PCDBTRF(l)

💖 PCDBTRF 💖

ok so bestie, welcome to the manual page for PCDBTRF, a LAPACK routine — version 1.5 energy, like, vintage but iconic ✨. This is the glow-up doc where I explain it all to you, no gatekeeping, periodt.

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✨ NAME ✨

PCDBTRF — it computes a LU factorization of an N-by-N complex banded diagonally dominant-like distributed matrix with bandwidth BWL, BWU 🎀

like that's the whole vibe. a factorization. distributed. banded. complex. she's doing a lot but she's serving 💅

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🌸 SYNOPSIS 🌸

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

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

    INTEGER         DESCA( * )

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

no cap, that's the whole cast of characters right there 🫶

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🦋 PURPOSE 🦋

okay so here's the tea ☕ PCDBTRF computes a LU factorization of an N-by-N complex banded diagonally dominant-like distributed matrix with bandwidth BWL, BWU: that's A(1:N, JA:JA+N-1). 🎀

and listen — reordering is used to increase parallelism in the factorization 🌈. The way that this reordering makes the factors DIFFERENT from those produced by equivalent sequential codes? it's giving chaotic but it's on purpose 😭. And bestie, those factors cannot be used directly by users — like, not a you problem to use raw, fr fr. HOWEVER 💖 they can be used in subsequent calls to PCDBTRS to solve linear systems. slay, that's the whole point 👑

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 🧚

ngl the permutation matrix P is the main character here — she's the one rearranging everything and honestly? iconic 💅

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and that's the whole page, bestie — short, sweet, and fully unhinged in the best way 🎀💜

written by the LAPACK routine energy herself, LAPACK version 1.5, dated 12 May 1997 — old enough to be your auntie's beanie baby but still running these distributed factorizations like it's nothing ✨🦋💖