F06FRF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06FRF

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
    9  Example

1  Purpose

F06FRF generates a real elementary reflection in the NAG (as opposed to LINPACK) style.

2  Specification

SUBROUTINE F06FRF ( N, ALPHA, X, INCX, TOL, ZETA)
INTEGER  N, INCX
REAL (KIND=nag_wp)  ALPHA, X(*), TOL, 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  Parameters

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  Further Comments

None.

9  Example

None.

F06FRF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012