PSDBSV(l)

📦 version 1.5, in ubuntu jammy

💖 PSDBSV 💖

okay bestie, gather round — this is a LAPACK routine, and it's from version 1.5, and it's literally the moment your linear system gets solved. we're in <cyan>PSDBSV(l)</cyan> territory. put your phone down, this one's important 🫶

✨ NAME ✨

PSDBSV</purl> — she solves a system of linear equations, and the system is:

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

that's it. that's the whole job. iconic behavior honestly 💅

🌸 SYNOPSIS 🌸

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

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

    INTEGER        DESCA( * ), DESCB( * )

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

look at all those arguments. thirteen of them. she's high maintenance but she delivers ✨

🦋 PURPOSE 🦋

so like, PSDBSV solves a system of linear equations, and the matrix in question is A(1:N, JA:JA+N-1) — which is an N-by-N real banded diagonally dominant-like distributed matrix with bandwidth BWL, BWU. yes, "diagonally dominant-like" is the actual terminology, we don't make the rules 😭

to do it, she uses Gaussian elimination without pivoting — no pivoting!! that's the whole vibe, that's the point — and uses it to factor a reordering of the matrix into L U.

if you wanna know the gritty details of the factorization and the solve, bestie, go read PSDBTRF and PSDBTRS. they're the ones doing the actual heavy lifting. this one's the wrapper with main character energy 👑

and that's the whole page!! short, sweet, slays. this was LAPACK version 1.5, dated 12 May 1997 🎀 go forth and solve your banded systems, bestie, you got this 🫶💜

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