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       LAPACK-3 - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric
       band matrix A


                          W, Z, LDZ, WORK, IWORK, IFAIL, INFO )


           INTEGER        IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N

           REAL           ABSTOL, VL, VU

           INTEGER        IFAIL( * ), IWORK( * )

           REAL           AB( LDAB, * ), Q( LDQ, * ), W( * ), WORK( * ), Z( LDZ, * )


       SSBEVX  computes  selected  eigenvalues  and, optionally, eigenvectors of a real symmetric
       band matrix A.  Eigenvalues and eigenvectors can
        be selected by specifying either a range of values or a range of
        indices for the desired eigenvalues.


        JOBZ    (input) CHARACTER*1
                = 'N':  Compute eigenvalues only;
                = 'V':  Compute eigenvalues and eigenvectors.

        RANGE   (input) CHARACTER*1
                = 'A': all eigenvalues will be found;
                = 'V': all eigenvalues in the half-open interval (VL,VU]
                will be found;
                = 'I': the IL-th through IU-th eigenvalues will be found.

        UPLO    (input) CHARACTER*1
                = 'U':  Upper triangle of A is stored;
                = 'L':  Lower triangle of A is stored.

        N       (input) INTEGER
                The order of the matrix A.  N >= 0.

        KD      (input) INTEGER
                The number of superdiagonals of the matrix A if UPLO = 'U',
                or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

        AB      (input/output) REAL array, dimension (LDAB, N)
                On entry, the upper or lower triangle of the symmetric band
                matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
                if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
                On exit, AB is overwritten by values generated during the
                reduction to tridiagonal form.  If UPLO = 'U', the first
                superdiagonal and the diagonal of the tridiagonal matrix T
                are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
                the diagonal and first subdiagonal of T are returned in the
                first two rows of AB.

        LDAB    (input) INTEGER
                The leading dimension of the array AB.  LDAB >= KD + 1.

        Q       (output) REAL array, dimension (LDQ, N)
                If JOBZ = 'V', the N-by-N orthogonal matrix used in the
                reduction to tridiagonal form.
                If JOBZ = 'N', the array Q is not referenced.

        LDQ     (input) INTEGER
                The leading dimension of the array Q.  If JOBZ = 'V', then
                LDQ >= max(1,N).

        VL      (input) REAL
                VU      (input) REAL
                If RANGE='V', the lower and upper bounds of the interval to
                be searched for eigenvalues. VL < VU.
                Not referenced if RANGE = 'A' or 'I'.

        IL      (input) INTEGER
                IU      (input) INTEGER
                If RANGE='I', the indices (in ascending order) of the
                smallest and largest eigenvalues to be returned.
                1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
                Not referenced if RANGE = 'A' or 'V'.

        ABSTOL  (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 + EPS *   max( |a|,|b| ) ,
                where EPS is the machine precision.  If ABSTOL is less than
                or equal to zero, then  EPS*|T|  will be used in its place,
                where |T| is the 1-norm of the tridiagonal matrix obtained
                by reducing AB to tridiagonal form.
                Eigenvalues will be computed most accurately when ABSTOL is
                set to twice the underflow threshold 2*SLAMCH('S'), not zero.
                If this routine returns with INFO>0, indicating that some
                eigenvectors did not converge, try setting ABSTOL to
                See "Computing Small Singular Values of Bidiagonal Matrices
                with Guaranteed High Relative Accuracy," by Demmel and
                Kahan, LAPACK Working Note #3.

        M       (output) INTEGER
                The total number of eigenvalues found.  0 <= M <= N.
                If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.

        W       (output) REAL array, dimension (N)
                The first M elements contain the selected eigenvalues in
                ascending order.

        Z       (output) REAL array, dimension (LDZ, max(1,M))
                If JOBZ = 'V', then if INFO = 0, 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 holding the eigenvector associated with 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.
                If JOBZ = 'N', then Z is not referenced.
                Note: the user must ensure that at least max(1,M) columns are
                supplied in the array Z; if RANGE = 'V', the exact value of M
                is not known in advance and an upper bound must be used.

        LDZ     (input) INTEGER
                The leading dimension of the array Z.  LDZ >= 1, and if
                JOBZ = 'V', LDZ >= max(1,N).

        WORK    (workspace) REAL array, dimension (7*N)

        IWORK   (workspace) INTEGER array, dimension (5*N)

        IFAIL   (output) INTEGER array, dimension (N)
                If JOBZ = 'V', then 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.
                If JOBZ = 'N', then IFAIL is not referenced.

        INFO    (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.

 LAPACK driver routine (version 3.2)        April 2011                            SSBEVX(3lapack)