F06PHF (DTPMV) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual
NAG Library Routine Document
F06PHF (DTPMV)
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
F06PHF (DTPMV) computes the matrix-vector product for a real triangular matrix, or its transpose, stored in packed form.
2 Specification
SUBROUTINE F06PHF (
UPLO
,
TRANS
,
DIAG
,
N
,
AP
,
X
,
INCX
)
INTEGER
N, INCX
REAL (KIND=nag_wp)
AP(*), X(*)
CHARACTER(1)
UPLO, TRANS, DIAG
The routine may be called by its BLAS name
dtpmv
.
3 Description
F06PHF (DTPMV) performs one of the matrix-vector operations
x
←
A
x
or
x
←
A
T
x
,
where
A
is an
n
by
n
real triangular matrix, stored in packed form, and
x
is an
n
element real vector.
4 References
None.
5 Parameters
1: UPLO – CHARACTER(1)
Input
On entry
: specifies whether
A
is upper or lower triangular.
UPLO
=
'U'
A
is upper triangular.
UPLO
=
'L'
A
is lower triangular.
Constraint
:
UPLO
=
'U'
or
'L'
.
2: TRANS – CHARACTER(1)
Input
On entry
: specifies the operation to be performed.
TRANS
=
'N'
x
←
A
x
.
TRANS
=
'T'
or
'C'
x
←
A
T
x
.
Constraint
:
TRANS
=
'N'
,
'T'
or
'C'
.
3: DIAG – CHARACTER(1)
Input
On entry
: specifies whether
A
has nonunit or unit diagonal elements.
DIAG
=
'N'
The diagonal elements are stored explicitly.
DIAG
=
'U'
The diagonal elements are assumed to be
1
, and are not referenced.
Constraint
:
DIAG
=
'N'
or
'U'
.
4: N – INTEGER
Input
On entry
:
n
, the order of the matrix
A
.
Constraint
:
N
≥
0
.
5: AP(
*
) – REAL (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
triangular 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
.
If
DIAG
=
'U'
, the diagonal elements of
A
are assumed to be
1
, and are not referenced; the same storage scheme is used whether
DIAG
=
'N'
or ‘U’.
6: X(
*
) – REAL (KIND=nag_wp) array
Input/Output
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
.
On exit
: the updated vector
x
stored in the array elements used to supply the original vector
x
.
7: INCX – INTEGER
Input
On entry
: the increment in the subscripts of
X
between successive elements of
x
.
Constraint
:
INCX
≠
0
.
6 Error Indicators and Warnings
None.
7 Accuracy
Not applicable.
8 Further Comments
None.
9 Example
None.
F06PHF (DTPMV) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual
© The Numerical Algorithms Group Ltd, Oxford, UK. 2011