          SUBROUTINE DTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
         $                   LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK,
         $                   IWORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          TRANS
          INTEGER            IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF,
         $                   LWORK, M, N
          DOUBLE PRECISION   DIF, SCALE
    *     ..
    *     .. Array Arguments ..
          INTEGER            IWORK( * )
          DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), C( LDC, * ),
         $                   D( LDD, * ), E( LDE, * ), F( LDF, * ),
         $                   WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DTGSYL solves the generalized Sylvester equation:
    *
    *              A * R - L * B = scale * C                 (1)
    *              D * R - L * E = scale * F
    *
    *  where R and L are unknown m-by-n matrices, (A, D), (B, E) and
    *  (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n,
    *  respectively, with real entries. (A, D) and (B, E) must be in
    *  generalized (real) Schur canonical form, i.e. A, B are upper quasi
    *  triangular and D, E are upper triangular.
    *
    *  The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output
    *  scaling factor chosen to avoid overflow.
    *
    *  In matrix notation (1) is equivalent to solve  Zx = scale b, where
    *  Z is defined as
    *
    *             Z = [ kron(In, A)  -kron(B', Im) ]         (2)
    *                 [ kron(In, D)  -kron(E', Im) ].
    *
    *  Here Ik is the identity matrix of size k and X' is the transpose of
    *  X. kron(X, Y) is the Kronecker product between the matrices X and Y.
    *
    *  If TRANS = 'T', DTGSYL solves the transposed system Z'*y = scale*b,
    *  which is equivalent to solve for R and L in
    *
    *              A' * R  + D' * L   = scale *  C           (3)
    *              R  * B' + L  * E'  = scale * (-F)
    *
    *  This case (TRANS = 'T') is used to compute an one-norm-based estimate
    *  of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D)
    *  and (B,E), using DLACON.
    *
    *  If IJOB >= 1, DTGSYL computes a Frobenius norm-based estimate
    *  of Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the
    *  reciprocal of the smallest singular value of Z. See [1-2] for more
    *  information.
    *
    *  This is a level 3 BLAS algorithm.
    *
    *  Arguments
    *  =========
    *
    *  TRANS   (input) CHARACTER*1
    *          = 'N', solve the generalized Sylvester equation (1).
    *          = 'T', solve the 'transposed' system (3).
    *
    *  IJOB    (input) INTEGER
    *          Specifies what kind of functionality to be performed.
    *           =0: solve (1) only.
    *           =1: The functionality of 0 and 3.
    *           =2: The functionality of 0 and 4.
    *           =3: Only an estimate of Dif[(A,D), (B,E)] is computed.
    *               (look ahead strategy IJOB  = 1 is used).
    *           =4: Only an estimate of Dif[(A,D), (B,E)] is computed.
    *               ( DGECON on sub-systems is used ).
    *          Not referenced if TRANS = 'T'.
    *
    *  M       (input) INTEGER
    *          The order of the matrices A and D, and the row dimension of
    *          the matrices C, F, R and L.
    *
    *  N       (input) INTEGER
    *          The order of the matrices B and E, and the column dimension
    *          of the matrices C, F, R and L.
    *
    *  A       (input) DOUBLE PRECISION array, dimension (LDA, M)
    *          The upper quasi triangular matrix A.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A. LDA >= max(1, M).
    *
    *  B       (input) DOUBLE PRECISION array, dimension (LDB, N)
    *          The upper quasi triangular matrix B.
    *
    *  LDB     (input) INTEGER
    *          The leading dimension of the array B. LDB >= max(1, N).
    *
    *  C       (input/output) DOUBLE PRECISION array, dimension (LDC, N)
    *          On entry, C contains the right-hand-side of the first matrix
    *          equation in (1) or (3).
    *          On exit, if IJOB = 0, 1 or 2, C has been overwritten by
    *          the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R,
    *          the solution achieved during the computation of the
    *          Dif-estimate.
    *
    *  LDC     (input) INTEGER
    *          The leading dimension of the array C. LDC >= max(1, M).
    *
    *  D       (input) DOUBLE PRECISION array, dimension (LDD, M)
    *          The upper triangular matrix D.
