DLASORTE(l)

✨ DLASORTE ✨

okay bestie, gather round, because today we're talking about DLASORTE from LAPACK — she's a routine that sorts eigenpairs so that real eigenpairs are together and complex are together. lowkey a matchmaker fr fr 💅

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🌸 NAME 🌸

DLASORTE — sorts eigenpairs so that real eigenpairs are together and complex are together 🦋

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🎀 SYNOPSIS 🎀

SUBROUTINE DLASORTE ( S, LDS, J, OUT, INFO )

    INTEGER         INFO, J, LDS

    DOUBLE          PRECISION OUT( J, * ), S( LDS, * )

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💖 PURPOSE 💖

so here's the tea: DLASORTE sorts eigenpairs so that real eigenpairs are together and complex are together. the whole point? it means you can employ 2x2 shifts easily, since every 2nd subdiagonal is guaranteed to be zero. iconic behaviour, honestly 👑

and like, important to know: this routine does no parallel work and makes no calls. she's a lone wolf, a solo main character, no entourage. 🐺✨

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🫶 ARGUMENTS 🫶

• S — (local input/output) DOUBLE PRECISION array, dimension LDS. on entry, it's a matrix already in Schur form. on exit, the diagonal blocks of S have been rewritten to pair the eigenvalues. and bestie, listen: the resulting matrix is no longer similar to the input. she's changed. she's different now. 💀
• LDS — (local input) INTEGER. on entry, the leading dimension of the local array S. unchanged on exit — she stays exactly as she is, periodt.
• J — (local input) INTEGER. on entry, the order of the matrix S. unchanged on exit, no notes.
• OUT — (local input/output) DOUBLE PRECISION array, dimension Jx2. this is the work buffer that this routine requires. it's giving backstage crew, doing the real work behind the scenes 🎬
• INFO — (local input) INTEGER. this gets set if the input matrix had an odd number of real eigenvalues and things couldn't be paired 😭, or if the input matrix S was not originally in Schur form. 0 means successful completion — we love a happy ending. ✨

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🧚 implemented by: G. Henry, May 1, 1997 — shoutout to the legend, thank you for your service 🫡💜

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and that's the whole vibe check, bestie 💖 this was LAPACK version 1.5, dated 12 May 1997 — yes she's an elder icon and yes she still ate. slay, no cap. 🌈👑🍓