# NAG FL Interfacef06etf (daxpyi)

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## 1Purpose

f06etf adds a scaled sparse real vector, stored in compressed form, to an unscaled real vector.

## 2Specification

Fortran Interface
 Subroutine f06etf ( nz, a, x, indx, y)
 Integer, Intent (In) :: nz, indx(*) Real (Kind=nag_wp), Intent (In) :: a, x(*) Real (Kind=nag_wp), Intent (Inout) :: y(*)
#include <nag.h>
 void f06etf_ (const Integer *nz, const double *a, const double x[], const Integer indx[], double y[])
The routine may be called by the names f06etf, nagf_blas_daxpyi or its BLAS name daxpyi.

## 3Description

f06etf 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.

## 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: $\mathbf{nz}$Integer Input
On entry: the number of nonzeros in the sparse vector $x$.
2: $\mathbf{a}$Real (Kind=nag_wp) Input
On entry: the scalar $\alpha$.
3: $\mathbf{x}\left(*\right)$Real (Kind=nag_wp) array Input
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: $\mathbf{indx}\left(*\right)$Integer array Input
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: $\mathbf{y}\left(*\right)$Real (Kind=nag_wp) array Input/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.

## 8Parallelism and Performance

f06etf is not threaded in any implementation.