SLAQR5(3)

💅 SLAQR5(3) 💅

okay so bestie, welcome to SLAQR5(3) from the Library Functions Manual — this is the LAPACK page for a real one: SLAQR5. It’s giving “small-bulge multi-shift QR sweep” main character energy, and honestly? Iconic. 🫶

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slaqr5.f

yes, that whole path is literally the NAME entry. no cap. 💅

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🌸 SYNOPSIS 🌸

💖 Functions/Subroutines 💖

subroutine SLAQR5 (wantt, wantz, kacc22, n, ktop, kbot, nshfts, sr, si,
    h, ldh, iloz, ihiz, z, ldz, v, ldv, u, ldu, nv, wv, ldwv, nh, wh,
    ldwh)
    SLAQR5 performs a single small-bulge multi-shift QR sweep.

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🦋 Function/Subroutine Documentation 🦋

🧚 subroutine SLAQR5 🧚

subroutine SLAQR5 (logical wantt, logical wantz, integer kacc22, integer n,
    integer ktop, integer kbot, integer nshfts, real, dimension( * ) sr,
    real, dimension( * ) si, real, dimension( ldh, * ) h, integer ldh,
    integer iloz, integer ihiz, real, dimension( ldz, * ) z, integer ldz,
    real, dimension( ldv, * ) v, integer ldv, real, dimension( ldu, * ) u,
    integer ldu, integer nv, real, dimension( ldwv, * ) wv, integer ldwv,
    integer nh, real, dimension( ldwh, * ) wh, integer ldwh)

SLAQR5 performs a single small-bulge multi-shift QR sweep. that’s the whole vibe, and it ate. ✨

Purpose:

!>
!>    SLAQR5, called by SLAQR0, performs a
!>    single small-bulge multi-shift QR sweep.
!>

Parameters

• WANTT — WANTT is LOGICAL. WANTT = .true. if the quasi-triangular Schur factor is being computed. WANTT is set to .false. otherwise.
• WANTZ — WANTZ is LOGICAL. WANTZ = .true. if the orthogonal 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.
  • = 0: SLAQR5 does not accumulate reflections and does not use matrix-matrix multiply to update far-from-diagonal matrix entries.
  • = 1: SLAQR5 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. 🫠
• 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.
• SR — SR is REAL array, dimension (NSHFTS).
• SI — SI is REAL array, dimension (NSHFTS). SR contains the real parts and SI contains the imaginary parts of the NSHFTS shifts of origin that define the multi-shift QR sweep. On output SR and SI may be reordered.
• H — H is REAL 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 REAL array, dimension (LDZ,IHIZ). If WANTZ = .TRUE., then the QR Sweep orthogonal 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 text says LDA is the leading dimension of Z just as declared in the calling procedure. LDZ >= N. yes bestie, it literally says LDA there — we’re keeping the detail exactly as it appears. 🙈
• V — V is REAL 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 REAL 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.
• NV — NV is INTEGER. NV is the number of rows in WV available for workspace. NV >= 1. (the original spells it agailable — keeping that exact energy 🍓)
• WV — WV is REAL 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 REAL array, dimension (LDWH,NH).
• LDWH — LDWH is INTEGER. Leading dimension of WH just as declared in the calling procedure. LDWH >= 2*NSHFTS.

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👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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🌈 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

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🔥 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).

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📌 Definition at line 262 of file slaqr5.f.

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💀 Author 💀

Generated automatically by Doxygen for LAPACK from the source code.

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💖 cute little footer sign-off: LAPACK, Version 3.12.0, and /home/abui...RC/slaqr5.f(3) — no date listed in the footer, just those source/version deets. periodt. 🫶