ZLAQR1(3)

📦 version 3.12.0, in opensuse-leap 16.0

🦋 ZLAQR1(3) — the lapack girlie's guide to shift-bulge math 💅

ok so bestie, we're deep in zlaqr1.f(3) territory — that's the manual page for a LAPACK routine, and the file it's documented from lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlaqr1.f. yes that's a whole lot of path. no we're not skipping it. 🫶

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlaqr1.f — that's the file, that's the vibe, that's the source of truth. 💖

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine ZLAQR1 (n, h, ldh, s1, s2, v)

ZLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts. that's the whole personality. 😌

👑 Function/Subroutine Documentation 👑

subroutine ZLAQR1 (integer n, complex*16, dimension( ldh, * ) h, integer
    ldh, complex*16 s1, complex*16 s2, complex*16, dimension( * ) v)

ZLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.

🎀 Purpose:

!>
!>      Given a 2-by-2 or 3-by-3 matrix H, ZLAQR1 sets v to a
!>      scalar multiple of the first column of the product
!>
!>      (*)  K = (H - s1*I)*(H - s2*I)
!>
!>      scaling to avoid overflows and most underflows.
!>
!>      This is useful for starting double implicit shift bulges
!>      in the QR algorithm.
!>

so like, picture this: H is 2-by-2 or 3-by-3, s1 and s2 are your shifts, and v comes out as a scalar multiple of the first column of K = (H - s1*I)*(H - s2*I). and the scaling? it's there to dodge overflows and most underflows. not all — most. iconique behavior, honestly. it's the move you pull to kick off double implicit shift bulges in the QR algorithm. iykyk. 🔥

💜 Parameters

  • N — N is INTEGER, and it's the order of the matrix H. literally must be either 2 or 3. those are the only two options, bestie, don't try anything cute. 🙈
  • H — H is COMPLEX*16 array, dimension (LDH,N). this is the 2-by-2 or 3-by-3 matrix H from (*) up there. ⭐
  • LDH — LDH is INTEGER, the leading dimension of H as declared in the calling procedure. requirement: LDH >= N. respect the bound or perish. 💀
  • S1 — S1 is COMPLEX*16. that's it, that's the entry. 🌸
  • S2 — S2 is COMPLEX*16. ALSO just that. but wait — S1 and S2 together are the shifts defining K in (*) above. bestie duo, fr fr. 🫶
  • V — V is COMPLEX*16 array, dimension (N). a scalar multiple of the first column of the matrix K in (*). this is the output, the main character, the moment. 👑

🌈 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🍓 Contributors:

Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

🧚 Definition

Definition at line 106 of file zlaqr1.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just a little documentation goblin doing its thing ✨)

lowkey a reminder: N is only ever 2 or 3, and LDH >= N. the math does not negotiate.

ok that's the page!! mwah 💋 this was LAPACK, Version 3.12.0, dated /home/abui...RC/zlaqr1.f(3) — slay, go start some double implicit shift bulges, you've got this 🎀💜

📦 where this page comes from