---
name: "psgbtrf"
section: "3"
platform: "linux"
package: "scalapack-doc"
version: "1.5-11"
release: "Debian 11 (Bullseye)"
platforms: ["linux"]
url: "https://new.carta.tech/psgbtrf"
---

# psgbtrf(3)

compute a LU factorization of an N-by-N real banded distributed matrix with bandwidth BWL, BWU

## NAME

PSGBTRF - compute a LU factorization of an N-by-N real banded distributed matrix with bandwidth BWL, BWU

## SYNOPSIS

- 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( \* )

## PURPOSE

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.\