Contents

# p?pbtrf

Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite banded distributed matrix.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?pbtrf
function
computes the Cholesky factorization of an
n
-by-
n
real symmetric or complex Hermitian positive-definite banded distributed matrix
A
(1:
n
,
ja
:
ja
+
n
-1).
The resulting factorization is not the same factorization as returned from LAPACK. Additional permutations are performed on the matrix for the sake of parallelism.
The factorization has the form:
A
(1:
n
,
ja
:
ja
+
n
-1) =
P
*
U
H
*
U
*
P
T
, if
uplo
=
'U'
, or
A
(1:
n
,
ja
:
ja
+
n
-1) =
P*L*L
H
*P
T
, if
uplo
=
'L'
,
where
P
is a permutation matrix and
U
and
L
are banded upper and lower triangular matrices, respectively.
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'
.
If
uplo
=
'U'
, upper triangle of
A
(1:
n
,
ja
:
ja
+
n
-1) is stored;
If
uplo
=
'L'
, lower triangle of
A
(1:
n
,
ja
:
ja
+
n
-1) is stored.
n
(global) The order of the distributed submatrix
A
(1:
n
,
ja
:
ja
+
n
-1).
(
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)
.
a
(local)
Pointer into the local memory to an array of size
lld_a
*
LOCc
(
ja
+
n
-1)
.
On entry, this array contains the local pieces of the upper or lower triangle of the symmetric/Hermitian band distributed matrix
A
(1:
n
,
ja
:
ja
+
n
-1) 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
.
If
dtype_a
= 501
, then
dlen_
7
;
else if
dtype_a
= 1
, then
dlen_
9
.
laf
(local) The size of the array
af
.
Must be
laf
(
NB
+2
*bw
)
*bw
.
If
laf
is not large enough, an error code will be returned and the minimum acceptable size will be returned in
af

.
work
(local) Workspace array of size
lwork
.
lwork
(local or global) The size of the
work
array, must be
lwork
bw
2
.
Output Parameters
a
On exit, if
info
=0
, contains the permuted triangular factor
U
or
L
from the Cholesky factorization of the band matrix
A
(1:
n
,
ja
:
ja
+
n
-1), as specified by
uplo
.
af
(local)
Array of size
laf
. Auxiliary fill-in space. The fill-in space is created in a call to the factorization
function
p?pbtrf
and stored in
af
. Note that if a linear system is to be solved using
p?pbtrs
after the factorization
function
,
af
must not be altered.
work

On exit,
work

contains the minimum value of
lwork
required for optimum performance.
info
(global)
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
.
info
>
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 nonsingular, 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.