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

NAME
  DSPEVX - compute selected eigenvalues	and, optionally, eigenvectors of a
  real symmetric matrix	A in packed storage

SYNOPSIS

  SUBROUTINE DSPEVX( JOBZ, RANGE, UPLO,	N, AP, VL, VU, IL, IU, ABSTOL, M, W,
		     Z,	LDZ, WORK, IWORK, IFAIL, INFO )

      CHARACTER	     JOBZ, RANGE, UPLO

      INTEGER	     IL, INFO, IU, LDZ,	M, N

      DOUBLE	     PRECISION ABSTOL, VL, VU

      INTEGER	     IFAIL( * ), IWORK(	* )

      DOUBLE	     PRECISION AP( * ),	W( * ),	WORK( *	), Z( LDZ, * )

PURPOSE
  DSPEVX computes selected eigenvalues and, optionally,	eigenvectors of	a
  real symmetric matrix	A in packed storage.  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.

  AP	  (input/output) DOUBLE	PRECISION array, dimension (N*(N+1)/2)
	  On entry, the	upper or lower triangle	of the symmetric matrix	A,
	  packed columnwise in a linear	array.	The j-th column	of A is
	  stored in the	array AP as follows: if	UPLO = 'U', AP(i + (j-1)*j/2)
	  = A(i,j) for 1<=i<=j;	if UPLO	= 'L', AP(i + (j-1)*(2*n-j)/2) =
	  A(i,j) for j<=i<=n.

	  On exit, AP is overwritten by	values generated during	the reduction
	  to tridiagonal form.	If UPLO	= 'U', the diagonal and	first
	  superdiagonal	of the tridiagonal matrix T overwrite the correspond-
	  ing elements of A, and if UPLO = 'L',	the diagonal and first subdi-
	  agonal of T overwrite	the corresponding elements of A.

  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 AP 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)
	  If INFO = 0, 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	(8*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.