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

📦 version 3.12.0, in opensuse-leap 16.0

okay so this is the Library Functions Manual page for /home/abui.../csyequb.f(3) — welcome, bestie. The header path is abbreviated like that; the NAME section below has the full source-path glow-up. ✨

🎀 NAME 🎀

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

that's it. that's the name. full source-path realness. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

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

💖 FUNCTION/SUBROUTINE DOCUMENTATION 💖

the main character signature is literally:

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

CSYEQUB — yes bestie, that's the icon. 👑

🎯 Purpose

okay so CSYEQUB 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. no cap, that's the whole purpose block. 🔥

🌈 Parameters

bestie, here's every parameter, no skips:

💅 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 COMPLEX 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, the original text says S there, not SCOND — I'm just reporting the vibes verbatim, bestie. 🙈

🧚 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 COMPLEX 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.

👑 Author

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

📚 References

Definition at line 131 of file csyequb.f.

🫶 AUTHOR 🫶

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and that's the whole page, bestie — source/version sign-off: LAPACK Version 3.12.0, footer path /home/abui.../csyequb.f(3), and no date is printed in that footer, so I'm not inventing one. periodt 💅🫶

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