Purpose
 =======
 
      LA_SPEVX / LA_HPEVX compute selected eigenvalues and, optionally,
 the corresponding eigenvectors of a real symmetric/complex hermitian
 matrix A in packed storage. Eigenvalues and eigenvectors can be
 selected by specifying either a range of values or a range of indices
 for the desired eigenvalues.
 
 =========
 
        SUBROUTINE LA_SPEVX / LA_HPEVX( AP, W, UPLO=uplo, Z=z, &
                 VL=vl, VU=vu, IL=il, IU=iu, M=m, IFAIL=ifail, &
                 ABSTOL=abstol, INFO=info )
          <type>(<wp>), INTENT(INOUT) :: AP(:)
          REAL(<wp>), INTENT(OUT) :: W(:)
          CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO
          <type>(<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
          <type> ::= REAL | COMPLEX
          <wp> ::= KIND(1.0) | KIND(1.0D0)
 
 Arguments
 =========
 
  AP      (input/output) REAL or COMPLEX array, shape (:) with size(AP)=
          n*(n+1)/2, where n is the order of A.
          On entry, the upper or lower triangle of matrix A in packed
          storage. The elements are stored columnwise as follows:
          if UPLO = 'U', AP(i+(j-1)*j/2)=A(i,j) for 1<=i<=j<=n;
          if UPLO = 'L', AP(i+(j-1)*(2*n-j)/2)=A(i,j) for 1<=j<=i<=n.
          On exit, AP is overwritten by values generated during the
          reduction of A to a tridiagonal matrix T . If UPLO = 'U', the
          diagonal and first superdiagonal of T overwrite the correspond-
          ing diagonals of A. If UPLO = 'L', the diagonal and first
          subdiagonal of T overwrite the corresponding diagonals of A.
  W       (output) REAL array, shape (:) with size(W) = n.
          The eigenvalues in ascending order.
  UPLO    Optional (input) CHARACTER(LEN=1).
          = 'U': Upper triangle of A is stored;
          = 'L': Lower triangle of A is stored.
          Default value: 'U'.
 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 
 	  the matrix 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<=size(A,1).
          Default values: IL = 1 and IU = size(A,1).
          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<=size(A,1).
          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>)*||T||1 will be used in its place, where
 	  ||T||1 is the l1 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*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.