NAG Library Routine Document

f06fuf (dlhous)

1
Purpose

f06fuf applies a LINPACK (as opposed to NAG) style real elementary reflection to a real vector.

2
Specification

Fortran Interface
Subroutine f06fuf ( n, z, incz, z1, alpha, x, incx)
Integer, Intent (In):: n, incz, incx
Real (Kind=nag_wp), Intent (In):: z(*), z1
Real (Kind=nag_wp), Intent (Inout):: alpha, x(*)
C Header Interface
#include <nagmk26.h>
void  f06fuf_ (const Integer *n, const double z[], const Integer *incz, const double *z1, double *alpha, double x[], const Integer *incx)

3
Description

f06fuf applies a real elementary reflection (Householder matrix) P, as generated by f06fsf, to a given real vector:
α x P α x  
where x is an n-element real vector and α a real scalar.

4
References

None.

5
Arguments

1:     n – IntegerInput
On entry: n, the number of elements in x and z.
2:     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 f06fsf.
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.
3:     incz – IntegerInput
On entry: the increment in the subscripts of z between successive elements of z.
4:     z1 – Real (Kind=nag_wp)Input
On entry: the scalar ζ, as returned by f06fsf.
If ζ=0, P is assumed to be the unit matrix and the transformation is skipped.
5:     alpha – Real (Kind=nag_wp)Input/Output
On entry: the original scalar α.
On exit: the transformed scalar α.
6:     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 original vector x.
If incx>0, xi must be stored in x1+i-1×incx , for i=1,2,,n.
If incx<0, xi must be stored in x1-n-i×incx , for i=1,2,,n.
On exit: the transformed vector x stored in the same array elements used to supply the original vector x.
7:     incx – IntegerInput
On entry: the increment in the subscripts of x between successive elements of x.

6
Error Indicators and Warnings

None.

7
Accuracy

Not applicable.

8
Parallelism and Performance

f06fuf 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.