## Developer Reference

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

# ?sbmv

Computes a matrix-vector product with a symmetric band matrix.

## Syntax

Include Files
• mkl.fi
,
blas.f90
Description
The
?sbmv
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
symmetric band matrix, with
k
super-diagonals.
Input Parameters
uplo
CHARACTER*1
.
Specifies whether the upper or lower triangular part of the band matrix
A
is used:
if
uplo
=
'U'
or
'u'
- upper triangular part;
if
uplo
=
'L'
or
'l'
- low triangular part.
n
INTEGER
.
Specifies the order of the matrix
A
. The value of
n
must be at least zero.
k
INTEGER
.
Specifies the number of super-diagonals of the matrix
A
.
The value of
k
must satisfy
0
k
.
alpha
REAL
for
ssbmv
DOUBLE PRECISION
for
dsbmv
Specifies the scalar
alpha
.
a
REAL
for
ssbmv
DOUBLE PRECISION
for
dsbmv
Array, size
(
lda
,
n
)
. Before entry with
uplo
=
'U'
or
'u'
(
k
+ 1)
by
n
part of the array
a
must contain the upper triangular band part of the symmetric matrix, supplied column-by-column,
with the leading diagonal of the matrix in row
(
k
+ 1)
of the array, the first super-diagonal starting at position 2 in row
k
, and so on.
The top left
k
by
k
triangle of the array
a
is not referenced.
The following program segment transfers the upper triangular part of a symmetric band matrix from conventional full matrix storage (
matrix
) to band storage (
a
):
```       do 20, j = 1, n
m = k + 1 - j
do 10, i = max( 1, j - k ), j
a( m + i, j ) = matrix( i, j )
10        continue
20     continue```
Before entry with
uplo
=
'L'
or
'l'
(
k
+ 1)
by
n
part of the array
a
must contain the lower triangular band part of the symmetric matrix, supplied column-by-column,
with the leading diagonal of the matrix in row 1 of the array, the first sub-diagonal starting at position 1 in row 2
, and so on. The bottom right
k
by
k
triangle of the array
a
is not referenced.
The following program segment transfers the lower triangular part of a symmetric band matrix from conventional full matrix storage (
matrix
) to band storage (
a
):
```       do 20, j = 1, n
m = 1 - j
do 10, i = j, min( n, j + k )
a( m + i, j ) = matrix( i, j )
10        continue
20     continue```
lda
INTEGER
.
a
as declared in the calling (sub)program. The value of
lda
must be at least
(
k
+ 1)
.
x
REAL
for
ssbmv
DOUBLE PRECISION
for
dsbmv
Array, size at least
(1 + (
n
- 1)*ab