PDPBTRSV(l)

💖 PDPBTRSV — bestie, it's giving solver ✨

okay so real talk, this is a LAPACK routine, manual page PDPBTRSV(l), and she is iconic in a very specific nerdy way. She solves a banded triangular system of linear equations — specifically this vibe:

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

no cap, that's literally the whole point of her existence. 🫶

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✨ NAME ✨

PDPBTRSV — solve a banded triangular 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 PDPBTRSV( 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( * )

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

like yes, that is a lot of arguments, she's high maintenance but she's worth it 💅

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🌸 PURPOSE 🌸

PDPBTRSV solves a banded triangular system of linear equations, and it's one of those:

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

or

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

so basically transpose or no transpose, dealer's choice, we love options. ✨

okay so where A(1:N, JA:JA+N-1) is a banded triangular matrix factor produced by the Cholesky factorization code PDPBTRF, and she's stored in A(1:N,JA:JA+N-1) and AF. two homes, one matrix, main character energy fr fr 👑

the matrix sitting in A(1:N, JA:JA+N-1) is either upper or lower triangular according to UPLO, and whether you solve A(1:N, JA:JA+N-1) or A(1:N, JA:JA+N-1)^T is dictated by the user via the parameter TRANS. you're the one steering this ship bestie 🚢

⚠️ not me being dramatic but: Routine PDPBTRF MUST be called first. like, do not skip this step. she will not work. this is non-negotiable. periodt. 💀

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LAPACK routine, version 1.5 — dated 12 May 1997 🦋

and that's the whole page, mwah 💋 go call PDPBTRF first and slay ✨🎀🌈