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### IMSL_NORM

IMSL_NORM

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

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|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 (xy).

## 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`

### 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 = 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`

## 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 (XY).

## Keywords

### INDEX_MAX (optional)

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 argument Y is specified, then the index of (XY) with the maximum modulus is stored.

### INF (optional)

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

### ONE (optional)

If present and nonzero, computes the 1-norm ## Version History

 6.4 Introduced

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