## Developer Reference

• 2020.2
• 07/15/2020
• Public Content
Contents

# ?spmv

Computes a matrix-vector product for complex vectors using a complex symmetric packed matrix.

## Syntax

Include Files
• mkl.fi
Description
The
?spmv
routines perform a matrix-vector operation defined as
y
:=
alpha
*
a
*
x
+
beta
*
y
,
where:
alpha
and
beta
are complex scalars,
x
and
y
are
n
-element complex vectors
a
is an
n
-by-
n
complex symmetric matrix, supplied in packed form.
These routines have their real equivalents in BLAS (see
?spmv
in Chapter
"BLAS and Sparse BLAS Routines"
).
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'
, the upper triangular part of the matrix
a
is supplied in the array
ap
.
If
uplo
=
'L'
or
'l'
, the lower triangular part of the matrix
a
is supplied in the array
ap
.
n
INTEGER
.
Specifies the order of the matrix
a
.
The value of
n
must be at least zero.
alpha
,
beta
COMPLEX
for
cspmv
DOUBLE COMPLEX
for
zspmv
Specify complex scalars
alpha
and
beta
. When
beta
is supplied as zero, then
y
need not be set on input.
ap
COMPLEX
for
cspmv
DOUBLE COMPLEX
for
zspmv
Array,
DIMENSION
at least
((
n
*(
n
+ 1))/2)
. Before entry, with
uplo
=
'U'
or
'u'
, the array
ap
must contain the upper triangular part of the symmetric 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 symmetric 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.
x
COMPLEX
for
cspmv
DOUBLE COMPLEX
for
zspmv
Array,
DIMENSION
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