```      SUBROUTINE DSPEVD( JOBZ, UPLO, N, AP, W, 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, UPLO
INTEGER            INFO, LDZ, LIWORK, LWORK, N
*     ..
*     .. Array Arguments ..
INTEGER            IWORK( * )
DOUBLE PRECISION   AP( * ), W( * ), WORK( * ), Z( LDZ, * )
*     ..
*
*  Purpose
*  =======
*
*  DSPEVD computes all the eigenvalues and, optionally, eigenvectors
*  of a real symmetric matrix A in packed storage. 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.
*
*  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.
*
*  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
*          On entry, the upper or lower triangle of the symmetric matrix
*          A, packed columnwise in a linear array.  The j-th column of A
*          is stored in the array AP as follows:
*          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
*          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
*
*          On exit, AP is overwritten by values generated during the
*          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
*          and first superdiagonal of the tridiagonal matrix T overwrite
*          the corresponding elements of A, and if UPLO = 'L', the
*          diagonal and first subdiagonal of T overwrite the
*          corresponding elements of A.
*
*  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/output) DOUBLE PRECISION array,
*                                         dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the required LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.
*          If N <= 1,               LWORK must be at least 1.
*          If JOBZ = 'N' and N > 1, LWORK must be at least 2*N.
*          If JOBZ = 'V' and N > 1, LWORK must be at least
*                                                 1 + 6*N + N**2.
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the required 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 required LIWORK.
*
*  LIWORK  (input) INTEGER
*          The dimension of the array IWORK.
*          If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
*          If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
*
*          If LIWORK = -1, then a workspace query is assumed; the
*          routine only calculates the required 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 an intermediate tridiagonal
*                form did not converge to zero.
*
*  =====================================================================
*
*     .. Parameters ..
DOUBLE PRECISION   ZERO, ONE
PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
LOGICAL            LQUERY, WANTZ
INTEGER            IINFO, INDE, INDTAU, INDWRK, ISCALE, LIWMIN,
\$                   LLWORK, LWMIN
DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
\$                   SMLNUM
*     ..
*     .. External Functions ..
LOGICAL            LSAME
DOUBLE PRECISION   DLAMCH, DLANSP
EXTERNAL           LSAME, DLAMCH, DLANSP
*     ..
*     .. External Subroutines ..
EXTERNAL           DOPMTR, DSCAL, DSPTRD, 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
IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
INFO = -1
ELSE IF( .NOT.( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) )
\$          THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
INFO = -7
END IF
*
IF( INFO.EQ.0 ) THEN
IF( N.LE.1 ) THEN
LIWMIN = 1
LWMIN = 1
ELSE
IF( WANTZ ) THEN
LIWMIN = 3 + 5*N
LWMIN = 1 + 6*N + N**2
ELSE
LIWMIN = 1
LWMIN = 2*N
END IF
END IF
IWORK( 1 ) = LIWMIN
WORK( 1 ) = LWMIN
*
IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -9
ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
INFO = -11
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DSPEVD', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
*     Quick return if possible
*
IF( N.EQ.0 )
\$   RETURN
*
IF( N.EQ.1 ) THEN
W( 1 ) = AP( 1 )
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 = DLANSP( 'M', UPLO, N, AP, 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
CALL DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
END IF
*
*     Call DSPTRD to reduce symmetric packed matrix to tridiagonal form.
*
INDE = 1
INDTAU = INDE + N
CALL DSPTRD( UPLO, N, AP, W, WORK( INDE ), WORK( INDTAU ), IINFO )
*
*     For eigenvalues only, call DSTERF.  For eigenvectors, first call
*     DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
*     tridiagonal matrix, then call DOPMTR to multiply it by the
*     Householder transformations represented in AP.
*
IF( .NOT.WANTZ ) THEN
CALL DSTERF( N, W, WORK( INDE ), INFO )
ELSE
INDWRK = INDTAU + N
LLWORK = LWORK - INDWRK + 1
CALL DSTEDC( 'I', N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
\$                LLWORK, IWORK, LIWORK, INFO )
CALL DOPMTR( 'L', UPLO, 'N', N, N, AP, WORK( INDTAU ), Z, LDZ,
\$                WORK( INDWRK ), IINFO )
END IF
*
*     If matrix was scaled, then rescale eigenvalues appropriately.
*
IF( ISCALE.EQ.1 )
\$   CALL DSCAL( N, ONE / SIGMA, W, 1 )
*
WORK( 1 ) = LWMIN
IWORK( 1 ) = LIWMIN
RETURN
*
*     End of DSPEVD
*
END

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