          SUBROUTINE ZTRSEN( JOB, COMPQ, SELECT, N, T, LDT, Q, LDQ, W, M, S,
         $                   SEP, WORK, LWORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
    *
    *     .. Scalar Arguments ..
          CHARACTER          COMPQ, JOB
          INTEGER            INFO, LDQ, LDT, LWORK, M, N
          DOUBLE PRECISION   S, SEP
    *     ..
    *     .. Array Arguments ..
          LOGICAL            SELECT( * )
          COMPLEX*16         Q( LDQ, * ), T( LDT, * ), W( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZTRSEN reorders the Schur factorization of a complex matrix
    *  A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in
    *  the leading positions on the diagonal of the upper triangular matrix
    *  T, and the leading columns of Q form an orthonormal basis of the
    *  corresponding right invariant subspace.
    *
    *  Optionally the routine computes the reciprocal condition numbers of
    *  the cluster of eigenvalues and/or the invariant subspace.
    *
    *  Arguments
    *  =========
    *
    *  JOB     (input) CHARACTER*1
    *          Specifies whether condition numbers are required for the
    *          cluster of eigenvalues (S) or the invariant subspace (SEP):
    *          = 'N': none;
    *          = 'E': for eigenvalues only (S);
    *          = 'V': for invariant subspace only (SEP);
    *          = 'B': for both eigenvalues and invariant subspace (S and
    *                 SEP).
    *
    *  COMPQ   (input) CHARACTER*1
    *          = 'V': update the matrix Q of Schur vectors;
    *          = 'N': do not update Q.
    *
    *  SELECT  (input) LOGICAL array, dimension (N)
    *          SELECT specifies the eigenvalues in the selected cluster. To
    *          select the j-th eigenvalue, SELECT(j) must be set to .TRUE..
    *
    *  N       (input) INTEGER
    *          The order of the matrix T. N >= 0.
    *
    *  T       (input/output) COMPLEX*16 array, dimension (LDT,N)
    *          On entry, the upper triangular matrix T.
    *          On exit, T is overwritten by the reordered matrix T, with the
    *          selected eigenvalues as the leading diagonal elements.
    *
    *  LDT     (input) INTEGER
    *          The leading dimension of the array T. LDT >= max(1,N).
    *
    *  Q       (input/output) COMPLEX*16 array, dimension (LDQ,N)
    *          On entry, if COMPQ = 'V', the matrix Q of Schur vectors.
    *          On exit, if COMPQ = 'V', Q has been postmultiplied by the
    *          unitary transformation matrix which reorders T; the leading M
    *          columns of Q form an orthonormal basis for the specified
    *          invariant subspace.
    *          If COMPQ = 'N', Q is not referenced.
    *
    *  LDQ     (input) INTEGER
    *          The leading dimension of the array Q.
    *          LDQ >= 1; and if COMPQ = 'V', LDQ >= N.
    *
    *  W       (output) COMPLEX*16 array, dimension (N)
    *          The reordered eigenvalues of T, in the same order as they
    *          appear on the diagonal of T.
    *
    *  M       (output) INTEGER
    *          The dimension of the specified invariant subspace.
    *          0 <= M <= N.
    *
    *  S       (output) DOUBLE PRECISION
    *          If JOB = 'E' or 'B', S is a lower bound on the reciprocal
    *          condition number for the selected cluster of eigenvalues.
    *          S cannot underestimate the true reciprocal condition number
    *          by more than a factor of sqrt(N). If M = 0 or N, S = 1.
    *          If JOB = 'N' or 'V', S is not referenced.
    *
    *  SEP     (output) DOUBLE PRECISION
    *          If JOB = 'V' or 'B', SEP is the estimated reciprocal
    *          condition number of the specified invariant subspace. If
    *          M = 0 or N, SEP = norm(T).
    *          If JOB = 'N' or 'E', SEP is not referenced.
    *
    *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) INTEGER
    *          The dimension of the array WORK.
    *          If JOB = 'N', LWORK >= 1;
    *          if JOB = 'E', LWORK = max(1,M*(N-M));
    *          if JOB = 'V' or 'B', LWORK >= max(1,2*M*(N-M)).
    *
    *          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.
