!-----------------------------------------------------------------
!
! Purpose
! =======
!
!  LA_SPGV | LA_HPGV computes all the eigenvalues and, optionally, the
!  eigenvectors of a real generalized symmetric-definite eigenproblem,
!  of the form
!  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
!  Here A and B are assumed to be symmetric, stored in packed format,
!  and B is also positive definite.
!
! =======
!
!   SUBROUTINE LA_SPGV / LA_HPGV_F90( AP, BP, W, ITYPE, UPLO, Z, INFO )
!      <type>(<wp>), INTENT(INOUT) :: AP(:), BP(:)
!      REAL(<wp>), INTENT(OUT) :: W(:)
!      INTEGER, INTENT(IN), OPTIONAL :: ITYPE
!      CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO
!      <type>(<wp>), INTENT(OUT), OPTIONAL :: Z(:,:)
!      INTEGER, INTENT(OUT), OPTIONAL :: INFO
!   where
!      <type> ::= REAL | COMPLEX
!      <wp>   ::= KIND(1.0) | KIND(1.0D0)
!
! Arguments
! =========
!
! AP   (input/output) REAL | 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, the contents of AP are destroyed.
!
! BP   (input/output) REAL | COMPLEX array, shape (:),
!      SIZE(BP) == (n*(n+1)/2).
!      On entry, the upper or lower triangle of the symmetric matrix
!      B, packed columnwise in a linear array.  The j-th column of B
!      is stored in the array BP as follows:
!      if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
!      if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
!      On exit, the triangular factor U or L from the Cholesky
!      factorization B = U**T*U or B = L*L**T, in the same storage
!      format as B.
!
!  W   (output) REAL array, shape (:), SIZE(W) == n, where
!       n*(n+1)/2 ==  SIZE(AP).
!      If INFO = 0, the eigenvalues in ascending order.
!
! ITYPE  Optional (input) INTEGER
!      Specifies the problem type to be solved:
!      = 1:  A*x = (lambda)*B*x
!      = 2:  A*B*x = (lambda)*x
!      = 3:  B*A*x = (lambda)*x
!      If ITYPE is not present ITYPE = 1 is assumed.
!
! UPLO  Optional (input) CHARACTER*1
!      = 'U':  Upper triangles of A and B are stored;
!      = 'L':  Lower triangles of A and B are stored.
!      If UPLO is not present UPLO = 'U' is assumed
!
! Z    Optional (output) REAL | COMPLEX array, shape (:,:),
!      SIZE(Z,1) == SIZE(Z,2) == n.
!      If INFO = 0, Z contains the matrix Z of eigenvectors.
!      The eigenvectors are normalized as follows:
!      if ITYPE = 1 or 2, Z**T*B*Z = I;
!      if ITYPE = 3, Z**T*inv(B)*Z = I.
!
! INFO Optional (output) INTEGER
!      = 0:  successful exit
!      < 0:  if INFO = -i, the i-th argument had an illegal value
!      > 0:  SPPTRF or SSPEV returned an error code:
!         <= n:  if INFO = i, SSPEV failed to converge;
!                i off-diagonal elements of an intermediate
!                tridiagonal form did not converge to zero.
!         > n:   if INFO = n + i, for 1 <= i <= n, then the leading
!                minor of order i of B is not positive definite.
!                The factorization of B could not be completed and
!                no eigenvalues or eigenvectors were computed.
!      If INFO is not present and an error occurs, then the program is
!         terminated with an error message.
!---------------------------------------------------------------------

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