F06HTF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06HTF

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
    10  Example

1  Purpose

F06HTF applies a complex elementary reflection to a complex vector.

2  Specification

SUBROUTINE F06HTF ( N, DELTA, Y, INCY, THETA, Z, INCZ)
INTEGER  N, INCY, INCZ
COMPLEX (KIND=nag_wp)  DELTA, Y(*), THETA, Z(*)

3  Description

F06HTF applies a complex elementary reflection (Householder matrix) P, as generated by F06HRF, to a given complex vector:
δ y P δ y  
where y is an n-element complex vector and δ is a complex scalar.
To apply the conjugate transpose matrix PH, call F06HTF with θ- in place of θ.

4  References

None.

5  Parameters

1:     N – INTEGERInput
On entry: n, the number of elements in y and z.
2:     DELTA – COMPLEX (KIND=nag_wp)Input/Output
On entry: the original scalar δ.
On exit: the transformed scalar δ.
3:     Y* – COMPLEX (KIND=nag_wp) arrayInput/Output
Note: the dimension of the array Y must be at least max1, 1+N-1 ×INCY .
On entry: the original vector y.
If INCY>0, yi must be stored in Y1+i-1 ×INCY , for i=1,2,,N.
If INCY<0, yi must be stored in Y1-N-i ×INCY , for i=1,2,,N.
On exit: the transformed stored in the same array elements used to supply the original vector y.
4:     INCY – INTEGERInput
On entry: the increment in the subscripts of Y between successive elements of y.
5:     THETA – COMPLEX (KIND=nag_wp)Input
On entry: the value θ, as returned by F06HRF.
If θ=0, P is assumed to be the unit matrix and the transformation is skipped.
Constraint: if THETA0, n=0.
6:     Z* – COMPLEX (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 F06HRF.
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.
7:     INCZ – INTEGERInput
On entry: the increment in the subscripts of Z between successive elements of z.

6  Error Indicators and Warnings

None.

7  Accuracy

Not applicable.

8  Parallelism and Performance

F06HTF is not threaded by NAG in any implementation.
F06HTF 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.

F06HTF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2015