zstemr.f

          SUBROUTINE ZSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
         $                   M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK,
         $                   IWORK, LIWORK, INFO )
          IMPLICIT NONE
    *
    *  -- LAPACK computational routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          JOBZ, RANGE
          LOGICAL            TRYRAC
          INTEGER            IL, INFO, IU, LDZ, NZC, LIWORK, LWORK, M, N
          DOUBLE PRECISION VL, VU
    *     ..
    *     .. Array Arguments ..
          INTEGER            ISUPPZ( * ), IWORK( * )
          DOUBLE PRECISION   D( * ), E( * ), W( * ), WORK( * )
          COMPLEX*16         Z( LDZ, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZSTEMR computes selected eigenvalues and, optionally, eigenvectors
    *  of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
    *  a well defined set of pairwise different real eigenvalues, the corresponding
    *  real eigenvectors are pairwise orthogonal.
    *
    *  The spectrum may be computed either completely or partially by specifying
    *  either an interval (VL,VU] or a range of indices IL:IU for the desired
    *  eigenvalues.
    *
    *  Depending on the number of desired eigenvalues, these are computed either
    *  by bisection or the dqds algorithm. Numerically orthogonal eigenvectors are
    *  computed by the use of various suitable L D L^T factorizations near clusters
    *  of close eigenvalues (referred to as RRRs, Relatively Robust
    *  Representations). An informal sketch of the algorithm follows.
    *
    *  For each unreduced block (submatrix) of T,
    *     (a) Compute T - sigma I  = L D L^T, so that L and D
    *         define all the wanted eigenvalues to high relative accuracy.
    *         This means that small relative changes in the entries of D and L
    *         cause only small relative changes in the eigenvalues and
    *         eigenvectors. The standard (unfactored) representation of the
    *         tridiagonal matrix T does not have this property in general.
    *     (b) Compute the eigenvalues to suitable accuracy.
    *         If the eigenvectors are desired, the algorithm attains full
    *         accuracy of the computed eigenvalues only right before
    *         the corresponding vectors have to be computed, see steps c) and d).
    *     (c) For each cluster of close eigenvalues, select a new
    *         shift close to the cluster, find a new factorization, and refine
    *         the shifted eigenvalues to suitable accuracy.
    *     (d) For each eigenvalue with a large enough relative separation compute
    *         the corresponding eigenvector by forming a rank revealing twisted
    *         factorization. Go back to (c) for any clusters that remain.
    *
    *  For more details, see:
    *  - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations
    *    to compute orthogonal eigenvectors of symmetric tridiagonal matrices,"
    *    Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.
    *  - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and
    *    Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25,
    *    2004.  Also LAPACK Working Note 154.
    *  - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric
    *    tridiagonal eigenvalue/eigenvector problem",
    *    Computer Science Division Technical Report No. UCB/CSD-97-971,
    *    UC Berkeley, May 1997.
    *
    *  Notes:
    *  1.ZSTEMR works only on machines which follow IEEE-754
    *  floating-point standard in their handling of infinities and NaNs.
    *  This permits the use of efficient inner loops avoiding a check for
    *  zero divisors.
    *
    *  2. LAPACK routines can be used to reduce a complex Hermitean matrix to
    *  real symmetric tridiagonal form.
    *
    *  (Any complex Hermitean tridiagonal matrix has real values on its diagonal
    *  and potentially complex numbers on its off-diagonals. By applying a
    *  similarity transform with an appropriate diagonal matrix
    *  diag(1,e^{i \phy_1}, ... , e^{i \phy_{n-1}}), the complex Hermitean
    *  matrix can be transformed into a real symmetric matrix and complex
    *  arithmetic can be entirely avoided.)
    *
    *  While the eigenvectors of the real symmetric tridiagonal matrix are real,
    *  the eigenvectors of original complex Hermitean matrix have complex entries
    *  in general.
    *  Since LAPACK drivers overwrite the matrix data with the eigenvectors,
    *  ZSTEMR accepts complex workspace to facilitate interoperability
    *  with ZUNMTR or ZUPMTR.
    *
    *  Arguments
    *  =========
    *
    *  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.
    *
    *  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
    *          T. On exit, D is overwritten.
    *
    *  E       (input/output) DOUBLE PRECISION array, dimension (N)
    *          On entry, the (N-1) subdiagonal elements of the tridiagonal
    *          matrix T in elements 1 to N-1 of E. E(N) need not be set on
    *          input, but is used internally as workspace.
    *          On exit, E is overwritten.
    *
    *  VL      (input) DOUBLE PRECISION
    *  VU      (input) DOUBLE PRECISION
    *          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.
    *          Not referenced if RANGE = 'A' or 'V'.
    *
    *  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) DOUBLE PRECISION array, dimension (N)
    *          The first M elements contain the selected eigenvalues in
    *          ascending order.
    *
    *  Z       (output) COMPLEX*16 array, dimension (LDZ, max(1,M) )
    *          If JOBZ = 'V', and if INFO = 0, then the first M columns of Z
    *          contain the orthonormal eigenvectors of the matrix T
