
 
 Purpose
 =======
 
    LA_STEVX computes selected eigenvalues and, optionally, the 
 corresponding 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.
 
 =========
 
        SUBROUTINE LA_STEVX( D, E, W, Z=z, VL=vl, VU=vu, &
                         IL=il, IU=iu, M=m, IFAIL=ifail, &
                         ABSTOL=abstol, INFO=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)
 
 Arguments
 =========
 
 D        (input/output) REAL array, shape (:) with size(D) = n, where n
          is the order of A.
          On entry, the diagonal elements of the matrix A.
          On exit, the original contents of D possibly multiplied by a 
          constant factor to avoid over/underflow in computing the
 	  eigenvalues.
 E        (input/output) REAL array, shape (:) with size(E) = n.
          On entry, the n-1 subdiagonal elements of A in E(1) to E(n-1).
 	  E(n) need not be set.
          On exit, the original contents of E possibly multiplied by a 
 	  constant factor to avoid over/underflow in computing the 
 	  eigenvalues.
 W        (output) REAL array with size(W) = n.
          The first M elements contain the selected eigenvalues in 
 	  ascending order.
 Z        Optional (output) REAL or COMPLEX array, shape (:,:) with 
          size(Z,1) = n and size(Z,2) = M.
          The first M columns of Z contain the orthonormal eigenvectors
 	  of A corresponding to the selected eigenvalues, with the i-th
 	  column of Z containing the eigenvector associated with the
          eigenvalue in 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.
          Note: The user must ensure that at least M columns are 
 	  supplied in the array Z. When the exact value of M is not 
 	  known in advance, an upper bound must be used. In all cases
 	  M <= n.
 VL,VU    Optional (input) REAL.
          The lower and upper bounds of the interval to be searched for 
 	  eigenvalues. VL < VU.
          default values: VL = -HUGE(<wp>) and VU = HUGE(<wp>), where 
 	  <wp> ::= KIND(1.0) | KIND(1.0D0).
          Note: Neither VL nor VU may be present if IL and/or IU is 
 	  present.
 IL,IU    Optional (input) INTEGER.
          The indices of the smallest and largest eigenvalues to be
 	  returned. The IL-th through IU-th eigenvalues will be found.
 	  1 <= IL <= IU <= n.
          Default values: IL = 1 and IU = n.
          Note: Neither IL nor IU may be present if VL and/or VU is 
 	  present.
          Note: All eigenvalues are calculated if none of the arguments
 	  VL, VU, IL and IU are present.
 M        Optional (output) INTEGER.
          The total number of eigenvalues found. 0 <= M <= n.
          Note: If IL and IU are present then M = IU - IL + 1.
 IFAIL    Optional (output) INTEGER array, shape (:) with 
          size(IFAIL) = n.
          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.
          Note: If Z is present then IFAIL should also be present.
 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 + EPSILON(1.0_<wp>) * max(|a|,|b|),
          where <wp> is the working precision. If ABSTOL <= 0, then
 	  EPSILON(1.0_<wp>) * ||A||1 will be used in its place. 
 	  Eigenvalues will be computed most accurately when ABSTOL is
 	  set to twice the underflow threshold 
 	  2 * LA_LAMCH(1.0_<wp>, 'Save minimum'), not zero.
          Default value: 0.0_<wp>.
          Note: If this routine returns with INFO > 0, then some 
 	  eigenvectors did not converge. Try setting ABSTOL to 
 	  2 * LA_LAMCH(1.0_<wp>, 'Save minimum').
 INFO     Optional (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.

