laqz1(3)

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🎀 laqz1 🎀

okay so bestie, this one is from the Library Functions Manual, and the manual name is literally laqz1 — it's a section 3 kinda situation (that's laqz1(3) if you're keeping score 💅). It's giving "step in ggev3, gges3" energy. Let's get into it 🌸

✨ NAME ✨

laqz1 — no cap, that's the name. And the vibe is: laqz1: step in ggev3, gges3. That's the whole name section, we love a concise icon 👑

🌈 SYNOPSIS 🌈

💜 Functions

subroutine claqz1 (ilq, ilz, k, istartm, istopm, ihi, a, lda, b, ldb, nq, qstart, q, ldq, nz, zstart, z, ldz) — this one's CLAQZ1
subroutine dlaqz1 (a, lda, b, ldb, sr1, sr2, si, beta1, beta2, v) — this one's DLAQZ1
subroutine slaqz1 (a, lda, b, ldb, sr1, sr2, si, beta1, beta2, v) — this one's SLAQZ1
subroutine zlaqz1 (ilq, ilz, k, istartm, istopm, ihi, a, lda, b, ldb, nq, qstart, q, ldq, nz, zstart, z, ldz) — and this one's ZLAQZ1

Like yes, there's four of them, one for each flavour of precision, and they all show up in the synopsis first because that's how we do 💖

🦋 Detailed Description 🦋

So the "Detailed Description" section exists, it's in the original, and it is — and I cannot stress this enough — completely empty. Not one word. Just the heading sitting there, main character energy, saying nothing. I respect it tbh 💀✨

🔥 Function Documentation 🔥

💅 subroutine claqz1

subroutine claqz1 (logical, intent(in) ilq, logical, intent(in) ilz,
    integer, intent(in) k, integer, intent(in) istartm, integer, intent(in)
    istopm, integer, intent(in) ihi, complex, dimension( lda, * ) a,
    integer, intent(in) lda, complex, dimension( ldb, * ) b, integer,
    intent(in) ldb, integer, intent(in) nq, integer, intent(in) qstart,
    complex, dimension( ldq, * ) q, integer, intent(in) ldq, integer,
    intent(in) nz, integer, intent(in) zstart, complex, dimension( ldz, * )
    z, integer, intent(in) ldz)

🫶 CLAQZ1

⭐ Purpose

CLAQZ1 chases a 1x1 shift bulge in a matrix pencil down a single position

that's it. that's the purpose. it's chasing a lil 1x1 shift bulge down exactly one position and honestly? go off 🦋

🍓 Parameters

ILQ — ILQ is LOGICAL. It decides whether or not we're updating the matrix Q. simple as that, no notes 💅
ILZ — ILZ is LOGICAL. Same deal but for the matrix Z — are we updating it or not? you decide, queen 👑
K — K is INTEGER. It's the index telling you where the bulge is hanging out. On entry, the bulge is located in (A(k+1,k),B(k+1,k)). On exit, the bulge is located in (A(k+2,k+1),B(k+2,k+1)). It literally moved one step, that's the whole gig 🚶‍♀️
ISTARTM — ISTARTM is INTEGER. That's the whole description. iconic minimalism ✨
ISTOPM — ISTOPM is INTEGER. Updates to (A,B) are restricted to (istartm:k+2,k:istopm). And it's assumed — without checking — that istartm <= k+1 and k+2 <= istopm. so like, it trusts you. don't make it regret that 🫶
IHI — IHI is INTEGER. once again, that's all it says 💀
A — A is COMPLEX array, dimension (LDA,N) 🎀
LDA — LDA is INTEGER. The leading dimension of A as declared in the calling procedure.
B — B is COMPLEX array, dimension (LDB,N) 🎀
LDB — LDB is INTEGER. The leading dimension of B as declared in the calling procedure.
NQ — NQ is INTEGER. The order of the matrix Q. periodt.
QSTART — QSTART is INTEGER. Start index of the matrix Q. Rotations are applied to columns k+2-qStart:k+3-qStart of Q. yes, exactly those ones 🌀
Q — Q is COMPLEX array, dimension (LDQ,NQ) 🎀
LDQ — LDQ is INTEGER. The leading dimension of Q as declared in the calling procedure.
NZ — NZ is INTEGER. The order of the matrix Z. slay.
ZSTART — ZSTART is INTEGER. Start index of the matrix Z. Rotations are applied to columns k+1-qStart:k+2-qStart of Z. (and yes, it genuinely says qStart in there — I'm just telling you what it says, I don't make the rules 🙈)
Z — Z is COMPLEX array, dimension (LDZ,NZ) 🎀
LDZ — LDZ is INTEGER. The leading dimension of Q as declared in the calling procedure. (again — it says Q. that's the original's whole thing, I'm not touching it 🫠)

