# NAG FL Interfacef06hdf (zaxpzy)

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## 1Purpose

f06hdf multiplies a complex vector by a scalar, preserving the input vector.

## 2Specification

Fortran Interface
 Subroutine f06hdf ( n, x, incx, y, incy)
 Integer, Intent (In) :: n, incx, incy Complex (Kind=nag_wp), Intent (In) :: alpha, x(*) Complex (Kind=nag_wp), Intent (Inout) :: y(*)
C Header Interface
#include <nag.h>
 void f06hdf_ (const Integer *n, const Complex *alpha, const Complex x[], const Integer *incx, Complex y[], const Integer *incy)
The routine may be called by the names f06hdf or nagf_blas_zaxpzy.

## 3Description

f06hdf performs the operation
 $y←αx$
where $x$ and $y$ are $n$-element complex vectors scattered with stride incx and incy respectively, and $\alpha$ is a complex scalar.

None.

## 5Arguments

1: $\mathbf{n}$Integer Input
On entry: $n$, the number of elements in $x$ and $y$.
2: $\mathbf{alpha}$Complex (Kind=nag_wp) Input
On entry: the scalar $\alpha$.
3: $\mathbf{x}\left(*\right)$Complex (Kind=nag_wp) array Input
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 $x$.
If ${\mathbf{incx}}>0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left(1+\left(\mathit{i}-1\right)×{\mathbf{incx}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incx}}<0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left(1-\left({\mathbf{n}}-\mathit{i}\right)×{\mathbf{incx}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of x are not referenced.
4: $\mathbf{incx}$Integer Input
On entry: the increment in the subscripts of x between successive elements of $x$.
5: $\mathbf{y}\left(*\right)$Complex (Kind=nag_wp) array Input/Output
Note: the dimension of the array y must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×|{\mathbf{incy}}|\right)$.
On entry: if $|{\mathbf{incy}}|\ne 1$, intermediate elements of y may contain values and will not be referenced; the other elements will be overwritten and need not be set.
On exit: the elements ${y}_{i}$ of the vector $y$ will be stored in y as follows.
If ${\mathbf{incy}}>0$, ${y}_{\mathit{i}}$ will be stored in ${\mathbf{y}}\left(1+\left(\mathit{i}-1\right)×{\mathbf{incy}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incy}}<0$, ${y}_{\mathit{i}}$ will be stored in ${\mathbf{y}}\left(1-\left({\mathbf{n}}-\mathit{i}\right)×{\mathbf{incy}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of y are unchanged.
6: $\mathbf{incy}$Integer Input
On entry: the increment in the subscripts of y between successive elements of $y$.

None.

Not applicable.

## 8Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
f06hdf is not threaded in any implementation.

None.

None.