f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_zaxpby (f16gcc)

## 1  Purpose

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

## 2  Specification

 #include #include
 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 $\alpha$ and $\beta$ are complex scalars. If $n$ is equal to zero, or if $\alpha$ is equal to zero and $\beta$ 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:     nIntegerInput
On entry: $n$, the number of elements in $x$ and $y$.
Constraint: ${\mathbf{n}}\ge 0$.
2:     alphaComplexInput
On entry: the scalar $\alpha$.
3:     x[$\mathit{dim}$]const ComplexInput
Note: the dimension, dim, of the array x must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incx}}\right|\right)$.
On entry: the $n$-element vector $x$.
If ${\mathbf{incx}}>0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left[\left(\mathit{i}-1\right)×{\mathbf{incx}}\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incx}}<0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left[\left({\mathbf{n}}-\mathit{i}\right)×\left|{\mathbf{incx}}\right|\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of x are not referenced.
4:     incxIntegerInput
On entry: the increment in the subscripts of x between successive elements of $x$.
Constraint: ${\mathbf{incx}}\ne 0$.
5:     betaComplexInput
On entry: the scalar $\beta$.
6:     y[$\mathit{dim}$]ComplexInput/Output
Note: the dimension, dim, of the array y must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incy}}\right|\right)$.
On entry: the $n$-element vector $y$.
If ${\mathbf{incy}}>0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{y}}\left[\left(\mathit{i}-1\right)×{\mathbf{incy}}\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incy}}<0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{y}}\left[\left({\mathbf{n}}-\mathit{i}\right)×\left|{\mathbf{incy}}\right|\right]$, 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:     incyIntegerInput
On entry: the increment in the subscripts of y between successive elements of $y$.
Constraint: ${\mathbf{incy}}\ne 0$.
8:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.
NE_INT
On entry, ${\mathbf{incx}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{incx}}\ne 0$.
On entry, ${\mathbf{incy}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{incy}}\ne 0$.
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\ge 0$.

## 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) is not threaded by NAG in any implementation.
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.

None.

## 10  Example

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

### 10.1  Program Text

Program Text (f16gcce.c)

### 10.2  Program Data

Program Data (f16gcce.d)

### 10.3  Program Results

Program Results (f16gcce.r)