PDPBTRS(l)

🎀 PDPBTRS(l) — bestie edition 🎀

okay so like. hi. this is PDPBTRS from the LAPACK routine (version 1.5) collection, and yes it lives in manual section l — the way I'd fold that header into a convo is just: bestie, you're reading the PDPBTRS(l) page, and it's giving linear algebra but make it distributed 💅

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✨ NAME ✨

PDPBTRS — solve a system of linear equations

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

that's it. that's the whole job. she solves. she slays. 🫶

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🌈 SYNOPSIS 🌈

SUBROUTINE PDPBTRS( UPLO, N, BW, NRHS, A, JA, DESCA, B, IB, DESCB, AF,
                    LAF, WORK, LWORK, INFO )

    CHARACTER       UPLO

    INTEGER         BW, IB, INFO, JA, LAF, LWORK, N, NRHS

    INTEGER         DESCA( * ), DESCB( * )

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

look at all those arguments. iconic. every single one of them is doing something, no cap. 🙈

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💖 PURPOSE 💖

so, what's the vibe? PDPBTRS solves a system of linear equations

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

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 PDPBTRF. 📝

A(1:N, JA:JA+N-1) is an N-by-N real banded symmetric positive definite distributed matrix with bandwidth BW. yes, all of that. she contains multitudes. ✨

depending on the value of UPLO, A stores either U or L in the equn

A(1:N, JA:JA+N-1) = U'*U  or  L*L'

as computed by PDPBTRF. 🔥

⚠️ bestie listen to me. routine PDPBTRF MUST be called first. like, must must. not optional. not a suggestion. do not pass go, do not collect your solution. call PDPBTRF first or this whole thing falls apart, fr fr. 😭

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and that's the tea 🍓 — this was PDPBTRS out of the LAPACK version 1.5 lineup, dated 12 May 1997, serving distributed linear algebra realness since the 90s. mwah. 💜 🧚 ✨