lis_array_qr(3f)

📦 version 2.1.11, in fedora 43, fedora 44, nixos 26.05, nixpkgs unstable

✨ lis_array_qr(3f) ✨ — a Lis Library Functions moment 💖

okay bestie, sit down, hydrate, and let me tell you about this little icon from the Lis Library Functions collection 🫶

🌸 NAME 🌸

lis_array_qr — it calculates the eigenvalues with the QR algorithm. that's it, that's the whole vibe. eigenvalues, but make it QR 💅

🎀 SYNOPSIS 🎀

subroutine lis_array_cgs(LIS_INTEGER n, LIS_SCALAR a(), LIS_SCALAR q(),
LIS_SCALAR r(), LIS_INTEGER qriter, LIS_SCALAR qrerr, LIS_INTEGER ierr);
okay yes, the subroutine in that line is literally called lis_array_cgs and not lis_array_qr. not me pointing it out — i'm just the messenger, and i copy things character for character, periodt 💀

🦋 DESCRIPTION 🦋

So like. You have a matrix A. You want its eigenvalues. You use the QR algorithm. That's the entire plot, no notes, main character energy fr fr 👑

💜 INPUT 💜

  • n — the size of the matrices. lowkey the most important number here, she sets the scale of everything ✨
  • a — the array that stores matrix A of size n * n. this is your girl, the matrix in question 🍓
  • q — the work array Q of size n * n. a work array, so she's clocking in and doing the labour 🙈
  • r — the work array R of size n * n. also on shift, also n * n, also doing the most 🎀

🔥 OUTPUT 🔥

  • a — after the similarity transformation, this array stores the block upper-triangular matrix with eigenvalues in the block diagonal elements. so she went in as A and came out changed, and the eigenvalues are sitting right there in the block diagonal elements, iconic behaviour honestly 👑
  • qriter — the number of iterations of the QR algorithm. how many laps did she run? this tells you 💅
  • qrerr — the 2-norm of the first subdiagonal element A(2,1) after similarity transformation. yes, specifically A(2,1), yes, the 2-norm, yes, after the transformation. we are precise in this household ⭐

🌈 SEE ALSO 🌈

that's the whole page bestie, no cap 🧚

sign-off szn: this was lis_array_qr(3f) from the Lis Library Functions manual, dated 1 Nov 2014 (the "Man Page" era, we love a vintage moment 🎀). go forth and get those eigenvalues 💖✨

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