🌸 Author

Thijs Steel, KU Leuven 👑

🌈 Date

May 2020

💜 Definition at line 171 of file claqz1.f.

🧚 subroutine dlaqz1

subroutine dlaqz1 (double precision, dimension( lda, * ), intent(in) a,
    integer, intent(in) lda, double precision, dimension( ldb, * ),
    intent(in) b, integer, intent(in) ldb, double precision, intent(in) sr1,
    double precision, intent(in) sr2, double precision, intent(in) si,
    double precision, intent(in) beta1, double precision, intent(in) beta2,
    double precision, dimension( * ), intent(out) v)

🫶 DLAQZ1

⭐ Purpose

Given a 3-by-3 matrix pencil (A,B), DLAQZ1 sets v to a scalar multiple of the first column of the product:

(*)  K = (A - (beta2*sr2 - i*si)*B)*B^(-1)*(beta1*A - (sr2 + i*si2)*B)*B^(-1).

It is assumed that either:

sr1 = sr2
si = 0

And why do we care? Because this is useful for starting double implicit shift bulges in the QZ algorithm. that's the tea ☕✨

🍓 Parameters

A — A is DOUBLE PRECISION array, dimension (LDA,N). It's the 3-by-3 matrix A in (*).
LDA — LDA is INTEGER. The leading dimension of A as declared in the calling procedure.
B — B is DOUBLE PRECISION array, dimension (LDB,N). It's the 3-by-3 matrix B in (*).
LDB — LDB is INTEGER. The leading dimension of B as declared in the calling procedure.
SR1 — SR1 is DOUBLE PRECISION. (that's the whole note, bestie 🎀)
SR2 — SR2 is DOUBLE PRECISION.
SI — SI is DOUBLE PRECISION.
BETA1 — BETA1 is DOUBLE PRECISION.
BETA2 — BETA2 is DOUBLE PRECISION.
V — V is DOUBLE PRECISION array, dimension (N). On the way out it's a scalar multiple of the first column of the matrix K in (*). so it's doing the actual delivering 💐

🌸 Author

Thijs Steel, KU Leuven 👑

🌈 Date

May 2020

💜 Definition at line 125 of file dlaqz1.f.

🦋 subroutine slaqz1

subroutine slaqz1 (real, dimension( lda, * ), intent(in) a, integer,
    intent(in) lda, real, dimension( ldb, * ), intent(in) b, integer,
    intent(in) ldb, real, intent(in) sr1, real, intent(in) sr2, real,
    intent(in) si, real, intent(in) beta1, real, intent(in) beta2, real,
    dimension( * ), intent(out) v)

🫶 SLAQZ1

⭐ Purpose

Given a 3-by-3 matrix pencil (A,B), SLAQZ1 sets v to a scalar multiple of the first column of the product:

(*)  K = (A - (beta2*sr2 - i*si)*B)*B^(-1)*(beta1*A - (sr2 + i*si2)*B)*B^(-1).

