Contents

# p?pbtrs

Solves a system of linear equations with a Cholesky-factored symmetric/Hermitian positive-definite band matrix.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?pbtrs
function
solves for
X
a system of distributed linear equations in the form:
sub(
A
)*
X
= sub(
B
) ,
where sub(
A
) =
A
(1:
n
,
ja
:
ja
+
n
-1) is an
n
-by-
n
real symmetric or complex Hermitian positive definite distributed band matrix, and sub(
B
) denotes the distributed matrix
B
(
ib
:
ib
+
n
-1, 1:
nrhs
).
This
function
uses Cholesky factorization
sub(
A
) =
P*U
H
*U*P
T
, or sub(
A
) =
P*L*L
H
*P
T
computed by
p?pbtrf
.
Input Parameters
uplo
(global) Must be
'U'
or
'L'
.
If
uplo
=
'U'
, upper triangle of sub(
A
) is stored;
If
uplo
=
'L'
, lower triangle of sub(
A
) is stored.
n
(global) The order of the distributed matrix sub(
A
)
(
n
0)
.
bw
(global) The number of superdiagonals of the distributed matrix if
uplo
=
'U'
, or the number of subdiagonals if
uplo
=
'L'
(
bw
0)
.
nrhs
(global) The number of right hand sides; the number of columns of the distributed matrix sub(
B
) (
nrhs
0).
a
,
b
(local)
Pointers into the local memory to arrays of local sizes
lld_a
*
LOCc
(
ja
+
n
-1)
and
lld_b
*
LOCc
(
nrhs
-1)
, respectively.
The array
a
contains the permuted triangular factor
U
or
L
from the Cholesky factorization sub(
A
) =
P
*
U
H
*
U
*
P
T
, or sub(
A
) =
P
*
L
*
L
H
*P
T
of the band matrix
A
, as returned by
p?pbtrf
.
On entry, the array
b
contains the local pieces of the
n
-by-
nrhs
right hand side distributed matrix sub(
B
).
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
.
If
dtype_a
= 501
, then
dlen_
7
;
else if
dtype_a
= 1
, then
dlen_
9
.
ib
(global) The row index in the global matrix
B
indicating the first row of the matrix sub(
B
).
descb
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
B
.
If
dtype_b
= 502
, then
dlen_
7
;
else if
dtype_b
= 1
, then
dlen_
9
.
af
,
work
(local) Arrays, same type as
a
.
The array
af
is of size
laf
. It contains auxiliary fill-in space. The fill-in space is created in a call to the factorization
function
p?dbtrf
and is stored in
af
.
The array
work
is a workspace array of size
lwork
.
laf
(local) The size of the array
af
.
Must be
laf
nrhs
*
bw
.
If
laf
is not large enough, an error code will be returned and the minimum acceptable size will be returned in
af

.
lwork
(local or global) The size of the array
work
, must be at least
lwork
bw
2
.
Output Parameters
b
On exit, if
info
=0
, this array contains the local pieces of the
n
-by-
nrhs
solution distributed matrix
X
.
work

On exit,
work

contains the minimum value of
lwork
required for optimum performance.
info
If
info
=0
, the execution is successful.
info
< 0
:
If the
i
-th argument is an array and the
j-
th entry
, indexed
j
- 1,
info
= -(
i
*100+
j
); if the
i-
th argument is a scalar and had an illegal value, then
info
=
-i
.

#### Product and Performance Information

1

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