SRC/claqr5.f(3)

💖 SRC/claqr5.f(3) 💖

okay bestie, welcome to the Library Functions Manual page for SRC/claqr5.f(3) — yes, the claqr5 one, and it’s giving full LAPACK main-character energy. no cap, we’re getting into a single small-bulge multi-shift QR sweep. 🦋

🌸 NAME 🌸

SRC/claqr5.f

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine claqr5 (wantt, wantz, kacc22, n, ktop, kbot, nshfts, s, h,
    ldh, iloz, ihiz, z, ldz, v, ldv, u, ldu, nv, wv, ldwv, nh, wh, ldwh)

CLAQR5 performs a single small-bulge multi-shift QR sweep.

🫶 Function/Subroutine Documentation 🫶

subroutine claqr5 (logical wantt, logical wantz, integer kacc22, integer n,
    integer ktop, integer kbot, integer nshfts, complex, dimension( * ) s,
    complex, dimension( ldh, * ) h, integer ldh, integer iloz, integer ihiz,
    complex, dimension( ldz, * ) z, integer ldz, complex, dimension( ldv, *
    ) v, integer ldv, complex, dimension( ldu, * ) u, integer ldu, integer
    nv, complex, dimension( ldwv, * ) wv, integer ldwv, integer nh, complex,
    dimension( ldwh, * ) wh, integer ldwh)

CLAQR5 performs a single small-bulge multi-shift QR sweep. periodt.

🌟 Purpose 🌟

okay so the purpose is literally this: CLAQR5 is called by CLAQR0 and performs a single small-bulge multi-shift QR sweep. that’s the whole vibe, bestie. 💅

🎀 Parameters 🎀

WANTT 💖

WANTT is LOGICAL. WANTT = .true. if the triangular Schur factor is being computed. WANTT is set to .false. otherwise. slay.

WANTZ 🦋

WANTZ is LOGICAL. WANTZ = .true. if the unitary Schur factor is being computed. WANTZ is set to .false. otherwise.

KACC22 🔥

KACC22 is INTEGER with value 0, 1, or 2. It specifies the computation mode of far-from-diagonal orthogonal updates. the tea:

• = 0: CLAQR5 does not accumulate reflections and does not use matrix-matrix multiply to update far-from-diagonal matrix entries.
• = 1: CLAQR5 accumulates reflections and uses matrix-matrix multiply to update the far-from-diagonal matrix entries.
• = 2: Same as KACC22 = 1. This option used to enable exploiting the 2-by-2 structure during matrix multiplications, but this is no longer supported.

⚠️ bestie, KACC22 = 2 is the same as KACC22 = 1; the old 2-by-2-structure trick is no longer supported. not me mourning the deprecated option 💀

N 🌈

N is INTEGER. N is the order of the Hessenberg matrix H upon which this subroutine operates.

KTOP 🎀

KTOP is INTEGER.

KBOT 💜

KBOT is INTEGER. These are the first and last rows and columns of an isolated diagonal block upon which the QR sweep is to be applied. It is assumed without a check that either KTOP = 1 or H(KTOP,KTOP-1) = 0 and either KBOT = N or H(KBOT+1,KBOT) = 0.

NSHFTS ✨

NSHFTS is INTEGER. NSHFTS gives the number of simultaneous shifts. NSHFTS must be positive and even. no odd numbers allowed, bestie 🫶

S 🍓

S is COMPLEX array, dimension (NSHFTS). S contains the shifts of origin that define the multi-shift QR sweep. On output S may be reordered.

H 🔥

H is COMPLEX array, dimension (LDH,N). On input H contains a Hessenberg matrix. On output a multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied to the isolated diagonal block in rows and columns KTOP through KBOT.

LDH 💅

LDH is INTEGER. LDH is the leading dimension of H just as declared in the calling procedure. LDH >= MAX(1,N).

ILOZ 🌸

ILOZ is INTEGER.

IHIZ 🦋

IHIZ is INTEGER. Specify the rows of Z to which transformations must be applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N.

Z 👑

Z is COMPLEX array, dimension (LDZ,IHIZ). If WANTZ = .TRUE., then the QR Sweep unitary similarity transformation is accumulated into Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. If WANTZ = .FALSE., then Z is unreferenced.

LDZ 💀

LDZ is INTEGER. The original line says LDA is the leading dimension of Z just as declared in the calling procedure. LDZ >= N. yes bestie, that LDA is the source’s little typo moment — iconic, honestly 🙈

V 🧚

V is COMPLEX array, dimension (LDV,NSHFTS/2).

LDV ⭐

LDV is INTEGER. LDV is the leading dimension of V as declared in the calling procedure. LDV >= 3.

U 💜

U is COMPLEX array, dimension (LDU,2*NSHFTS).

LDU 😭

LDU is INTEGER. LDU is the leading dimension of U just as declared in the in the calling subroutine. LDU >= 2*NSHFTS. yes, “in the in the” is really in there — no cap 💀

NV 🌈

NV is INTEGER. NV is the number of rows in WV agailable for workspace. NV >= 1. that’s the original spelling, bestie — agailable ate and left no crumbs 🍓

WV 🎀

WV is COMPLEX array, dimension (LDWV,2*NSHFTS).

LDWV 💖

LDWV is INTEGER. LDWV is the leading dimension of WV as declared in the in the calling subroutine. LDWV >= NV.

NH ✨

NH is INTEGER. NH is the number of columns in array WH available for workspace. NH >= 1.

WH 🦋

WH is COMPLEX array, dimension (LDWH,NH).

LDWH 🔥

LDWH is INTEGER. Leading dimension of WH just as declared in the calling procedure. LDWH >= 2*NSHFTS.

👑 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
• Lars Karlsson, Daniel Kressner, and Bruno Lang
• Thijs Steel, Department of Computer science, KU Leuven, Belgium

📚 References: 📚

• K. Braman, R. Byers and R. Mathias, The Multi-Shift QR Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 Performance, SIAM Journal of Matrix Analysis, volume 23, pages 929--947, 2002.
• Lars Karlsson, Daniel Kressner, and Bruno Lang, Optimally packed chains of bulges in multishift QR algorithms. ACM Trans. Math. Softw. 40, 2, Article 12 (February 2014).

Definition at line 254 of file claqr5.f.

💻 Author 💻

Generated automatically by Doxygen for LAPACK from the source code.

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that’s the whole page, bestie — stay slay and may your QR sweeps be small-bulge and multi-shift 💖✨ signed, your LAPACK bestie: source SRC/claqr5.f(3), LAPACK Version 3.12.0 🎀