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LAPACK version 3.0
dstevx(3)

PURPOSE
  DSTEVX - compute selected eigenvalues and, optionally, eigenvectors of a
  real symmetric tridiagonal matrix A

SYNTAX
  SUBROUTINE DSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, W, Z,
		     LDZ, WORK, IWORK, IFAIL, INFO )

      CHARACTER	     JOBZ, RANGE

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

      DOUBLE	     PRECISION ABSTOL, VL, VU

      INTEGER	     IFAIL( * ), IWORK( * )

      DOUBLE	     PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )

DESCRIPTION
  DSTEVX computes selected eigenvalues and, optionally, eigenvectors of a
  real symmetric tridiagonal matrix A. Eigenvalues and eigenvectors 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.

  N	  (input) INTEGER
	  The order of the matrix.  N >= 0.

  D	  (input/output) DOUBLE PRECISION array, dimension (N)
	  On entry, the n diagonal elements of the tridiagonal matrix A.  On
	  exit, D may be multiplied by a constant factor chosen to avoid
	  over/underflow in computing the eigenvalues.

  E	  (input/output) DOUBLE PRECISION array, dimension (N)
	  On entry, the (n-1) subdiagonal elements of the tridiagonal matrix
	  A in elements 1 to N-1 of E; E(N) need not be set.  On exit, E may
	  be multiplied by a constant factor chosen to avoid over/underflow
	  in computing the eigenvalues.

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

  IL	  (input) INTEGER
	  IU	  (input) INTEGER If RANGE='I', the indices (in ascending
	  order) of the smallest and largest eigenvalues to be returned.  1
	  <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.  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.

	  Eigenvalues will be computed most accurately when ABSTOL is set to
	  twice the underflow threshold 2*DLAMCH('S'), not zero.  If this
	  routine returns with INFO>0, indicating that some eigenvectors did
	  not converge, try setting ABSTOL to 2*DLAMCH('S').

	  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 A corresponding to the
	  selected eigenvalues, with the i-th column of Z holding the
	  eigenvector associated with W(i).  If an eigenvector fails to
	  converge (INFO > 0), then that column of Z contains the latest
	  approximation to the eigenvector, 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 (5*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
	  eigenvectors 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.