F06FTF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06FTF

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.

 Contents

    1  Purpose
    7  Accuracy
    10  Example

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 δ a real scalar.

4  References

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 δ.
On exit: the transformed scalar δ.
3:     Y* – REAL (KIND=nag_wp) arrayInput/Output
Note: the dimension of the array Y must be at least max1, 1+N-1 ×INCY .
On entry: the original vector y.
If INCY>0, yi must be stored in Y1+i-1 ×INCY , for i=1,2,,N.
If INCY<0, yi must be stored in Y1-N-i ×INCY , for i=1,2,,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 ζ, as returned by F06FRF.
If ζ=0, P is assumed to be the unit matrix and the transformation is skipped.
Constraint: if ZETA=0.0, N=0.
6:     Z* – REAL (KIND=nag_wp) arrayInput
Note: the dimension of the array Z must be at least max1, 1+N-1 ×INCZ .
On entry: the vector z, as returned by F06FRF.
If INCZ>0, zi must be stored in Z1+i-1×INCZ , for i=1,2,,N.
If INCZ<0, zi must be stored in Z1-N-i×INCZ , for i=1,2,,N.
7:     INCZ – INTEGERInput
On entry: the increment in the subscripts of Z between successive elements of z.

6  Error Indicators and Warnings

None.

7  Accuracy

Not applicable.

8  Parallelism and Performance

F06FTF is not threaded by NAG in any implementation.
F06FTF 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.

9  Further Comments

None.

10  Example

None.

F06FTF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2015