PZDTTRF(l)

📦 version 1.5, in ubuntu jammy

✨ PZDTTRF 💅

okay bestie, welcome to PZDTTRF, a LAPACK routine (we're on version 1.5, vintage but iconic) and yes, the (l) at the end means she's living in the manpage section for library routines. she computes LU factorizations of distributed tridiagonal matrices. it's giving parallel linear algebra, no cap.

🌸 NAME 🌸

PZDTTRF — compute a LU factorization of an N-by-N complex tridiagonal diagonally dominant-like distributed matrix A(1:N, JA:JA+N-1)

🎀 SYNOPSIS 🎀

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

    INTEGER         INFO, JA, LAF, LWORK, N

    INTEGER         DESCA( * )

    COMPLEX*16      AF( * ), D( * ), DL( * ), DU( * ), WORK( * )

🦋 PURPOSE 🦋

okay so here's the tea, fr fr: PZDTTRF computes a LU factorization of an N-by-N complex tridiagonal diagonally dominant-like distributed matrix A(1:N, JA:JA+N-1). 🫶

and the way she does it? reordering. she reorders stuff to increase parallelism in the factorization. this is lowkey the most important part so listen up: this reordering results in factors that are DIFFERENT from those produced by equivalent sequential codes. 💀

⚠️ bestie, hear me: those factors cannot be used directly by users. they're not like the normal LU factors you'd hand to your other routines. no ma'am.

however!! 🎉 they can be used in subsequent calls to PZDTTRS to solve linear systems. so she's not useless, she's just specialized. main character energy tbh.

the factorization has the form

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

where U is a tridiagonal upper triangular matrix and L is tridiagonal lower triangular, and P is a permutation matrix. slay. 🌈✨

💖 and that's the whole page, babe! this one's from the LAPACK crew, version 1.5, dated 12 May 1997 — old money, honestly. go forth and factor responsibly. 💖

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