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *
    *  Further Details
    *  ===============
    *
    *  ZTRSEN first collects the selected eigenvalues by computing a unitary
    *  transformation Z to move them to the top left corner of T. In other
    *  words, the selected eigenvalues are the eigenvalues of T11 in:
    *
    *                Z'*T*Z = ( T11 T12 ) n1
    *                         (  0  T22 ) n2
    *                            n1  n2
    *
    *  where N = n1+n2 and Z' means the conjugate transpose of Z. The first
    *  n1 columns of Z span the specified invariant subspace of T.
    *
    *  If T has been obtained from the Schur factorization of a matrix
    *  A = Q*T*Q', then the reordered Schur factorization of A is given by
    *  A = (Q*Z)*(Z'*T*Z)*(Q*Z)', and the first n1 columns of Q*Z span the
    *  corresponding invariant subspace of A.
    *
    *  The reciprocal condition number of the average of the eigenvalues of
    *  T11 may be returned in S. S lies between 0 (very badly conditioned)
    *  and 1 (very well conditioned). It is computed as follows. First we
    *  compute R so that
    *
    *                         P = ( I  R ) n1
    *                             ( 0  0 ) n2
    *                               n1 n2
    *
    *  is the projector on the invariant subspace associated with T11.
    *  R is the solution of the Sylvester equation:
    *
    *                        T11*R - R*T22 = T12.
    *
    *  Let F-norm(M) denote the Frobenius-norm of M and 2-norm(M) denote
    *  the two-norm of M. Then S is computed as the lower bound
    *
    *                      (1 + F-norm(R)**2)**(-1/2)
    *
    *  on the reciprocal of 2-norm(P), the true reciprocal condition number.
    *  S cannot underestimate 1 / 2-norm(P) by more than a factor of
    *  sqrt(N).
    *
    *  An approximate error bound for the computed average of the
    *  eigenvalues of T11 is
    *
    *                         EPS * norm(T) / S
    *
    *  where EPS is the machine precision.
    *
    *  The reciprocal condition number of the right invariant subspace
    *  spanned by the first n1 columns of Z (or of Q*Z) is returned in SEP.
    *  SEP is defined as the separation of T11 and T22:
    *
    *                     sep( T11, T22 ) = sigma-min( C )
    *
    *  where sigma-min(C) is the smallest singular value of the
    *  n1*n2-by-n1*n2 matrix
    *
    *     C  = kprod( I(n2), T11 ) - kprod( transpose(T22), I(n1) )
    *
    *  I(m) is an m by m identity matrix, and kprod denotes the Kronecker
    *  product. We estimate sigma-min(C) by the reciprocal of an estimate of
    *  the 1-norm of inverse(C). The true reciprocal 1-norm of inverse(C)
    *  cannot differ from sigma-min(C) by more than a factor of sqrt(n1*n2).
    *
    *  When SEP is small, small changes in T can cause large changes in
    *  the invariant subspace. An approximate bound on the maximum angular
    *  error in the computed right invariant subspace is
    *
    *                      EPS * norm(T) / SEP
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ZERO, ONE
          PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            LQUERY, WANTBH, WANTQ, WANTS, WANTSP
          INTEGER            IERR, K, KASE, KS, LWMIN, N1, N2, NN
          DOUBLE PRECISION   EST, RNORM, SCALE
    *     ..
    *     .. Local Arrays ..
          INTEGER            ISAVE( 3 )
          DOUBLE PRECISION   RWORK( 1 )
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          DOUBLE PRECISION   ZLANGE
          EXTERNAL           LSAME, ZLANGE
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA, ZLACN2, ZLACPY, ZTREXC, ZTRSYL
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, SQRT
    *     ..
    *     .. Executable Statements ..
    *
    *     Decode and test the input parameters.
    *
          WANTBH = LSAME( JOB, 'B' )
          WANTS = LSAME( JOB, 'E' ) .OR. WANTBH
          WANTSP = LSAME( JOB, 'V' ) .OR. WANTBH
          WANTQ = LSAME( COMPQ, 'V' )
    *
    *     Set M to the number of selected eigenvalues.
