```      SUBROUTINE DSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
\$                  INFO )
*
*  -- LAPACK driver routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          JOBZ, UPLO
INTEGER            INFO, KD, LDAB, LDZ, N
*     ..
*     .. Array Arguments ..
DOUBLE PRECISION   AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
*     ..
*
*  Purpose
*  =======
*
*  DSBEV computes all the eigenvalues and, optionally, eigenvectors of
*  a real symmetric band matrix A.
*
*  Arguments
*  =========
*
*  JOBZ    (input) CHARACTER*1
*          = 'N':  Compute eigenvalues only;
*          = 'V':  Compute eigenvalues and eigenvectors.
*
*  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) DOUBLE PRECISION 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.
*
*  W       (output) DOUBLE PRECISION array, dimension (N)
*          If INFO = 0, the eigenvalues in ascending order.
*
*  Z       (output) DOUBLE PRECISION array, dimension (LDZ, N)
*          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
*          eigenvectors of the matrix A, with the i-th column of Z
*          holding the eigenvector associated with W(i).
*          If JOBZ = 'N', then Z is not referenced.
*
*  LDZ     (input) INTEGER
*          The leading dimension of the array Z.  LDZ >= 1, and if
*          JOBZ = 'V', LDZ >= max(1,N).
*
*  WORK    (workspace) DOUBLE PRECISION array, dimension (max(1,3*N-2))
*
*  INFO    (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.
*
*  =====================================================================
*
*     .. Parameters ..
DOUBLE PRECISION   ZERO, ONE
PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
*     ..
*     .. Local Scalars ..
LOGICAL            LOWER, WANTZ
INTEGER            IINFO, IMAX, INDE, INDWRK, ISCALE
DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
\$                   SMLNUM
*     ..
*     .. External Functions ..
LOGICAL            LSAME
DOUBLE PRECISION   DLAMCH, DLANSB
EXTERNAL           LSAME, DLAMCH, DLANSB
*     ..
*     .. External Subroutines ..
EXTERNAL           DLASCL, DSBTRD, DSCAL, DSTEQR, DSTERF, XERBLA
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          SQRT
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
WANTZ = LSAME( JOBZ, 'V' )
LOWER = LSAME( UPLO, 'L' )
*
INFO = 0
IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
INFO = -1
ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( KD.LT.0 ) THEN
INFO = -4
ELSE IF( LDAB.LT.KD+1 ) THEN
INFO = -6
ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
INFO = -9
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DSBEV ', -INFO )
RETURN
END IF
*
*     Quick return if possible
*
IF( N.EQ.0 )
\$   RETURN
*
IF( N.EQ.1 ) THEN
IF( LOWER ) THEN
W( 1 ) = AB( 1, 1 )
ELSE
W( 1 ) = AB( KD+1, 1 )
END IF
IF( WANTZ )
\$      Z( 1, 1 ) = ONE
RETURN
END IF
*
*     Get machine constants.
*
SAFMIN = DLAMCH( 'Safe minimum' )
EPS = DLAMCH( 'Precision' )
SMLNUM = SAFMIN / EPS
BIGNUM = ONE / SMLNUM
RMIN = SQRT( SMLNUM )
RMAX = SQRT( BIGNUM )
*
*     Scale matrix to allowable range, if necessary.
*
ANRM = DLANSB( 'M', UPLO, N, KD, AB, LDAB, WORK )
ISCALE = 0
IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
ISCALE = 1
SIGMA = RMIN / ANRM
ELSE IF( ANRM.GT.RMAX ) THEN
ISCALE = 1
SIGMA = RMAX / ANRM
END IF
IF( ISCALE.EQ.1 ) THEN
IF( LOWER ) THEN
CALL DLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
ELSE
CALL DLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
END IF
END IF
*
*     Call DSBTRD to reduce symmetric band matrix to tridiagonal form.
*
INDE = 1
INDWRK = INDE + N
CALL DSBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, WORK( INDE ), Z, LDZ,
\$             WORK( INDWRK ), IINFO )
*
*     For eigenvalues only, call DSTERF.  For eigenvectors, call SSTEQR.
*
IF( .NOT.WANTZ ) THEN
CALL DSTERF( N, W, WORK( INDE ), INFO )
ELSE
CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
\$                INFO )
END IF
*
*     If matrix was scaled, then rescale eigenvalues appropriately.
*
IF( ISCALE.EQ.1 ) THEN
IF( INFO.EQ.0 ) THEN
IMAX = N
ELSE
IMAX = INFO - 1
END IF
CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
END IF
*
RETURN
*
*     End of DSBEV
*
END

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