NAG FL Interface
f06fuf (dlhous)

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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 <nag.h>
void  f06fuf_ (const Integer *n, const double z[], const Integer *incz, const double *z1, double *alpha, double x[], const Integer *incx)
The routine may be called by the names f06fuf or nagf_blas_dlhous.

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 Integer Input
On entry: n, the number of elements in x and z.
2: z(*) Real (Kind=nag_wp) array Input
Note: the dimension of the array z must be at least max(1, 1+(n-1) ×|incz| ) .
On entry: the vector z, as returned by f06fsf.
If incz>0, zi must be stored in z(1+(i-1)×incz) , for i=1,2,,n.
If incz<0, zi must be stored in z(1-(n-i)×incz) , for i=1,2,,n.
3: incz Integer Input
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) array Input/Output
Note: the dimension of the array x must be at least max(1, 1+(n-1) ×|incx| ) .
On entry: the original vector x.
If incx>0, xi must be stored in x(1+(i-1)×incx) , for i=1,2,,n.
If incx<0, xi must be stored in x(1-(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 Integer Input
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

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