    *          corresponding to the selected eigenvalues, with the i-th
    *          column of Z holding the eigenvector associated with W(i).
    *          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 can be computed with a workspace
    *          query by setting NZC = -1, see below.
    *
    *  LDZ     (input) INTEGER
    *          The leading dimension of the array Z.  LDZ >= 1, and if
    *          JOBZ = 'V', then LDZ >= max(1,N).
    *
    *  NZC     (input) INTEGER
    *          The number of eigenvectors to be held in the array Z.
    *          If RANGE = 'A', then NZC >= max(1,N).
    *          If RANGE = 'V', then NZC >= the number of eigenvalues in (VL,VU].
    *          If RANGE = 'I', then NZC >= IU-IL+1.
    *          If NZC = -1, then a workspace query is assumed; the
    *          routine calculates the number of columns of the array Z that
    *          are needed to hold the eigenvectors.
    *          This value is returned as the first entry of the Z array, and
    *          no error message related to NZC is issued by XERBLA.
    *
    *  ISUPPZ  (output) INTEGER ARRAY, dimension ( 2*max(1,M) )
    *          The support of the eigenvectors in Z, i.e., the indices
    *          indicating the nonzero elements in Z. The i-th computed eigenvector
    *          is nonzero only in elements ISUPPZ( 2*i-1 ) through
    *          ISUPPZ( 2*i ). This is relevant in the case when the matrix
    *          is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0.
    *
    *  TRYRAC  (input/output) LOGICAL
    *          If TRYRAC.EQ..TRUE., indicates that the code should check whether
    *          the tridiagonal matrix defines its eigenvalues to high relative
    *          accuracy.  If so, the code uses relative-accuracy preserving
    *          algorithms that might be (a bit) slower depending on the matrix.
    *          If the matrix does not define its eigenvalues to high relative
    *          accuracy, the code can uses possibly faster algorithms.
    *          If TRYRAC.EQ..FALSE., the code is not required to guarantee
    *          relatively accurate eigenvalues and can use the fastest possible
    *          techniques.
    *          On exit, a .TRUE. TRYRAC will be set to .FALSE. if the matrix
    *          does not define its eigenvalues to high relative accuracy.
    *
    *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
    *          On exit, if INFO = 0, WORK(1) returns the optimal
    *          (and minimal) LWORK.
    *
    *  LWORK   (input) INTEGER
    *          The dimension of the array WORK. LWORK >= max(1,18*N)
    *          if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.
    *          If LWORK = -1, then a workspace query is assumed; the routine
    *          only calculates the optimal size of the WORK array, returns
    *          this value as the first entry of the WORK array, and no error
    *          message related to LWORK is issued by XERBLA.
    *
    *  IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
    *          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
    *
    *  LIWORK  (input) INTEGER
    *          The dimension of the array IWORK.  LIWORK >= max(1,10*N)
    *          if the eigenvectors are desired, and LIWORK >= max(1,8*N)
    *          if only the eigenvalues are to be computed.
    *          If LIWORK = -1, then a workspace query is assumed; the
    *          routine only calculates the optimal size of the IWORK array,
    *          returns this value as the first entry of the IWORK array, and
    *          no error message related to LIWORK is issued by XERBLA.
    *
    *  INFO    (output) INTEGER
    *          On exit, INFO
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *          > 0:  if INFO = 1X, internal error in DLARRE,
    *                if INFO = 2X, internal error in ZLARRV.
    *                Here, the digit X = ABS( IINFO ) < 10, where IINFO is
    *                the nonzero error code returned by DLARRE or
    *                ZLARRV, respectively.
    *
    *
    *  Further Details
    *  ===============
    *
    *  Based on contributions by
    *     Beresford Parlett, University of California, Berkeley, USA
    *     Jim Demmel, University of California, Berkeley, USA
    *     Inderjit Dhillon, University of Texas, Austin, USA
    *     Osni Marques, LBNL/NERSC, USA
    *     Christof Voemel, University of California, Berkeley, USA
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ZERO, ONE, FOUR, MINRGP
          PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0,
         $                     FOUR = 4.0D0,
         $                     MINRGP = 1.0D-3 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            ALLEIG, INDEIG, LQUERY, VALEIG, WANTZ, ZQUERY
          INTEGER            I, IBEGIN, IEND, IFIRST, IIL, IINDBL, IINDW,
         $                   IINDWK, IINFO, IINSPL, IIU, ILAST, IN, INDD,
         $                   INDE2, INDERR, INDGP, INDGRS, INDWRK, ITMP,
         $                   ITMP2, J, JBLK, JJ, LIWMIN, LWMIN, NSPLIT,
         $                   NZCMIN, OFFSET, WBEGIN, WEND
          DOUBLE PRECISION   BIGNUM, CS, EPS, PIVMIN, R1, R2, RMAX, RMIN,
         $                   RTOL1, RTOL2, SAFMIN, SCALE, SMLNUM, SN,
         $                   THRESH, TMP, TNRM, WL, WU
    *     ..
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          DOUBLE PRECISION   DLAMCH, DLANST
          EXTERNAL           LSAME, DLAMCH, DLANST
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DCOPY, DLAE2, DLAEV2, DLARRC, DLARRE, DLARRJ,
         $                   DLARRR, DLASRT, DSCAL, XERBLA, ZLARRV, ZSWAP
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, MIN, SQRT

