ZLAQZ3(3)

💖 ZLAQZ3(3) — LAPACK Library Functions Manual 💖

okay so bestie, welcome to the ZLAQZ3(3) page from the LAPACK Library Functions Manual ✨ no cap, this is a Fortran subroutine page and it's giving big linear-algebra main character energy.

🌸 NAME 🌸

The name is literally this file path, bestie:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlaqz3.f

🦋 SYNOPSIS 🦋

It lives under Functions/Subroutines 🫶 and the call looks like this:

subroutine ZLAQZ3 (ilschur, ilq, ilz, n, ilo, ihi, nshifts,
           nblock_desired, alpha, beta, a, lda, b, ldb, q, ldq, z, ldz, qc,
           ldqc, zc, ldzc, work, lwork, info)
           ZLAQZ3

💅 FUNCTION/SUBROUTINE DOCUMENTATION 💅

Full signature, every intent and dimension exactly as the page says — yes, even the goofy spacing, periodt:

subroutine ZLAQZ3 (logical, intent(in) ilschur, logical, intent(in) ilq,
       logical, intent(in) ilz, integer, intent(in) n, integer, intent(in) ilo,
       integer, intent(in) ihi, integer, intent(in) nshifts, integer,
       intent(in) nblock_desired, complex*16, dimension( * ), intent(inout)
       alpha, complex*16, dimension( * ), intent(inout) beta, complex*16,
       dimension( lda, * ), intent(inout) a, integer, intent(in) lda,
       complex*16, dimension( ldb, * ), intent(inout) b, integer, intent(in)
       ldb, complex*16, dimension( ldq,         * ), intent(inout) q, integer,
       intent(in) ldq, complex*16, dimension( ldz, * ), intent(inout) z,
       integer, intent(in) ldz, complex*16, dimension( ldqc, * ), intent(inout)
       qc, integer, intent(in) ldqc, complex*16, dimension( ldzc, * ),
       intent(inout) zc, integer, intent(in) ldzc, complex*16, dimension( * ),
       intent(inout) work, integer, intent(in) lwork, integer, intent(out)
       info)
       ZLAQZ3

🎀 Purpose 🎀

The source comment is short and iconic:

!> ZLAQZ3 Executes a single multishift QZ sweep

That's the whole vibe: one multishift QZ sweep, bestie 🌈.

🍓 Parameters 🍓

• ILSCHUR — ILSCHUR is LOGICAL. It decides whether or not to update the full Schur form, iykyk.
• ILQ — ILQ is LOGICAL. It decides whether or not to update the matrix Q.
• ILZ — ILZ is LOGICAL. It decides whether or not to update the matrix Z.
• N — N is INTEGER. The order of the matrices A, B, Q, and Z. N >= 0.
• ILO — ILO is INTEGER. That's it, that's the whole description on the page.
• IHI — IHI is INTEGER. Same energy: no extra description given.
• NSHIFTS — NSHIFTS is INTEGER. The desired number of shifts to use.
• NBLOCK_DESIRED — NBLOCK_DESIRED is INTEGER. The desired size of the computational windows.
• ALPHA — ALPHA is COMPLEX*16 array. The doc says SR contains the alpha parts of the shifts to use. Keeping SR exactly as written, no cap.
• BETA — BETA is COMPLEX*16 array. The doc says SS contains the scale of the shifts to use. Keeping SS exactly too.
• A — A is COMPLEX*16 array, dimension (LDA, N).
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max( 1, N ).
• B — B is COMPLEX*16 array, dimension (LDB, N).
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max( 1, N ).
• Q — Q is COMPLEX*16 array, dimension (LDQ, N).
• LDQ — LDQ is INTEGER. No extra description on the page.
• Z — Z is COMPLEX*16 array, dimension (LDZ, N).
• LDZ — LDZ is INTEGER. No extra description on the page.
• QC — QC is COMPLEX*16 array, dimension (LDQC, NBLOCK_DESIRED).
• LDQC — LDQC is INTEGER. No extra description on the page.
• ZC — ZC is COMPLEX*16 array, dimension (LDZC, NBLOCK_DESIRED).
• LDZC — LDZC is INTEGER. The page literally says LDZ is INTEGER here, so I'm preserving that typo exactly. Not me fixing it, bestie 💀.
• WORK — WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO >= 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= max(1,N).
  • If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
• INFO — INFO is INTEGER.
  • = 0: successful exit.
  • < 0: if INFO = -i, the i-th argument had an illegal value.

👑 AUTHOR 👑

Thijs Steel, KU Leuven.

⭐ DATE ⭐

May 2020.

Definition at line 204 of file zlaqz3.f.

🌈 AUTHOR (the Doxygen one) 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page 💜 this was LAPACK Version 3.12.0, dated May 2020, and the footer path is /home/abui...RC/zlaqz3.f(3) — catch u later, bestie 🫶✨