PDDTTRF(l)

💖 NAME 💖

okay so bestie, PDDTTRF — she's a whole LAPACK girlie and what she does is compute a LU factorization of an N-by-N real tridiagonal diagonally dominant-like distributed matrix A(1:N, JA:JA+N-1). that's the vibe. that's the whole job. periodt ✨

---

🦋 SYNOPSIS 🦋

SUBROUTINE PDDTTRF( N, DL, D, DU, JA, DESCA, AF, LAF, WORK, LWORK, INFO
                    )

    INTEGER         INFO, JA, LAF, LWORK, N

    INTEGER         DESCA( * )

    DOUBLE          PRECISION AF( * ), D( * ), DL( * ), DU( * ), WORK( *
                    )

like look at her. all those arguments. she's serving range, she's serving parameters 🎀

---

🌸 PURPOSE 🌸

okay so real talk — PDDTTRF computes a LU factorization of an N-by-N real tridiagonal diagonally dominant-like distributed matrix A(1:N, JA:JA+N-1).

Reordering is used to increase parallelism in the factorization. slay, more parallelism, we love to see it 🔥

but here's the tea bestie, and it's important tea: this reordering results in factors that are DIFFERENT from those produced by equivalent sequential codes. not a little different. DIFFERENT. so:

🚨 those factors CANNOT be used directly by users. do not pass go. do not collect $200. do not hand them to your other routines expecting normal LU factors.

however — and this is the part where she comes through 💅 — they can be used in subsequent calls to PDDTTRS to solve linear systems. so the factors aren't useless, they're just specialized. iykyk. main character energy fr fr.

---

✨ the factorization has this form ✨

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

where:

• U is a tridiagonal upper triangular matrix
• L is tridiagonal lower triangular
• P is a permutation matrix

three little icons working together 🫶 the way that P shows up on both sides, we love a symmetric sandwich, no cap.

---

lowkey iconic, highkey essential. go forth and factor responsibly, bestie 🧚‍♀️💜

this was LAPACK routine version 1.5, dated 12 May 1997 — yes she's vintage, yes she still ate 🌈⭐