Purpose
 =======
 
    LA_SBGV, LA_SBGVD, LA_HBGV and LA_HBGVD compute all eigenvalues and,
 optionally, all eigenvectors of the generalized eigenvalue problem
                    A*z = lambda*B*z,
 where A and B are real symmetric in the cases of LA_SBGV and LA_SBGVD 
 and complex Hermitian in the cases of LA_HBGV and LA_HBGVD. Matrix B
 is positive definite. Matrices A and B are stored in a band format.
    LA_SBGVD and LA_HBGVD use a divide and conquer algorithm. If 
 eigenvectors are desired, they can be much faster than LA_SBGV and 
 LA_HBGV for large matrices but use more workspace.
 
 =========
 
         SUBROUTINE LA_SBGV / LA_SBGVD / LA_HBGV / LA_HBGVD( AB, BB, &
                                        W, UPLO=uplo, Z=z, INFO=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 or COMPLEX array, shape (:,:) with 
         size(AB,1) = ka + 1 and size(AB,2) = n, where ka is the number
 	 of subdiagonals or superdiagonals in the band and n is the 
    	 order of A and B.
         On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') 
 	 triangle of matrix A in band storage. The ka + 1 diagonals of
 	 A are stored in the rows of AB so that the j-th column of A
         is stored in the j-th column of AB as follows:
         if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j,
 	                                           1<=j<=n
         if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka),
 	                                           1<=j<=n.
         On exit, the contents of AB are destroyed.
 BB      (input/output) REAL or COMPLEX array, shape (:,:) with 
         size(BB,1) = kb + 1 and size(BB,2) = n, where kb is the number
 	 of subdiagonals or superdiagonals in the band of B.
         On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
 	 triangle of matrix B in band storage. The kb + 1 diagonals of
 	 B are stored in the rows of BB so that the j-th column of B
         is stored in the j-th column of BB as follows:
         if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j,
 	                                           1<=j<=n
         if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb),
 	                                           1<=j<=n.
         On exit, the factor S from the split Cholesky factorization
 	 B = S^H*S.
 W       (output) REAL array, shape (:) with size(W) = n.
         The eigenvalues in ascending order.
 UPLO    Optional (input) CHARACTER(LEN=1).
           = 'U': Upper triangles of A and B are stored;
           = 'L': Lower triangles of A and B are stored.
         Default value: 'U'.
 Z       Optional (output) REAL or COMPLEX square array, shape (:,:)
         with size(Z,1) = n.
         The matrix Z of eigenvectors, normalized so that Z^H*B*Z = I.
 INFO    Optional (output) INTEGER.
         = 0: successful exit.
         < 0: if INFO = -i, the i-th argument had an illegal value.
         > 0: the algorithm failed to converge or matrix B is not
 	 positive definite:
            <= n: if INFO = i, 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.