    *
    *  LDD     (input) INTEGER
    *          The leading dimension of the array D. LDD >= max(1, M).
    *
    *  E       (input) DOUBLE PRECISION array, dimension (LDE, N)
    *          The upper triangular matrix E.
    *
    *  LDE     (input) INTEGER
    *          The leading dimension of the array E. LDE >= max(1, N).
    *
    *  F       (input/output) DOUBLE PRECISION array, dimension (LDF, N)
    *          On entry, F contains the right-hand-side of the second matrix
    *          equation in (1) or (3).
    *          On exit, if IJOB = 0, 1 or 2, F has been overwritten by
    *          the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L,
    *          the solution achieved during the computation of the
    *          Dif-estimate.
    *
    *  LDF     (input) INTEGER
    *          The leading dimension of the array F. LDF >= max(1, M).
    *
    *  DIF     (output) DOUBLE PRECISION
    *          On exit DIF is the reciprocal of a lower bound of the
    *          reciprocal of the Dif-function, i.e. DIF is an upper bound of
    *          Dif[(A,D), (B,E)] = sigma_min(Z), where Z as in (2).
    *          IF IJOB = 0 or TRANS = 'T', DIF is not touched.
    *
    *  SCALE   (output) DOUBLE PRECISION
    *          On exit SCALE is the scaling factor in (1) or (3).
    *          If 0 < SCALE < 1, C and F hold the solutions R and L, resp.,
    *          to a slightly perturbed system but the input matrices A, B, D
    *          and E have not been changed. If SCALE = 0, C and F hold the
    *          solutions R and L, respectively, to the homogeneous system
    *          with C = F = 0. Normally, SCALE = 1.
    *
    *  WORK    (workspace/output) DOUBLE PRECISION 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. LWORK > = 1.
    *          If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*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) INTEGER array, dimension (M+N+6)
    *
    *  INFO    (output) INTEGER
    *            =0: successful exit
    *            <0: If INFO = -i, the i-th argument had an illegal value.
    *            >0: (A, D) and (B, E) have common or close eigenvalues.
    *
    *  Further Details
    *  ===============
    *
    *  Based on contributions by
    *     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
    *     Umea University, S-901 87 Umea, Sweden.
    *
    *  [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
    *      for Solving the Generalized Sylvester Equation and Estimating the
    *      Separation between Regular Matrix Pairs, Report UMINF - 93.23,
    *      Department of Computing Science, Umea University, S-901 87 Umea,
    *      Sweden, December 1993, Revised April 1994, Also as LAPACK Working
    *      Note 75.  To appear in ACM Trans. on Math. Software, Vol 22,
    *      No 1, 1996.
    *
    *  [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester
    *      Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal.
    *      Appl., 15(4):1045-1060, 1994
    *
    *  [3] B. Kagstrom and L. Westin, Generalized Schur Methods with
    *      Condition Estimators for Solving the Generalized Sylvester
    *      Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7,
    *      July 1989, pp 745-751.
    *
    *  =====================================================================
    *  Replaced various illegal calls to DCOPY by calls to DLASET.
    *  Sven Hammarling, 1/5/02.
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ZERO, ONE
          PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            LQUERY, NOTRAN
          INTEGER            I, IE, IFUNC, IROUND, IS, ISOLVE, J, JE, JS, K,
         $                   LINFO, LWMIN, MB, NB, P, PPQQ, PQ, Q
          DOUBLE PRECISION   DSCALE, DSUM, SCALE2, SCALOC
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          EXTERNAL           LSAME, ILAENV
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DGEMM, DLACPY, DLASET, DSCAL, DTGSY2, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          DBLE, MAX, SQRT
    *     ..
    *     .. Executable Statements ..
