SRC/claqr1.f(3)

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💖 SRC/claqr1.f — Library Functions Manual 💖

okay bestie, this is the page for SRC/claqr1.f, from the Library Functions Manual. It's giving LAPACK, it's giving QR-algorithm starter energy, and it's literally about a tiny helper that sets up shift bulges. Let's go. 🦋

✨ NAME ✨

SRC/claqr1.f

✨ 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. ✨

💖 Purpose 💖

Given a 2-by-2 or 3-by-3 matrix H, CLAQR1 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. No cap, that overflow avoidance matters. 😭

This is useful for starting double implicit shift bulges in the QR algorithm. Main character QR behavior, honestly. 👑

🌈 Parameters 🌈

⭐ N

N is INTEGER Order of the matrix H. N must be either 2 or 3.

⭐ H

H is COMPLEX array, dimension (LDH,N) The 2-by-2 or 3-by-3 matrix H in (*).

⭐ LDH

LDH is INTEGER The leading dimension of H as declared in the calling procedure. LDH >= N

⭐ S1

S1 is COMPLEX

⭐ S2

S2 is COMPLEX

S1 and S2 are the shifts defining K in (*) above.

⭐ V

V is COMPLEX array, dimension (N) A scalar multiple of the first column of the matrix K in (*).

🫶 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 at line 106 of file claqr1.f. 🔥

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

okay that's the whole thing, bestie. Footer vibes: LAPACK Version 3.12.0, SRC/claqr1.f(3) — periodt. 💜

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