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) arrayOutput: On exit: the $n$ -element vector $w$ .
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 DocumentF16GHF (BLAS_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

NAG Library Routine Document

F16GHF (BLAS_ZWAXPBY)