SPBEQU(l)		LAPACK routine (version	1.1)		    SPBEQU(l)

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

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 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) 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 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) 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	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) 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 i-th argument	had an illegal value.
	  > 0:	if INFO	= i, the i-th diagonal entry is	nonpositive.