    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          WANTZ = LSAME( JOBZ, 'V' )
          ALLEIG = LSAME( RANGE, 'A' )
          VALEIG = LSAME( RANGE, 'V' )
          INDEIG = LSAME( RANGE, 'I' )
    *
          LQUERY = ( ( LWORK.EQ.-1 ).OR.( LIWORK.EQ.-1 ) )
          ZQUERY = ( NZC.EQ.-1 )
          TRYRAC = ( INFO.NE.0 )

    *     DSTEMR needs WORK of size 6*N, IWORK of size 3*N.
    *     In addition, DLARRE needs WORK of size 6*N, IWORK of size 5*N.
    *     Furthermore, ZLARRV needs WORK of size 12*N, IWORK of size 7*N.
          IF( WANTZ ) THEN
             LWMIN = 18*N
             LIWMIN = 10*N
          ELSE
    *        need less workspace if only the eigenvalues are wanted
             LWMIN = 12*N
             LIWMIN = 8*N
          ENDIF

          WL = ZERO
          WU = ZERO
          IIL = 0
          IIU = 0

          IF( VALEIG ) THEN
    *        We do not reference VL, VU in the cases RANGE = 'I','A'
    *        The interval (WL, WU] contains all the wanted eigenvalues.
    *        It is either given by the user or computed in DLARRE.
             WL = VL
             WU = VU
          ELSEIF( INDEIG ) THEN
    *        We do not reference IL, IU in the cases RANGE = 'V','A'
             IIL = IL
             IIU = IU
          ENDIF
    *
          INFO = 0
          IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
             INFO = -1
          ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
             INFO = -2
          ELSE IF( N.LT.0 ) THEN
             INFO = -3
          ELSE IF( VALEIG .AND. N.GT.0 .AND. WU.LE.WL ) THEN
             INFO = -7
          ELSE IF( INDEIG .AND. ( IIL.LT.1 .OR. IIL.GT.N ) ) THEN
             INFO = -8
          ELSE IF( INDEIG .AND. ( IIU.LT.IIL .OR. IIU.GT.N ) ) THEN
             INFO = -9
          ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
             INFO = -13
          ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
             INFO = -17
          ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
             INFO = -19
          END IF
    *
    *     Get machine constants.
    *
          SAFMIN = DLAMCH( 'Safe minimum' )
          EPS = DLAMCH( 'Precision' )
          SMLNUM = SAFMIN / EPS
          BIGNUM = ONE / SMLNUM
          RMIN = SQRT( SMLNUM )
          RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
    *
          IF( INFO.EQ.0 ) THEN
             WORK( 1 ) = LWMIN
             IWORK( 1 ) = LIWMIN
    *
             IF( WANTZ .AND. ALLEIG ) THEN
                NZCMIN = N
             ELSE IF( WANTZ .AND. VALEIG ) THEN
                CALL DLARRC( 'T', N, VL, VU, D, E, SAFMIN,
         $                            NZCMIN, ITMP, ITMP2, INFO )
             ELSE IF( WANTZ .AND. INDEIG ) THEN
                NZCMIN = IIU-IIL+1
             ELSE
    *           WANTZ .EQ. FALSE.
                NZCMIN = 0
             ENDIF
             IF( ZQUERY .AND. INFO.EQ.0 ) THEN
                Z( 1,1 ) = NZCMIN
             ELSE IF( NZC.LT.NZCMIN .AND. .NOT.ZQUERY ) THEN
                INFO = -14
             END IF
          END IF

