# NAG Library Routine Document

## 1Purpose

f06htf applies a complex elementary reflection to a complex vector.

## 2Specification

Fortran Interface
 Subroutine f06htf ( n, y, incy, z, incz)
 Integer, Intent (In) :: n, incy, incz Complex (Kind=nag_wp), Intent (In) :: theta, z(*) Complex (Kind=nag_wp), Intent (Inout) :: delta, y(*)
#include nagmk26.h
 void f06htf_ (const Integer *n, Complex *delta, Complex y[], const Integer *incy, const Complex *theta, const Complex z[], const Integer *incz)

## 3Description

f06htf applies a complex elementary reflection (Householder matrix) $P$, as generated by f06hrf, to a given complex vector:
 $δ y ←P δ y$
where $y$ is an $n$-element complex vector and $\delta$ is a complex scalar.
To apply the conjugate transpose matrix ${P}^{\mathrm{H}}$, call f06htf with $\stackrel{-}{\theta }$ in place of $\theta$.

None.

## 5Arguments

1:     $\mathbf{n}$ – IntegerInput
On entry: $n$, the number of elements in $y$ and $z$.
2:     $\mathbf{delta}$ – Complex (Kind=nag_wp)Input/Output
On entry: the original scalar $\delta$.
On exit: the transformed scalar $\delta$.
3:     $\mathbf{y}\left(*\right)$ – Complex (Kind=nag_wp) arrayInput/Output
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 original 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 $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
On exit: the transformed stored in the same array elements used to supply the original vector $y$.
4:     $\mathbf{incy}$ – IntegerInput
On entry: the increment in the subscripts of y between successive elements of $y$.
5:     $\mathbf{theta}$ – Complex (Kind=nag_wp)Input
On entry: the value $\theta$, as returned by f06hrf.
If $\theta =0$, $P$ is assumed to be the unit matrix and the transformation is skipped.
Constraint: if ${\mathbf{theta}}\le 0$, $n=0$.
6:     $\mathbf{z}\left(*\right)$ – Complex (Kind=nag_wp) arrayInput
Note: the dimension of the array z must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incz}}\right|\right)$.
On entry: the vector $z$, as returned by f06hrf.
If ${\mathbf{incz}}>0$, ${z}_{\mathit{i}}$ must be stored in ${\mathbf{z}}\left(1+\left(\mathit{i}-1\right)×{\mathbf{incz}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incz}}<0$, ${z}_{\mathit{i}}$ must be stored in ${\mathbf{z}}\left(1-\left({\mathbf{n}}-\mathit{i}\right)×{\mathbf{incz}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
7:     $\mathbf{incz}$ – IntegerInput
On entry: the increment in the subscripts of z between successive elements of $z$.

None.

Not applicable.

## 8Parallelism and Performance

f06htf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.