# NAG Library Routine Document

## 1Purpose

f06gaf (zdotu) computes the scalar product of two complex vectors.

## 2Specification

Fortran Interface
 Function f06gaf ( n, x, incx, y, incy)
 Complex (Kind=nag_wp) :: f06gaf Integer, Intent (In) :: n, incx, incy Complex (Kind=nag_wp), Intent (In) :: x(*), y(*)
#include nagmk26.h
 Complex f06gaf_ (const Integer *n, const Complex x[], const Integer *incx, const Complex y[], const Integer *incy)
The routine may be called by its BLAS name zdotu.

## 3Description

f06gaf (zdotu) returns, via the function name, the value of the scalar product
 $xTy$
where $x$ and $y$ are $n$-element complex vectors scattered with stride incx and incy respectively.

## 4References

Lawson C L, Hanson R J, Kincaid D R and Krogh F T (1979) Basic linear algebra supbrograms for Fortran usage ACM Trans. Math. Software 5 308–325

## 5Arguments

1:     $\mathbf{n}$ – IntegerInput
On entry: $n$, the number of elements in $x$ and $y$.
2:     $\mathbf{x}\left(*\right)$ – Complex (Kind=nag_wp) arrayInput
Note: the dimension 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 ${\mathbf{x}}\left(1+\left(\mathit{i}-1\right)×{\mathbf{incx}}\right)$, 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.
3:     $\mathbf{incx}$ – IntegerInput
On entry: the increment in the subscripts of x between successive elements of $x$.
4:     $\mathbf{y}\left(*\right)$ – Complex (Kind=nag_wp) arrayInput
Note: the dimension 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 ${\mathbf{y}}\left(1+\left(\mathit{i}-1\right)×{\mathbf{incy}}\right)$, 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.
5:     $\mathbf{incy}$ – IntegerInput
On entry: the increment in the subscripts of y between successive elements of $y$.

None.

Not applicable.

## 8Parallelism and Performance

f06gaf (zdotu) is not threaded in any implementation.