It is assumed that either:

sr1 = sr2
si = 0

This is useful for starting double implicit shift bulges in the QZ algorithm. same energy, different precision 💅

🍓 Parameters

A — A is REAL array, dimension (LDA,N). The 3-by-3 matrix A in (*).
LDA — LDA is INTEGER. The leading dimension of A as declared in the calling procedure.
B — B is REAL array, dimension (LDB,N). The 3-by-3 matrix B in (*).
LDB — LDB is INTEGER. The leading dimension of B as declared in the calling procedure.
SR1 — SR1 is REAL. yep 🎀
SR2 — SR2 is REAL.
SI — SI is REAL.
BETA1 — BETA1 is REAL.
BETA2 — BETA2 is REAL.
V — V is REAL array, dimension (N). A scalar multiple of the first column of the matrix K in (*). 💐

🌸 Author

Thijs Steel, KU Leuven 👑

🌈 Date

May 2020

💜 Definition at line 125 of file slaqz1.f.

🎀 subroutine zlaqz1

subroutine zlaqz1 (logical, intent(in) ilq, logical, intent(in) ilz,
    integer, intent(in) k, integer, intent(in) istartm, integer, intent(in)
    istopm, integer, intent(in) ihi, complex*16, dimension( lda, * ) a,
    integer, intent(in) lda, complex*16, dimension( ldb, * ) b, integer,
    intent(in) ldb, integer, intent(in) nq, integer, intent(in) qstart,
    complex*16, dimension( ldq, * ) q, integer, intent(in) ldq, integer,
    intent(in) nz, integer, intent(in) zstart, complex*16, dimension( ldz, *
    ) z, integer, intent(in) ldz)

🫶 ZLAQZ1

⭐ Purpose

ZLAQZ1 chases a 1x1 shift bulge in a matrix pencil down a single position

same little bulge, same single position, but make it COMPLEX*16 💅✨

🍓 Parameters

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.
K — K is INTEGER. Index indicating the position of the bulge. On entry, the bulge is located in (A(k+1,k),B(k+1,k)). On exit, the bulge is located in (A(k+2,k+1),B(k+2,k+1)). it moved, that's the update 📍
ISTARTM — ISTARTM is INTEGER.
ISTOPM — ISTOPM is INTEGER. Updates to (A,B) are restricted to (istartm:k+2,k:istopm). It is assumed without checking that istartm <= k+1 and k+2 <= istopm. again — no checking, so behave 🫶
IHI — IHI is INTEGER.
A — A is COMPLEX*16 array, dimension (LDA,N) 🎀
LDA — LDA is INTEGER. The leading dimension of A as declared in the calling procedure.
B — B is COMPLEX*16 array, dimension (LDB,N) 🎀
LDB — LDB is INTEGER. The leading dimension of B as declared in the calling procedure.
NQ — NQ is INTEGER. The order of the matrix Q.
QSTART — QSTART is INTEGER. Start index of the matrix Q. Rotations are applied to columns k+2-qStart:k+3-qStart of Q.
Q
Q — Q is a COMPLEX*16 array, dimension (LDQ,NQ). 💅
LDQ — LDQ is INTEGER; the leading dimension of Q as declared in the calling procedure. ✨
NZ — NZ is INTEGER; the order of the matrix Z. 🦋
ZSTART — ZSTART is INTEGER; start index of the matrix Z. Rotations are applied to columns k+1-qStart:k+2-qStart of Z. 🎀
Z — Z is a COMPLEX*16 array, dimension (LDZ,NZ). 🌸
LDZ — LDZ is INTEGER; the leading dimension of Q as declared in the calling procedure. 💖

👑 AUTHOR 👑

Thijs Steel, KU Leuven

📅 DATE 📅

May 2020

Definition at line 171 of file zlaqz1.f.

🤖 AUTHOR 🤖

Generated automatically by Doxygen for LAPACK from the source code.

Source/version check, bestie: LAPACK, Version 3.12.0, dated May 2020 — laqz1(3) signing off! 🎀💖✨

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms