SRC/dgeequ.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

💖 NAME 💖

okay so bestie, this is the manual page for SRC/dgeequ.f — yes, the SRC/dgeequ.f(3) one — and it lives in the Library Functions Manual. It’s giving “linear algebra glow-up” energy, and we’re gonna read it together 💅✨

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

🧚 Function/Subroutine Documentation 🧚

subroutine dgeequ (integer m, integer n, double precision, dimension( lda, *
       ) a, integer lda, double precision, dimension( * ) r, double precision,
       dimension( * ) c, double precision rowcnd, double precision colcnd,
       double precision amax, integer info)
    DGEEQU

🌸 Purpose 🌸

okay so DGEEQU 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 returns 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 it works well in practice. no cap, that’s the whole vibe check 😌

🎀 Parameters 🎀

  • M — M is INTEGER. It’s the number of rows of matrix A, and M >= 0. 👑
  • N — N is INTEGER. It’s the number of columns of matrix A, and N >= 0. 🌸
  • A — A is DOUBLE PRECISION array, dimension (LDA,N). This is the M-by-N matrix whose equilibration factors are to be computed. 💖
  • LDA — LDA is INTEGER. It’s the leading dimension of the array A, and LDA >= max(1,M). ✨
  • R — R is DOUBLE PRECISION array, dimension (M). If INFO = 0 or INFO > M, R contains the row scale factors for A. 🦋
  • C — C is DOUBLE PRECISION array, dimension (N). If INFO = 0, C contains the column scale factors for A. 🎀
  • ROWCND — ROWCND is DOUBLE PRECISION. If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest R(i) to the largest R(i). If ROWCND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by R. 💅
  • COLCND — COLCND is DOUBLE PRECISION. 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. 🫧
  • AMAX — AMAX is DOUBLE PRECISION. It’s the absolute value of the largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled. 🔥
  • INFO — INFO is INTEGER:
    • = 0: successful exit ✅
    • < 0: if INFO = -i, the i-th argument had an illegal value 💀
    • > 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 dgeequ.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

kisses, bestie 🫶💖 — this was SRC/dgeequ.f(3) from LAPACK Version 3.12.0, and your fave Unix bestie is obsessed with how clean that scaling logic is. bye! 💋✨

📦 where this page comes from