!-----------------------------------------------------------------
!
! Purpose
! =======
!
! LA_SPEVD / LA_HPEVD computes all the eigenvalues and, optionally,
! eigenvectors of a real symmetric matrix A in packed storage. If
! eigenvectors are desired, it uses a divide and conquer algorithm.
! The divide and conquer algorithm makes very mild assumptions about
! floating point arithmetic. It will work on machines with a guard
! digit in add/subtract, or on those binary machines without guard
! digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
! Cray-2. It could conceivably fail on hexadecimal or decimal machines
! without guard digits, but we know of none.
!
! Arguments
! =========
!
! SUBROUTINE LA_SPEVD / LA_HPEV( AP, W, UPLO, Z, INFO )
!    <type>(<wp>), INTENT(INOUT) :: AP(:)
!    REAL(<wp>), INTENT(OUT) :: W(:)
!    CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO
!    <type>(<wp>), INTENT(OUT), OPTIONAL :: Z(:,:)
!    INTEGER, INTENT(OUT), OPTIONAL :: INFO
!    <type> ::= REAL | COMPLEX
!    <wp>   ::= KIND(1.0) | KIND(1.0D0)
!
! =====================
!
! AP   (input/output) either REAL or COMPLEX array, shape (:),
!      SIZE(AP) == (n*(n+1)/2).
!      On entry, the upper or lower triangle of the symmetric matrix
!      A, packed columnwise in a linear array.  The j-th column of A
!      is stored in the array AP as follows:
!      if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
!      if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
!      On exit, AP is overwritten by values generated during the
!      reduction to tridiagonal form.  If UPLO = 'U', the diagonal
!      and first superdiagonal of the tridiagonal matrix T overwrite
!      the corresponding elements of A, and if UPLO = 'L', the
!      diagonal and first subdiagonal of T overwrite the
!      corresponding elements of A.
!      INFO = -1 if SIZE(AP) < 0 or SIZE(AP) /= n*(n+1)/2.
!
! W    (output) either REAL or COMPLEX array, shape (:),
!      SIZE(W) == n, where = n*(n+1)/2 ==  SIZE(AP).
!      If INFO = 0, the eigenvalues in ascending order.
!      INFO = -2 if SIZE(W) /= n.
!
! UPLO Optional (input) CHARACTER*1
!      = 'U':  Upper triangle of A is stored;
!      = 'L':  Lower triangle of A is stored.
!      If UPLO is not present UPLO = 'U' is assumed.
!      INFO -3 if UPLO /= 'U' nor 'L'.
!
! Z    Optional (output) either REAL or COMPLEX rectangular array,
!      shape either (:,:), size(Z,1) == n and size(Z,2) == n.
!      Z contains the orthonormal eigenvectors of the matrix A,
!      with the i-th column of Z holding the eigenvector associated
!      with W(i).
!      INFO = -4 if SIZE(Z,1) and SIZE(Z,2) /= n.
!
! INFO Optional (output) INTEGER
!      = 0:  successful exit.
!      < 0:  if INFO = -i, the i-th argument had an illegal value.
!      > 0:  if INFO = i, the algorithm failed to converge; i
!            off-diagonal elements of an intermediate tridiagonal
!            form did not converge to zero.
!      If INFO is not present and an error occurs, then the program is
!      terminated with an error message.
!
!-------------------------------------

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