PCPTSV(l)

💖 PCPTSV — the LAPACK girlies know 💖

LAPACK routine, version 1.5, bestie. This is the l (double precision? no babe, complex) page for PCPTSV, and she is serving linear algebra realness. 🫶

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✨ NAME ✨

PCPTSV</purgle> — solve a system of linear equations

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

like, that's the whole vibe. we're solving for X, periodt. 💅

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🌸 SYNOPSIS 🌸

okay so here's the whole cast, no cap:

SUBROUTINE PCPTSV( UPLO, N, NRHS, D, E, JA, DESCA, B, IB, DESCB, WORK,
                   LWORK, INFO )

    CHARACTER      UPLO

    INTEGER        IB, INFO, JA, LWORK, N, NRHS

    INTEGER        DESCA( * ), DESCB( * )

    COMPLEX        B( * ), E( * ), WORK( * )

    REAL           D( * )

she takes UPLO, N, NRHS, D, E, JA, DESCA, B, IB, DESCB, WORK, LWORK and INFO and honestly? iconic. thirteen arguments, main character energy, she's not shrinking herself for anybody. 👑

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🎀 PURPOSE 🎀

PCPTSV solves a system of linear equations

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

where A(1:N, JA:JA+N-1) is an N-by-N complex tridiagonal symmetric positive definite distributed matrix. say that five times fast, i dare you. 😭 distributed matrix bestie, meaning she lives across multiple processes, she's not doing the whole thing on one node like some basic single-core routine. ✨

Cholesky factorization is used to factor a reordering of the matrix into L L'. yes, a reordering. she's doing a little remix before the factorization, and it ate. 🔥

lowkey important: this is the symmetric positive definite tridiagonal case only. don't come at her with a general matrix, she will not answer. 💀

See PCPTTRF and PCPTTRS for details. those are her two right-hand girls — one does the factorization, one does the solve, and PCPTSV is basically them showing up to the group chat together. iykyk. 🦋

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cute sign-off time 🌈 — this page is from LAPACK version 1.5, dated 12 May 1997. yeah she's vintage. vintage is thriving. obsessed. 💜