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

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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


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


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:

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):
Element of (x-y) with maximum modulus:


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.



Vector for which the norm is to be computed.


If present, IMSL_NORM computes the norm of (XY).


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

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