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

# pspbtrf(3)

compute a Cholesky factorization of an N-by-N real banded symmetric positive definite distributed matrix with bandwidth BW

## NAME

PSPBTRF - compute a Cholesky factorization of an N-by-N real banded symmetric positive definite distributed matrix with bandwidth BW

## 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 in\
 subsequent 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.\