NAG Library Routine Document

f16ghf  (zwaxpby)

 Contents

    1  Purpose
    7  Accuracy

1
Purpose

f16ghf (blas_zwaxpby) computes the sum of two scaled vectors, preserving input, for complex scalars and vectors.

2
Specification

Fortran Interface
Subroutine f16ghf ( n, alpha, x, incx, beta, y, incy, w, incw)
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 αx+βy,  
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:     x1+n-1×incx – Complex (Kind=nag_wp) arrayInput
On entry: the n-element vector x.
If incx>0, xi must be stored in xi-1×incx+1, for i=1,2,,n.
If incx<0, xi must be stored in xn-i×incx+1, for i=1,2,,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: incx0.
5:     beta – Complex (Kind=nag_wp)Input
On entry: the scalar β.
6:     y1+n-1×incy – Complex (Kind=nag_wp) arrayInput
On entry: the n-element vector y.
If incy>0, yi must be stored in yi-1×incy+1, for i=1,2,,n.
If incy<0, yi must be stored in yn-i×incy+1, for i=1,2,,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: incy0.
8:     w1+n-1×incw – Complex (Kind=nag_wp) arrayInput/Output
On entry: if incw1, 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 wi of the vector w will be stored in w as follows.
If incw>0, wi is in wi-1×incw+1, for i=1,2,,n.
If incw<0, wi is in wn-i×incw+1, for i=1,2,,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: incw0.

6
Error Indicators and Warnings

If incx=0 or incy=0 or 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
α=3+2i,   x = -6+1.2i,3.7+4.5i,-4+2.1iT , β=-i,   y = -5.1,6.4-5i,-3-2.4iT .  
x and y, and also the sum vector w, are stored in reverse order.

10.1
Program Text

Program Text (f16ghfe.f90)

10.2
Program Data

Program Data (f16ghfe.d)

10.3
Program Results

Program Results (f16ghfe.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017