# NAG FL Interfacef06grf (zdotui)

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## 1Purpose

f06grf computes the scalar product of an unconjugated sparse complex vector with a complex vector.

## 2Specification

Fortran Interface
 Function f06grf ( nz, x, indx, y)
 Complex (Kind=nag_wp) :: f06grf Integer, Intent (In) :: nz, indx(*) Complex (Kind=nag_wp), Intent (In) :: x(*), y(*)
#include <nag.h>
 Complex f06grf_ (const Integer *nz, const Complex x[], const Integer indx[], const Complex y[])
The routine may be called by the names f06grf, nagf_blas_zdotui or its BLAS name zdotui.

## 3Description

f06grf returns, via the function name, the value of the scalar product
 $xTy$
where $x$ is a sparse complex vector stored in compressed form, and $y$ is a complex vector in full storage form.
Dodson D S, Grimes R G and Lewis J G (1991) Sparse extensions to the Fortran basic linear algebra subprograms ACM Trans. Math. Software 17 253–263

## 5Arguments

1: $\mathbf{nz}$Integer Input
On entry: the number of nonzeros in the sparse vector $x$.
2: $\mathbf{x}\left(*\right)$Complex (Kind=nag_wp) array Input
Note: the dimension of the array x must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nz}}\right)$.
On entry: the compressed vector $x$. x contains ${x}_{i}$ for $i\in J$.
3: $\mathbf{indx}\left(*\right)$Integer array Input
Note: the dimension of the array indx must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nz}}\right)$.
On entry: indx must contain the set of indices $J$.
4: $\mathbf{y}\left(*\right)$Complex (Kind=nag_wp) array Input
Note: the dimension of the array y must be at least $\underset{\mathit{k}}{\mathrm{max}}\phantom{\rule{0.25em}{0ex}}\left\{{\mathbf{indx}}\left(\mathit{k}\right)\right\}$.
On entry: the vector $y$. Only elements corresponding to indices in indx are accessed.

None.

Not applicable.