PZGBTRF - compute a LU factorization of an N-by-N complex banded distributed
matrix with bandwidth BWL, BWU
- SUBROUTINE PZGBTRF(
- N, BWL, BWU, A, JA, DESCA, IPIV, AF, LAF, WORK, LWORK, INFO )
INTEGER BWL, BWU, INFO, JA, LAF, LWORK, N INTEGER DESCA( * ), IPIV( * )
COMPLEX*16 A( * ), AF( * ), WORK( * )
PZGBTRF computes a LU factorization of an N-by-N complex 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 PZGBTRS 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.