ZPBEQU(l)		LAPACK routine (version	1.1)		    ZPBEQU(l)

NAME
  ZPBEQU - compute row and column scalings intended to equilibrate a Hermi-
  tian positive	definite band matrix A and reduce its condition	number (with
  respect to the two-norm)

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 two-norm).  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	con-
  dition 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 j-th column	of A is
	  stored in the	j-th column of the array AB as follows:	if UPLO	=
	  'U', AB(kd+1+i-j,j) =	A(i,j) for max(1,j-kd)<=i<=j; if UPLO =	'L',
	  AB(1+i-j,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	larg-
	  est 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 i-th argument	had an illegal value.
	  > 0:	if INFO	= i, the i-th diagonal entry is	nonpositive.