F16GCF (BLAS_ZAXPBY) (PDF version)
F16 Chapter Contents
F16 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F16GCF (BLAS_ZAXPBY)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+ Contents

    1  Purpose
    7  Accuracy

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 αx+βy,
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×INCX) – COMPLEX (KIND=nag_wp) arrayInput
On entry: the n-element vector x.
If INCX>0, xi must be stored in X1+i-1×INCX, for i=1,2,,N.
If INCX<0, xi must be stored in X1-N-i×INCX, for i=1,2,,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: INCX0.
5:     BETA – COMPLEX (KIND=nag_wp)Input
On entry: the scalar β.
6:     Y(1+N-1×INCY) – COMPLEX (KIND=nag_wp) arrayInput/Output
On entry: the n-element vector y.
If INCY>0, yi must be stored in Y1+i-1×INCY, for i=1,2,,N.
If INCY<0, yi must be stored in Y1-N-i×INCY, for i=1,2,,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: INCY0.

6  Error Indicators and Warnings

If INCX=0 or 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  Further Comments

None.

9  Example

This example computes the result of a scaled vector accumulation for
α=3+2i,   x = -4+2.1i,3.7+4.5i,-6+1.2iT , β=-i,   y = -3-2.4i,6.4-5i,-5.1T .

9.1  Program Text

Program Text (f16gcfe.f90)

9.2  Program Data

Program Data (f16gcfe.d)

9.3  Program Results

Program Results (f16gcfe.r)


F16GCF (BLAS_ZAXPBY) (PDF version)
F16 Chapter Contents
F16 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012