NAG FL Interface
f06fsf (dlhousg)

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1 Purpose

f06fsf generates a real elementary reflection in the LINPACK (as opposed to NAG) style.

2 Specification

Fortran Interface
Subroutine f06fsf ( n, alpha, x, incx, tol, z1)
Integer, Intent (In) :: n, incx
Real (Kind=nag_wp), Intent (In) :: tol
Real (Kind=nag_wp), Intent (Inout) :: alpha, x(*)
Real (Kind=nag_wp), Intent (Out) :: z1
C Header Interface
#include <nag.h>
void  f06fsf_ (const Integer *n, double *alpha, double x[], const Integer *incx, const double *tol, double *z1)
The routine may be called by the names f06fsf or nagf_blas_dlhousg.

3 Description

f06fsf generates details of a real elementary reflection (Householder matrix), P, such that
P ( α x )=( β 0 )  
where P is orthogonal, α and β are real scalars, and x is an n-element real vector.
P is given in the form
P=I-1ζ ( ζ z ) ( ζ zT ) ,  
where z is an n-element real vector and ζ is a real scalar. (This form is compatible with that used by LINPACK.)
If the elements of x are all zero, or if the elements of x are all less than tol×|α| in absolute value, then ζ is set to 0 and P can be taken to be the unit matrix. Otherwise ζ always lies in the range (1,2).

4 References


5 Arguments

1: n Integer Input
On entry: n, the number of elements in x and z.
2: alpha Real (Kind=nag_wp) Input/Output
On entry: the scalar α.
On exit: the scalar β.
3: x(*) Real (Kind=nag_wp) array Input/Output
Note: the dimension of the array x must be at least max(1, 1+(n-1) ×incx ) .
On entry: the n-element vector x. xi must be stored in x(1+(i-1)×incx), for i=1,2,,n.
Intermediate elements of x are not referenced.
On exit: the referenced elements are overwritten by details of the real elementary reflection.
4: incx Integer Input
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx>0.
5: tol Real (Kind=nag_wp) Input
On entry: the value tol.
If tol is not in the range (0,1) , the value 0 is used for tol.
6: z1 Real (Kind=nag_wp) Output
On exit: the scalar ζ.

6 Error Indicators and Warnings


7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
f06fsf 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


10 Example