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

💅 dsyequb.f — like, the whole manual page, bestie 🫶

okay so this is a page from the Library Functions Manual for /home/abui.../dsyequb.f(3), and ngl it's giving big "LAPACK internals" energy. it's a Fortran source file page, and the actual file lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsyequb.f 💖

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsyequb.f — yes bestie, the NAME section is literally just the path. iconic, honestly. 👑

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine DSYEQUB (uplo, n, a, lda, s, scond, amax, work, info) — DSYEQUB 🦋

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💜 Function/Subroutine Documentation 💜

so here's the full signature, no cap:

subroutine DSYEQUB (character uplo, integer n, double precision, dimension(
    lda, * ) a, integer lda, double precision, dimension( * ) s, double
precision scond, double precision amax, double precision, dimension( * )
work, integer info)

DSYEQUB ✨

🎀 Purpose 🎀

!> !> DSYEQUB 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. !>

like, literally it's out here balancing your symmetric matrix so the condition number stops being dramatic 😭 it uses the BIN algorithm (refs below, iykyk), and the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) ends up with a condition number within a factor N of the smallest possible one over all diagonal scalings. ate. 💅

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🦋 Parameters 🦋

• UPLO — UPLO is CHARACTER*1. which triangle are we vibing with?
  • = '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. (zero is allowed, she's valid 💀)
• A — A is DOUBLE PRECISION array, dimension (LDA,N). the N-by-N symmetric matrix whose scaling factors are to be computed. main character matrix energy 👑
• LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N). don't skip this one fr fr.
• S — S is DOUBLE PRECISION array, dimension (N). If INFO = 0, S contains the scale factors for A. 🍓
• SCOND — SCOND is DOUBLE PRECISION. 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. so like, if this checks out, don't bother — she's fine as is 💅
• AMAX — AMAX is DOUBLE PRECISION. largest absolute value of any matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled. 🚨 like, actual warning territory.
• WORK — WORK is DOUBLE PRECISION array, dimension (2*N). yes, 2*N, not N. respect the workspace.
• INFO — INFO is INTEGER. the vibe check:
  • = 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.

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🧚 Author 🧚

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

the whole squad co-signed this one 🫶

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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 law 📚✨

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🌈 Where she lives 🌈

Definition at line 130 of file dsyequb.f.

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💖 Author (the meta one) 💖

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just a robot doing her little thing 🤖💅)

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okay and that's the whole page, periodt. 🎀 this footer slays: LAPACK, Version 3.12.0, dated /home/abui.../dsyequb.f(3) — go off, queen 👑💜