NAG Library Routine Document

F16GCF (BLAS_ZAXPBY)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

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

F16GCF (BLAS_ZAXPBY) computes the sum of two scaled vectors, for complex scalars and vectors.

2 Specification

SUBROUTINE F16GCF (

N, ALPHA, X, INCX, BETA, Y, INCY)

INTEGER	N, INCX, INCY
COMPLEX (KIND=nag_wp)	ALPHA, X(1+(N-1)ABS(INCX)), BETA, Y(1+(N-1)ABS(INCY))

The routine may be called by its BLAST name blas_zaxpby.

3 Description

F16GCF (BLAS_ZAXPBY) performs the operation

y \leftarrow α x + β y,

where

x

and

y

are

n

-element complex vectors, and

α

and

β

are complex scalars. If

n

is less than or 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 http://www.netlib.org/blas/blast-forum/blas-report.pdf

5 Parameters

1: $N$ – INTEGERInput: On entry: $n$ , the number of elements in $x$ and $y$ .
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.
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/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: $INCY$ – INTEGERInput: 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

F16GCF (BLAS_ZAXPBY) is not threaded by NAG in any implementation.

F16GCF (BLAS_ZAXPBY) 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 + 2 i, & x = {(- 4 + 2.1 i, 3.7 + 4.5 i, - 6 + 1.2 i)}^{T}, \\ β = - i, & y = {(- 3 - 2.4 i, 6.4 - 5 i, - 5.1)}^{T} . \end{matrix}

NAG Library Routine DocumentF16GCF (BLAS_ZAXPBY)