# NAG Library Routine Document

## 1Purpose

f06kef multiplies a complex vector by the reciprocal of a real scalar.

## 2Specification

Fortran Interface
 Subroutine f06kef ( n, x, incx)
 Integer, Intent (In) :: n, incx Real (Kind=nag_wp), Intent (In) :: alpha Complex (Kind=nag_wp), Intent (Inout) :: x(*)
#include nagmk26.h
 void f06kef_ (const Integer *n, const double *alpha, Complex x[], const Integer *incx)

## 3Description

f06kef performs the operation
 $x←1 α x$
where $x$ is an $n$-element complex vector and $\alpha$ is a real nonzero scalar scattered with stride incx.

None.

## 5Arguments

1:     $\mathbf{n}$ – IntegerInput
On entry: $n$, the number of elements in $x$.
2:     $\mathbf{alpha}$ – Real (Kind=nag_wp)Input
On entry: the scalar $\alpha$.
Constraint: ${\mathbf{alpha}}\ne 0.0$.
3:     $\mathbf{x}\left(*\right)$ – Complex (Kind=nag_wp) arrayInput/Output
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.
On exit: the updated vector $x$, stored in the same array elements used to supply the original vector.
4:     $\mathbf{incx}$ – 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

f06kef makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.