NORM Function (PV-WAVE Extreme Advantage)

Signal Processing Toolkit User Guide > Reference (G to P) > NORM Function (PV-WAVE Extreme Advantage)

Computes various norms of an array, or the difference of two arrays.

Usage

result = NORM(x [, y])

Input Parameters

x—An array for which the norm is to be computed.

y—(optional) If present, NORM computes the norm of (x – y).

Returned Value

result—The requested norm of the input array. If the norm cannot be computed, NaN is returned.

Keywords

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

Inf—If present and nonzero, computes the infinity norm max|xi|.

One—If present and nonzero, computes the 1-norm:

Discussion

By default, NORM computes the Euclidean norm as follows:

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

is returned. If the keyword Inf is set, the infinity norm:

max|xi|

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).

Example 1

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

x = [1.0, 3.0, -2.0, 4.0]

n = NORM(x)

PM, n, Title = 'Euclidean norm of x:'

Example 2

This example computes max | xi – yi | and prints the norm and index.

x = [1.0, 3.0, -2.0, 4.0]

y = [4.0, 2.0, -1.0, -5.0]

n = 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:'

Version 2017.0