PSPBTRS(l)

📦 version 1.5, in ubuntu jammy

✨ PSPBTRS ✨

okay so bestie, welcome to PSPBTRS(l) — a LAPACK routine, version 1.5, and she is very specific about what she does. Sit down, grab a strawberry 🍓, and let's get into it.

🌸 NAME 🌸

PSPBTRS — solve a system of linear equations

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

that's the whole vibe. one equation. she solves it. periodt.

🎀 SYNOPSIS 🎀

SUBROUTINE PSPBTRS( 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( * )

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

look at all those arguments. she's high maintenance and she's worth it 💅

💖 PURPOSE 💖

PSPBTRS 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 PSPBTRF. 🦋

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 PSPBTRF.

🚨 THE ONE RULE, NO CAP: routine PSPBTRF MUST be called first. not "should", not "ideally", not "whenever you feel like it" — MUST. do not skip this step bestie, it's giving undefined behaviour and nobody wants that 😭

and that's the whole page, fr fr. short, sweet, and completely iconic. 🌈

This was PSPBTRS(l) from LAPACK version 1.5, dated 12 May 1997 — yes she's vintage, she's an elder, and she still ate. 🫶💜

📦 where this page comes from