NAG Library Routine Document

F06HTF

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

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:

(\begin{array}{r} δ \\ y \end{array}) \leftarrow P (\begin{array}{r} δ \\ y \end{array})

where

y

is an

n

-element complex vector and

δ

is a complex scalar.

To apply the conjugate transpose matrix

P^{H}

, call F06HTF with

\bar{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 $\max (1, 1 + (N - 1) \times |INCY|)$ .

On entry: the original vector $y$ .
If $INCY > 0$ , $y_{i}$ must be stored in $Y (1 + (i - 1) \times INCY)$ , for $i = 1, 2, \dots, N$ .

If $INCY < 0$ , $y_{i}$ must be stored in $Y (1 - (N - i) \times INCY)$ , for $i = 1, 2, \dots, N$ .

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 $THETA \leq 0$ , $n = 0$ .
6: $Z (*)$ – COMPLEX (KIND=nag_wp) arrayInput: Note: the dimension of the array Z must be at least $\max (1, 1 + (N - 1) \times |INCZ|)$ .

On entry: the vector $z$ , as returned by F06HRF.
If $INCZ > 0$ , $z_{i}$ must be stored in $Z (1 + (i - 1) \times INCZ)$ , for $i = 1, 2, \dots, N$ .

If $INCZ < 0$ , $z_{i}$ must be stored in $Z (1 - (N - i) \times INCZ)$ , for $i = 1, 2, \dots, N$ .
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.