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

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

CHARACTER
UPLO

INTEGER
INFO, KD, LDAB, N

DOUBLE
PRECISION AMAX, SCOND

DOUBLE
PRECISION S( * )

COMPLEX*16
AB( LDAB, * )
PURPOSE
ZPBEQU computes row and column scalings intended to equilibrate a
Hermitian 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) COMPLEX*16 array, dimension (LDAB,N)

The upper or lower triangle of the Hermitian 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) DOUBLE PRECISION array, dimension (N)

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

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) 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, the ith diagonal element is nonpositive.