# NAG FL Interfacef06epf (drot)

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## 1Purpose

f06epf applies a real plane rotation to two real vectors.

## 2Specification

Fortran Interface
 Subroutine f06epf ( n, x, incx, y, incy, c, s)
 Integer, Intent (In) :: n, incx, incy Real (Kind=nag_wp), Intent (In) :: c, s Real (Kind=nag_wp), Intent (Inout) :: x(*), y(*)
#include <nag.h>
 void f06epf_ (const Integer *n, double x[], const Integer *incx, double y[], const Integer *incy, const double *c, const double *s)
The routine may be called by the names f06epf, nagf_blas_drot or its BLAS name drot.

## 3Description

f06epf applies a real plane rotation to two $n$-element real vectors $x$ and $y$ with respective strides incx and incy:
 $( xT yT ) ← ( c s -s c ) ( xT yT ) .$
The plane rotation has the form generated by f06aaf or f06baf.

## 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: $\mathbf{n}$Integer Input
On entry: $n$, the number of elements in $x$ and $y$.
2: $\mathbf{x}\left(*\right)$Real (Kind=nag_wp) array Input/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 $x$.
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.
On exit: the transformed vector $x$ stored in the array elements used to supply the original vector $x$.
Intermediate elements of x are unchanged.
3: $\mathbf{incx}$Integer Input
On entry: the increment in the subscripts of x between successive elements of $x$.
4: $\mathbf{y}\left(*\right)$Real (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: the $n$-element vector $y$.
If ${\mathbf{incy}}>0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{y}}\left(1+\left(\mathit{i}-1\right)×{\mathbf{incy}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incy}}<0$, ${y}_{\mathit{i}}$ must 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 not referenced.
On exit: the transformed vector $y$ stored in the array elements used to supply the original vector $y$.
Intermediate elements of y are unchanged.
5: $\mathbf{incy}$Integer Input
On entry: the increment in the subscripts of y between successive elements of $y$.
6: $\mathbf{c}$Real (Kind=nag_wp) Input
On entry: the value $c$, the cosine of the rotation.
7: $\mathbf{s}$Real (Kind=nag_wp) Input
On entry: the value $s$, the sine of the rotation.

None.

Not applicable.