!-----------------------------------------------------------------
!
! Purpose
! =======
!
!  LA_SBGV | LA_HBSV computes all the eigenvalues, and optionally,
!  the eigenvectors of a real generalized symmetric-definite banded
!  eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are
!  assumed to be symmetric and banded, and B is also positive definite.
!
! =========
!
!   SUBROUTINE LA_SBGV / LA_HBGV( AB, BB, W, UPLO, Z, INFO )
!      <type>(<wp>), INTENT(INOUT) :: AB(:,:), BB(:,:)
!      REAL(<wp>), INTENT(OUT) :: W(:)
!      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
! =========
!
! AB  (input/output) REAL / COMPLEX array, shape (:,:),
!     SIZE(AB,1) == ka+1, SIZE(AB,2) == n.
!     On entry, the upper or lower triangle of the symmetric band
!     matrix A, stored in the first ka+1 rows of the array.  The
!     j-th column of A is stored in the j-th column of the array AB
!     as follows:
!     if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
!     if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).
!     On exit, the contents of AB are destroyed.
!
! BB  (input/output) REAL / COMPLEX array, shape (:,:),
!     SIZE(BB,1) == kb+1, SIZE(BB,2) == n.
!     On entry, the upper or lower triangle of the symmetric band
!     matrix B, stored in the first kb+1 rows of the array.  The
!     j-th column of B is stored in the j-th column of the array BB
!     as follows:
!     if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
!     if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).
!     On exit, the factor S from the split Cholesky factorization
!     B = S**T*S.
!
! W   (output) REAL array, hape (:), SIZE(W) == n.
!     If INFO = 0, the eigenvalues in ascending order.
!
! 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 UPLU = '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,
!     with the i-th column of Z holding the eigenvector
!     associated with W(i). The eigenvectors are normalized
!     so that Z**T*B*Z = I.
!
! INFO  Optional (output) INTEGER
!     = 0:  successful exit
!     < 0:  if INFO = -i, the i-th argument had an illegal value
!     > 0:  if INFO = i, and i is:
!        <= n:  the algorithm 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 SPBSTF
!               returned INFO = i: 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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