# NAG FL Interfacef06htf (zhous)

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## 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 <nag.h>
 void f06htf_ (const Integer *n, Complex *delta, Complex y[], const Integer *incy, const Complex *theta, const Complex z[], const Integer *incz)
The routine may be called by the names f06htf or nagf_blas_zhous.

## 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 $\overline{\theta }$ in place of $\theta$.

None.

## 5Arguments

1: $\mathbf{n}$Integer Input
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) array Input/Output
Note: the dimension of the array y must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×|{\mathbf{incy}}|\right)$.
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 vector stored in the same array elements used to supply the original vector $y$.
4: $\mathbf{incy}$Integer Input
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 ${\mathbf{n}}=0$, $\mathrm{Re}\left({\mathbf{theta}}\right)\le 0.0$.
6: $\mathbf{z}\left(*\right)$Complex (Kind=nag_wp) array Input
Note: the dimension of the array z must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×|{\mathbf{incz}}|\right)$.
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: $\mathbf{incz}$Integer Input
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.