F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06GAF (ZDOTU)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

F06GAF (ZDOTU) computes the scalar product of two complex vectors.

## 2  Specification

 FUNCTION F06GAF ( N, X, INCX, Y, INCY)
 COMPLEX (KIND=nag_wp) F06GAF
 INTEGER N, INCX, INCY COMPLEX (KIND=nag_wp) X(*), Y(*)
The routine may be called by its BLAS name zdotu.

## 3  Description

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.
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

## 5  Parameters

1:     $\mathrm{N}$ – INTEGERInput
On entry: $n$, the number of elements in $x$ and $y$.
2:     $\mathrm{X}\left(*\right)$ – 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:     $\mathrm{INCX}$ – INTEGERInput
On entry: the increment in the subscripts of X between successive elements of $x$.
4:     $\mathrm{Y}\left(*\right)$ – 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:     $\mathrm{INCY}$ – INTEGERInput
On entry: the increment in the subscripts of Y between successive elements of $y$.

None.

Not applicable.

Not applicable.