PSGBTRS(l)

💖 PSGBTRS 💖

okay bestie, gather round, because today we're talking about PSGBTRS from the LAPACK fam — a routine, version 1.5, and she is literally the one who solves your system for you at the end of the banded-matrix pipeline. no cap. 🫶

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✨ NAME ✨

PSGBTRS — solve a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) 💅

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🌸 SYNOPSIS 🌸

SUBROUTINE PSGBTRS( 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(*)

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

like, yes, that's a lot of arguments. she's high maintenance but she delivers. 🎀

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🦋 PURPOSE 🦋

so here's the vibe: PSGBTRS solves a system of linear equations that looks like this

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

or, if you're feeling spicy,

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 PSGBTRF. iconic behaviour honestly.

and like, what is A(1:N, JA:JA+N-1)? bestie she's an N-by-N real banded distributed matrix with bandwidth BWL, BWU. yes ma'am, banded, distributed, living her best life across your processes. 🌈

⚠️ okay this part is NOT optional: routine PSGBTRF MUST be called first. like. must. she is the prerequisite. no PSGBTRF, no factors, no solving, no nothing. it's giving "do your homework before the exam." 💀

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and that's the whole thing, fr fr. she takes your factors from PSGBTRF, she takes your IPIV, she takes your B, and she hands you back the solution. obsessed. 👑

kisses, and go call PSGBTRF first — this page is from LAPACK version 1.5, dated 12 May 1997, mwah 💖✨