SRC/dgbequb.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

💅 SRC/dgbequb.f 💅

okay so bestie, we're looking at SRC/dgbequb.f(3) — a page straight out of the LAPACK Library Functions Manual, and honestly? she's giving linear algebra icon. it's DGBEQUB, a Fortran subroutine that does scaling math, and yes it has a lot of arguments. don't panic. we got this. 🫶

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine dgbequb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info) — that's her! that's DGBEQUB 🎀

📜 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 — say it with me: dee-gee-bee-ee-kew-bee. iconic name, no notes. 👑

🎯 Purpose 🎯

okay so here's the whole vibe, fr fr:

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.

so basically it's trying to make your matrix chill — scale it down so nothing is screaming too loud. 💆

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.

lowkey can't promise the condition number goes down, but she tries her best and honestly that's enough. 🙈

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).

this is the main character difference between her and DGEEQU — power of the radix only, so no extra rounding errors, but the scaled entries live between sqrt(radix) and 1/sqrt(radix) instead of hovering around 1. iykyk. ✨

🌸 Parameters 🌸

grab a snack, bestie, because there are twelve of these. all facts, no cap:

  • M — M is INTEGER. The number of rows of the matrix A. M >= 0. 🔢
  • N — N is INTEGER. The number of columns of the matrix A. N >= 0. 🔢
  • KL — KL is INTEGER. The number of subdiagonals within the band of A. KL >= 0. 📏
  • KU — KU is INTEGER. The number of superdiagonals within the band of A. KU >= 0. 📏
  • 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)

this indexing situation is a whole journey but it's exactly right, copy it character for character please 🫶

  • 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. 🧐
  • 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. Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled. ⚠️
  • INFO — INFO is INTEGER, and she's the vibe check of the whole operation:
    • = 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 💀
no cap, an exactly-zero row or column is a real situation. check your INFO before you trust anything, bestie.

👑 Author 👑

these absolute legends wrote her:

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

definition at line 158 of file dgbequb.f. that's the receipts. 📍

🌟 Author (the other one) 🌟

generated automatically by Doxygen for LAPACK from the source code. so she's not hand-written, she's curated. 💅

🎀 that's the whole page, bestie. go scale something responsibly. 🎀

LAPACK · Version 3.12.0 · SRC/dgbequb.f(3) — mwah, hope this helped, slay, periodt 💖✨🦋

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