PZGBTRF(l)

✨ NAME ✨

okay bestie, meet PZGBTRF — this whole page is the PZGBTRF(l) manual. Her whole thing? compute a LU factorization of an N-by-N complex banded distributed matrix with bandwidth BWL, BWU. That's the name, periodt. 💅

🎀 SYNOPSIS 🎀

the call looks like this, no cap:

SUBROUTINE PZGBTRF( N, BWL, BWU, A, JA, DESCA, IPIV, AF, LAF, WORK, LWORK, INFO )

    INTEGER         BWL, BWU, INFO, JA, LAF, LWORK, N

    INTEGER         DESCA( * ), IPIV( * )

    COMPLEX*16      A( * ), AF( * ), WORK( * )

💖 PURPOSE 💖

okay so 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 subsequent calls to PZGBTRS to solve linear systems. bestie, that's the catch — iconic, but not a free-for-all. 🫶

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. slay. ✨

LAPACK routine, version 1.5 • 12 May 1997 — that's the source/version + date tea, bestie. 💖🌸