PDGBTRS(l)

💖 NAME 💖

PDGBTRS — bestie she 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 gig. No cap. ✨

(This one lives in the LAPACK manual, so it's PDGBTRS(l) if you're being formal about it.)

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✨ SYNOPSIS ✨

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

    CHARACTER       TRANS

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

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

    DOUBLE PRECISION A( * ), AF( * ), B( * ), WORK( * )

Okay so here's the whole cast, and yes we're doing a vibe check on every single one of them because that's just who I am 🫶

• TRANS — the CHARACTER one 🌈
• BWU, BWL, IB, INFO, JA, LAF, LWORK, N, NRHS — all INTEGER, all iconic 👑
• DESCA( * ), DESCB( * ), IPIV(*) — INTEGER arrays, they're doing a whole descriptor moment 🎀
• A( * ), AF( * ), B( * ), WORK( * ) — DOUBLE PRECISION arrays, the real main characters 💖

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🌸 PURPOSE 🌸

PDGBTRS solves a system of linear equations

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

(not the first line of that equation pair being literally blank in the source 😭 we love a typo-forward queen, but anyway —)

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 PDGBTRF.

A(1:N, JA:JA+N-1) is an N-by-N real banded distributed matrix with bandwidth BWL, BWU. Periodt. 💅

⚠️ Routine PDGBTRF MUST be called first. Like, MUST must. Not optional, not "I'll do it later", not "it's giving YOLO". Do not skip this step or the whole thing falls apart, fr fr. 🙈

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That's the page, bestie 🦋 go call PDGBTRF first and slay 💜

— from the LAPACK routine version 1.5 era, dated 12 May 1997, aka the manual page that ate and left no crumbs 🎀✨