
DGBEQU(l) ) DGBEQU(l)
NAME
DGBEQU  compute row and column scalings intended to equilibrate an MbyN band matrix A
and reduce its condition number
SYNOPSIS
SUBROUTINE DGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO )
INTEGER INFO, KL, KU, LDAB, M, N
DOUBLE PRECISION AMAX, COLCND, ROWCND
DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * )
PURPOSE
DGBEQU computes row and column scalings intended to equilibrate an MbyN band matrix A
and reduce its condition number. R returns the row scale factors and C the column scale
factors, chosen to try to make the largest element in each row and column of the matrix B
with elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
R(i) and C(j) are restricted to be between SMLNUM = smallest safe number and BIGNUM =
largest safe number. Use of these scaling factors is not guaranteed to reduce the condi
tion number of A but works well in practice.
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) DOUBLE PRECISION array, dimension (LDAB,N)
The band matrix A, stored 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,j
ku)<=i<=min(m,j+kl).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
R (output) DOUBLE PRECISION array, dimension (M)
If INFO = 0, or INFO > M, R contains the row scale factors for A.
C (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, C contains the column scale factors for A.
ROWCND (output) DOUBLE PRECISION
If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest R(i) to the
largest R(i). If ROWCND >= 0.1 and AMAX is neither too large nor too small, it is
not worth scaling by R.
COLCND (output) DOUBLE PRECISION
If INFO = 0, COLCND contains the ratio of the smallest C(i) to the largest C(i).
If COLCND >= 0.1, it is not worth scaling by C.
AMAX (output) DOUBLE PRECISION
Absolute value of largest matrix element. If AMAX is very close to overflow or
very close to underflow, the matrix should be scaled.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: if INFO = i, and i is
<= M: the ith row of A is exactly zero
> M: the (iM)th column of A is exactly zero
LAPACK version 3.0 15 June 2000 DGBEQU(l) 
