DGEEQU(3)

💅 dgeequ.f(3) — Library Functions Manual

okay so this is the dgeequ.f(3) page from the Library Functions Manual, and we’re about to get into some matrix-equilibration business. stay with me bestie, it’s actually kinda iconic ✨

🎀 NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgeequ.f — that’s the file path, no cap 💖

✨ SYNOPSIS

🦋 Functions/Subroutines

• subroutine DGEEQU (m, n, a, lda, r, c, rowcnd, colcnd, amax, info) — DGEEQU, our main character 👑

🌸 Function/Subroutine Documentation

💖 DGEEQU

   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 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. literally the goal 💅

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.

Caveat bestie: using these scaling factors is not guaranteed to reduce the condition number of A, but it works well in practice. so like, it’s giving “trust me it usually slays” 😭

🌈 Parameters

• M — INTEGER; the number of rows of the matrix A. M >= 0.
• N — INTEGER; the number of columns of the matrix A. N >= 0.
• A — DOUBLE PRECISION array, dimension (LDA,N); the M-by-N matrix whose equilibration factors are to be computed.
• LDA — INTEGER; the leading dimension of the array A. LDA >= max(1,M).
• R — DOUBLE PRECISION array, dimension (M); if INFO = 0 or INFO > M, R contains the row scale factors for A.
• C — DOUBLE PRECISION array, dimension (N); if INFO = 0, C contains the column scale factors for A.
• ROWCND — 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 — 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 — DOUBLE PRECISION; absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.
• INFO — INTEGER; here’s the tea:
  • = 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.

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Okay bestie, that’s the whole page! Source/version tea: LAPACK Version 3.12.0, page path /home/abui...RC/dgeequ.f(3) — now go equilibrate responsibly 💖✨