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

💅 NAME 💅

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

okay so bestie, this is a page from the LAPACK Library Functions Manual (section 3, the library-call girlies 🎀), and it's literally all about one little file: zsyequb.f. That's it. That's the name. slay.

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✨ SYNOPSIS ✨

Functions/Subroutines

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

ZSYEQUB — that's her. that's the girl. 👑

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🦋 Function/Subroutine Documentation 🦋

subroutine ZSYEQUB (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, complex*16, dimension( * ) work, integer info)

ZSYEQUB 💫

🌸 Purpose 🌸

!>
!> ZSYEQUB 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 what she does, fr fr: she computes row and column scalings that equilibrate a symmetric matrix A (with respect to the Euclidean norm, no cap) and reduce its condition number. The scale factors S come from the BIN algorithm (the references are down below, iykyk) 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 mathematically iconic. 🧚

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🎀 Parameters 🎀

• UPLO — is CHARACTER*1. our triangle indicator bestie:
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — is INTEGER. The order of the matrix A. N >= 0.
• A — is COMPLEX*16 array, dimension (LDA,N). The N-by-N symmetric matrix whose scaling factors are to be computed. she's the main character here ngl 💜
• LDA — is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• S — is DOUBLE PRECISION array, dimension (N). If INFO = 0, S contains the scale factors for A.
• 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. (like, don't even bother, bestie 🙈)
• 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. ⚠️
• WORK — is COMPLEX*16 array, dimension (2*N). just her little workspace, nothing to see here 🫶
• 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.

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👑 Author 👑

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

(the academic royalty collab we didn't know we needed 🫡)

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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

go read the source, bestie. citations are literally self-care. 📚

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Definition at line 131 of file zsyequb.f.

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💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just vibes 🤖✨)

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

and that's the whole page diva 💅 tysm for reading, mwah 🍓💜