          IF( INFO.NE.0 ) THEN
    *
             CALL XERBLA( 'ZSTEMR', -INFO )
    *
             RETURN
          ELSE IF( LQUERY .OR. ZQUERY ) THEN
             RETURN
          END IF
    *
    *     Handle N = 0, 1, and 2 cases immediately
    *
          M = 0
          IF( N.EQ.0 )
         $   RETURN
    *
          IF( N.EQ.1 ) THEN
             IF( ALLEIG .OR. INDEIG ) THEN
                M = 1
                W( 1 ) = D( 1 )
             ELSE
                IF( WL.LT.D( 1 ) .AND. WU.GE.D( 1 ) ) THEN
                   M = 1
                   W( 1 ) = D( 1 )
                END IF
             END IF
             IF( WANTZ.AND.(.NOT.ZQUERY) ) THEN
                Z( 1, 1 ) = ONE
                ISUPPZ(1) = 1
                ISUPPZ(2) = 1
             END IF
             RETURN
          END IF
    *
          IF( N.EQ.2 ) THEN
             IF( .NOT.WANTZ ) THEN
                CALL DLAE2( D(1), E(1), D(2), R1, R2 )
             ELSE IF( WANTZ.AND.(.NOT.ZQUERY) ) THEN
                CALL DLAEV2( D(1), E(1), D(2), R1, R2, CS, SN )
             END IF
             IF( ALLEIG.OR.
         $      (VALEIG.AND.(R2.GT.WL).AND.
         $                  (R2.LE.WU)).OR.
         $      (INDEIG.AND.(IIL.EQ.1)) ) THEN
                M = M+1
                W( M ) = R2
                IF( WANTZ.AND.(.NOT.ZQUERY) ) THEN
                   Z( 1, M ) = -SN
                   Z( 2, M ) = CS
    *              Note: At most one of SN and CS can be zero.
                   IF (SN.NE.ZERO) THEN
                      IF (CS.NE.ZERO) THEN
                         ISUPPZ(2*M-1) = 1
                         ISUPPZ(2*M-1) = 2
                      ELSE
                         ISUPPZ(2*M-1) = 1
                         ISUPPZ(2*M-1) = 1
                      END IF
                   ELSE
                      ISUPPZ(2*M-1) = 2
                      ISUPPZ(2*M) = 2
                   END IF
                ENDIF
             ENDIF
             IF( ALLEIG.OR.
         $      (VALEIG.AND.(R1.GT.WL).AND.
         $                  (R1.LE.WU)).OR.
         $      (INDEIG.AND.(IIU.EQ.2)) ) THEN
                M = M+1
                W( M ) = R1
                IF( WANTZ.AND.(.NOT.ZQUERY) ) THEN
                   Z( 1, M ) = CS
                   Z( 2, M ) = SN
    *              Note: At most one of SN and CS can be zero.
                   IF (SN.NE.ZERO) THEN
                      IF (CS.NE.ZERO) THEN
                         ISUPPZ(2*M-1) = 1
                         ISUPPZ(2*M-1) = 2
                      ELSE
                         ISUPPZ(2*M-1) = 1
                         ISUPPZ(2*M-1) = 1
                      END IF
                   ELSE
                      ISUPPZ(2*M-1) = 2
                      ISUPPZ(2*M) = 2
                   END IF
                ENDIF
             ENDIF
             RETURN
          END IF

