SPBEQU(3)
computes row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the twonorm)
SYNOPSIS
 SUBROUTINE SPBEQU(

UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO )

CHARACTER
UPLO

INTEGER
INFO, KD, LDAB, N

REAL
AMAX, SCOND

REAL
AB( LDAB, * ), S( * )
PURPOSE
SPBEQU computes row and column scalings intended to equilibrate a
symmetric positive definite band matrix A and reduce its condition
number (with respect to the twonorm). S contains the scale factors,
S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This
choice of S puts the condition number of B within a factor N of the
smallest possible condition number over all possible diagonal
scalings.
ARGUMENTS
 UPLO (input) CHARACTER*1

= 'U': Upper triangular of A is stored;
= 'L': Lower triangular of A is stored.
 N (input) INTEGER

The order of the matrix A. N >= 0.
 KD (input) INTEGER

The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 0.
 AB (input) REAL array, dimension (LDAB,N)

The upper or lower triangle of the symmetric band matrix A,
stored in the first KD+1 rows of the array. The jth column
of A is stored in the jth column of the array AB as follows:
if UPLO = 'U', AB(kd+1+ij,j) = A(i,j) for max(1,jkd)<=i<=j;
if UPLO = 'L', AB(1+ij,j) = A(i,j) for j<=i<=min(n,j+kd).
 LDAB (input) INTEGER

The leading dimension of the array A. LDAB >= KD+1.
 S (output) REAL array, dimension (N)

If INFO = 0, S contains the scale factors for A.
 SCOND (output) REAL

If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i). If SCOND >= 0.1 and AMAX is neither too
large nor too small, it is not worth scaling by S.
 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, the ith diagonal element is nonpositive.