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))

C Header Interface

#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.

3 Description

f16ecf performs the operation

y \leftarrow α x + β y

where

x

and

y

are

n

-element real vectors, and

α

and

β

real scalars. If

n

is equal to zero, or if

α

is equal to zero and

β

is equal to

1

, this routine returns immediately.

4 References

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

5 Arguments

1: $n$ – Integer Input: On entry: $n$ , the number of elements in $x$ and $y$ .
2: $alpha$ – Real (Kind=nag_wp) Input: On entry: the scalar $α$ .
3: $x (1 + (n - 1) \times | incx |)$ – Real (Kind=nag_wp) array Input: On entry: the $n$ -element vector $x$ .
If $incx > 0$ , $x_{i}$ must be stored in $x ((i - 1) \times incx + 1)$ , for $i = 1, 2, \dots, n$ .

If $incx < 0$ , $x_{i}$ must be stored in $x ((n - i) \times | incx | + 1)$ , for $i = 1, 2, \dots, n$ .

Intermediate elements of x are not referenced. If $n = 0$ , x is not referenced.
4: $incx$ – Integer Input: On entry: the increment in the subscripts of x between successive elements of $x$ .

Constraint: $incx \neq 0$ .
5: $beta$ – Real (Kind=nag_wp) Input: On entry: the scalar $β$ .
6: $y (1 + (n - 1) \times | incy |)$ – Real (Kind=nag_wp) array Input/Output: On entry: the $n$ -element vector $y$ .
If $incy > 0$ , $y_{i}$ must be stored in $y ((i - 1) \times incy + 1)$ , for $i = 1, 2, \dots, n$ .

If $incy < 0$ , $y_{i}$ must be stored in $y ((n - i) \times | incy | + 1)$ , for $i = 1, 2, \dots, n$ .

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: $incy$ – Integer Input: On entry: the increment in the subscripts of y between successive elements of $y$ .

Constraint: $incy \neq 0$ .

6 Error Indicators and Warnings

incx = 0

incy = 0

, an error message is printed and program execution is terminated.

7 Accuracy

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

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

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.

9 Further Comments

None.

10 Example

This example computes the result of a scaled vector accumulation for

\begin{matrix} α = 3, & x = {(−6, 4.5, 3.7, 2.1, −4)}^{T}, \\ β = −1, & y = {(- 5.1, −5, 6.4, - 2.4, −3)}^{T} . \end{matrix}

x

and

y

are stored in reverse order.

f16ec: FL CL CPP AD PY MB

NAG FL Interfacef16ecf (daxpby)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
f16ecf (daxpby)