SRC/dlaqgb.f(3)

✨ NAME ✨

SRC/dlaqgb.f — okay bestie, this one is from the Library Functions Manual, and it's all about the dlaqgb subroutine. No cap. 🫶

🌈 SYNOPSIS 🌈

💫 Functions/Subroutines 💫

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

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

💖 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. That's the whole vibe. ✨

🎯 Purpose 🎯

Okay so the purpose is literally this: 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. That's the main character energy. 🌈

📦 Parameters 📦

• M — M is INTEGER. The number of rows of the matrix A. M >= 0. Rows go brrr. 💙
• N — N is INTEGER. The number of columns of the matrix A. N >= 0. Columns understood. 💚
• KL — KL is INTEGER. The number of subdiagonals within the band of A. KL >= 0. Subdiagonal realness. 💜
• KU — KU is INTEGER. The number of superdiagonals within the band of A. KU >= 0. Superdiagonal supremacy. 🍑
• 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(m,j+kl). On exit, the equilibrated matrix, in the same storage format as A. See EQUED for the form of the equilibrated matrix. Storage format tea. 🦋
• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDA >= KL+KU+1. Yes, that's the exact constraint on the page — keep it. 💀
• R — R is DOUBLE PRECISION array, dimension (M). The row scale factors for A. Row factors, iconic. 🎀
• C — C is DOUBLE PRECISION array, dimension (N). The column scale factors for A. Column factors, also iconic. 🌸
• ROWCND — ROWCND is DOUBLE PRECISION. Ratio of the smallest R(i) to the largest R(i). Ratio check. ⭐
• COLCND — COLCND is DOUBLE PRECISION. Ratio of the smallest C(i) to the largest C(i). Another ratio check. ✨
• AMAX — AMAX is DOUBLE PRECISION. Absolute value of largest matrix entry. Biggest entry energy. 🔥
• 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).

🧠 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. Threshold behavior, periodt. 🔥
• 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. Size-based scaling check. ⭐

👑 Author 👑

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

Definition at line 157 of file dlaqgb.f.

🤖 Author (the Doxygen one) 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that's the whole page — it's from LAPACK Version 3.12.0. Stay equilibrated and iconic! 💅✨🎀