F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06ETF (DAXPYI)

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

F06ETF (DAXPYI) adds a scaled sparse real vector, stored in compressed form, to an unscaled real vector.

## 2  Specification

 SUBROUTINE F06ETF ( NZ, A, X, INDX, Y)
 INTEGER NZ, INDX(*) REAL (KIND=nag_wp) A, X(*), Y(*)
The routine may be called by its BLAS name daxpyi.

## 3  Description

F06ETF (DAXPYI) performs the operation
 $y←αx+y$
where $x$ is a sparse real vector, stored in compressed form, and $y$ is a real vector in full storage form.

## 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:     A – REAL (KIND=nag_wp)Input
On entry: the scalar $\alpha$.
3:     X($*$) – REAL (KIND=nag_wp) arrayInput
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 $x$.
4:     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.
5:     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 elements corresponding to indices in INDX are accessed.
On exit: the updated vector $y$.

None.

Not applicable.