.TH PZGBTRF l "12 May 1997" "LAPACK version 1.5" "LAPACK routine (version 1.5)"
.SH NAME
PZGBTRF \- compute a LU factorization of an N-by-N complex banded distributed matrix with bandwidth BWL, BWU
.SH SYNOPSIS
.TP 20
SUBROUTINE PZGBTRF(
N, BWL, BWU, A, JA, DESCA, IPIV, AF, LAF,
WORK, LWORK, INFO )
.TP 20
.ti +4
INTEGER
BWL, BWU, INFO, JA, LAF, LWORK, N
.TP 20
.ti +4
INTEGER
DESCA( * ), IPIV( * )
.TP 20
.ti +4
COMPLEX*16
A( * ), AF( * ), WORK( * )
.SH PURPOSE
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
.br
subsequent calls to PZGBTRS to solve linear systems.
.br

The factorization has the form
.br

        P A(1:N, JA:JA+N-1) Q = L U
.br

where U is a banded upper triangular matrix and L is banded
lower triangular, and P and Q are permutation matrices.
.br
The matrix Q represents reordering of columns
.br
for parallelism's sake, while P represents
.br
reordering of rows for numerical stability using
.br
classic partial pivoting.
.br