SRC/zlaqr1.f(3)

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✨ NAME ✨

SRC/zlaqr1.f — that's the whole name section, bestie. 🫶

🌈 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. 💖

🦋 Function/Subroutine Documentation 🦋

🌸 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 is there to avoid overflows and most underflows. ✨ This is useful for starting double implicit shift bulges in the QR algorithm. 🔥

🍓 Parameters

• N — N is INTEGER. It's the order of the matrix H, and N must be either 2 or 3. 👑
• H — H is COMPLEX*16 array, dimension (LDH,N). This is the 2-by-2 or 3-by-3 matrix H in (*). 🦋
• LDH — LDH is INTEGER. It's 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). This is 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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