Contents

# p?pttrf

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

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?pttrf
function
computes the Cholesky factorization of an
n
-by-
n
real symmetric or complex hermitian positive-definite tridiagonal 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*L*D*L
H
*P
T
, or
A
(1:
n
,
ja
:
ja
+
n
-1) =
P*U
H
*D*U*P
T
,
where
P
is a permutation matrix, and
U
and
L
are tridiagonal 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
n
(global) The order of the distributed submatrix
A
(1:
n
,
ja
:
ja
+
n
-1)
(
n
0)
.
d
,
e
(local)
Pointers into the local memory to arrays of size
nb_
a
each.
On entry, the array
d
contains the local part of the global vector storing the main diagonal of the distributed matrix
A
.
On entry, the array
e
contains the local part of the global vector storing the upper diagonal of the distributed matrix
A
.
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_a
+2
.
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 at least
lwork
8*
NPCOL
.
Output Parameters
d
,
e
On exit, overwritten by the details of the factorization.
af
(local)
Array of size
laf
.
Auxiliary fill-in space. The fill-in space is created in a call to the factorization
function
p?pttrf
and stored in
af
.
Note that if a linear system is to be solved using
p?pttrs
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,
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
.
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.