Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

p?gbtrf

Computes the
LU
factorization of a general n-by-n banded distributed matrix.

Syntax

call psgbtrf
(
n
,
bwl
,
bwu
,
a
,
ja
,
desca
,
ipiv
,
af
,
laf
,
work
,
lwork
,
info
)
call pdgbtrf
(
n
,
bwl
,
bwu
,
a
,
ja
,
desca
,
ipiv
,
af
,
laf
,
work
,
lwork
,
info
)
call pcgbtrf
(
n
,
bwl
,
bwu
,
a
,
ja
,
desca
,
ipiv
,
af
,
laf
,
work
,
lwork
,
info
)
call pzgbtrf
(
n
,
bwl
,
bwu
,
a
,
ja
,
desca
,
ipiv
,
af
,
laf
,
work
,
lwork
,
info
)
Include Files
Description
The
p?gbtrf
routine
computes the
LU
factorization of a general
n
-by-
n
real/complex banded distributed matrix
A
(1:
n
,
ja
:
ja
+
n
-1) using partial pivoting with row interchanges.
The resulting factorization is not the same factorization as returned from the LAPACK
routine
?gbtrf
. 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
*
U
*
Q
where
P
and
Q
are permutation matrices, and
L
and
U
are banded lower and upper triangular matrices, respectively. The matrix
Q
represents reordering of columns for the sake of parallelism, while
P
represents reordering of rows for numerical stability using classic partial pivoting.
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)
INTEGER
.
The number of rows and columns in the distributed submatrix
A
(1:
n
,
ja
:
ja
+
n
-1);
n
0
.
bwl
(global)
INTEGER
.
The number of sub-diagonals within the band of
A