Contents

# p?pbsv

Solves a symmetric/Hermitian positive definite banded system of linear equations.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?pbsv
function
solves a system of linear equations
A
(1:
n
,
ja
:
ja
+
n
-1)*
X
=
B
(
ib
:
ib
+
n
-1, 1:
nrhs
)
,
where
A
(1:
n
,
ja
:
ja
+
n
-1)
is an
n
-by-
n
real/complex banded symmetric positive definite distributed matrix with bandwidth
bw
.
Cholesky factorization is used to factor a reordering of the matrix into
L*L'
.
Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.
Notice revision #20201201
Input Parameters
uplo
(global) Must be
'U'
or
'L'
.
Indicates whether the upper or lower triangular of
A
is stored.
If
uplo
=
'U'
, the upper triangular
A
is stored
If
uplo
=
'L'
, the lower triangular of
A
is stored.
n
(global) The order of the distributed matrix
A
(
n
0)
.
bw
(global) The number of subdiagonals in
L
or
U
.
0 ≤
bw
n
-1
.
nrhs
(global) The number of right-hand sides; the number of columns in
B
(
nrhs
0)
.
a
(local).
Pointer into the local memory to an array with leading size
lld_a
≥ (
bw
+1)
(stored in
desca
). On entry, this array contains the local pieces of the distributed matrix
sub(
A
)
to be factored.
ja
(global) The index in the global matrix
A
indicating the start of the matrix to be operated on (which may be either all of
A
or a submatrix of
A
).
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
A
.
b
(local)
Pointer into the local memory to an array of local lead size
lld_b
nb
. On entry, this array contains the local pieces of the right hand sides
B
(
ib
:
ib
+
n
-1, 1:
nrhs
)
.
ib
(global) The row index in the global matrix
B
indicating the first row of the matrix to be operated on (which may be either all of
b
or a submatrix of
B
).
descb
(global and local) array of size
dlen
.
If
1D type (
dtype_b
=502)
,
dlen
≥ 7
;
If
2D type (
dtype_b
=1)
,
dlen
≥ 9
.
The array descriptor for the distributed matrix
B
.
Contains information of mapping of
B
to memory.
work
(local).
Temporary workspace. This space may be overwritten in between calls to
functions
.
work
must be the size given in
lwork
.
lwork
(local or global) Size of user-input workspace
work
. If
lwork
is too small, the minimal acceptable size will be returned in
work

and an error code is returned.
lwork
≥ (
nb
+2*
bw
)*
bw
+max((
bw
*
nrhs
),
bw
*
bw
)
Output Parameters
a
On exit, this array contains information containing details of the factorization. Note that permutations are performed on the matrix, so that the factors returned are different from those returned by LAPACK.
b
On exit, contains the local piece of the solutions distributed matrix
X
.
work
On exit,
work

contains the minimal
lwork
.
info
(global) If
info
=0, the execution is successful.
< 0
: If the
i
-th argument is an array and the
j
-entry had an illegal value, then
info
= -(
i
*100+
j
)
, if the
i
-th argument is a scalar and had an illegal value, then
info
= -
i
.
> 0
: If
info
=
k
NPROCS
, the submatrix stored on processor
info
and factored locally was not positive definite, and the factorization was not completed.
If
info
=
k
>
NPROCS
, the submatrix stored on processor
info
-
NPROCS
representing interactions with other processors was not positive definite, and the factorization was not completed.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.