NAG CL Interface
f16ghc (zwaxpby)

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1 Purpose

f16ghc computes the sum of two scaled vectors, preserving input, for complex scalars and vectors.

2 Specification

#include <nag.h>
void  f16ghc (Integer n, Complex alpha, const Complex x[], Integer incx, Complex beta, const Complex y[], Integer incy, Complex w[], Integer incw, NagError *fail)
The function may be called by the names: f16ghc, nag_blast_zwaxpby or nag_zwaxpby.

3 Description

f16ghc 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 https://www.netlib.org/blas/blast-forum/blas-report.pdf

5 Arguments

1: n Integer Input
On entry: n, the number of elements in x, y and w.
Constraint: n0.
2: alpha Complex Input
On entry: the scalar α.
3: x[dim] const Complex Input
Note: the dimension, dim, of the array x must be at least max(1,1+(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 Integer Input
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
5: beta Complex Input
On entry: the scalar β.
6: y[dim] const Complex Input
Note: the dimension, dim, of the array y must be at least max(1,1+(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. If β=0.0 or n=0, y is not referenced and may be NULL.
7: incy Integer Input
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.
8: w[dim] Complex Input/Output
Note: the dimension, dim, of the array w must be at least max(1,1+(n-1)×|incw|).
On entry: if |incw|1, 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 w[(i-1)×incw], for i=1,2,,n.
If incw<0, wi is in w[(n-i)×|incw|], for i=1,2,,n.
Intermediate elements of w are not referenced.
9: incw Integer Input
On entry: the increment in the subscripts of w between successive elements of w.
Constraint: incw0.
10: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, incw=value.
Constraint: incw0.
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 8 in the Introduction to the NAG Library CL Interface 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

Background information to multithreading can be found in the Multithreading documentation.
f16ghc 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+2.1i) T , β=-i,   y = (-5.1,6.4-5i,-3-2.4i) T .  
x and y, and also the sum vector w, are stored in reverse order.

10.1 Program Text

Program Text (f16ghce.c)

10.2 Program Data

Program Data (f16ghce.d)

10.3 Program Results

Program Results (f16ghce.r)