NAG Library Routine Document

F06HTF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

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:

(\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 $z$ .