# NAG Library Routine Document

## 1Purpose

f16ehf (blas_dwaxpby) computes the sum of two scaled vectors, preserving input, for real scalars and vectors.

## 2Specification

Fortran Interface
 Subroutine f16ehf ( n, x, incx, beta, y, incy, w, incw)
 Integer, Intent (In) :: n, incx, incy, incw Real (Kind=nag_wp), Intent (In) :: alpha, x(1+(n-1)*ABS(incx)), beta, y(1+(n-1)*ABS(incy)) Real (Kind=nag_wp), Intent (Inout) :: w(1+(n-1)*ABS(incw))
#include nagmk26.h
 void f16ehf_ (const Integer *n, const double *alpha, const double x[], const Integer *incx, const double *beta, const double y[], const Integer *incy, double w[], const Integer *incw)
The routine may be called by its BLAST name blas_dwaxpby.

## 3Description

f16ehf (blas_dwaxpby) performs the operation
 $w ← αx+βy,$
where $x$ and $y$ are $n$-element real vectors, and $\alpha$ and $\beta$ are real scalars.

## 4References

Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee http://www.netlib.org/blas/blast-forum/blas-report.pdf

## 5Arguments

1:     $\mathbf{n}$ – IntegerInput
On entry: $n$, the number of elements in $x$, $y$ and $w$.
2:     $\mathbf{alpha}$ – Real (Kind=nag_wp)Input
On entry: the scalar $\alpha$.
3:     $\mathbf{x}\left(1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incx}}\right|\right)$ – Real (Kind=nag_wp) arrayInput
On entry: the $n$-element vector $x$.
If ${\mathbf{incx}}>0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left(\left(\mathit{i}-1\right)×{\mathbf{incx}}+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incx}}<0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left(\left({\mathbf{n}}-\mathit{i}\right)×\left|{\mathbf{incx}}\right|+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of x are not referenced. If ${\mathbf{n}}=0$, x is not referenced.
4:     $\mathbf{incx}$ – IntegerInput
On entry: the increment in the subscripts of x between successive elements of $x$.
Constraint: ${\mathbf{incx}}\ne 0$.
5:     $\mathbf{beta}$ – Real (Kind=nag_wp)Input
On entry: the scalar $\beta$.
6:     $\mathbf{y}\left(1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incy}}\right|\right)$ – Real (Kind=nag_wp) arrayInput
On entry: the $n$-element vector $y$.
If ${\mathbf{incy}}>0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{y}}\left(\left(\mathit{i}-1\right)×{\mathbf{incy}}+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incy}}<0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{y}}\left(\left({\mathbf{n}}-\mathit{i}\right)×\left|{\mathbf{incy}}\right|+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of y are not referenced. If $\beta =0.0$ or ${\mathbf{n}}=0$, y is not referenced.
7:     $\mathbf{incy}$ – IntegerInput
On entry: the increment in the subscripts of y between successive elements of $y$.
Constraint: ${\mathbf{incy}}\ne 0$.
8:     $\mathbf{w}\left(1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incw}}\right|\right)$ – Real (Kind=nag_wp) arrayInput/Output
On entry: if $\left|{\mathbf{incw}}\right|\ne 1$, intermediate elements of w may contain values and will not be referenced; the other elements will be overwritten and need not be set.
On exit: the elements ${w}_{i}$ of the vector $w$ will be stored in w as follows.
If ${\mathbf{incw}}>0$, ${w}_{i}$ is in ${\mathbf{w}}\left(\left(\mathit{i}-1\right)×{\mathbf{incw}}+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incw}}<0$, ${w}_{i}$ is in ${\mathbf{w}}\left(\left({\mathbf{n}}-\mathit{i}\right)×\left|{\mathbf{incw}}\right|+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of w are not referenced.
9:     $\mathbf{incw}$ – IntegerInput
On entry: the increment in the subscripts of w between successive elements of $w$.
Constraint: ${\mathbf{incw}}\ne 0$.

## 6Error Indicators and Warnings

If ${\mathbf{incx}}=0$ or ${\mathbf{incy}}=0$ or ${\mathbf{incw}}=0$, an error message is printed and program execution is terminated.

## 7Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)).

## 8Parallelism and Performance

f16ehf (blas_dwaxpby) is not threaded in any implementation.

None.

## 10Example

This example computes the result of a scaled vector accumulation for
 $α=3, x = -6,4.5,3.7,2.1,-4T , β=-1, y = -5.1,-5,6.4,-2.4,-3T .$
$x$ and $y$, and also the sum vector $w$, are stored in reverse order.

### 10.1Program Text

Program Text (f16ehfe.f90)

### 10.2Program Data

Program Data (f16ehfe.d)

### 10.3Program Results

Program Results (f16ehfe.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017