ZLAQGE(3)

✨ ZLAQGE(3) — like, the row-and-column glow-up for your matrix ✨

okay so bestie, welcome to the Library Functions Manual 💅 this page is all about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlaqge.f and honestly? she's a little legend. sit down, grab a snack 🍓, we're talking equilibration.

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlaqge.f — that's the whole name, yes it's a whole file path, no I don't make the rules 🙈 that's just how the generated page do.

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🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine ZLAQGE (m, n, a, lda, r, c, rowcnd, colcnd, amax, equed) — ZLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ. slay.

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👑 Function/Subroutine Documentation 👑

💜 the subroutine herself

subroutine ZLAQGE (integer m, integer n, complex*16, dimension( lda, * ) a,
    integer lda, double precision, dimension( * ) r, double precision,
    dimension( * ) c, double precision rowcnd, double precision colcnd,
    double precision amax, character equed)

ZLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ. that's the whole vibe. main character energy fr fr 🔥

🎀 Purpose:

ZLAQGE equilibrates a general M by N matrix A using the row and column scaling factors in the vectors R and C.

literally just: A gets a little makeover using R and C. glow-up via vectors. obsessed. ✨

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🌈 Parameters

• M

M is INTEGER The number of rows of the matrix A. M >= 0.

how many rows, bestie. zero is allowed, we don't judge 💖

• N

N is INTEGER The number of columns of the matrix A. N >= 0.

how many columns. also allowed to be zero. equal opportunity 🫶

• A

A is COMPLEX*16 array, dimension (LDA,N) On entry, the M by N matrix A. On exit, the equilibrated matrix. See EQUED for the form of the equilibrated matrix.

she goes in as herself and comes out equilibrated 💅 check EQUED if you wanna know exactly which form she's serving.

• LDA

LDA is INTEGER The leading dimension of the array A. LDA >= max(M,1).

leading dimension, and yes the max(M,1) is real — not me being dramatic, that's the actual constraint ⭐

• R

R is DOUBLE PRECISION array, dimension (M) The row scale factors for A.

row scale factors. one per row. iconic 🌸

• C

C is DOUBLE PRECISION array, dimension (N) The column scale factors for A.

column scale factors. one per column. also iconic 🦋

• ROWCND

ROWCND is DOUBLE PRECISION Ratio of the smallest R(i) to the largest R(i).

tiniest row factor over biggest row factor. the ratio that tells you how row-ily unhinged things are 😭

• COLCND

COLCND is DOUBLE PRECISION Ratio of the smallest C(i) to the largest C(i).

same situation but for the columns. smallest C(i) over largest C(i). periodt.

• AMAX

AMAX is DOUBLE PRECISION Absolute value of largest matrix entry.

the absolute value of the biggest entry in the whole matrix. the head cheerleader of numbers 👑

• EQUED

EQUED is CHARACTER*1 Specifies the form of equilibration that was done. = 'N': No equilibration = 'R': Row equilibration, i.e., A has been premultiplied by diag(R). = 'C': Column equilibration, i.e., A has been postmultiplied by diag(C). = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).

the receipt 🧾 — tells you which flavor of glow-up actually happened:

• 'N' — no equilibration, she woke up like this
• 'R' — row equilibration, A got premultiplied by diag(R)
• 'C' — column equilibration, A got postmultiplied by diag(C)
• 'B' — both, so A was replaced by diag(R) * A * diag(C), full glam 💅✨

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🧚 Internal Parameters:

THRESH is a threshold value used to decide if row or column scaling should be done based on the ratio of the row or column scaling factors. If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column scaling is done.

so THRESH is the vibe check 🫶 ratio too small? scaling happens. that's it.

LARGE and SMALL are threshold values used to decide if row scaling should be done based on the absolute size of the largest matrix element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.

LARGE and SMALL are also vibe checks, but for the absolute size of the largest matrix element — if AMAX > LARGE or AMAX < SMALL, row scaling gets done. no cap 💯

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⭐ Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

the whole academic-and-NAG friend group wrote this, we stan 🌈

Definition at line 141 of file zlaqge.f.

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💫 Author (yes, again)

Generated automatically by Doxygen for LAPACK from the source code. it's giving auto-generated but make it cute 🤖🎀

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quick reminder bestie 💖: EQUED is output — it's telling you what was done, not asking you what to do. don't come for me, that's just what the parameters say.

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🌸 written by the LAPACK girlies, Version 3.12.0, straight outta /home/abui...RC/zlaqge.f(3) — mwah, see you in the next manpage, bestie 💜🦋✨