SGEEQU(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 SGEEQU(3) — the whole manual page, bestie

okay so this is the man page for SGEEQU(3), and it lives in the LAPACK fam — Version 3.12.0 to be exact. The source file is:

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

and it's filed under the Library Functions Manual. Buckle up, we're getting into matrix equilibration and honestly? it's giving main character energy. 🎀

✨ NAME ✨

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

like, yes, the NAME section is literally just the path to the file. no notes. iconic behaviour. 💀

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine SGEEQU (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)
    SGEEQU

🌸 Function/Subroutine Documentation 🌸

subroutine SGEEQU (integer m, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) r, real, dimension( * ) c, real
    rowcnd, real colcnd, real amax, integer info)

<b>SGEEQU</b>

💖 Purpose 💖

!> !> SGEEQU computes row and column scalings intended to equilibrate an !> M-by-N matrix A and reduce its condition number. R returns the row !> scale factors and C the column scale factors, chosen to try to make !> the largest element in each row and column of the matrix B with !> elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1. !> !> R(i) and C(j) are restricted to be between SMLNUM = smallest safe !> number and BIGNUM = largest safe number. Use of these scaling !> factors is not guaranteed to reduce the condition number of A but !> works well in practice. !>

so basically it's out here trying to make your matrix behave — scale each row and column so the biggest element in each one lands at absolute value 1. R is your row scalers, C is your column scalers, and the whole thing rides on B(i,j)=R(i)*A(i,j)*C(j). Also super important: R(i) and C(j) are restricted to live between SMLNUM (smallest safe number) and BIGNUM (largest safe number). and ngl, using these factors is not guaranteed to reduce the condition number of A — it just works well in practice, bestie. no cap. 🙈

🌈 Parameters 🌈

  • M — INTEGER, the number of rows of the matrix A. Must be M >= 0. yes zero is allowed, we love an empty-ish matrix.
  • N — INTEGER, the number of columns of the matrix A. Must be N >= 0. same deal, zero is chill.
  • A — REAL array, dimension (LDA,N). This is the M-by-N matrix whose equilibration factors are to be computed. it's the star of the show, the main character, the moment. 👑
  • C... wait no, order! let me not skip. 💀
  • LDA — INTEGER, the leading dimension of the array A. Must be LDA >= max(1,M). don't mess with this one, fr fr.
  • R — REAL array, dimension (M). If INFO = 0 or INFO > M, R contains the row scale factors for A.
  • C — REAL array, dimension (N). If INFO = 0, C contains the column scale factors for A. (notice the difference: C only shows up when INFO = 0, not INFO > M. iykyk.)
  • ROWCND — REAL. If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest R(i) to the largest R(i). And like, if ROWCND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by R. so just... don't bother, girl.
  • COLCND — REAL. If INFO = 0, COLCND contains the ratio of the smallest C(i) to the largest C(i). If COLCND >= 0.1, it is not worth scaling by C. same vibe check, different axis. 🦋
  • AMAX — REAL. Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled. that's the danger zone, bestie, take it seriously. 😭
  • INFO — INTEGER, the receipts:
    • = 0: successful exit 🎉
    • < 0: if INFO = -i, the i-th argument had an illegal value — like, you passed something bad and it's telling you which one
    • > 0: if INFO = i, and i is
      • <= M: the i-th row of A is exactly zero
      • > M: the (i-M)-th column of A is exactly zero

🧚 Author 🧚

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

Definition at line 137 of file sgeequ.f.

⭐ Author (yes, again) ⭐

Generated automatically by Doxygen for LAPACK from the source code.

and that's the whole page, bestie — LAPACK Version 3.12.0, dated to that path up there, generated by Doxygen from the source, slay. 🫶✨

📦 where this page comes from