.TH SGBEQU 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) "
.SH NAME
SGBEQU - row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number
.SH SYNOPSIS
.TP 19
SUBROUTINE SGBEQU(
M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
AMAX, INFO )
.TP 19
.ti +4
INTEGER
INFO, KL, KU, LDAB, M, N
.TP 19
.ti +4
REAL
AMAX, COLCND, ROWCND
.TP 19
.ti +4
REAL
AB( LDAB, * ), C( * ), R( * )
.SH PURPOSE
SGBEQU computes row and column scalings intended to equilibrate an
M-by-N 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.
.br
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 condition number of A but
works well in practice.
.br
.SH ARGUMENTS
.TP 8
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
.TP 8
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
.TP 8
KL (input) INTEGER
The number of subdiagonals within the band of A. KL >= 0.
.TP 8
KU (input) INTEGER
The number of superdiagonals within the band of A. KU >= 0.
.TP 8
AB (input) REAL array, dimension (LDAB,N)
The band matrix A, stored 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).
.TP 8
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
.TP 8
R (output) REAL array, dimension (M)
If INFO = 0, or INFO > M, R contains the row scale factors
for A.
.TP 8
C (output) REAL array, dimension (N)
If INFO = 0, C contains the column scale factors for A.
.TP 8
ROWCND (output) REAL
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.
.TP 8
COLCND (output) REAL
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.
.TP 8
AMAX (output) REAL
Absolute value of largest matrix element. If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value
.br
> 0: if INFO = i, and i is
.br
<= M: the i-th row of A is exactly zero
.br
> M: the (i-M)-th column of A is exactly zero