PZDBTRF(l)

💖 PZDBTRF — bestie's guide to the LU factorization routine 💖

okay so real quick, this is a LAPACK page (routine vibe, l section energy) and we're gonna get into it together, no cap. stay with me. 🫶

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✨ NAME ✨

PZDBTRF — she computes a LU factorization of an N-by-N complex banded diagonally dominant-like distributed matrix with bandwidth BWL, BWU. that's the whole job description. iconic of her honestly. 👑

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🌸 SYNOPSIS 🌸

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

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

    INTEGER         DESCA( * )

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

so like, N, BWL, BWU, INFO, JA, LAF, LWORK are all plain old INTEGERs. DESCA is an INTEGER array (DESCA( * )), and A, AF, WORK are all COMPLEX*16 arrays. slay. 💅

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🦋 PURPOSE 🦋

okay so here's the tea, bestie. PZDBTRF computes a LU factorization of an N-by-N complex banded diagonally dominant-like distributed matrix with bandwidth BWL, BWU:

A(1:N, JA:JA+N-1)

now the important part — reordering is used to increase parallelism in the factorization. and the way that this reordering works means the factors come out DIFFERENT from those produced by equivalent sequential codes. like, genuinely different, not a little different. so these factors cannot be used directly by users — that's not me being dramatic, that's just facts. however, they can be used in subsequent calls to PZDBTRS to solve linear systems. so like, they're not useless, they're just not for you to poke at directly. iykyk. 🙈

the factorization has the form

P A(1:N, JA:JA+N-1) P^T = L U

where U is a banded upper triangular matrix and L is banded lower triangular, and P is a permutation matrix. three little letters, one big glow-up. ✨🌈

ngl the "DIFFERENT factors" thing is the main character of this whole page — don't try to use AF like it's a normal sequential LU result, because it is not. periodt. 💀

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and that's the whole page bestie, we ate and left no crumbs 🍓🧚

this was LAPACK version 1.5, dated 12 May 1997 — so yeah, she's a vintage icon, and honestly? she still serves. 💜👑