SRC/slaqgb.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

✨ SRC/slaqgb.f ✨

okay bestie, so this is one of those LAPACK pages — it lives in the Library Functions Manual and honestly? it's giving "quiet hero of numerical linear algebra." it's a .f file, so yes, it's Fortran, and yes, she's iconic for it. 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • subroutine slaqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed) — SLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. slay 💖

🎀 Function/Subroutine Documentation 🎀

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

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

SLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. she's the glow-up phase of your matrix, no cap ✨

🦋 Purpose 🦋

!> !> SLAQGB 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 basically: band matrix A walks in looking a lil unbalanced, and SLAQGB is like "bestie, we're fixing that" using the row factors in R and the column factors in C. periodt. 💜

👑 Parameters 👑

  • M — M is INTEGER. the number of rows of the matrix A. M >= 0.
!> 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.
!> 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.
!> 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.
!> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 0. >
  • AB — AB is REAL array, dimension (LDAB,N).
!> AB is REAL 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(m,j+kl) !> !> On exit, the equilibrated matrix, in the same storage format !> as A. See EQUED for the form of the equilibrated matrix. >

on entry she's holding your matrix A in band storage, rows 1 to KL+KU+1. on exit she's holding the equilibrated matrix, same storage format as A — check EQUED for exactly what form it took. 🔥

  • LDAB — LDAB is INTEGER. the leading dimension of the array AB. LDA >= KL+KU+1.
!> LDAB is INTEGER !> The leading dimension of the array AB. LDA >= KL+KU+1. >
  • R — R is REAL array, dimension (M). the row scale factors for A.
!> R is REAL array, dimension (M) !> The row scale factors for A. >
  • C — C is REAL array, dimension (N). the column scale factors for A.
!> C is REAL array, dimension (N) !> The column scale factors for A. >
  • ROWCND — ROWCND is REAL. ratio of the smallest R(i) to the largest R(i).
!> ROWCND is REAL !> Ratio of the smallest R(i) to the largest R(i). >
  • COLCND — COLCND is REAL. ratio of the smallest C(i) to the largest C(i).
!> COLCND is REAL !> Ratio of the smallest C(i) to the largest C(i). >
  • AMAX — AMAX is REAL. absolute value of largest matrix entry.
!> AMAX is REAL !> Absolute value of largest matrix entry. >
  • EQUED — EQUED is CHARACTER*1. specifies the form of equilibration that was done. this is the receipts section, bestie — read it carefully 🫶
!> 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 like: '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), and 'B' = both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C). all four are valid, don't @ me 💅

🌈 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 vibe check: it decides whether row or column scaling happens, 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. 💫

and then LARGE and SMALL are threshold values that decide whether 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. she's thorough like that. ⭐

💖 Author 💖

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

Definition at line 157 of file slaqgb.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code. (yes, the page has two Author sections — that's just how she is, we don't question it 🙈)

later bestie!! 🌸💜🦋✨ this lil page came to you from LAPACK, Version 3.12.0, dated SRC/slaqgb.f(3) — go balance some matrices, you've got this 💅🎀

📦 where this page comes from