SRC/dlaqr1.f(3)

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🌈 SRC/dlaqr1.f 🌈

okay bestie, this page is from the Library Functions Manual, and it’s all about a Fortran subroutine that does one very specific little job. No cap, it’s giving “small but iconic” 💅.

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

  • subroutine dlaqr1 (n, h, ldh, sr1, si1, sr2, si2, v) — DLAQR1 sets a scalar multiple of the first column of the product of a 2-by-2 or 3-by-3 matrix H and the specified shifts. Slay.

🦋 Function/Subroutine Documentation 🦋

🌸 Function signature 🌸

subroutine dlaqr1 (integer n, double precision, dimension( ldh, * ) h,
       integer ldh, double precision sr1, double precision si1, double
       precision sr2, double precision si2, double precision, dimension( * ) v)

DLAQR1 sets a scalar multiple of the first column of the product of a 2-by-2 or 3-by-3 matrix H and the specified shifts. That’s the whole assignment, and it ate 💖.

💜 Purpose 💜

Given a 2-by-2 or 3-by-3 matrix H, DLAQR1 sets v to a scalar multiple of the first column of the product

(*)  K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)

and it does this scaling to avoid overflows and most underflows. Very “protect the math at all costs” energy, honestly 🫶.

It is assumed that either

  • 1) sr1 = sr2 and si1 = -si2

or

  • 2) si1 = si2 = 0.

This is useful for starting double implicit shift bulges in the QR algorithm. Yes bestie, “double implicit shift bulges” is the real phrase, and it’s lowkey iconic 😭.

🎀 Parameters 🎀

  • N — INTEGER. Order of the matrix H. N must be either 2 or 3.
  • H — DOUBLE PRECISION array, dimension (LDH,N). The 2-by-2 or 3-by-3 matrix H in (*).
  • LDH — INTEGER. The leading dimension of H as declared in the calling procedure. LDH >= N.
  • SR1 — DOUBLE PRECISION.
  • SI1 — DOUBLE PRECISION.
  • SR2 — DOUBLE PRECISION.
  • SI2 — DOUBLE PRECISION. The shifts in (*).
  • V — DOUBLE PRECISION 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 120 of file dlaqr1.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

Cute sign-off, bestie: this footer says LAPACK, Version 3.12.0, and SRC/dlaqr1.f(3) — no separate date shown, just the source/version vibe check 💜✨.

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