F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06FTF

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

F06FTF applies a NAG (as opposed to LINPACK) style real elementary reflection to a real vector.

## 2  Specification

 SUBROUTINE F06FTF ( N, DELTA, Y, INCY, ZETA, Z, INCZ)
 INTEGER N, INCY, INCZ REAL (KIND=nag_wp) DELTA, Y(*), ZETA, Z(*)

## 3  Description

F06FTF applies a real elementary reflection (Householder matrix) $P$, as generated by F06FRF, to a given real vector:
 $δ y ←P δ y ,$
where $y$ is an $n$-element real vector and $\delta$ a real scalar.
None.

## 5  Parameters

1:     N – INTEGERInput
On entry: $n$, the number of elements in $y$ and $z$.
2:     DELTA – REAL (KIND=nag_wp)Input/Output
On entry: the original scalar $\delta$.
On exit: the transformed scalar $\delta$.
3:     Y($*$) – REAL (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:     ZETA – REAL (KIND=nag_wp)Input
On entry: the scalar $\zeta$, as returned by F06FRF.
If $\zeta =0$, $P$ is assumed to be the unit matrix and the transformation is skipped.
Constraint: if ${\mathbf{ZETA}}=0.0$, ${\mathbf{N}}=0$.
6:     Z($*$) – REAL (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 F06FRF.
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.