NAG Library Function Document

nag_zaxpby (f16gcc)

 Contents

    1  Purpose
    7  Accuracy

1
Purpose

nag_zaxpby (f16gcc) computes the sum of two scaled vectors, for complex scalars and vectors.

2
Specification

#include <nag.h>
#include <nagf16.h>
void  nag_zaxpby (Integer n, Complex alpha, const Complex x[], Integer incx, Complex beta, Complex y[], Integer incy, NagError *fail)

3
Description

nag_zaxpby (f16gcc) 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 equal to zero, or if α is equal to zero and β is equal to 1, this function 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
Arguments

1:     n IntegerInput
On entry: n, the number of elements in x and y.
Constraint: n0.
2:     alpha ComplexInput
On entry: the scalar α.
3:     x[dim] const ComplexInput
Note: the dimension, dim, of the array x must be at least max1,1+n-1×incx.
On entry: the n-element vector x.
If incx>0, xi must be stored in x[i-1×incx], for i=1,2,,n.
If incx<0, xi must be stored in x[n-i×incx], for i=1,2,,n.
Intermediate elements of x are not referenced. If n=0, x is not referenced and may be NULL.
4:     incx IntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
5:     beta ComplexInput
On entry: the scalar β.
6:     y[dim] ComplexInput/Output
Note: the dimension, dim, of the array y must be at least max1,1+n-1×incy.
On entry: the n-element vector y.
If incy>0, yi must be stored in y[i-1×incy], for i=1,2,,n.
If incy<0, yi must be stored in y[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.
8:     fail NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6
Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, incx=value.
Constraint: incx0.
On entry, incy=value.
Constraint: incy0.
On entry, n=value.
Constraint: n0.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

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

nag_zaxpby (f16gcc) 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 function. 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
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 are stored in reverse order.

10.1
Program Text

Program Text (f16gcce.c)

10.2
Program Data

Program Data (f16gcce.d)

10.3
Program Results

Program Results (f16gcce.r)

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