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
    9  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 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 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  Further Comments

None.

9  Example

None.

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

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