# NAG C Library Function Document

## 1Purpose

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

## 2Specification

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

## 3Description

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.

## 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 $x$ and $y$.
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:    $\mathbf{y}\left[\mathit{dim}\right]$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:    $\mathbf{incy}$IntegerInput
On entry: the increment in the subscripts of y between successive elements of $y$.
Constraint: ${\mathbf{incy}}\ne 0$.
8:    $\mathbf{fail}$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.
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: ${\mathbf{n}}\ge 0$.
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_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.

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 $y$ are stored in reverse order.

### 10.1Program Text

Program Text (f16gcce.c)

### 10.2Program Data

Program Data (f16gcce.d)

### 10.3Program Results

Program Results (f16gcce.r)