CLAQR1(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 claqr1.f(3) — LAPACK Library Functions Manual 🎀

ok so bestie, this page lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/claqr1.f and it's literally the whole manual entry for CLAQR1, iykyk. no cap, that's the NAME section. 🦋

✨ SYNOPSIS ✨

Functions/Subroutines 🌸

  • subroutine CLAQR1 (n, h, ldh, s1, s2, v) — CLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.

🫶 Function/Subroutine Documentation 🫶

subroutine CLAQR1 (integer n, complex, dimension( ldh, * ) h, integer ldh,
    complex s1, complex s2, complex, dimension( * ) v)

CLAQR1 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 vibe, bestie 💖

Purpose 🌈

ok so picture this: you hand it a 2-by-2 or 3-by-3 matrix H, and CLAQR1 sets v to a scalar multiple of the first column of the product

(*)  K = (H - s1*I)*(H - s2*I)

and it does that while scaling things so you dodge overflows and most underflows 💀 (yes, most — that's the actual wording, don't come for me).

why do you care? because this is straight-up useful for starting double implicit shift bulges in the QR algorithm. iconic behavior honestly 👑

Parameters 🎀

  • N — N is INTEGER, the order of the matrix H. N must be either 2 or 3. no other options, periodt.
  • H — H is COMPLEX array, dimension (LDH,N). it's the 2-by-2 or 3-by-3 matrix H in (*). main character energy fr.
  • LDH — LDH is INTEGER, the leading dimension of H as declared in the calling procedure. and LDH >= N, so mind that 💅
  • S1 — S1 is COMPLEX.
  • S2 — S2 is COMPLEX.
    • S1 and S2 are the shifts defining K in (*) above. the way these two little icons define the whole product 😭
  • V — V is COMPLEX array, dimension (N). a scalar multiple of the first column of the matrix K in (*). that's the output, slay.

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. legends, honestly 🫶

Definition at line 106 of file claqr1.f. ⭐

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. not me being auto-generated 😭

ok that's the whole page bestie, go forth and bulge those double implicit shifts 💅✨

cute little sign-off: this was LAPACK, Version 3.12.0, dated /home/abui...RC/claqr1.f(3) — mwah 🍓
📦 where this page comes from