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

💅 DGBEQUB — like, the band-matrix equilibration queen ✨

okay bestie, so this page is from the LAPACK manual (a <cyan>Library Functions Manual</cyan> situation), and it's literally all about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgbequb.f. yes that's a whole path, no I'm not shortening it, it's the icon's full government name 🎀

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🌸 SYNOPSIS 🌸

✨ Functions/Subroutines ✨

• subroutine DGBEQUB (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info) — that's the whole squad, we'll meet every single one of them 💖
• DGBEQUB — the main character herself 👑

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🦋 Function/Subroutine Documentation 🦋

subroutine DGBEQUB (integer m, integer n, integer kl, integer ku, double
    precision, dimension( ldab, * ) ab, integer ldab, double precision,
    dimension( * ) r, double precision, dimension( * ) c, double precision
    rowcnd, double precision colcnd, double precision amax, integer info)

DGBEQUB — again, the moment, the legend 🫶

🌈 Purpose 🌈

okay so here's the tea, and I mean this exactly how the original says it:

DGBEQUB 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 an absolute value of at most the radix. 🔥

R(i) and C(j) are restricted to be a power of the radix 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. ngl, "works well in practice" is such a mood 💀

This routine differs from DGEEQU by restricting the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled entries' magnitudes are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix). ✨ like, the vibes shift, but the math stays valid, iykyk

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🎀 Parameters 🎀

• M — M is INTEGER. The number of rows of the matrix A. M >= 0. rows are literally her whole personality 💅
• N — N is INTEGER. The number of columns of the matrix A. N >= 0. columns too, she contains multitudes 🌸
• KL — KL is INTEGER. The number of subdiagonals within the band of A. KL >= 0. the under-band, if you will 🦋
• KU — KU is INTEGER. The number of superdiagonals within the band of A. KU >= 0. the over-band, iconic, opposite energy ⭐
• AB — AB is DOUBLE PRECISION array, dimension (LDAB,N). On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows:

AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)

copy that indexing exactly bestie, do not freestyle it 😭

• LDAB — LDAB is INTEGER. The leading dimension of the array A. LDAB >= 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. so like, if it's already chill, leave it alone 💅
• 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. same energy, different axis ✨
• AMAX — AMAX is 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. this is your vibe check for danger, do not ignore it 👑
• 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 💀

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🌟 Author 🌟

the legends themselves, no cap:

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

Definition at line 158 of file dgbequb.f. 📍

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💜 Author (yes, another one) 💜

Generated automatically by Doxygen for LAPACK from the source code. the robots did this one, respect 🤖✨

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ok bestie real talk: those INFO > 0 cases mean a whole row or column is exactly zero, which is genuinely a problem, not a cute quirk. and remember INFO < 0 means an argument was illegal. read your INFO before you trust your R and C, fr fr 🚨

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LAPACK · Version 3.12.0 · /home/abui.../dgbequb.f(3) — mwah, that's the page, ily, go equilibrate something 💖🎀🦋🌸