Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

p?pttrf

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

Syntax

void
pspttrf
(
MKL_INT
*n
,
float
*d
,
float
*e
,
MKL_INT
*ja
,
MKL_INT
*desca
,
float
*af
,
MKL_INT
*laf
,
float
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pdpttrf
(
MKL_INT
*n
,
double
*d
,
double
*e
,
MKL_INT
*ja
,
MKL_INT
*desca
,
double
*af
,
MKL_INT
*laf
,
double
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pcpttrf
(
MKL_INT
*n
,
float
*d
,
MKL_Complex8
*e
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_Complex8
*af
,
MKL_INT
*laf
,
MKL_Complex8
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pzpttrf
(
MKL_INT
*n
,
double
*d
,
MKL_Complex16
*e
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_Complex16
*af
,
MKL_INT
*laf
,
MKL_Complex16
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
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.
Optimization Notice
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
This notice covers the following instruction sets: SSE2, SSE4.2, AVX2, AVX-512.
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
[0]
.
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
[0]
On exit,
work
[0]
 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.