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LAPACK version 3.0
dsyevx(3)

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

SYNTAX
  SUBROUTINE DSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL, M,
		     W, Z, LDZ, WORK, LWORK, IWORK, IFAIL, INFO )

      CHARACTER	     JOBZ, RANGE, UPLO

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

      DOUBLE	     PRECISION ABSTOL, VL, VU

      INTEGER	     IFAIL( * ), IWORK( * )

      DOUBLE	     PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )

DESCRIPTION
  DSYEVX computes selected eigenvalues and, optionally, eigenvectors of a
  real symmetric 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.

  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.

  A	  (input/output) DOUBLE PRECISION array, dimension (LDA, N)
	  On entry, the symmetric matrix A.  If UPLO = 'U', the leading N-
	  by-N upper triangular part of A contains the upper triangular part
	  of the matrix A.  If UPLO = 'L', the leading N-by-N lower
	  triangular part of A contains the lower triangular part of the
	  matrix A.  On exit, the lower triangle (if UPLO='L') or the upper
	  triangle (if UPLO='U') of A, including the diagonal, is destroyed.

  LDA	  (input) INTEGER
	  The leading dimension of the array A.	 LDA >= max(1,N).

  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 obtained by reducing A to
	  tridiagonal form.

	  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)
	  On normal exit, 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, 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/output) DOUBLE PRECISION array, dimension (LWORK)
	  On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

  LWORK	  (input) INTEGER
	  The length of the array WORK.	 LWORK >= max(1,8*N).  For optimal
	  efficiency, LWORK >= (NB+3)*N, where NB is the max of the blocksize
	  for DSYTRD and DORMTR returned by ILAENV.

	  If LWORK = -1, then a workspace query is assumed; the routine only
	  calculates the optimal size of the WORK array, returns this value
	  as the first entry of the WORK array, and no error message related
	  to LWORK is issued by XERBLA.

  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.