SLAQZ3(3)

🌸 NAME 🌸

Bestie, welcome to SLAQZ3(3) from the LAPACK Library Functions Manual. The source file for this whole vibe is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slaqz3.f

That's the path, no cap. 🫶

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🦋 SYNOPSIS 🦋

Functions/Subroutines

recursive subroutine SLAQZ3 (ilschur, ilq, ilz, n, ilo, ihi, nw, a, lda,
    b, ldb, q, ldq, z, ldz, ns, nd, alphar, alphai, beta, qc, ldqc, zc,
    ldzc, work, lwork, rec, info)

SLAQZ3 — that's the routine, bestie. 💅

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💖 Function/Subroutine Documentation 💖

Here's the full signature in all its recursive glory, character-for-character:

recursive subroutine SLAQZ3 (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) nw, real,
    dimension( lda, * ), intent(inout) a, integer, intent(in) lda, real,
    dimension( ldb, * ), intent(inout) b, integer, intent(in) ldb, real,
    dimension( ldq, * ), intent(inout) q, integer, intent(in) ldq, real,
    dimension( ldz, * ), intent(inout) z, integer, intent(in) ldz, integer,
    intent(out) ns, integer, intent(out) nd, real, dimension( * ),
    intent(inout) alphar, real, dimension( * ), intent(inout) alphai, real,
    dimension( * ), intent(inout) beta, real, dimension( ldqc, * ) qc,
    integer, intent(in) ldqc, real, dimension( ldzc, * ) zc, integer,
    intent(in) ldzc, real, dimension( * ) work, integer, intent(in) lwork,
    integer, intent(in) rec, integer, intent(out) info)

SLAQZ3 — yes, the routine name pops up again. Main character energy. 👑

Purpose

Literal source-comment moment:

!>
!> SLAQZ3 performs AED
!>

That's the whole purpose line, bestie. It performs AED. Periodt. ✨

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🎀 Parameters 🎀

• ILSCHUR — ILSCHUR is LOGICAL. Determines whether or not to update the full Schur form. 💅
• ILQ — ILQ is LOGICAL. Determines whether or not to update the matrix Q.
• ILZ — ILZ is LOGICAL. Determines 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 description.
• IHI — IHI is INTEGER. ILO and IHI mark the rows and columns of (A,B) which are to be normalized.
• NW — NW is INTEGER. The desired size of the deflation window.
• A — A is REAL array, dimension (LDA, N).
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max( 1, N ).
• B — B is REAL array, dimension (LDB, N).
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max( 1, N ).
• Q — Q is REAL array, dimension (LDQ, N).
• LDQ — LDQ is INTEGER. No extra lore here, that's literally it.
• Z — Z is REAL array, dimension (LDZ, N).
• LDZ — LDZ is INTEGER. Also just that.
• NS — NS is INTEGER. The number of unconverged eigenvalues available to use as shifts. 🔥
• ND — ND is INTEGER. The number of converged eigenvalues found.
• ALPHAR — ALPHAR is REAL array, dimension (N). The real parts of each scalar alpha defining an eigenvalue of GNEP.
• ALPHAI — ALPHAI is REAL array, dimension (N). The imaginary parts of each scalar alpha defining an eigenvalue of GNEP. If ALPHAI(j) is zero, then the j-th eigenvalue is real; if positive, then the j-th and (j+1)-st eigenvalues are a complex conjugate pair, with ALPHAI(j+1) = -ALPHAI(j). 🌀
• BETA — BETA is REAL array, dimension (N). The scalars beta that define the eigenvalues of GNEP. Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and beta = BETA(j) represent the j-th eigenvalue of the matrix pair (A,B), in one of the forms lambda = alpha/beta or mu = beta/alpha.

Since either lambda or mu may overflow, they should not, in general, be computed. ⚠️

• QC — QC is REAL array, dimension (LDQC, NW).
• LDQC — LDQC is INTEGER. Simple. Clean. Iconic.
• ZC — ZC is REAL array, dimension (LDZC, NW).
• LDZC — LDZ is INTEGER. Yes bestie, the source literally says LDZ here under LDZC — copy-paste energy, but we're keeping it exactly as written. 🙈
• WORK — WORK is REAL 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.

• REC — REC is INTEGER. REC indicates the current recursion level. Should be set to 0 on first call. 🪆
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

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👑 Author 👑

Thijs Steel, KU Leuven

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🎀 Date 🎀

May 2020

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Definition at line 234 of file slaqz3.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Okay that's the whole page, bestie 🫶. Cute sign-off: LAPACK, Version 3.12.0, May 2020, page path /home/abui...RC/slaqz3.f(3). Now go slay those eigenvalues ✨💅 periodt.