IDL Analyst Reference Guide: Math and Statistics Utilities

IMSL_NORM

The IMSL_NORM function computes various norms of a vector or the difference of two vectors.

Syntax

Result = IMSL_NORM(x[, y] [, INDEX_MAX=variable] [, INF=value] [, ONE=value] )

Return Value

The requested norm of the input vector. If the norm cannot be computed, NaN is returned.

Arguments

x

Vector for which the norm is to be computed.

y

If present, IMSL_NORM computes the norm of (x – y).

Keywords

INDEX_MAX

Named variable into which the index of the element of x with the maximum modulus is stored. If Index_Max is used, then the keyword Inf also must be used. If the parameter y is specified, then the index of (x – y) with the maximum modulus is stored.

INF

If present and nonzero, computes the infinity norm max|x_i|.

ONE

If present and nonzero, computes the 1-norm

Discussion

By default, IMSL_NORM computes the Euclidean norm as follows:

If the keyword One is set, then the 1-norm:

is returned. If the keyword Inf is set, the infinity norm max|x_i| is returned. In the case of the infinity norm, the index of the element with maximum modulus also is returned.

If the parameter y is specified, the computations of the norms described above are performed on (x – y).

Examples

Example 1

In this example, the Euclidean norm of an input vector is computed.

x = [ 1.0, 3.0, -2.0, 4.0 ]  
n = IMSL_NORM(x)  
PM, n, Title = 'Euclidean norm of x:'   
  
Euclidean norm of x:  
      5.47723  

x = [1.0, 3.0, -2.0, 4.0]  
y = [4.0, 2.0, -1.0, -5.0]  
n = IMSL_NORM(x, y, /Inf, Index_Max = imax)  
PM, n, Title = 'Infinity norm of (x-y):'  
PM, imax, Title = 'Element of (x-y) with maximum modulus:'  
  
Infinity norm of (x-y):  
      9.00000  
Element of (x-y) with maximum modulus:  
           3