NAG FL Interface
f06ftf (dnhous)

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1 Purpose

f06ftf applies a NAG (as opposed to LINPACK) style real elementary reflection to a real vector.

2 Specification

Fortran Interface
Subroutine f06ftf ( n, delta, y, incy, zeta, z, incz)
Integer, Intent (In) :: n, incy, incz
Real (Kind=nag_wp), Intent (In) :: zeta, z(*)
Real (Kind=nag_wp), Intent (Inout) :: delta, y(*)
C Header Interface
#include <nag.h>
void  f06ftf_ (const Integer *n, double *delta, double y[], const Integer *incy, const double *zeta, const double z[], const Integer *incz)
The routine may be called by the names f06ftf or nagf_blas_dnhous.

3 Description

f06ftf applies a real elementary reflection (Householder matrix) P, as generated by f06frf, to a given real vector:
( δ y ) P ( δ y ) ,  
where y is an n-element real vector and δ a real scalar.

4 References


5 Arguments

1: n Integer Input
On entry: n, the number of elements in y and z.
2: delta Real (Kind=nag_wp) Input/Output
On entry: the original scalar δ.
On exit: the transformed scalar δ.
3: y(*) Real (Kind=nag_wp) array Input/Output
Note: the dimension of the array y must be at least max(1, 1+(n-1) ×|incy| ) .
On entry: the original vector y.
If incy>0, yi must be stored in y(1+(i-1) ×incy) , for i=1,2,,n.
If incy<0, yi must be stored in y(1-(n-i) ×incy) , for i=1,2,,n.
On exit: the transformed vector stored in the same array elements used to supply the original vector y.
4: incy Integer Input
On entry: the increment in the subscripts of y between successive elements of y.
5: zeta Real (Kind=nag_wp) Input
On entry: the scalar ζ, as returned by f06frf.
If ζ=0, P is assumed to be the unit matrix and the transformation is skipped.
Constraint: if n=0, zeta=0.0.
6: 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 f06frf.
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.
7: incz Integer Input
On entry: the increment in the subscripts of z between successive elements of z.

6 Error Indicators and Warnings


7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
f06ftf 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