F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06HMF (ZROT)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

F06HMF (ZROT) applies a real plane rotation to two complex vectors.

## 2  Specification

 SUBROUTINE F06HMF ( N, CX, INCX, CY, INCY, C, S)
 INTEGER N, INCX, INCY REAL (KIND=nag_wp) C COMPLEX (KIND=nag_wp) CX(*), CY(*), S
The routine may be called by its LAPACK name zrot.

## 3  Description

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.

## 5  Parameters

1:     N – INTEGERInput
On entry: $n$, the number of elements in $x$ and $y$.
2:     CX($*$) – 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:     INCX – INTEGERInput
On entry: the increment in the subscripts of CX between successive elements of $x$.
4:     CY($*$) – 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:     INCY – INTEGERInput
On entry: the increment in the subscripts of CY between successive elements of $y$.
6:     C – REAL (KIND=nag_wp)Input
On entry: the value $c$, the cosine of the rotation.
7:     S – COMPLEX (KIND=nag_wp)Input
On entry: the value $s$, the sine of the rotation.

None.

Not applicable.