NAG FL Interfacef16ehf (dwaxpby)

1Purpose

f16ehf 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 <nag.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 the names f16ehf, nagf_blast_dwaxpby or its BLAST name blas_dwaxpby.

3Description

f16ehf 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 https://www.netlib.org/blas/blast-forum/blas-report.pdf

5Arguments

1: $\mathbf{n}$Integer Input
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) array Input
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: $\mathbf{incx}$Integer Input
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) array Input
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: $\mathbf{incy}$Integer Input
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) array Input/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: $\mathbf{incw}$Integer Input
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 is not threaded in any implementation.

None.

10Example

This example computes the result of a scaled vector accumulation for
 $α=3, x = -6,4.5,3.7,2.1,-4 T , β=-1, y = -5.1,-5,6.4,-2.4,-3 T .$
$x$ 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)