F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06EXF (DROTI)

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

F06EXF (DROTI) applies a real plane rotation to a sparse real vector and a real vector.

## 2  Specification

 SUBROUTINE F06EXF ( NZ, X, INDX, Y, C, S)
 INTEGER NZ, INDX(*) REAL (KIND=nag_wp) X(*), Y(*), C, S
The routine may be called by its BLAS name droti.

## 3  Description

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.

## 4  References

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

## 5  Parameters

1:     NZ – INTEGERInput
On entry: the number of nonzeros in the sparse vector $x$.
2:     X($*$) – 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:     INDX($*$) – 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:     Y($*$) – 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:     C – REAL (KIND=nag_wp)Input
On entry: the value $c$, the cosine of the rotation.
6:     S – REAL (KIND=nag_wp)Input
On entry: the value $s$, the sine of the rotation.

None.

Not applicable.