```      SUBROUTINE DSTEVD( JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
\$                   LIWORK, INFO )
*
*  -- LAPACK driver routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          JOBZ
INTEGER            INFO, LDZ, LIWORK, LWORK, N
*     ..
*     .. Array Arguments ..
INTEGER            IWORK( * )
DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )
*     ..
*
*  Purpose
*  =======
*
*  DSTEVD computes all eigenvalues and, optionally, eigenvectors of a
*  real symmetric tridiagonal matrix. If eigenvectors are desired, it
*  uses a divide and conquer algorithm.
*
*  The divide and conquer algorithm makes very mild assumptions about
*  floating point arithmetic. It will work on machines with a guard
*  digit in add/subtract, or on those binary machines without guard
*  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*  Cray-2. It could conceivably fail on hexadecimal or decimal machines
*  without guard digits, but we know of none.
*
*  Arguments
*  =========
*
*  JOBZ    (input) CHARACTER*1
*          = 'N':  Compute eigenvalues only;
*          = 'V':  Compute eigenvalues and eigenvectors.
*
*  N       (input) INTEGER
*          The order of the matrix.  N >= 0.
*
*  D       (input/output) DOUBLE PRECISION array, dimension (N)
*          On entry, the n diagonal elements of the tridiagonal matrix
*          A.
*          On exit, if INFO = 0, the eigenvalues in ascending order.
*
*  E       (input/output) DOUBLE PRECISION array, dimension (N-1)
*          On entry, the (n-1) subdiagonal elements of the tridiagonal
*          matrix A, stored in elements 1 to N-1 of E.
*          On exit, the contents of E are destroyed.
*
*  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 D(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/output) DOUBLE PRECISION array,
*                                         dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.
*          If JOBZ  = 'N' or N <= 1 then LWORK must be at least 1.
*          If JOBZ  = 'V' and N > 1 then LWORK must be at least
*                         ( 1 + 4*N + N**2 ).
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal sizes of the WORK and IWORK
*          arrays, returns these values as the first entries of the WORK
*          and IWORK arrays, and no error message related to LWORK or
*          LIWORK is issued by XERBLA.
*
*  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
*          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
*
*  LIWORK  (input) INTEGER
*          The dimension of the array IWORK.
*          If JOBZ  = 'N' or N <= 1 then LIWORK must be at least 1.
*          If JOBZ  = 'V' and N > 1 then LIWORK must be at least 3+5*N.
*
*          If LIWORK = -1, then a workspace query is assumed; the
*          routine only calculates the optimal sizes of the WORK and
*          IWORK arrays, returns these values as the first entries of
*          the WORK and IWORK arrays, and no error message related to
*          LWORK or LIWORK is issued by XERBLA.
*
*  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 E did not converge to zero.
*
*  =====================================================================
*
*     .. Parameters ..
DOUBLE PRECISION   ZERO, ONE
PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
*     ..
*     .. Local Scalars ..
LOGICAL            LQUERY, WANTZ
INTEGER            ISCALE, LIWMIN, LWMIN
DOUBLE PRECISION   BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
\$                   TNRM
*     ..
*     .. External Functions ..
LOGICAL            LSAME
DOUBLE PRECISION   DLAMCH, DLANST
EXTERNAL           LSAME, DLAMCH, DLANST
*     ..
*     .. External Subroutines ..
EXTERNAL           DSCAL, DSTEDC, DSTERF, XERBLA
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          SQRT
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
WANTZ = LSAME( JOBZ, 'V' )
LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
*
INFO = 0
LIWMIN = 1
LWMIN = 1
IF( N.GT.1 .AND. WANTZ ) THEN
LWMIN = 1 + 4*N + N**2
LIWMIN = 3 + 5*N
END IF
*
IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
INFO = -6
END IF
*
IF( INFO.EQ.0 ) THEN
WORK( 1 ) = LWMIN
IWORK( 1 ) = LIWMIN
*
IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -8
ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
INFO = -10
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DSTEVD', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
*     Quick return if possible
*
IF( N.EQ.0 )
\$   RETURN
*
IF( N.EQ.1 ) THEN
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.
*
ISCALE = 0
TNRM = DLANST( 'M', N, D, E )
IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
ISCALE = 1
SIGMA = RMIN / TNRM
ELSE IF( TNRM.GT.RMAX ) THEN
ISCALE = 1
SIGMA = RMAX / TNRM
END IF
IF( ISCALE.EQ.1 ) THEN
CALL DSCAL( N, SIGMA, D, 1 )
CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
END IF
*
*     For eigenvalues only, call DSTERF.  For eigenvalues and
*     eigenvectors, call DSTEDC.
*
IF( .NOT.WANTZ ) THEN
CALL DSTERF( N, D, E, INFO )
ELSE
CALL DSTEDC( 'I', N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
\$                INFO )
END IF
*
*     If matrix was scaled, then rescale eigenvalues appropriately.
*
IF( ISCALE.EQ.1 )
\$   CALL DSCAL( N, ONE / SIGMA, D, 1 )
*
WORK( 1 ) = LWMIN
IWORK( 1 ) = LIWMIN
*
RETURN
*
*     End of DSTEVD
*
END

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