F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06HTF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

F06HTF applies a complex elementary reflection to a complex vector.

## 2  Specification

 SUBROUTINE F06HTF ( N, DELTA, Y, INCY, THETA, Z, INCZ)
 INTEGER N, INCY, INCZ COMPLEX (KIND=nag_wp) DELTA, Y(*), THETA, Z(*)

## 3  Description

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.

## 5  Parameters

1:     N – INTEGERInput
On entry: $n$, the number of elements in $y$ and $z$.
2:     DELTA – COMPLEX (KIND=nag_wp)Input/Output
On entry: the original scalar $\delta$.
On exit: the transformed scalar $\delta$.
3:     Y($*$) – 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:     INCY – INTEGERInput
On entry: the increment in the subscripts of Y between successive elements of $y$.
5:     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:     Z($*$) – 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:     INCZ – INTEGERInput
On entry: the increment in the subscripts of Z between successive elements of $z$.

None.

Not applicable.