NAG Library Routine Document

f06frf (dnhousg)

1
Purpose

f06frf generates a real elementary reflection in the NAG (as opposed to LINPACK) style.

2
Specification

Fortran Interface
Subroutine f06frf ( n, alpha, x, incx, tol, zeta)
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):: zeta
C Header Interface
#include <nagmk26.h>
void  f06frf_ (const Integer *n, double *alpha, double x[], const Integer *incx, const double *tol, double *zeta)

3
Description

f06frf 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- ζ z ζ zT ,  
where z is an n-element real vector and ζ is a real scalar.
If x is such that
maxximaxtol,εα  
where ε is the machine precision and tol is a user-supplied tolerance, then ζ is set to 0, and P can be taken to be the unit matrix. Otherwise 1ζ2.

4
References

None.

5
Arguments

1:     n – IntegerInput
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) arrayInput/Output
Note: the dimension of the array x must be at least max1, 1+n-1 ×incx .
On entry: the n-element vector x. xi must be stored in x1+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 – IntegerInput
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.
6:     zeta – Real (Kind=nag_wp)Output
On exit: the scalar ζ.

6
Error Indicators and Warnings

None.

7
Accuracy

Not applicable.

8
Parallelism and Performance

f06frf 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.