NAG FL Interfacef06gaf (zdotu)

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1Purpose

f06gaf 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 <nag.h>
 Complex f06gaf_ (const Integer *n, const Complex x[], const Integer *incx, const Complex y[], const Integer *incy)
The routine may be called by the names f06gaf, nagf_blas_zdotu or its BLAS name zdotu.

3Description

f06gaf 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: $\mathbf{n}$Integer Input
On entry: $n$, the number of elements in $x$ and $y$.
2: $\mathbf{x}\left(*\right)$Complex (Kind=nag_wp) array Input
Note: the dimension of the array x must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×|{\mathbf{incx}}|\right)$.
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: $\mathbf{incx}$Integer Input
On entry: the increment in the subscripts of x between successive elements of $x$.
4: $\mathbf{y}\left(*\right)$Complex (Kind=nag_wp) array Input
Note: the dimension of the array y must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×|{\mathbf{incy}}|\right)$.
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: $\mathbf{incy}$Integer Input
On entry: the increment in the subscripts of y between successive elements of $y$.

None.

Not applicable.

8Parallelism and Performance

f06gaf is not threaded in any implementation.