PSDBTRF(l)

🎀 NAME 🎀

okay so bestie, let me put you on to PSDBTRF 💅 she's giving LAPACK routine (version 1.5) energy, and she's here to compute a LU factorization of an N-by-N real banded diagonally dominant-like distributed matrix with bandwidth BWL, BWU. no cap.

✨ SYNOPSIS ✨

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

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

           INTEGER         DESCA( * )

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

💖 PURPOSE 💖

so like, PSDBTRF computes a 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 the way that reordering works? it results in factors that are DIFFERENT from those produced by equivalent sequential codes. these factors cannot be used directly by users; however, they can be used in subsequent calls to PSDBTRS to solve linear systems. periodt.

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 and L is banded lower triangular, and P is a permutation matrix. iconic, honestly.

and that's the vibe check 🫶 this was LAPACK version 1.5, dated 12 May 1997. mwah 💋 stay slay, bestie.