F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06ECF (DAXPY)

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

F06ECF (DAXPY) adds a scaled real vector to an unscaled real vector.

## 2  Specification

 SUBROUTINE F06ECF ( N, ALPHA, X, INCX, Y, INCY)
 INTEGER N, INCX, INCY REAL (KIND=nag_wp) ALPHA, X(*), Y(*)
The routine may be called by its BLAS name daxpy.

## 3  Description

F06ECF (DAXPY) performs the operation
 $y←αx+y$
where $x$ and $y$ are $n$-element real vectors scattered with stride INCX and INCY respectively, and $\alpha$ is a real scalar.

## 4  References

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

## 5  Parameters

1:     N – INTEGERInput
On entry: $n$, the number of elements in $x$ and $y$.
2:     ALPHA – 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 $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{N}}-1\right)×\left|{\mathbf{INCX}}\right|\right)$.
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.
4:     INCX – INTEGERInput
On entry: the increment in the subscripts of X between successive elements of $x$.
5:     Y($*$) – REAL (KIND=nag_wp) arrayInput/Output
Note: the dimension of the array Y must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{N}}-1\right)×\left|{\mathbf{INCY}}\right|\right)$.
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 updated vector $y$ stored in the array elements used to supply the original vector $y$.
Intermediate elements of Y are unchanged.
6:     INCY – INTEGERInput
On entry: the increment in the subscripts of Y between successive elements of $y$.

None.

Not applicable.