laqr1(3)

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version 3.12.1 · 9 versions
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okay bestie, welcome to laqr1(3) from the Library Functions Manual — the page about a tiny but iconic step in hseqr 💅✨

🎀 NAME 🎀

laqr1 — laqr1: step in hseqr 💖

🌸 SYNOPSIS 🌸

💖 Functions 💖

  • 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.
  • subroutine dlaqr1 (n, h, ldh, sr1, si1, sr2, si2, v) — DLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.
  • subroutine slaqr1 (n, h, ldh, sr1, si1, sr2, si2, v) — SLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.
  • 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.

🌈 DETAILED DESCRIPTION 🌈

the detailed description is basically the function docs below, bestie — keep scrolling for the full tea 🫖🫶

👑 FUNCTION DOCUMENTATION 👑

🧚 subroutine claqr1 🧚

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 ✨

okay so, 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. ✨

this is useful for starting double implicit shift bulges in the QR algorithm. 💅

🎀 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.

💫 subroutine dlaqr1 💫

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 2-by-2 or 3-by-3 matrix H and specified shifts.

✨ Purpose ✨

okay so, 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)

scaling to avoid overflows and most underflows. 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. 💅

🎀 Parameters 🎀

  • N — N is INTEGER; order of the matrix H. N must be either 2 or 3.
  • H — H is DOUBLE PRECISION 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.
  • SR1 — SR1 is DOUBLE PRECISION.
  • SI1 — SI1 is DOUBLE PRECISION.
  • SR2 — SR2 is DOUBLE PRECISION.
  • SI2 — SI2 is DOUBLE PRECISION; the shifts in (*).
  • V — V is 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.

🌸 subroutine slaqr1 🌸

subroutine slaqr1 (integer n, real, dimension( ldh, * ) h, integer ldh, real sr1, real si1, real sr2, real si2, real, dimension( * ) v)

SLAQR1 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 ✨

okay so, given a 2-by-2 or 3-by-3 matrix H, SLAQR1 sets v to a scalar multiple of the first column of the product

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

scaling to avoid overflows and most underflows. 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. 💅

🎀 Parameters 🎀

  • N — N is INTEGER; order of the matrix H. N must be either 2 or 3.
  • H — H is REAL 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.
  • SR1 — SR1 is REAL.
  • SI1 — SI1 is REAL.
  • SR2 — SR2 is REAL.
  • SI2 — SI2 is REAL; the shifts in (*).
  • V — V is REAL 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 slaqr1.f.

🦋 subroutine zlaqr1 🦋

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 ✨

okay so, 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. 💅

🎀 Parameters 🎀

  • N — N is INTEGER; order of the matrix H. N must be either 2 or 3.
  • H — H is COMPLEX*16 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*16.
  • S2 — S2 is COMPLEX*16; S1 and S2 are the shifts defining K in (*) above.
  • V — V is COMPLEX*16 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 zlaqr1.f.

📜 AUTHOR 📜

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