DLAQGB(3)

🌸 NAME 🌸

okay so bestie, this page is from the Library Functions Manual, and it's all about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlaqgb.f ✨

✨ SYNOPSIS ✨

🌈 Functions/Subroutines

• subroutine DLAQGB (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed) — literally iconic: DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. 💅

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

💖 Function/Subroutine Documentation 💖

subroutine DLAQGB (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, character equed)

DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. 🫶

🎯 Purpose

okay so the Purpose is giving main-character energy: DLAQGB 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. ✨

🧸 Parameters

• M — M is INTEGER; it's the number of rows of the matrix A. M >= 0. 🌸
• N — N is INTEGER; it's the number of columns of the matrix A. N >= 0. 🦋
• KL — KL is INTEGER; it's the number of subdiagonals within the band of A. KL >= 0. 💜
• KU — KU is INTEGER; it's the number of superdiagonals within the band of A. KU >= 0. ⭐
• AB — AB is a DOUBLE PRECISION array, dimension (LDAB,N). On entry, it's 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, it's the equilibrated matrix, in the same storage format as A. See EQUED for the form of the equilibrated matrix. 💖
• LDAB — LDAB is INTEGER; it's the leading dimension of the array AB. The page says LDA >= KL+KU+1. 🫧

ngl, the page literally says LDA >= KL+KU+1 here — keeping it exactly as written, bestie. 🫶

• R — R is a DOUBLE PRECISION array, dimension (M). The row scale factors for A. 🌈
• C — C is a DOUBLE PRECISION array, dimension (N). The column scale factors for A. 🎀
• ROWCND — ROWCND is DOUBLE PRECISION; ratio of the smallest R(i) to the largest R(i). 🌸
• COLCND — COLCND is DOUBLE PRECISION; ratio of the smallest C(i) to the largest C(i). 🦋
• AMAX — AMAX is DOUBLE PRECISION; absolute value of largest matrix entry. ⭐
• EQUED — EQUED is CHARACTER*1; it 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).

🫧 Internal Parameters

• THRESH — 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 — 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. 💀

👑 Author

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

📍 Definition

Definition at line 157 of file dlaqgb.f. 🎯

🌟 Author

Generated automatically by Doxygen for LAPACK from the source code. 🪄

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and that's the whole page, bestie 💖 this is LAPACK Version 3.12.0, source path /home/abui...RC/dlaqgb.f(3) — the footer doesn't list a date, so that's the whole sign-off. slay, bye! 🎀✨