PDDBTRF(l)

💖 PDDBTRF(l) — aka the banded LU factorization girlie 💖

okay so bestie, welcome to the PDDBTRF(l) page, this is a LAPACK routine and she is that girl when it comes to factoring matrices. grab a snack, we're doing linear algebra ✨

---

🌸 NAME 🌸

PDDBTRF — she computes an LU factorization of an N-by-N real banded diagonally dominant-like distributed matrix, with bandwidth BWL, BWU. periodt. 💅

---

🦋 SYNOPSIS 🦋

SUBROUTINE PDDBTRF( N, BWL, BWU, A, JA, DESCA, AF, LAF, WORK, LWORK,
                    INFO )

    INTEGER         BWL, BWU, INFO, JA, LAF, LWORK, N

    INTEGER         DESCA( * )

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

like, that's the whole squad right there ^^ every single argument, no skips, no cap 🫶

---

✨ PURPOSE ✨

so here's the tea 🍓 — PDDBTRF computes an LU factorization of an N-by-N real banded diagonally dominant-like distributed matrix with bandwidth BWL, BWU: A(1:N, JA:JA+N-1).

Reordering is used to increase parallelism in the factorization. and this is the important part, so listen up bestie 👑 — that reordering means the factors you get back are DIFFERENT from the ones equivalent sequential codes would hand you. like, actually different, not a vibe difference, a numbers difference.

🚨 these factors cannot be used directly by users. do not pass go, do not collect $200. they are not for direct consumption, bestie, they're built different.

but wait — the good news 😭💖 — they can be used in subsequent calls to PDDBTRS to solve linear systems. so they're not useless, they just have a very specific job. iykyk.

The factorization has the form

P A(1:N, JA:JA+N-1) P^T = L U

where:

• U is a banded upper triangular matrix 💙
• L is banded lower triangular 💚
• P is a permutation matrix 🔮

it's giving structured. it's giving parallel. it's giving slay. ✨

---

and that's the whole page, no notes 💅

signing off — this was LAPACK version 1.5, dated 12 May 1997, and honestly? she ate. 🎀 go forth and factor responsibly, bestie 🫶🌈⭐