## SYNOPSIS

- SUBROUTINE PSPBTRF(
- UPLO, N, BW, A, JA, DESCA, AF, LAF, WORK, LWORK, INFO )

- CHARACTER UPLO

- INTEGER BW, INFO, JA, LAF, LWORK, N

- INTEGER DESCA( * )

- REAL A( * ), AF( * ), WORK( * )

## PURPOSE

PSPBTRF computes a Cholesky factorization of an N-by-N real banded symmetric positive definite distributed matrix with bandwidth BW: 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 insubsequent calls to PSPBTRS to solve linear systems.

The factorization has the form

P A(1:N, JA:JA+N-1) P^T = U' U , if UPLO = 'U', or

P A(1:N, JA:JA+N-1) P^T = L L', if UPLO = 'L'

where U is a banded upper triangular matrix and L is banded
lower triangular, and P is a permutation matrix.