CLAQGB(l) ) CLAQGB(l)NAME
CLAQGB - equilibrate a general M by N band matrix A with KL subdiago‐
nals and KU superdiagonals using the row and scaling factors in the
vectors R and C
SYNOPSIS
SUBROUTINE CLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX,
EQUED )
CHARACTER EQUED
INTEGER KL, KU, LDAB, M, N
REAL AMAX, COLCND, ROWCND
REAL C( * ), R( * )
COMPLEX AB( LDAB, * )
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.
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 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 (input) INTEGER
The leading dimension of the array AB. LDA >= KL+KU+1.
R (output) REAL array, dimension (M)
The row scale factors for A.
C (output) REAL array, dimension (N)
The column scale factors for A.
ROWCND (output) REAL
Ratio of the smallest R(i) to the largest R(i).
COLCND (output) REAL
Ratio of the smallest C(i) to the largest C(i).
AMAX (input) REAL
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 post‐
multiplied by diag(C). = 'B': Both row and column equilibra‐
tion, i.e., A has been replaced by diag(R) * A * diag(C).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 ele‐
ment. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
LAPACK version 3.0 15 June 2000 CLAQGB(l)
