# 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.