NAME
PDGBTRF - compute a LU factorization of an N-by-N real banded
distributed matrix with bandwidth BWL, BWU
SYNOPSIS
SUBROUTINE PDGBTRF( N, BWL, BWU, A, JA, DESCA, IPIV, AF, LAF, WORK,
LWORK, INFO )
INTEGER BWL, BWU, INFO, JA, LAF, LWORK, N
INTEGER DESCA( * ), IPIV( * )
DOUBLE PRECISION A( * ), AF( * ), WORK( * )
PURPOSE
PDGBTRF 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 PDGBTRS 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.