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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804