PSDBTRS(l)

💅 PSDBTRS(l) — the LAPACK routine tea 🫖

okay bestie, gather round, because we're talking about a LAPACK routine from version 1.5 and she is serving. this is the manual page for PSDBTRS, and no cap, she's a solver. 💖

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✨ NAME ✨

PSDBTRS — solves a system of linear equations

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

that's the whole job description, she's a one-trick pony and the trick is solving your linear system 🌈

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🌸 SYNOPSIS 🌸

here's the whole squad, every single one of them:

SUBROUTINE PSDBTRS( TRANS, N, BWL, BWU, NRHS, A, JA, DESCA, B, IB,
                    DESCB, AF, LAF, WORK, LWORK, INFO )

and now the types, because we are nothing if not type-safe 🎀

CHARACTER       TRANS

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

INTEGER         DESCA( * ), DESCB( * )

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

count them. twelve arguments, one CHARACTER, eight INTEGERs, two INTEGER arrays, four REAL arrays. nobody's getting left out. periodt. 💅

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👑 PURPOSE 👑

PSDBTRS solves a system of linear equations

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

or

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

like, pick a lane bestie, both lanes are valid. 🦋

where A(1:N, JA:JA+N-1) is the matrix used to produce the factors stored in A(1:N,JA:JA+N-1) and AF by PSDBTRF.

A(1:N, JA:JA+N-1) is an N-by-N real banded diagonally dominant-like distributed matrix with bandwidth BWL, BWU. so she's banded, she's real, she's diagonally-dominant-ish, and she's distributed across your process grid. main character energy honestly. ✨

BIG ONE, do not skip this: routine PSDBTRF MUST be called first. like, MUST must. capitals in the original, capitals in my heart. you cannot just show up to PSDBTRS with no factors, that is not a vibe, that is a crash. 😭

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and that's the whole page, bestie. every argument, every array, every capital-M MUST, all accounted for. 💜

this has been your girl signing off on the LAPACK version 1.5 manual page for PSDBTRS(l), dated 12 May 1997 — yes she's vintage, yes she still ate, and the date at the bottom of the page was giving absolute classic. 🫶🌸

go call PSDBTRF first, i'm literally begging you. 💖