CLAQGB(3)

💅 claqgb.f(3) — Library Functions Manual 💅

okay bestie, this is the manual page for claqgb.f(3) from the Library Functions Manual. It's giving LAPACK routine energy, and we are keeping every single technical crumb. No cap. 💖

🎀 NAME 🎀

The NAME section is literally a path, which is iconic and chaotic in equal measure:

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/SRC/claqgb.f

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

The summary tea: CLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

🦋 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)

Yep, same summary again because the page says it twice: CLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. 💅

🌈 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.

🌸 Parameters 🌸

• M — M is INTEGER. It's the number of rows of the matrix A. Constraint: M >= 0.
• N — N is INTEGER. It's the number of columns of the matrix A. Constraint: N >= 0.
• KL — KL is INTEGER. The number of subdiagonals within the band of A. Constraint: KL >= 0.
• KU — KU is INTEGER. The number of superdiagonals within the band of A. Constraint: KU >= 0.
• AB — AB is COMPLEX 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.

• LDAB — LDAB is INTEGER. The leading dimension of the array AB. Constraint, exactly as written: LDA >= KL+KU+1.
• R — 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.
• ROWCND — 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).
• AMAX — AMAX is REAL. Absolute value of largest matrix entry.
• 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.
• 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 at line 158 of file claqgb.f.

👑 Author (Doxygen's little cameo) 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie 🫶. Footer source/version/date tea: LAPACK, Version 3.12.0, and the path /home/abui...RC/claqgb.f(3) — and no date is printed there on this page. 💖