SRC/zsyequb.f(3)

🎀 SRC/zsyequb.f(3) — LAPACK Library Functions Manual 🎀

okay so bestie, welcome to the SRC/zsyequb.f(3) page from the LAPACK Library Functions Manual. this is the whole glow-up of ZSYEQUB, and we are keeping every single detail, no cap. 💅✨

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💖 NAME 💖

SRC/zsyequb.f

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines

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

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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. 🔥

🎀 Parameters

• UPLO — CHARACTER*1. tells us which triangle of A is stored:
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — INTEGER. The order of the matrix A. N >= 0.
• A — COMPLEX*16 array, dimension (LDA,N). The N-by-N symmetric matrix whose scaling factors are to be computed.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• S — DOUBLE PRECISION array, dimension (N). If INFO = 0, S contains the scale factors for A.
• SCOND — 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.

bestie, the page literally says S in that SCOND paragraph, so I am keeping it exactly as written. 💀

• AMAX — 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 — COMPLEX*16 array, dimension (2*N).
• INFO — INTEGER. the exit-status 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.

👑 Author

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

📚 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

📍 Definition at line 131 of file zsyequb.f.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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💖 okay that's the whole page, bestie — LAPACK Version 3.12.0, source SRC/zsyequb.f(3). byeee, go equilibrate something iconic 🫶✨