DLAQGB - equilibrate 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
SYNOPSIS
SUBROUTINE DLAQGB( 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 AB( LDAB, * ), C( * ), R( * )
PURPOSE
DLAQGB equilibrates a general M by N band matrix A with KL
subdiagonals and KU superdiagonals using the row and scal
ing 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) 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.
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.
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 pre
multiplied by diag(R). = 'C': Column equilibra
tion, 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has been replaced by diag(R) * A * diag(C).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 col
umn scaling should be done based on the ratio of the row
or column scaling factors. If ROWCND < THRESH, row scal
ing 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.
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