
ZLAQGB(l) ) ZLAQGB(l)
NAME
ZLAQGB  equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiag
onals using the row and scaling factors in the vectors R and C
SYNOPSIS
SUBROUTINE ZLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, EQUED )
CHARACTER EQUED
INTEGER KL, KU, LDAB, M, N
DOUBLE PRECISION AMAX, COLCND, ROWCND
DOUBLE PRECISION C( * ), R( * )
COMPLEX*16 AB( LDAB, * )
PURPOSE
ZLAQGB equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiago
nals using the row and scaling factors in the vectors R and C.
ARGUMENTS
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
KL (input) INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU (input) INTEGER
The number of superdiagonals within the band of A. KU >= 0.
AB (input/output) COMPLEX*16 array, dimension (LDAB,N)
On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The jth column of
A is stored in the jth column of the array AB as follows: AB(ku+1+ij,j) = A(i,j)
for max(1,jku)<=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 (input) INTEGER
The leading dimension of the array AB. LDA >= KL+KU+1.
R (output) DOUBLE PRECISION array, dimension (M)
The row scale factors for A.
C (output) DOUBLE PRECISION array, dimension (N)
The column scale factors for A.
ROWCND (output) DOUBLE PRECISION
Ratio of the smallest R(i) to the largest R(i).
COLCND (output) DOUBLE PRECISION
Ratio of the smallest C(i) to the largest C(i).
AMAX (input) DOUBLE PRECISION
Absolute value of largest matrix entry.
EQUED (output) 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row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).
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.
LAPACK version 3.0 15 June 2000 ZLAQGB(l) 
