# NAG CL Interfacef16ghc (zwaxpby)

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## 1Purpose

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

## 2Specification

 #include
 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.

## 3Description

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

## 5Arguments

1: $\mathbf{n}$Integer Input
On entry: $n$, the number of elements in $x$, $y$ and $w$.
Constraint: ${\mathbf{n}}\ge 0$.
2: $\mathbf{alpha}$Complex Input
On entry: the scalar $\alpha$.
3: $\mathbf{x}\left[\mathit{dim}\right]$const Complex Input
Note: the dimension, dim, of the array x must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×|{\mathbf{incx}}|\right)$.
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 ${\mathbf{x}}\left[\left({\mathbf{n}}-\mathit{i}\right)×|{\mathbf{incx}}|\right]$, 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: $\mathbf{incx}$Integer Input
On entry: the increment in the subscripts of x between successive elements of $x$.
Constraint: ${\mathbf{incx}}\ne 0$.
5: $\mathbf{beta}$Complex Input
On entry: the scalar $\beta$.
6: $\mathbf{y}\left[\mathit{dim}\right]$const Complex Input
Note: the dimension, dim, of the array y must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×|{\mathbf{incy}}|\right)$.
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 ${\mathbf{y}}\left[\left({\mathbf{n}}-\mathit{i}\right)×|{\mathbf{incy}}|\right]$, 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: $\mathbf{incy}$Integer Input
On entry: the increment in the subscripts of y between successive elements of $y$.
Constraint: ${\mathbf{incy}}\ne 0$.
8: $\mathbf{w}\left[\mathit{dim}\right]$Complex Input/Output
Note: the dimension, dim, of the array w must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×|{\mathbf{incw}}|\right)$.
On entry: if $|{\mathbf{incw}}|\ne 1$, 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 ${\mathbf{w}}\left[\left({\mathbf{n}}-\mathit{i}\right)×|{\mathbf{incw}}|\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of w are not referenced.
9: $\mathbf{incw}$Integer Input
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 7 in the Introduction to the NAG Library CL Interface).

## 6Error 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.
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 8 in the Introduction to the NAG Library CL Interface 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

f16ghc is not threaded in any implementation.

None.

## 10Example

This example computes the result of a scaled vector accumulation for
 $α=3+2i, x = (-6+1.2i,3.7+4.5i,-4+2.1i) T , β=-i, y = (-5.1,6.4-5i,-3-2.4i) T .$
$x$ and $y$, and also the sum vector $w$, are stored in reverse order.

### 10.1Program Text

Program Text (f16ghce.c)

### 10.2Program Data

Program Data (f16ghce.d)

### 10.3Program Results

Program Results (f16ghce.r)