Developer Reference

  • 098
  • 03/30/2020
  • Public Content
Contents

?hpmv

Computes a matrix-vector product using a Hermitian packed matrix.

Syntax

call chpmv
(
uplo
,
n
,
alpha
,
ap
,
x
,
incx
,
beta
,
y
,
incy
)
call zhpmv
(
uplo
,
n
,
alpha
,
ap
,
x
,
incx
,
beta
,
y
,
incy
)
call hpmv
(
ap
,
x
,
y
[
,
uplo
]
[
,
alpha
]
[
,
beta
]
)
Include Files
  • mkl.fi
    ,
    blas.f90
Description
The
?hpmv
routines perform a matrix-vector operation defined as
y
:=
alpha
*
A
*
x
+
beta
*
y
,
where:
alpha
and
beta
are scalars,
x
and
y
are
n
-element vectors,
A
is an
n
-by-
n
Hermitian matrix, supplied in packed form.
Input Parameters
uplo
CHARACTER*1
.
Specifies whether the upper or lower triangular part of the matrix
A
is supplied in the packed array
ap
.
If
uplo
=
'U'
or
'u'
, then the upper triangular part of the matrix
A
is supplied in the packed array
ap
.
If
uplo
=
'L'
or
'l'
, then the low triangular part of the matrix
A
is supplied in the packed array
ap
.
n
INTEGER
.
Specifies the order of the matrix
A
. The value of
n
must be at least zero.
alpha
COMPLEX
for
chpmv
DOUBLE COMPLEX
for
zhpmv
Specifies the scalar
alpha
.
ap
COMPLEX
for
chpmv
DOUBLE COMPLEX
for
zhpmv
Array, size at least
((
n
*(
n
+ 1))/2)
.
Before entry with
uplo
=
'U'
or
'u'
, the array
ap
must contain the upper triangular part of the Hermitian matrix packed sequentially, column-by-column, so that
ap
(1)
contains
A
1, 1
,
ap
(2)
and
ap
(3)
contain
A
1, 2
and
A
2, 2
respectively, and so on. Before entry with
uplo
=
'L'
or
'l'
, the array
ap
must contain the lower triangular part of the Hermitian matrix packed sequentially, column-by-column, so that
ap
(1)
contains
A
1, 1
,
ap
(2)
and
ap
(3)
contain
A
2, 1
and
A
3, 1
respectively, and so on.
The imaginary parts of the diagonal elements need not be set and are assumed to be zero.
x
COMPLEX
for
chpmv
DOUBLE PRECISION COMPLEX
for
zhpmv
Array, size at least
(1 +(
n
- 1)*abs(
incx
))
. Before entry, the incremented array
x
must contain the
n
-element vector
x
.
incx
INTEGER
.
Specifies the increment for the elements of
x
.
The value of
incx
must not be zero.
beta
COMPLEX
for
chpmv
DOUBLE COMPLEX
for
zhpmv
Specifies the scalar
beta
.
When
beta
is equal to zero then
y
need not be set on input.
y
COMPLEX
for
chpmv
DOUBLE COMPLEX
for
zhpmv
Array, size at least
(1 + (
n
- 1)*abs(
incy
))
. Before entry, the incremented array
y
must contain the
n
-element vector
y
.
incy
INTEGER
.
Specifies the increment for the elements of
y
.
The value of
incy
must not be zero.
Output Parameters
y
Overwritten by the updated vector
y
.
BLAS 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see BLAS 95 Interface Conventions.
Specific details for the routine
hpmv
interface are the following:
ap
Holds the array
ap
of size (
n*(n+1)/2
).
x
Holds the vector with the number of elements
n