!-----------------------------------------------------------------
!
! Purpose
! =======
!
!  LA_STEVX 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
! =========
!
!  SUBROUTINE LA_STEVX( D, E, W, Z, VL, VU, IL, IU, &
!                       M, IFAIL, ABSTOL, INFO )
!     REAL(<wp>), INTENT(INOUT) :: D(:), E(:)
!     REAL(<wp>), INTENT(OUT) :: W(:)
!     REAL(<wp>), INTENT(OUT), OPTIONAL :: Z(:,:)
!     REAL(<wp>), INTENT(IN), OPTIONAL :: VL, VU
!     INTEGER, INTENT(IN), OPTIONAL :: IL, IU
!     INTEGER, INTENT(OUT), OPTIONAL :: M
!     INTEGER, INTENT(OUT), OPTIONAL :: IFAIL(:)
!     REAL(<wp>), INTENT(IN), OPTIONAL :: ABSTOL
!     INTEGER, INTENT(OUT), OPTIONAL :: INFO
!  where
!     <wp>   ::= KIND(1.0) | KIND(1.0D0)
!
! ===================
!
! D    (input/output) REAL array, shape (:), where SIZE(D)
!      indicates the matrix rank (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) REAL array, shape (:), where
!      SIZE(E) == SIZE(D).
!      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.
!
! W    (output) REAL array, where SIZE(W) == n.
!      The first M elements contain the selected eigenvalues in
!      ascending order.
!
! Z    Optional (output) REAL array, SIZE(Z,1) == SIZE(Z,2) == n.
!      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.
!
! VL   Optional (input) REAL
! VU   Optional (input) REAL
!      The lower and upper bounds of the interval to be searched for
!      eigenvalues. VL < VU.
!      If VL is not present VL = -HUGE(<wp>) is assumed.
!      If VU is not present VU =  HUGE(<wp>) is assumed.
!
! IL   Optional (input) INTEGER
! IU   Optional (input) INTEGER
!      The indices (in ascending order) of the smallest and largest
!      eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0;
!      If IL is not present IL = 1 is assumed.
!      If IU is not present IU = n is assumed.
!
! M    Optional (output) INTEGER
!      The total number of eigenvalues found.  0 <= M <= N.
!
! IFAIL Optional (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.
!
! ABSTOL  Optional (input) REAL
!      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*_LAMCH('S'), not zero.
!      If this routine returns with INFO>0, indicating that some
!      eigenvectors did not converge, try setting ABSTOL to
!      2*_LAMCH('S').
!      If ABSTOL is not present then ABSTOL = 2*_LAMCH('S') is assumed.
!      _LAMCH ::= SLAMCH | DLAMCH.
!
!      See "Computing Small Singular Values of Bidiagonal Matrices
!      with Guaranteed High Relative Accuracy," by Demmel and
!      Kahan, LAPACK Working Note #3.
!
! 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.
!      If INFO is not present and an error occurs, then the program is
!              terminated with an error message.
!-------------------------------------

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