NAG Library Function Document

nag_dwaxpby (f16ehc)

void	nag_dwaxpby (Integer n, double alpha, const double x[], Integer incx, double beta, const double y[], Integer incy, double w[], Integer incw, NagError *fail)

3 Description

nag_dwaxpby (f16ehc) performs the operation

w \leftarrow α x + β y,

where

x

and

y

are

n

-element real vectors, and

α

and

β

are real scalars.

4 References

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

5 Arguments

1: n – IntegerInput: On entry: $n$ , the number of elements in $x$ , $y$ and $w$ .

Constraint: $n \geq 0$ .
2: alpha – doubleInput: On entry: the scalar $α$ .
3: x[ $\dim$ ] – const doubleInput: Note: the dimension, dim, of the array x must be at least $\max (1, 1 + (n - 1) \times |incx|)$ .
On entry: the $n$ -element vector $x$ .
If $incx > 0$ , $x_{i}$ must be stored in $x [(i - 1) \times |incx|]$ , for $i = 1, 2, \dots, n$ .

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

Intermediate elements of x are not referenced.
4: incx – IntegerInput: On entry: the increment in the subscripts of x between successive elements of $x$ .
Constraint: $incx \neq 0$ .
5: beta – doubleInput: On entry: the scalar $β$ .
6: y[ $\dim$ ] – const doubleInput: Note: the dimension, dim, of the array y must be at least $\max (1, 1 + (n - 1) \times |incy|)$ .
On entry: the $n$ -element vector $y$ .
If $incy > 0$ , $y_{i}$ must be stored in $y [1 + (i - 1) \times incy - 1]$ , for $i = 1, 2, \dots, n$ .

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

Intermediate elements of y are not referenced.
7: incy – IntegerInput: On entry: the increment in the subscripts of y between successive elements of $y$ .
Constraint: $incy \neq 0$ .
8: w[ $\dim$ ] – doubleOutput: Note: the dimension, dim, of the array w must be at least $\max (1, 1 + (n - 1) \times |incw|)$ .

On exit: the $n$ -element vector $w$ .
If $incw > 0$ , $w_{i}$ is in $w [1 + (i - 1) \times incw - 1]$ , for $i = 1, 2, \dots, n$ .

If $incw < 0$ , $w_{i}$ is in $w [1 + (n - i) \times incw - 1]$ , for $i = 1, 2, \dots, n$ .

Intermediate elements of w are not referenced.
9: incw – IntegerInput: On entry: the increment in the subscripts of w between successive elements of $w$ .
Constraint: $incw \neq 0$ .
10: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_BAD_PARAM: On entry, argument $⟨value⟩$ had an illegal value.
NE_INT: On entry, $incw = ⟨value⟩$ .
Constraint: $incw \neq 0$ .
On entry, $incx = ⟨value⟩$ .
Constraint: $incx \neq 0$ .
On entry, $incy = ⟨value⟩$ .
Constraint: $incy \neq 0$ .
On entry, $n = ⟨value⟩$ .
Constraint: $n \geq 0$ .

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

Not applicable.

9 Further Comments

None.

10 Example

This example computes the result of a scaled vector accumulation for

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

NAG Library Function Documentnag_dwaxpby (f16ehc)

+− Contents

1 Purpose

2 Specification