    *     Continue with general N

          INDGRS = 1
          INDERR = 2*N + 1
          INDGP = 3*N + 1
          INDD = 4*N + 1
          INDE2 = 5*N + 1
          INDWRK = 6*N + 1
    *
          IINSPL = 1
          IINDBL = N + 1
          IINDW = 2*N + 1
          IINDWK = 3*N + 1
    *
    *     Scale matrix to allowable range, if necessary.
    *     The allowable range is related to the PIVMIN parameter; see the
    *     comments in DLARRD.  The preference for scaling small values
    *     up is heuristic; we expect users' matrices not to be close to the
    *     RMAX threshold.
    *
          SCALE = ONE
          TNRM = DLANST( 'M', N, D, E )
          IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
             SCALE = RMIN / TNRM
          ELSE IF( TNRM.GT.RMAX ) THEN
             SCALE = RMAX / TNRM
          END IF
          IF( SCALE.NE.ONE ) THEN
             CALL DSCAL( N, SCALE, D, 1 )
             CALL DSCAL( N-1, SCALE, E, 1 )
             TNRM = TNRM*SCALE
             IF( VALEIG ) THEN
    *           If eigenvalues in interval have to be found,
    *           scale (WL, WU] accordingly
                WL = WL*SCALE
                WU = WU*SCALE
             ENDIF
          END IF
    *
    *     Compute the desired eigenvalues of the tridiagonal after splitting
    *     into smaller subblocks if the corresponding off-diagonal elements
    *     are small
    *     THRESH is the splitting parameter for DLARRE
    *     A negative THRESH forces the old splitting criterion based on the
    *     size of the off-diagonal. A positive THRESH switches to splitting
    *     which preserves relative accuracy.
    *
          IF( TRYRAC ) THEN
    *        Test whether the matrix warrants the more expensive relative approach.
             CALL DLARRR( N, D, E, IINFO )
          ELSE
    *        The user does not care about relative accurately eigenvalues
             IINFO = -1
          ENDIF
    *     Set the splitting criterion
          IF (IINFO.EQ.0) THEN
             THRESH = EPS
          ELSE
             THRESH = -EPS
    *        relative accuracy is desired but T does not guarantee it
             TRYRAC = .FALSE.
          ENDIF
    *
          IF( TRYRAC ) THEN
    *        Copy original diagonal, needed to guarantee relative accuracy
             CALL DCOPY(N,D,1,WORK(INDD),1)
          ENDIF
    *     Store the squares of the offdiagonal values of T
          DO 5 J = 1, N-1
             WORK( INDE2+J-1 ) = E(J)**2
     5    CONTINUE

    *     Set the tolerance parameters for bisection
          IF( .NOT.WANTZ ) THEN
    *        DLARRE computes the eigenvalues to full precision.
             RTOL1 = FOUR * EPS
             RTOL2 = FOUR * EPS
          ELSE
    *        DLARRE computes the eigenvalues to less than full precision.
    *        ZLARRV will refine the eigenvalue approximations, and we only
    *        need less accurate initial bisection in DLARRE.
    *        Note: these settings do only affect the subset case and DLARRE
             RTOL1 = SQRT(EPS)
             RTOL2 = MAX( SQRT(EPS)*5.0D-3, FOUR * EPS )
          ENDIF
          CALL DLARRE( RANGE, N, WL, WU, IIL, IIU, D, E,
         $             WORK(INDE2), RTOL1, RTOL2, THRESH, NSPLIT,
         $             IWORK( IINSPL ), M, W, WORK( INDERR ),
         $             WORK( INDGP ), IWORK( IINDBL ),
         $             IWORK( IINDW ), WORK( INDGRS ), PIVMIN,
         $             WORK( INDWRK ), IWORK( IINDWK ), IINFO )
          IF( IINFO.NE.0 ) THEN
             INFO = 10 + ABS( IINFO )
             RETURN
          END IF
    *     Note that if RANGE .NE. 'V', DLARRE computes bounds on the desired
    *     part of the spectrum. All desired eigenvalues are contained in
    *     (WL,WU]

