ZLAQR3(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 ZLAQR3(3) 💅

okay so bestie, welcome to the Library Functions Manual entry for /home/abui...RC/zlaqr3.f(3) — yes that's the real header, we're not copying it, we're honoring it. This is the page for ZLAQR3, an absolute icon of a subroutine that does aggressive early deflation. no cap. 🎀

🦋 NAME 🦋

The file in question, in all its glorious path-ness:

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/SRC/zlaqr3.f

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine ZLAQR3 (wantt, wantz, n, ktop, kbot, nw, h, ldh, iloz, ihiz,
    z, ldz, ns, nd, sh, v, ldv, nh, t, ldt, nv, wv, ldwv, work, lwork)

ZLAQR3 performs the unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation). it's giving main character energy, honestly 👑

💜 Function/Subroutine Documentation 💜

subroutine ZLAQR3 (logical wantt, logical wantz, integer n, integer ktop,
    integer kbot, integer nw, complex*16, dimension( ldh, * ) h, integer
    ldh, integer iloz, integer ihiz, complex*16, dimension( ldz, * ) z,
    integer ldz, integer ns, integer nd, complex*16, dimension( * ) sh,
    complex*16, dimension( ldv, * ) v, integer ldv, integer nh, complex*16,
    dimension( ldt, * ) t, integer ldt, integer nv, complex*16, dimension(
    ldwv, * ) wv, integer ldwv, complex*16, dimension( * ) work, integer
    lwork)

ZLAQR3 performs the unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation). same energy, second mention, because she deserves it 🫶

🔥 Purpose 🔥

okay so, aggressive early deflation, bestie:

ZLAQR3 accepts as input an upper Hessenberg matrix H and performs an unitary similarity transformation designed to detect and deflate fully converged eigenvalues from a trailing principal submatrix. On output H has been over-written by a new Hessenberg matrix that is a perturbation of an unitary similarity transformation of H. It is to be hoped that the final version of H has many zero subdiagonal entries. 🤞 like, manifesting that for you fr fr.

🎀 Parameters 🎀

  • WANTT — WANTT is LOGICAL. If .TRUE., then the Hessenberg matrix H is fully updated so that the triangular Schur factor may be computed (in cooperation with the calling subroutine). If .FALSE., then only enough of H is updated to preserve the eigenvalues. 💫
  • WANTZ — WANTZ is LOGICAL. If .TRUE., then the unitary matrix Z is updated so that the unitary Schur factor may be computed (in cooperation with the calling subroutine). If .FALSE., then Z is not referenced. she's simply not invited to the function 💀
  • N — N is INTEGER. The order of the matrix H and (if WANTZ is .TRUE.) the order of the unitary matrix Z. 📐
  • KTOP — KTOP is INTEGER. It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0. KBOT and KTOP together determine an isolated block along the diagonal of the Hessenberg matrix. the duo we didn't know we needed 🫶
  • KBOT — KBOT is INTEGER. It is assumed without a check that either KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together determine an isolated block along the diagonal of the Hessenberg matrix. ngl "without a check" is so real of her 🙈
  • NW — NW is INTEGER. Deflation window size. 1 <= NW <= (KBOT-KTOP+1). 📏 keep it in range bestie.
  • H — H is COMPLEX*16 array, dimension (LDH,N). On input the initial N-by-N section of H stores the Hessenberg matrix undergoing aggressive early deflation. On output H has been transformed by a unitary similarity transformation, perturbed, and the returned to Hessenberg form that (it is to be hoped) has some zero subdiagonal entries. glow-up arc complete ✨
  • LDH — LDH is INTEGER. Leading dimension of H just as declared in the calling subroutine. N <= LDH. 🧚
  • ILOZ — ILOZ is INTEGER. that's it, that's the whole description. she said minimal effort, maximum vibe 💅
  • 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*16 array, dimension (LDZ,N). IF WANTZ is .TRUE., then on output, the unitary similarity transformation mentioned above has been accumulated into Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. If WANTZ is .FALSE., then Z is unreferenced. not read, not written, not perceived 👑
  • LDZ — LDZ is INTEGER. The leading dimension of Z just as declared in the calling subroutine. 1 <= LDZ. ⭐
  • NS — NS is INTEGER. The number of unconverged (ie approximate) eigenvalues returned in SR and SI that may be used as shifts by the calling subroutine. (yes, SR and SI, we're quoting her exactly, don't come for me 😭)
  • ND — ND is INTEGER. The number of converged eigenvalues uncovered by this subroutine. found them, they were converged the whole time 🌈
  • SH — SH is COMPLEX*16 array, dimension (KBOT). On output, approximate eigenvalues that may be used for shifts are stored in SH(KBOT-ND-NS+1) through SR(KBOT-ND). Converged eigenvalues are stored in SH(KBOT-ND+1) through SH(KBOT). (again with the SR, that's literally what the original says, keeping it verbatim 🫶)
  • V — V is COMPLEX*16 array, dimension (LDV,NW). An NW-by-NW work array. just vibing in the background 💜
  • LDV — LDV is INTEGER. The leading dimension of V just as declared in the calling subroutine. NW <= LDV. 🎀
  • NH — NH is INTEGER. The number of columns of T. NH >= NW. 📊
  • T — T is COMPLEX*16 array, dimension (LDT,NW). no further notes, she's mysterious like that 🦋
  • LDT — LDT is INTEGER. The leading dimension of T just as declared in the calling subroutine. NW <= LDT. 🧚
  • NV — NV is INTEGER. The number of rows of work array WV available for workspace. NV >= NW. 💫
  • WV — WV is COMPLEX*16 array, dimension (LDWV,NW). (that's it, that's all she wrote 💅)
  • LDWV — LDWV is INTEGER. The leading dimension of W just as declared in the calling subroutine. NW <= LDV. ⚠️ note: it really does say "W" and it really does say LDV — I'm not touching that, that's canon.
  • WORK — WORK is COMPLEX*16 array, dimension (LWORK). On exit, WORK(1) is set to an estimate of the optimal value of LWORK for the given values of N, NW, KTOP and KBOT. 📈
  • LWORK — LWORK is INTEGER. The dimension of the work array WORK. LWORK = 2*NW suffices, but greater efficiency may result from larger values of LWORK.
If LWORK = -1, then a workspace query is assumed; ZLAQR3 only estimates the optimal workspace size for the given values of N, NW, KTOP and KBOT. The estimate is returned in WORK(1). No error message related to LWORK is issued by XERBLA. Neither H nor Z are accessed. 🕵️ like, they're not even looked at. iconique.

🌟 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. absolute legends, we stan 🫶

⭐ Definition at line 264 of file zlaqr3.f. ⭐

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. (a bot wrote this, and honestly? it ate 🤖✨)

and that's the whole page babes — LAPACK Version 3.12.0, /home/abui...RC/zlaqr3.f(3), no facts dropped, no flags merged, periodt 💅

📦 where this page comes from