    *
          M = 0
          DO 10 K = 1, N
             IF( SELECT( K ) )
         $      M = M + 1
       10 CONTINUE
    *
          N1 = M
          N2 = N - M
          NN = N1*N2
    *
          INFO = 0
          LQUERY = ( LWORK.EQ.-1 )
    *
          IF( WANTSP ) THEN
             LWMIN = MAX( 1, 2*NN )
          ELSE IF( LSAME( JOB, 'N' ) ) THEN
             LWMIN = 1
          ELSE IF( LSAME( JOB, 'E' ) ) THEN
             LWMIN = MAX( 1, NN )
          END IF
    *
          IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.WANTS .AND. .NOT.WANTSP )
         $     THEN
             INFO = -1
          ELSE IF( .NOT.LSAME( COMPQ, 'N' ) .AND. .NOT.WANTQ ) THEN
             INFO = -2
          ELSE IF( N.LT.0 ) THEN
             INFO = -4
          ELSE IF( LDT.LT.MAX( 1, N ) ) THEN
             INFO = -6
          ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.N ) ) THEN
             INFO = -8
          ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
             INFO = -14
          END IF
    *
          IF( INFO.EQ.0 ) THEN
             WORK( 1 ) = LWMIN
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'ZTRSEN', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( M.EQ.N .OR. M.EQ.0 ) THEN
             IF( WANTS )
         $      S = ONE
             IF( WANTSP )
         $      SEP = ZLANGE( '1', N, N, T, LDT, RWORK )
             GO TO 40
          END IF
    *
    *     Collect the selected eigenvalues at the top left corner of T.
    *
          KS = 0
          DO 20 K = 1, N
             IF( SELECT( K ) ) THEN
                KS = KS + 1
    *
    *           Swap the K-th eigenvalue to position KS.
    *
                IF( K.NE.KS )
         $         CALL ZTREXC( COMPQ, N, T, LDT, Q, LDQ, K, KS, IERR )
             END IF
       20 CONTINUE
    *
          IF( WANTS ) THEN
    *
    *        Solve the Sylvester equation for R:
    *
    *           T11*R - R*T22 = scale*T12
    *
             CALL ZLACPY( 'F', N1, N2, T( 1, N1+1 ), LDT, WORK, N1 )
             CALL ZTRSYL( 'N', 'N', -1, N1, N2, T, LDT, T( N1+1, N1+1 ),
         $                LDT, WORK, N1, SCALE, IERR )
    *
    *        Estimate the reciprocal of the condition number of the cluster
    *        of eigenvalues.
    *
             RNORM = ZLANGE( 'F', N1, N2, WORK, N1, RWORK )
             IF( RNORM.EQ.ZERO ) THEN
                S = ONE
             ELSE
                S = SCALE / ( SQRT( SCALE*SCALE / RNORM+RNORM )*
         $          SQRT( RNORM ) )
             END IF
          END IF
    *
          IF( WANTSP ) THEN
    *
    *        Estimate sep(T11,T22).
    *
             EST = ZERO
             KASE = 0
       30    CONTINUE
             CALL ZLACN2( NN, WORK( NN+1 ), WORK, EST, KASE, ISAVE )
             IF( KASE.NE.0 ) THEN
                IF( KASE.EQ.1 ) THEN
    *
    *              Solve T11*R - R*T22 = scale*X.
    *
                   CALL ZTRSYL( 'N', 'N', -1, N1, N2, T, LDT,
         $                      T( N1+1, N1+1 ), LDT, WORK, N1, SCALE,
         $                      IERR )
                ELSE
    *
    *              Solve T11'*R - R*T22' = scale*X.
    *
                   CALL ZTRSYL( 'C', 'C', -1, N1, N2, T, LDT,
         $                      T( N1+1, N1+1 ), LDT, WORK, N1, SCALE,
         $                      IERR )
                END IF
                GO TO 30
             END IF
    *
             SEP = SCALE / EST
          END IF
    *
       40 CONTINUE
    *
    *     Copy reordered eigenvalues to W.
    *
          DO 50 K = 1, N
             W( K ) = T( K, K )
       50 CONTINUE
    *
          WORK( 1 ) = LWMIN
    *
          RETURN
    *
    *     End of ZTRSEN
    *
          END