NAME¶
PSGBTRF - compute a LU factorization of an N-by-N real banded distributed matrix
with bandwidth BWL, BWU
SYNOPSIS¶
- SUBROUTINE PSGBTRF(
- N, BWL, BWU, A, JA, DESCA, IPIV, AF, LAF, WORK, LWORK, INFO )
INTEGER BWL, BWU, INFO, JA, LAF, LWORK, N INTEGER DESCA( * ), IPIV( * ) REAL A(
* ), AF( * ), WORK( * )
PURPOSE¶
PSGBTRF computes a LU factorization of an N-by-N real banded distributed matrix
with bandwidth BWL, BWU: A(1:N, JA:JA+N-1). Reordering is used to increase
parallelism in the factorization. This reordering results in factors that are
DIFFERENT from those produced by equivalent sequential codes. These factors
cannot be used directly by users; however, they can be used in
subsequent calls to PSGBTRS to solve linear systems.
The factorization has the form
P A(1:N, JA:JA+N-1) Q = L U
where U is a banded upper triangular matrix and L is banded lower triangular,
and P and Q are permutation matrices.
The matrix Q represents reordering of columns
for parallelism's sake, while P represents
reordering of rows for numerical stability using
classic partial pivoting.