# NAG C Library Function Document

## 1Purpose

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

## 2Specification

 #include #include
 void nag_zwaxpby (Integer n, Complex alpha, const Complex x[], Integer incx, Complex beta, const Complex y[], Integer incy, Complex w[], Integer incw, NagError *fail)

## 3Description

nag_zwaxpby (f16ghc) performs the operation
 $w ← αx+βy,$
where $x$ and $y$ are $n$-element complex vectors, and $\alpha$ and $\beta$ are complex scalars.

## 4References

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

## 5Arguments

1:    $\mathbf{n}$IntegerInput
On entry: $n$, the number of elements in $x$, $y$ and $w$.
Constraint: ${\mathbf{n}}\ge 0$.
2:    $\mathbf{alpha}$ComplexInput
On entry: the scalar $\alpha$.
3:    $\mathbf{x}\left[\mathit{dim}\right]$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. If ${\mathbf{n}}=0$, x is not referenced and may be NULL.
4:    $\mathbf{incx}$IntegerInput
On entry: the increment in the subscripts of x between successive elements of $x$.
Constraint: ${\mathbf{incx}}\ne 0$.
5:    $\mathbf{beta}$ComplexInput
On entry: the scalar $\beta$.
6:    $\mathbf{y}\left[\mathit{dim}\right]$const ComplexInput
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. If $\beta =0.0$ or ${\mathbf{n}}=0$, y is not referenced and may be NULL.
7:    $\mathbf{incy}$IntegerInput
On entry: the increment in the subscripts of y between successive elements of $y$.
Constraint: ${\mathbf{incy}}\ne 0$.
8:    $\mathbf{w}\left[\mathit{dim}\right]$ComplexInput/Output
Note: the dimension, dim, of the array w must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incw}}\right|\right)$.
On entry: if $\left|{\mathbf{incw}}\right|\ne 1$, 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 ${w}_{i}$ of the vector $w$ will be stored in w as follows.
If ${\mathbf{incw}}>0$, ${w}_{i}$ is in ${\mathbf{w}}\left[\left(\mathit{i}-1\right)×{\mathbf{incw}}\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incw}}<0$, ${w}_{i}$ is in ${\mathbf{w}}\left[\left({\mathbf{n}}-\mathit{i}\right)×\left|{\mathbf{incw}}\right|\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of w are not referenced.
9:    $\mathbf{incw}$IntegerInput
On entry: the increment in the subscripts of w between successive elements of $w$.
Constraint: ${\mathbf{incw}}\ne 0$.
10:  $\mathbf{fail}$NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

## 6Error 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 $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{incw}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{incw}}\ne 0$.
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: ${\mathbf{n}}\ge 0$.
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.

## 7Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)).

## 8Parallelism and Performance

nag_zwaxpby (f16ghc) is not threaded in any implementation.

None.

## 10Example

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 $y$, and also the sum vector $w$, are stored in reverse order.

### 10.1Program Text

Program Text (f16ghce.c)

### 10.2Program Data

Program Data (f16ghce.d)

### 10.3Program Results

Program Results (f16ghce.r)