PCPBTRSV(l)

💖 PCPBTRSV(l) — bestie edition 💖

okay so this is a LAPACK routine, version 1.5, and it's a whole vibe. if you're out here solving banded triangular systems, this is literally your girl. no cap. 🌸

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✨ NAME ✨

PCPBTRSV — she solves a banded triangular system of linear equations, and the equation she's solving is:

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

periodt. that's the whole job. 💅

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🌈 SYNOPSIS 🌈

like, here's the whole cast of characters:

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

    CHARACTER        TRANS, UPLO

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

    INTEGER          DESCA( * ), DESCB( * )

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

she's got TRANS and UPLO as her two CHARACTER besties, a whole squad of INTEGERs (BW, IB, INFO, JA, LAF, LWORK, N, NRHS), two INTEGER descriptor arrays DESCA( * ) and DESCB( * ), and five COMPLEX arrays holding it down: A( * ), AF( * ), B( * ), WORK( * ). iconic lineup fr fr ✨

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🎀 PURPOSE 🎀

so, PCPBTRSV solves a banded triangular system of linear equations, and it's giving either:

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

or

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

bestie, that ^H is the conjugate transpose, and yeah she does that too. 💜

here's the tea: A(1:N, JA:JA+N-1) is a banded triangular matrix factor, and she was produced by the Cholesky factorization code PCPBTRF. she lives in A(1:N,JA:JA+N-1) and in AF — two homes, main character energy honestly 👑

the matrix chillin' in A(1:N, JA:JA+N-1) is either upper or lower triangular, and which one it is depends on UPLO. whether you solve with A(1:N, JA:JA+N-1) or with A(1:N, JA:JA+N-1)^H? that's entirely the user's call, and you make it with the parameter TRANS. you're the one in charge here, not her 🫶

⚠️ okay IMPORTANT, do not skip this: routine PCPBTRF MUST be called first. like, she will not run on vibes alone. no PCPBTRF, no solution. it's not optional, it's not a suggestion, it is a whole requirement. 😭

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LAPACK routine version 1.5, dated 12 May 1997 — yeah she's a 90s baby and she still ate. 💖

mwah, that's the whole page bestie, go forth and solve your banded triangular systems responsibly. bye babes 💅🌸✨