          IF( WANTZ ) THEN
    *
    *        Compute the desired eigenvectors corresponding to the computed
    *        eigenvalues
    *
             CALL ZLARRV( N, WL, WU, D, E,
         $                PIVMIN, IWORK( IINSPL ), M,
         $                1, M, MINRGP, RTOL1, RTOL2,
         $                W, WORK( INDERR ), WORK( INDGP ), IWORK( IINDBL ),
         $                IWORK( IINDW ), WORK( INDGRS ), Z, LDZ,
         $                ISUPPZ, WORK( INDWRK ), IWORK( IINDWK ), IINFO )
             IF( IINFO.NE.0 ) THEN
                INFO = 20 + ABS( IINFO )
                RETURN
             END IF
          ELSE
    *        DLARRE computes eigenvalues of the (shifted) root representation
    *        ZLARRV returns the eigenvalues of the unshifted matrix.
    *        However, if the eigenvectors are not desired by the user, we need
    *        to apply the corresponding shifts from DLARRE to obtain the
    *        eigenvalues of the original matrix.
             DO 20 J = 1, M
                ITMP = IWORK( IINDBL+J-1 )
                W( J ) = W( J ) + E( IWORK( IINSPL+ITMP-1 ) )
     20      CONTINUE
          END IF
    *

          IF ( TRYRAC ) THEN
    *        Refine computed eigenvalues so that they are relatively accurate
    *        with respect to the original matrix T.
             IBEGIN = 1
             WBEGIN = 1
             DO 39  JBLK = 1, IWORK( IINDBL+M-1 )
                IEND = IWORK( IINSPL+JBLK-1 )
                IN = IEND - IBEGIN + 1
                WEND = WBEGIN - 1
    *           check if any eigenvalues have to be refined in this block
     36         CONTINUE
                IF( WEND.LT.M ) THEN
                   IF( IWORK( IINDBL+WEND ).EQ.JBLK ) THEN
                      WEND = WEND + 1
                      GO TO 36
                   END IF
                END IF
                IF( WEND.LT.WBEGIN ) THEN
                   IBEGIN = IEND + 1
                   GO TO 39
                END IF

                OFFSET = IWORK(IINDW+WBEGIN-1)-1
                IFIRST = IWORK(IINDW+WBEGIN-1)
                ILAST = IWORK(IINDW+WEND-1)
                RTOL2 = FOUR * EPS
                CALL DLARRJ( IN,
         $                   WORK(INDD+IBEGIN-1), WORK(INDE2+IBEGIN-1),
         $                   IFIRST, ILAST, RTOL2, OFFSET, W(WBEGIN),
         $                   WORK( INDERR+WBEGIN-1 ),
         $                   WORK( INDWRK ), IWORK( IINDWK ), PIVMIN,
         $                   TNRM, IINFO )
                IBEGIN = IEND + 1
                WBEGIN = WEND + 1
     39      CONTINUE
          ENDIF
    *
    *     If matrix was scaled, then rescale eigenvalues appropriately.
    *
          IF( SCALE.NE.ONE ) THEN
             CALL DSCAL( M, ONE / SCALE, W, 1 )
          END IF
    *
    *     If eigenvalues are not in increasing order, then sort them,
    *     possibly along with eigenvectors.
    *
          IF( NSPLIT.GT.1 ) THEN
             IF( .NOT. WANTZ ) THEN
                CALL DLASRT( 'I', M, W, IINFO )
                IF( IINFO.NE.0 ) THEN
                   INFO = 3
                   RETURN
                END IF
             ELSE
                DO 60 J = 1, M - 1
                   I = 0
                   TMP = W( J )
                   DO 50 JJ = J + 1, M
                      IF( W( JJ ).LT.TMP ) THEN
                         I = JJ
                         TMP = W( JJ )
                      END IF
     50            CONTINUE
                   IF( I.NE.0 ) THEN
                      W( I ) = W( J )
                      W( J ) = TMP
                      IF( WANTZ ) THEN
                         CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
                         ITMP = ISUPPZ( 2*I-1 )
                         ISUPPZ( 2*I-1 ) = ISUPPZ( 2*J-1 )
                         ISUPPZ( 2*J-1 ) = ITMP
                         ITMP = ISUPPZ( 2*I )
                         ISUPPZ( 2*I ) = ISUPPZ( 2*J )
                         ISUPPZ( 2*J ) = ITMP
                      END IF
                   END IF
     60         CONTINUE
             END IF
          ENDIF
    *
    *
          WORK( 1 ) = LWMIN
          IWORK( 1 ) = LIWMIN
          RETURN
    *
    *     End of ZSTEMR
    *
          END