CGESC2(3)

💅 CGESC2(3) — like, the complex getc2 solver, bestie

okay so first things first: this is a page from the Library Functions Manual (LAPACK girlies, we're in section 3, the library-functions section, mwah 💖). And lowkey the file it's documenting is literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgesc2.f

like that's it, that's the absolute path, no notes ✨

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgesc2.f

yep. that's the whole NAME section. it's giving minimalism, it's giving "the file speaks for itself" 💀

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine CGESC2 (n, a, lda, rhs, ipiv, jpiv, scale) — CGESC2 solves a system of linear equations using the LU factorization with complete pivoting computed by sgetc2.

(spot the lowercase s there? yeah. we literally keep it. copying it exactly, no cap 🫶)

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🦋 Function/Subroutine Documentation 🦋

subroutine CGESC2 (integer n, complex, dimension( lda, * ) a, integer lda,
    complex, dimension( * ) rhs, integer, dimension( * ) ipiv, integer,
    dimension( * ) jpiv, real scale)

CGESC2 solves a system of linear equations using the LU factorization with complete pivoting computed by sgetc2.

🎀 Purpose 🎀

okay here's the whole vibe, straight from the source comment block:

!>
!> CGESC2 solves a system of linear equations
!>
!>           A * X = scale* RHS
!>
!> with a general N-by-N matrix A using the LU factorization with
!> complete pivoting computed by CGETC2.
!>
!>

so like — you already got A factorized by CGETC2, and now you want the solve. that's the whole job, bestie. main character energy honestly 💅

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🌈 Parameters 🌈

• N

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

• A

!>          A is COMPLEX array, dimension (LDA, N)
!>          On entry, the  LU part of the factorization of the n-by-n
!>          matrix A computed by CGETC2:  A = P * L * U * Q
!>

like — on entry it's already the LU part. don't come in here with a fresh matrix, that's not the assignment 🙈

• LDA

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

that LDA >= max(1, N) is not a suggestion, it's a lifestyle. respect it or enjoy your undefined behaviour 🔥

• RHS

!>          RHS is COMPLEX array, dimension N.
!>          On entry, the right hand side vector b.
!>          On exit, the solution vector X.
!>

the glow-up is real: goes in as b, comes out as X. ate and left no crumbs ✨

• IPIV

!>          IPIV is INTEGER array, dimension (N).
!>          The pivot indices; for 1 <= i <= N, row i of the
!>          matrix has been interchanged with row IPIV(i).
!>

• JPIV

!>          JPIV is INTEGER array, dimension (N).
!>          The pivot indices; for 1 <= j <= N, column j of the
!>          matrix has been interchanged with column JPIV(j).
!>

rows go through IPIV, columns go through JPIV. complete pivoting means both get shuffled, iykyk 🌀

• SCALE

!>          SCALE is REAL
!>           On exit, SCALE contains the scale factor. SCALE is chosen
!>           0 <= SCALE <= 1 to prevent overflow in the solution.
!>

the anti-overflow queen 👑 she clamps herself between 0 and 1 so your solution doesn't explode. iconic, honestly.

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💖 Author 💖

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

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🧚 Contributors: 🧚

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

shoutout to Bo and Peter, the founders of the function, fr fr 🫶

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⭐ one more thing ⭐

Definition at line 114 of file cgesc2.f.

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💜 Author (yes, a second one, don't @ me) 💜

Generated automatically by Doxygen for LAPACK from the source code.

like... the robot wrote this section, not a human. we love a machine-made author credit, slay 🤖✨

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and that's the whole page, bestie — bye!! this was LAPACK, Version 3.12.0, and the header/footer vibe was cgesc2.f(3) all along. 🍓 see u in the next manpage 💅