# NAG Library Routine Document

## 1Purpose

f06exf (droti) applies a real plane rotation to a sparse real vector and a real vector.

## 2Specification

Fortran Interface
 Subroutine f06exf ( nz, x, indx, y, c, s)
 Integer, Intent (In) :: nz, indx(*) Real (Kind=nag_wp), Intent (In) :: c, s Real (Kind=nag_wp), Intent (Inout) :: x(*), y(*)
#include nagmk26.h
 void f06exf_ (const Integer *nz, double x[], const Integer indx[], double y[], const double *c, const double *s)
The routine may be called by its BLAS name droti.

## 3Description

f06exf (droti) applies a real plane rotation to a sparse real vector $x$ stored in compressed form and a real vector $y$ in full storage form:
 $xT yT ← c s -s c xT yT .$
The plane rotation has the form generated by f06aaf (drotg) or f06baf.

## 4References

Dodson D S, Grimes R G and Lewis J G (1991) Sparse extensions to the Fortran basic linear algebra subprograms ACM Trans. Math. Software 17 253–263

## 5Arguments

1:     $\mathbf{nz}$ – IntegerInput
On entry: the number of nonzeros in the sparse vector $x$.
2:     $\mathbf{x}\left(*\right)$ – Real (Kind=nag_wp) arrayInput/Output
Note: the dimension of the array x must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nz}}\right)$.
On entry: the nonzero elements of the sparse vector $x$.
On exit: the transformed vector $x$.
3:     $\mathbf{indx}\left(*\right)$ – Integer arrayInput
Note: the dimension of the array indx must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nz}}\right)$.
On entry: ${\mathbf{indx}}\left(\mathit{i}\right)$ must contain the index of ${\mathbf{x}}\left(\mathit{i}\right)$ in the sparse vector $x$, for $\mathit{i}=1,2,\dots ,{\mathbf{nz}}$.
Constraint: the indices must be distinct.
4:     $\mathbf{y}\left(*\right)$ – Real (Kind=nag_wp) arrayInput/Output
Note: the dimension of the array y must be at least $\underset{\mathit{k}}{\mathrm{max}}\phantom{\rule{0.25em}{0ex}}\left\{{\mathbf{indx}}\left(\mathit{k}\right)\right\}$.
On entry: the vector $y$. Only the elements corresponding to indices in indx are referenced.
On exit: the transformed vector $y$. Only elements corresponding to indices in indx are altered.
5:     $\mathbf{c}$ – Real (Kind=nag_wp)Input
On entry: the value $c$, the cosine of the rotation.
6:     $\mathbf{s}$ – Real (Kind=nag_wp)Input
On entry: the value $s$, the sine of the rotation.

None.

Not applicable.

## 8Parallelism and Performance

f06exf (droti) is not threaded in any implementation.

None.

## 10Example

None.
© The Numerical Algorithms Group Ltd, Oxford, UK. 2017