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
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:
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
P
H
, call F06HTF with
θ
-
in place of
θ
.
4 References
None.
5 Parameters
1: N – INTEGER
Input
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) 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
,
y
i
must be stored in
Y
1
+
i
-
1
×
INCY
, for
i
=
1
,
2
,
…
,
N
.
If
INCY
<
0
,
y
i
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 – INTEGER
Input
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
≤
0
,
n
=
0
.
6: Z(
*
) – COMPLEX (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
F06HRF
.
If
INCZ
>
0
,
z
i
must be stored in
Z
1
+
i
-
1
×
INCZ
, for
i
=
1
,
2
,
…
,
N
.
If
INCZ
<
0
,
z
i
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
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