NAG Library Routine Document

Integer, Intent (In)	::	n, incx, incy, incw
Complex (Kind=nag_wp), Intent (In)	::	alpha, x(1+(n-1)ABS(incx)), beta, y(1+(n-1)ABS(incy))
Complex (Kind=nag_wp), Intent (Inout)	::	w(1+(n-1)*ABS(incw))

C Header Interface

#include <nagmk26.h>

void	f16ghf_ (const Integer n, const Complex alpha, const Complex x[], const Integer incx, const Complex beta, const Complex y[], const Integer incy, Complex w[], const Integer incw)

The routine may be called by its BLAST name blas_zwaxpby.

3

Description

f16ghf (blas_zwaxpby) performs the operation

w \leftarrow α x + β y,

where

x

and

y

are

n

-element complex vectors, and

α

and

β

are complex 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 $w$ .
2: $alpha$ – Complex (Kind=nag_wp)Input: On entry: the scalar $α$ .
3: $x (1 + (n - 1) \times |incx|)$ – Complex (Kind=nag_wp) arrayInput: 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: $incx$ – IntegerInput: On entry: the increment in the subscripts of x between successive elements of $x$ .

Constraint: $incx \neq 0$ .
5: $beta$ – Complex (Kind=nag_wp)Input: On entry: the scalar $β$ .
6: $y (1 + (n - 1) \times |incy|)$ – Complex (Kind=nag_wp) arrayInput: 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. If $β = 0.0$ or $n = 0$ , y is not referenced.
7: $incy$ – IntegerInput: On entry: the increment in the subscripts of y between successive elements of $y$ .

Constraint: $incy \neq 0$ .
8: $w (1 + (n - 1) \times |incw|)$ – Complex (Kind=nag_wp) arrayInput/Output: On entry: if $|incw| \neq 1$ , 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 $incw > 0$ , $w_{i}$ is in $w ((i - 1) \times incw + 1)$ , for $i = 1, 2, \dots, n$ .

If $incw < 0$ , $w_{i}$ is in $w ((n - i) \times |incw| + 1)$ , 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: $incw \neq 0$ .

6

Error Indicators and Warnings

incx = 0

incy = 0

incw = 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

f16ghf (blas_zwaxpby) is not threaded in any implementation.

9

Further Comments

None.

10

Example

This example computes the result of a scaled vector accumulation for

\begin{matrix} α = 3 + 2 i, & x = {(- 6 + 1.2 i, 3.7 + 4.5 i, - 4 + 2.1 i)}^{T}, \\ β = - i, & y = {(- 5.1, 6.4 - 5 i, - 3 - 2.4 i)}^{T} . \end{matrix}

x

and

y

, and also the sum vector

w

, are stored in reverse order.

NAG Library Routine Document

f16ghf (blas_zwaxpby) (zwaxpby)

▸▿ 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

1

Purpose

2

Specification