ZLAQR5(3)

💅 ZLAQR5(3) — Library Functions Manual 💅

Okay so this is the Library Functions Manual page for ZLAQR5(3), and the header path is literally /home/abui...RC/zlaqr5.f(3). Bestie, it’s giving “serious Fortran business,” but make it cute: this whole page is about one subroutine doing a small-bulge multi-shift QR sweep. Let’s go. ✨

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlaqr5.f

That’s the file path, no cap.

🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines 🎀

subroutine ZLAQR5 (wantt, wantz, kacc22, n, ktop, kbot, nshfts, s, h,
    ldh, iloz, ihiz, z, ldz, v, ldv, u, ldu, nv, wv, ldwv, nh, wh, ldwh)

ZLAQR5 performs a single small-bulge multi-shift QR sweep. That’s the whole vibe. 👑

💖 Function/Subroutine Documentation 💖

subroutine ZLAQR5 (logical wantt, logical wantz, integer kacc22, integer n,
    integer ktop, integer kbot, integer nshfts, complex*16, dimension( * )
    s, complex*16, dimension( ldh, * ) h, integer ldh, integer iloz, integer
    ihiz, complex*16, dimension( ldz, * ) z, integer ldz, complex*16,
    dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldu, * ) u,
    integer ldu, integer nv, complex*16, dimension( ldwv, * ) wv, integer
    ldwv, integer nh, complex*16, dimension( ldwh, * ) wh, integer ldwh)

ZLAQR5 performs a single small-bulge multi-shift QR sweep. Yes, again — it’s the main character. 💅

🎯 Purpose 🎯

ZLAQR5, called by ZLAQR0, performs a single small-bulge multi-shift QR sweep. Periodt.

🧩 Parameters 🧩

• WANTT — LOGICAL. WANTT = .true. if the triangular Schur factor is being computed. WANTT is set to .false. otherwise.
• WANTZ — LOGICAL. WANTZ = .true. if the unitary Schur factor is being computed. WANTZ is set to .false. otherwise.
• KACC22 — INTEGER with value 0, 1, or 2. Specifies the computation mode of far-from-diagonal orthogonal updates.
  • = 0: ZLAQR5 does not accumulate reflections and does not use matrix-matrix multiply to update far-from-diagonal matrix entries.
  • = 1: ZLAQR5 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 — INTEGER. N is the order of the Hessenberg matrix H upon which this subroutine operates.
• KTOP — INTEGER.
• KBOT — 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 — INTEGER. NSHFTS gives the number of simultaneous shifts. NSHFTS must be positive and even.
• S — COMPLEX*16 array, dimension (NSHFTS). S contains the shifts of origin that define the multi-shift QR sweep. On output S may be reordered.
• H — COMPLEX*16 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 — INTEGER. LDH is the leading dimension of H just as declared in the calling procedure. LDH >= MAX(1,N).
• ILOZ — INTEGER.
• IHIZ — INTEGER. Specify the rows of Z to which transformations must be applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N.
• Z — COMPLEX*16 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 — INTEGER. The page says LDA is the leading dimension of Z just as declared in the calling procedure. LDZ >= N.
• V — COMPLEX*16 array, dimension (LDV,NSHFTS/2).
• LDV — INTEGER. LDV is the leading dimension of V as declared in the calling procedure. LDV >= 3.
• U — COMPLEX*16 array, dimension (LDU,2*NSHFTS).
• LDU — INTEGER. LDU is the leading dimension of U just as declared in the in the calling subroutine. LDU >= 2*NSHFTS.
• NV — INTEGER. NV is the number of rows in WV agailable for workspace. NV >= 1.
• WV — COMPLEX*16 array, dimension (LDWV,2*NSHFTS).
• LDWV — INTEGER. LDWV is the leading dimension of WV as declared in the in the calling subroutine. LDWV >= NV.
• NH — INTEGER. NH is the number of columns in array WH available for workspace. NH >= 1.
• WH — COMPLEX*16 array, dimension (LDWH,NH).
• LDWH — 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 zlaqr5.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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Catch you later, bestie 🫶 — this one’s from LAPACK Version 3.12.0 and the footer path is /home/abui...RC/zlaqr5.f(3). No date on the page, so I’m not inventing one. Mwah 💋