SRC/claqgb.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

🌸 SRC/claqgb.f(3) — Library Functions Manual 🌸

okay bestie, welcome to the glow-up zone ✨ this is a page from the Library Functions Manual, and it's all about one iconic little Fortran subroutine that does matrix makeovers. no cap, she's serving scaling realness 💅

🎀 NAME 🎀

SRC/claqgb.f

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine claqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax,
    equed)

CLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. literally her whole personality 💖

👑 Function/Subroutine Documentation 👑

subroutine claqgb (integer m, integer n, integer kl, integer ku, complex,
    dimension( ldab, * ) ab, integer ldab, real, dimension( * ) r, real,
    dimension( * ) c, real rowcnd, real colcnd, real amax, character equed)

CLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. she's not doing the math herself, she's applying the looks that sgbequ curated 🫶

✨ Purpose ✨

!>
!> CLAQGB equilibrates a general M by N band matrix A with KL
!> subdiagonals and KU superdiagonals using the row and scaling factors
!> in the vectors R and C.
!>

so like, she takes your band matrix A — M by N, with KL subdiagonals and KU superdiagonals — and equilibrates it using those row and scaling factors hanging out in the R and C vectors. main character energy fr fr 🌈

💅 Parameters 💅

  • M — M is INTEGER, and it's the number of rows of the matrix A. M >= 0. keep it non-negative, bestie 🙈
  • N — N is INTEGER, the number of columns of the matrix A. N >= 0. again, no negatives please 💀
  • KL — KL is INTEGER, the number of subdiagonals within the band of A. KL >= 0. yes queen, stay non-negative ⭐
  • KU — KU is INTEGER, the number of superdiagonals within the band of A. KU >= 0. same vibe, same rule 🎀
  • AB — AB is COMPLEX array, dimension (LDAB,N). on entry, this is 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 like this:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)

on exit, it's the equilibrated matrix, in the same storage format as A. see EQUED for the form of the equilibrated matrix. she went in, got the glow-up, kept the same outfit 💖

  • LDAB — LDAB is INTEGER, the leading dimension of the array AB. LDA >= KL+KU+1. (yes, it says LDA, we're keeping it exactly as written — no editing the sacred text, bestie 😭)
  • R — R is REAL array, dimension (M). the row scale factors for A. iconic little row receipts 🧚
  • C — C is REAL array, dimension (N). the column scale factors for A. matching column receipts, we love a coordinated set 💜
  • ROWCND — ROWCND is REAL. ratio of the smallest R(i) to the largest R(i). it's giving imbalance report 🔥
  • COLCND — COLCND is REAL. ratio of the smallest C(i) to the largest C(i). same energy, column edition 🌸
  • AMAX — AMAX is REAL. absolute value of largest matrix entry. the biggest vibe in the room, literally 💀
  • EQUED — EQUED is CHARACTER*1. specifies the form of equilibration that was done:
    • = 'N': No equilibration
    • = 'R': Row equilibration, i.e., A has been premultiplied by diag(R).
    • = 'C': Column equilibration, i.e., A has been postmultiplied by diag(C).
    • = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).

so 'N' is no glow-up, 'R' is row-only, 'C' is column-only, and 'B' is the full both-sides slay 👑✨

🍓 Internal Parameters 🍓

!>  THRESH is a threshold value used to decide if row or column scaling
!>  should be done based on the ratio of the row or column scaling
!>  factors.  If ROWCND < THRESH, row scaling is done, and if
!>  COLCND < THRESH, column scaling is done.
!>
!>  LARGE and SMALL are threshold values used to decide if row scaling
!>  should be done based on the absolute size of the largest matrix
!>  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
!>

so THRESH is the cutoff that decides whether row or column scaling gets the green light, based on the ratio of the row or column scaling factors. if ROWCND < THRESH, row scaling is done; if COLCND < THRESH, column scaling is done. and LARGE and SMALL are thresholds deciding whether row scaling happens based on the absolute size of the largest matrix element — if AMAX > LARGE or AMAX < SMALL, row scaling is done. iykyk, the thresholds are doing all the decision-making behind the scenes 🌀

🌈 Author 🌈

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

⭐ Definition ⭐

Definition at line 158 of file claqgb.f.

💖 Author (again, but the generated one) 💖

Generated automatically by Doxygen for LAPACK from the source code. she was born from automation, and honestly? iconic 🎀

lowkey a whole serve: LAPACK · Version 3.12.0 · SRC/claqgb.f(3) — and that's the tea, bestie. drink up 🍵💅✨
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