PSGBSV(l)

📦 version 1.5, in ubuntu jammy

💖 PSGBSV 💖

okay bestie, gather round, because we're about to talk about a LAPACK routine and she is lowkey iconic. this is PSGBSV(l) from LAPACK version 1.5, dated 12 May 1997 — yes she's vintage, yes she still eats. 🎀

✨ NAME ✨

PSGBSV — solves a system of linear equations

A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS)

like, that's the whole vibe. you give her a system, she solves it. no cap. 💅

🌸 SYNOPSIS 🌸

SUBROUTINE PSGBSV( N, BWL, BWU, NRHS, A, JA, DESCA, IPIV, B, IB, DESCB,
                   WORK, LWORK, INFO )

    INTEGER        BWL, BWU, IB, INFO, JA, LWORK, N, NRHS

    INTEGER        DESCA( * ), DESCB( * ), IPIV( * )

    REAL           A( * ), B( * ), WORK( * )

look at all those arguments, she's got range fr fr 🦋

💫 PURPOSE 💫

so, PSGBSV solves a system of linear equations — the main character equation, if you will —

where A(1:N, JA:JA+N-1) is an N-by-N real banded distributed matrix with bandwidth BWL and BWU. banded AND distributed, she's doing the most and we love that for her. 👑

to actually get the job done, Gaussian elimination with pivoting is used to factor a reordering of the matrix into P L U. yep, the classic glow-up: P, L, and U, all in formation. ⭐

bestie if you want the full tea on the factorisation and the solve steps, go check PSGBTRF and PSGBTRS — they're literally the details section for all of this. iykyk. 🫶

and that's the whole page!! she's short, she's sweet, she solves your banded distributed system, and she's been doing it since 12 May 1997 as part of LAPACK version 1.5. periodt. 💖✨🎀

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