# NAG Library Routine Document

## 1Purpose

f06ejf (dnrm2) returns the Euclidean norm of the $n$-element real vector $x$.

## 2Specification

Fortran Interface
 Function f06ejf ( n, x, incx)
 Real (Kind=nag_wp) :: f06ejf Integer, Intent (In) :: n, incx Real (Kind=nag_wp), Intent (In) :: x(*)
#include nagmk26.h
 double f06ejf_ ( const Integer *n, const double x[], const Integer *incx)
The routine may be called by its BLAS name dnrm2.

## 3Description

f06ejf (dnrm2) returns, via the function name, the Euclidean norm
 $x2=xTx$
of the $n$-element real vector $x$ scattered with stride incx.

## 4References

Lawson C L, Hanson R J, Kincaid D R and Krogh F T (1979) Basic linear algebra supbrograms for Fortran usage ACM Trans. Math. Software 5 308–325

## 5Arguments

1:     $\mathbf{n}$ – IntegerInput
On entry: $n$, the number of elements in $x$.
2:     $\mathbf{x}\left(*\right)$ – Real (Kind=nag_wp) arrayInput
Note: the dimension of the array x must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×{\mathbf{incx}}\right)$.
On entry: the $n$-element vector $x$. ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left(1+\left(\mathit{i}-1\right)×{\mathbf{incx}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of x are not referenced.
3:     $\mathbf{incx}$ – IntegerInput
On entry: the increment in the subscripts of x between successive elements of $x$.
Constraint: ${\mathbf{incx}}>0$.

None.

Not applicable.

## 8Parallelism and Performance

f06ejf (dnrm2) is not threaded in any implementation.