F16 Chapter Contents
F16 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF16GCF (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.

## 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 $\alpha$ and $\beta$ are complex scalars. If $n$ is less than or equal to zero, or if $\alpha$ is equal to zero and $\beta$ is equal to $1$, this routine returns immediately.
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 $\alpha$.
3:     X($1+\left({\mathbf{N}}-1\right)×\left|{\mathbf{INCX}}\right|$) – COMPLEX (KIND=nag_wp) arrayInput
On entry: the $n$-element vector $x$.
If ${\mathbf{INCX}}>0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{X}}\left(1+\left(\mathit{i}-1\right)×{\mathbf{INCX}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{N}}$.
If ${\mathbf{INCX}}<0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{X}}\left(1-\left({\mathbf{N}}-\mathit{i}\right)×{\mathbf{INCX}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{N}}$.
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: ${\mathbf{INCX}}\ne 0$.
5:     BETA – COMPLEX (KIND=nag_wp)Input
On entry: the scalar $\beta$.
6:     Y($1+\left({\mathbf{N}}-1\right)×\left|{\mathbf{INCY}}\right|$) – COMPLEX (KIND=nag_wp) arrayInput/Output
On entry: the $n$-element vector $y$.
If ${\mathbf{INCY}}>0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{Y}}\left(1+\left(\mathit{i}-1\right)×{\mathbf{INCY}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{N}}$.
If ${\mathbf{INCY}}<0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{Y}}\left(1-\left({\mathbf{N}}-\mathit{i}\right)×{\mathbf{INCY}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{N}}$.
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: ${\mathbf{INCY}}\ne 0$.

## 6  Error Indicators and Warnings

If ${\mathbf{INCX}}=0$ or ${\mathbf{INCY}}=0$, 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)).

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)