# NAG Library Routine Document

## 1Purpose

f06hmf (zrot) applies a plane rotation with a real cosine and complex sine to two complex vectors.

## 2Specification

Fortran Interface
 Subroutine f06hmf ( n, cx, incx, cy, incy, c, s)
 Integer, Intent (In) :: n, incx, incy Real (Kind=nag_wp), Intent (In) :: c Complex (Kind=nag_wp), Intent (In) :: s Complex (Kind=nag_wp), Intent (Inout) :: cx(*), cy(*)
#include <nagmk26.h>
 void f06hmf_ (const Integer *n, Complex cx[], const Integer *incx, Complex cy[], const Integer *incy, const double *c, const Complex *s)
The routine may be called by its LAPACK name zrot.

## 3Description

f06hmf (zrot) applies a plane rotation, where the cosine is real and the sine is complex, to two $n$-element complex vectors $x$ and $y$:
 $xT yT ← c s -s- c xT yT .$

None.

## 5Arguments

1:     $\mathbf{n}$ – IntegerInput
On entry: $n$, the number of elements in $x$ and $y$.
2:     $\mathbf{cx}\left(*\right)$ – Complex (Kind=nag_wp) arrayInput/Output
Note: the dimension of the array cx must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incx}}\right|\right)$.
On entry: the $n$-element vector $x$.
If ${\mathbf{incx}}>0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{cx}}\left(1+\left(\mathit{i}-1\right)×{\mathbf{incx}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incx}}<0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{cx}}\left(1-\left({\mathbf{n}}-\mathit{i}\right)×{\mathbf{incx}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of cx are not referenced.
On exit: the transformed vector $x$ stored in the array elements used to supply the original vector $x$.
Intermediate elements of cx are unchanged.
3:     $\mathbf{incx}$ – IntegerInput
On entry: the increment in the subscripts of cx between successive elements of $x$.
4:     $\mathbf{cy}\left(*\right)$ – Complex (Kind=nag_wp) arrayInput/Output
Note: the dimension of the array cy must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incy}}\right|\right)$.
On entry: the $n$-element vector $y$.
If ${\mathbf{incy}}>0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{cy}}\left(1+\left(\mathit{i}-1\right)×{\mathbf{incy}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incy}}<0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{cy}}\left(1-\left({\mathbf{n}}-\mathit{i}\right)×{\mathbf{incy}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of cy are not referenced.
On exit: the transformed vector $y$.
Intermediate elements of cy are unchanged.
5:     $\mathbf{incy}$ – IntegerInput
On entry: the increment in the subscripts of cy between successive elements of $y$.
6:     $\mathbf{c}$ – Real (Kind=nag_wp)Input
On entry: the value $c$, the cosine of the rotation.
7:     $\mathbf{s}$ – Complex (Kind=nag_wp)Input
On entry: the value $s$, the sine of the rotation.

None.

Not applicable.

## 8Parallelism and Performance

f06hmf (zrot) is not threaded in any implementation.