DSBEVX(l)	     LAPACK driver routine (version 1.1)	    DSBEVX(l)

NAME
  DSBEVX - compute selected eigenvalues	and, optionally, eigenvectors of a
  real symmetric band matrix A

SYNOPSIS

  SUBROUTINE DSBEVX( JOBZ, RANGE, UPLO,	N, KD, AB, LDAB, Q, LDQ, VL, VU, IL,
		     IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO	)

      CHARACTER	     JOBZ, RANGE, UPLO

      INTEGER	     IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N

      DOUBLE	     PRECISION ABSTOL, VL, VU

      INTEGER	     IFAIL( * ), IWORK(	* )

      DOUBLE	     PRECISION AB( LDAB, * ), Q( LDQ, *	), W( *	), WORK( * ),
		     Z(	LDZ, * )

PURPOSE
  DSBEVX computes selected eigenvalues and, optionally,	eigenvectors of	a
  real symmetric band matrix A.	 Eigenvalues/vectors can be selected by
  specifying either a range of values or a range of indices for	the desired
  eigenvalues.

ARGUMENTS

  JOBZ	  (input) CHARACTER*1
	  = 'N':  Compute eigenvalues only;
	  = 'V':  Compute eigenvalues and eigenvectors.

  RANGE	  (input) CHARACTER*1
	  = 'A': all eigenvalues will be found;
	  = 'V': all eigenvalues in the	half-open interval (VL,VU] will	be
	  found; = 'I':	the IL-th through IU-th	eigenvalues will be found.

  UPLO	  (input) CHARACTER*1
	  = 'U':  Upper	triangle of A is stored;
	  = 'L':  Lower	triangle 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/output) DOUBLE	PRECISION array, dimension (LDAB, N)
	  On entry, 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).

	  On exit, AB is overwritten by	values generated during	the reduction
	  to tridiagonal form.	If UPLO	= 'U', the first superdiagonal and
	  the diagonal of the tridiagonal matrix T are returned	in rows	KD
	  and KD+1 of AB, and if UPLO =	'L', the diagonal and first subdiago-
	  nal of T are returned	in the first two rows of AB.

  LDAB	  (input) INTEGER
	  The leading dimension	of the array AB.  LDAB >= KD + 1.

  Q	  (output) DOUBLE PRECISION array, dimension (LDQ, N)
	  If JOBZ = 'V', the N-by-N orthogonal matrix used in the reduction
	  to tridiagonal form.	If JOBZ	= 'N', the array Q is not referenced.

  LDQ	  (input) INTEGER
	  The leading dimension	of the array Q.	 If JOBZ = 'V',	then LDQ >=
	  max(1,N).

  VL	  (input) DOUBLE PRECISION
	  If RANGE='V',	the lower bound	of the interval	to be searched for
	  eigenvalues.	Not referenced if RANGE	= 'A' or 'I'.

  VU	  (input) DOUBLE PRECISION
	  If RANGE='V',	the upper bound	of the interval	to be searched for
	  eigenvalues.	Not referenced if RANGE	= 'A' or 'I'.

  IL	  (input) INTEGER
	  If RANGE='I',	the index (from	smallest to largest) of	the smallest
	  eigenvalue to	be returned.  IL >= 1.	Not referenced if RANGE	= 'A'
	  or 'V'.

  IU	  (input) INTEGER
	  If RANGE='I',	the index (from	smallest to largest) of	the largest
	  eigenvalue to	be returned.  min(IL,N)	<= IU <= N.  Not referenced
	  if RANGE = 'A' or 'V'.

  ABSTOL  (input) DOUBLE PRECISION
	  The absolute error tolerance for the eigenvalues.  An	approximate
	  eigenvalue is	accepted as converged when it is determined to lie in
	  an interval [a,b] of width less than or equal	to

	  ABSTOL + EPS *   max(	|a|,|b|	) ,

	  where	EPS is the machine precision.  If ABSTOL is less than or
	  equal	to zero, then  EPS*|T|	will be	used in	its place, where |T|
	  is the 1-norm	of the tridiagonal matrix obtained by reducing AB to
	  tridiagonal form.

	  See "Computing Small Singular	Values of Bidiagonal Matrices with
	  Guaranteed High Relative Accuracy," by Demmel	and Kahan, LAPACK
	  Working Note #3.

  M	  (output) INTEGER
	  The total number of eigenvalues found.  0 <= M <= N.	If RANGE =
	  'A', M = N, and if RANGE = 'I', M = IU-IL+1.

  W	  (output) DOUBLE PRECISION array, dimension (N)
	  The first M elements contain the selected eigenvalues	in ascending
	  order.

  Z	  (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M))
	  If JOBZ = 'V', then if INFO =	0, the first M columns of Z contain
	  the orthonormal eigenvectors of the matrix corresponding to the
	  selected eigenvalues.	 If an eigenvector fails to converge, then
	  that column of Z contains the	latest approximation to	the eigenvec-
	  tor, and the index of	the eigenvector	is returned in IFAIL.  If
	  JOBZ = 'N', then Z is	not referenced.	 Note: the user	must ensure
	  that at least	max(1,M) columns are supplied in the array Z; if
	  RANGE	= 'V', the exact value of M is not known in advance and	an
	  upper	bound must be used.

  LDZ	  (input) INTEGER
	  The leading dimension	of the array Z.	 LDZ >=	1, and if JOBZ = 'V',
	  LDZ >= max(1,N).

  WORK	  (workspace) DOUBLE PRECISION array, dimension	(7*N)

  IWORK	  (workspace) INTEGER array, dimension (5*N)

  IFAIL	  (output) INTEGER array, dimension (N)
	  If JOBZ = 'V', then if INFO =	0, the first M elements	of IFAIL are
	  zero.	 If INFO > 0, then IFAIL contains the indices of the eigen-
	  vectors that failed to converge.  If JOBZ = 'N', then	IFAIL is not
	  referenced.

  INFO	  (output) INTEGER
	  = 0:	successful exit.
	  < 0:	if INFO	= -i, the i-th argument	had an illegal value.
	  > 0:	if INFO	= i, then i eigenvectors failed	to converge.  Their
	  indices are stored in	array IFAIL.