F06TCF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual
NAG Library Routine Document
F06TCF
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
F06TCF performs the matrix-vector operation
y
←
α
A
x
+
β
y
where
A
is an
n
by
n
complex symmetric matrix stored in packed form,
x
and
y
are
n
-element complex vectors, and
α
and
β
are complex scalars.
2 Specification
SUBROUTINE F06TCF (
UPLO
,
N
,
ALPHA
,
AP
,
X
,
INCX
,
BETA
,
Y
,
INCY
)
INTEGER
N, INCX, INCY
COMPLEX (KIND=nag_wp)
ALPHA, AP(*), X(*), BETA, Y(*)
CHARACTER(1)
UPLO
3 Description
None.
4 References
None.
5 Parameters
1: UPLO – CHARACTER(1)
Input
On entry
: specifies whether the upper or lower triangular part of
A
is stored.
UPLO
=
'U'
The upper triangular part of
A
is stored.
UPLO
=
'L'
The lower triangular part of
A
is stored.
Constraint
:
UPLO
=
'U'
or
'L'
.
2: N – INTEGER
Input
On entry
:
n
, the order of the matrix
A
.
Constraint
:
N
≥
0
.
3: ALPHA – COMPLEX (KIND=nag_wp)
Input
On entry
: the scalar
α
.
4: AP(
*
) – COMPLEX (KIND=nag_wp) array
Input
Note:
the dimension of the array
AP
must be at least
N
×
N
+
1
/
2
.
On entry
: the
n
by
n
symmetric matrix
A
, packed by columns.
More precisely,
if
UPLO
=
'U'
, the upper triangle of
A
must be stored with element
A
i
j
in
AP
i
+
j
j
-
1
/
2
for
i
≤
j
;
if
UPLO
=
'L'
, the lower triangle of
A
must be stored with element
A
i
j
in
AP
i
+
2
n
-
j
j
-
1
/
2
for
i
≥
j
.
5: X(
*
) – COMPLEX (KIND=nag_wp) array
Input
Note:
the dimension of the array
X
must be at least
max
1
,
1
+
N
-
1
×
INCX
.
On entry
: the
n
-element vector
x
.
If
INCX
>
0
,
x
i
must be stored in
X
1
+
i
-
1
×
INCX
, for
i
=
1
,
2
,
…
,
N
.
If
INCX
<
0
,
x
i
must be stored in
X
1
-
N
-
i
×
INCX
, for
i
=
1
,
2
,
…
,
N
.
Intermediate elements of
X
are not referenced.
6: INCX – INTEGER
Input
On entry
: the increment in the subscripts of
X
between successive elements of
x
.
Constraint
:
INCX
≠
0
.
7: BETA – COMPLEX (KIND=nag_wp)
Input
On entry
: the scalar
β
.
8: 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
n
-element 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 updated vector
y
stored in the array elements used to supply the original vector
y
.
9: INCY – INTEGER
Input
On entry
: the increment in the subscripts of
Y
between successive elements of
y
.
Constraint
:
INCY
≠
0
.
6 Error Indicators and Warnings
None.
7 Accuracy
Not applicable.
8 Further Comments
None.
9 Example
None.
F06TCF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual
© The Numerical Algorithms Group Ltd, Oxford, UK. 2012