SYNOPSIS
 SUBROUTINE SGBEQUB(
 M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO )
 IMPLICIT NONE
 INTEGER INFO, KL, KU, LDAB, M, N
 REAL AMAX, COLCND, ROWCND
 REAL AB( LDAB, * ), C( * ), R( * )
PURPOSE
SGBEQUB computes row and column scalings intended to equilibrate an MbyN 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 an absolute value of at most the radix.R(i) and C(j) are restricted to be a power of the radix 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.
This routine differs from SGEEQU by restricting the scaling factors to a power of the radix. Baring over and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled entries' magnitured are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix).
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)
 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(N,j+kl)
 LDAB (input) INTEGER
 The leading dimension of the array A. LDAB >= max(1,M).
 R (output) REAL array, dimension (M)
 If INFO = 0 or INFO > M, R contains the row scale factors for A.
 C (output) REAL array, dimension (N)
 If INFO = 0, C contains the column scale factors for A.
 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.
 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.
 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.
 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