SRC/zlaqgb.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

okay so bestie, welcome to the Library Functions Manual page for SRC/zlaqgb.f — aka the zlaqgb subroutine's very own corner of LAPACK. It's giving band-matrix glow-up, and we're gonna read it together. 💅✨

💖 NAME 💖

SRC/zlaqgb.f — that's the file, bestie. This page documents the zlaqgb subroutine.

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

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

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

🎀 Function/Subroutine Documentation 🎀

subroutine zlaqgb (integer m, integer n, integer kl, integer ku, complex*16,
    dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )
    r, double precision, dimension( * ) c, double precision rowcnd, double
    precision colcnd, double precision amax, character equed)

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

🦋 Purpose 🦋

ZLAQGB 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. The number of rows of the matrix A. M >= 0.

N

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.

KU

KU is INTEGER. The number of superdiagonals within the band of A. KU >= 0.

AB

AB is COMPLEX*16 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. LDA >= KL+KU+1.

R

R is DOUBLE PRECISION array, dimension (M). The row scale factors for A.

C

C is 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. 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 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.

🫶 Author 🫶

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

Definition at line 158 of file zlaqgb.f.

🫶 Author 🫶

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that's the whole page, bestie 💖 — LAPACK Version 3.12.0, SRC/zlaqgb.f(3). periodt. 💅✨

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