# NAG FL Interfacef16ecf (daxpby)

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## 1Purpose

f16ecf computes the sum of two scaled vectors, for real vectors and scalars.

## 2Specification

Fortran Interface
 Subroutine f16ecf ( n, x, incx, beta, y, incy)
 Integer, Intent (In) :: n, incx, incy Real (Kind=nag_wp), Intent (In) :: alpha, x(1+(n-1)*ABS(incx)), beta Real (Kind=nag_wp), Intent (Inout) :: y(1+(n-1)*ABS(incy))
#include <nag.h>
 void f16ecf_ (const Integer *n, const double *alpha, const double x[], const Integer *incx, const double *beta, double y[], const Integer *incy)
The routine may be called by the names f16ecf, nagf_blast_daxpby or its BLAST name blas_daxpby.

## 3Description

f16ecf performs the operation
 $y←α x+β y$
where $x$ and $y$ are $n$-element real vectors, and $\alpha$ and $\beta$ real scalars. If $n$ is equal to zero, or if $\alpha$ is equal to zero and $\beta$ is equal to $1$, this routine returns immediately.

## 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 $x$ and $y$.
2: $\mathbf{alpha}$Real (Kind=nag_wp) Input
On entry: the scalar $\alpha$.
3: $\mathbf{x}\left(1+\left({\mathbf{n}}-1\right)×|{\mathbf{incx}}|\right)$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 ${\mathbf{x}}\left(\left({\mathbf{n}}-\mathit{i}\right)×|{\mathbf{incx}}|+1\right)$, 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: $\mathbf{y}\left(1+\left({\mathbf{n}}-1\right)×|{\mathbf{incy}}|\right)$Real (Kind=nag_wp) array Input/Output
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 ${\mathbf{y}}\left(\left({\mathbf{n}}-\mathit{i}\right)×|{\mathbf{incy}}|+1\right)$, 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.
7: $\mathbf{incy}$Integer Input
On entry: the increment in the subscripts of y between successive elements of $y$.
Constraint: ${\mathbf{incy}}\ne 0$.

## 6Error Indicators and Warnings

If ${\mathbf{incx}}=0$ or ${\mathbf{incy}}=0$, 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

f16ecf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

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 $y$ are stored in reverse order.

### 10.1Program Text

Program Text (f16ecfe.f90)

### 10.2Program Data

Program Data (f16ecfe.d)

### 10.3Program Results

Program Results (f16ecfe.r)