}])

Return Value

Returns the Euclidean or infinity norm of a vector or an array. This function always returns a float or double value.

Arguments

A

A can be either a real or complex vector, or a real or complex two-dimensional array.

Keywords

DOUBLE

Set this keyword to force the result to be returned as double precision. The default is to return a single-precision result if the input is single precision, or double precision otherwise. Internally, all computations are done using double-precision arithmetic.

LNORM

Set this keyword to indicate which norm to compute. If A is a vector, then the possible values of this keyword are:

Table 3-95: LNORM Keyword Values (Vector) 

Table 3-95: LNORM Keyword Values (Vector) 

Value	Description
0	Compute the norm, defined as MAX(ABS(A)).
1	Compute the L1 norm, defined as TOTAL(ABS(A)).
2	Compute the L2 norm, defined as SQRT(TOTAL(ABS(A)^2)). This is the default.
n	Compute the Ln norm, defined as (TOTAL(ABS(A)^n))^(1/n) where n is any number, float-point or integer.

If A is a two-dimensional array, then the possible values of this keyword are:

Examples

; Define an n-element complex vector A:  
A = [COMPLEX(1, 0), COMPLEX(2,-2), COMPLEX(-3,1)]  
  
; Compute the Euclidean norm of A and print:  
PRINT, 'Euclidian Norm of A =', NORM(A)  
  
; Define an m by n complex array B:   
B = [[COMPLEX(1, 0), COMPLEX(2,-2), COMPLEX(-3,1)], $  
     [COMPLEX(1,-2), COMPLEX(2, 2), COMPLEX(1, 0)]]  
  
;Compute the Infinity norm of B and print.  
PRINT, 'Infinity Norm of B =', NORM(B, /DOUBLE)  

IDL prints:

Euclidian Norm of A =    4.35890  
Infinity Norm of B =    6.9907048