psgbtrf (3)

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( * )

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.