CQRT12(3)

🌸 cqrt12.f(3) — bestie edition 🌸

okay so this is a page from the Library Functions Manual for cqrt12.f(3), and it's literally the glow-up documentation for one little LAPACK testing helper. it's not a huge man page but it's our man page, and we're gonna read it together. grab a snack 🍓

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/cqrt12.f

yeah that's the whole name. it's a path. she's long, she's giving filesystem realness, and she is iconic for it 💅

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🦋 SYNOPSIS 🦋

Functions/Subroutines

real function CQRT12 (m, n, a, lda, s, work, lwork, rwork)

CQRT12 — that's her, that's the whole function, no notes 👑

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🎀 Function/Subroutine Documentation 🎀

real function CQRT12 (integer m, integer n, complex, dimension( lda, * ) a,
    integer lda, real, dimension( * ) s, complex, dimension( lwork ) work,
    integer lwork, real, dimension( * ) rwork)

CQRT12

💖 Purpose:

ok so the vibe of this function, fr fr:

!>
!> CQRT12 computes the singular values `svlues' of the upper trapezoid
!> of A(1:M,1:N) and returns the ratio
!>
!>      || svlues -s ||/( ||s||*eps*max(M,N) )
!>

yes bestie, the original really does spell it svlues — that's a choice, we are keeping it exactly as written, no cap 🙈 it computes the singular values of the upper trapezoid of A(1:M,1:N) and hands you back that ratio. the !> stuff is just Fortran doc-comment glitter ✨

🌈 Parameters

• M — M is INTEGER. the number of rows of the matrix A. that's the up-and-down count, iykyk.
• N — N is INTEGER. the number of columns of the matrix A. that's the left-and-right count 🫶
• A — A is COMPLEX array, dimension (LDA,N). it's the M-by-N matrix A, but heads up: only the upper trapezoid is referenced. she does not read the whole thing, only the glow-up triangle part 💅
• LDA — LDA is INTEGER. the leading dimension of the array A. respect her dimensions.
• S — S is REAL array, dimension (min(M,N)). the singular values of the matrix A. these are the values your heart desires 💖
• WORK — WORK is COMPLEX array, dimension (LWORK). a workspace. she works, okay? 💀
• LWORK — LWORK is INTEGER. the length of the array WORK. and here's the actual tea, the size requirement:

LWORK >= M*N + 2*min(M,N) + max(M,N).

do not disrespect this, the math said what it said 📐✨

• RWORK — RWORK is REAL array, dimension (4*min(M,N)). more workspace, but make it real-number flavored.

👑 Author

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

the whole squad came together for this one, we love a collab 🌈🫶

⭐ Definition at line 95 of file cqrt12.f.

literally line 95, go look, she's there 💅

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

so nobody hand-wrote this page — Doxygen did it, automatically, like a little robot bestie 🤖✨ (we still appreciate her tho)

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and that's the whole page, bestie!! 🎀 one last thing, the cute lil' sign-off at the bottom: this is LAPACK, Version 3.12.0, and the page is from /home/abui...IN/cqrt12.f(3). slay, go test those singular values, mwah 💖🦋🌸