/home/abui.../ssyequb.f(3)

💅 ssyequb.f(3) — Library Functions Manual, bestie 🎀

okay so this is a manpage for /home/abui.../ssyequb.f(3) and it lives in the Library Functions Manual section, and honestly? it's giving "LAPACK source file that got its own glamorous little documentation era." ✨

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🌸 NAME 🌸

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

like... that's the whole name. a whole path. she's an icon, she contains multitudes (and also lapack-3.12.0 twice, no cap 💀).

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine SSYEQUB (uplo, n, a, lda, s, scond, amax, work, info)

SSYEQUB — that's her. that's the subroutine. 🫶

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🦋 Function/Subroutine Documentation 🦋

subroutine SSYEQUB (character uplo, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) s, real scond, real amax, real,
    dimension( * ) work, integer info)

SSYEQUB 🔥 (yes the full signature is right there, i did not skip it, i would never 😤)

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💖 Purpose 💖

!> !> SSYEQUB computes row and column scalings intended to equilibrate a !> symmetric matrix A (with respect to the Euclidean norm) and reduce !> its condition number. The scale factors S are computed by the BIN !> algorithm (see references) so that the scaled matrix B with elements !> B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of !> the smallest possible condition number over all possible diagonal !> scalings. !>

so basically: bestie, this subroutine computes row and column scalings that equilibrate a symmetric matrix A (with respect to the Euclidean norm) and reduce its condition number 😌✨. the scale factors S get computed by the BIN algorithm (check the references section, i'm getting to it 👀) so that the scaled matrix B — with elements B(i,j) = S(i)*A(i,j)*S(j) — has a condition number within a factor N of the smallest possible condition number over all possible diagonal scalings. it's giving "make the matrix behave" energy, fr fr 💅

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🎀 Parameters 🎀

• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — N is INTEGER
  • The order of the matrix A. N >= 0.
• A — A is REAL array, dimension (LDA,N)
  • The N-by-N symmetric matrix whose scaling factors are to be computed.
• LDA — LDA is INTEGER
  • The leading dimension of the array A. LDA >= max(1,N).
• S — S is REAL array, dimension (N)
  • If INFO = 0, S contains the scale factors for A.
• SCOND — SCOND is REAL
  • If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S. (yes it says S here, i'm telling you exactly what it says 🫶)
• AMAX — AMAX is REAL
  • Largest absolute value of any matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.
• WORK — WORK is REAL array, dimension (2*N)
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, the i-th diagonal element is nonpositive.

💀 heads up: INFO < 0 means an argument was illegal (INFO = -i → the i-th one), and INFO > 0 means INFO = i and the i-th diagonal element is nonpositive. not a vibe, but now you know.

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👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

(the whole squad showed up, we love a collaborative era 🌈)

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⭐ References: ⭐

Livne, O.E. and Golub, G.H., "Scaling by Binormalization", Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004. DOI 10.1023/B:NUMA.0000016606.32820.69 Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

like, cite your sources bestie, it's the BIN algorithm lore 📚✨

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🧚 Definition 🧚

Definition at line 130 of file ssyequb.f.

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🌷 Author 🌷

Generated automatically by Doxygen for LAPACK from the source code.

(not a human author, a generated author — main character energy but make it automation 🤖💅)

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LAPACK · Version 3.12.0 · /home/abui.../ssyequb.f(3)

and that's the whole page bestie!! 🍓 go scale those symmetric matrices, slay, periodt 💜🦋