    *
    *     Decode and test input parameters
    *
          INFO = 0
          NOTRAN = LSAME( TRANS, 'N' )
          LQUERY = ( LWORK.EQ.-1 )
    *
          IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
             INFO = -1
          ELSE IF( NOTRAN ) THEN
             IF( ( IJOB.LT.0 ) .OR. ( IJOB.GT.4 ) ) THEN
                INFO = -2
             END IF
          END IF
          IF( INFO.EQ.0 ) THEN
             IF( M.LE.0 ) THEN
                INFO = -3
             ELSE IF( N.LE.0 ) THEN
                INFO = -4
             ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
                INFO = -6
             ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
                INFO = -8
             ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
                INFO = -10
             ELSE IF( LDD.LT.MAX( 1, M ) ) THEN
                INFO = -12
             ELSE IF( LDE.LT.MAX( 1, N ) ) THEN
                INFO = -14
             ELSE IF( LDF.LT.MAX( 1, M ) ) THEN
                INFO = -16
             END IF
          END IF
    *
          IF( INFO.EQ.0 ) THEN
             IF( NOTRAN ) THEN
                IF( IJOB.EQ.1 .OR. IJOB.EQ.2 ) THEN
                   LWMIN = MAX( 1, 2*M*N )
                ELSE
                   LWMIN = 1
                END IF
             ELSE
                LWMIN = 1
             END IF
             WORK( 1 ) = LWMIN
    *
             IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
                INFO = -20
             END IF
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'DTGSYL', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( M.EQ.0 .OR. N.EQ.0 ) THEN
             SCALE = 1
             IF( NOTRAN ) THEN
                IF( IJOB.NE.0 ) THEN
                   DIF = 0
                END IF
             END IF
             RETURN
          END IF
    *
    *     Determine optimal block sizes MB and NB
    *
          MB = ILAENV( 2, 'DTGSYL', TRANS, M, N, -1, -1 )
          NB = ILAENV( 5, 'DTGSYL', TRANS, M, N, -1, -1 )
    *
          ISOLVE = 1
          IFUNC = 0
          IF( NOTRAN ) THEN
             IF( IJOB.GE.3 ) THEN
                IFUNC = IJOB - 2
                CALL DLASET( 'F', M, N, ZERO, ZERO, C, LDC )
                CALL DLASET( 'F', M, N, ZERO, ZERO, F, LDF )
             ELSE IF( IJOB.GE.1 ) THEN
                ISOLVE = 2
             END IF
          END IF
    *
          IF( ( MB.LE.1 .AND. NB.LE.1 ) .OR. ( MB.GE.M .AND. NB.GE.N ) )
         $     THEN
    *
             DO 30 IROUND = 1, ISOLVE
    *
    *           Use unblocked Level 2 solver
    *
                DSCALE = ZERO
                DSUM = ONE
                PQ = 0
                CALL DTGSY2( TRANS, IFUNC, M, N, A, LDA, B, LDB, C, LDC, D,
         $                   LDD, E, LDE, F, LDF, SCALE, DSUM, DSCALE,
         $                   IWORK, PQ, INFO )
                IF( DSCALE.NE.ZERO ) THEN
                   IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN
                      DIF = SQRT( DBLE( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) )
                   ELSE
                      DIF = SQRT( DBLE( PQ ) ) / ( DSCALE*SQRT( DSUM ) )
                   END IF
                END IF
    *
                IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN
                   IF( NOTRAN ) THEN
                      IFUNC = IJOB
                   END IF
                   SCALE2 = SCALE
                   CALL DLACPY( 'F', M, N, C, LDC, WORK, M )
                   CALL DLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M )
                   CALL DLASET( 'F', M, N, ZERO, ZERO, C, LDC )
                   CALL DLASET( 'F', M, N, ZERO, ZERO, F, LDF )
                ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN
                   CALL DLACPY( 'F', M, N, WORK, M, C, LDC )
                   CALL DLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF )
                   SCALE = SCALE2
                END IF
       30    CONTINUE
    *
             RETURN
          END IF
    *
    *     Determine block structure of A
    *
          P = 0
          I = 1
       40 CONTINUE
          IF( I.GT.M )
         $   GO TO 50
          P = P + 1
          IWORK( P ) = I
          I = I + MB
          IF( I.GE.M )
         $   GO TO 50
          IF( A( I, I-1 ).NE.ZERO )
         $   I = I + 1
          GO TO 40
       50 CONTINUE
    *
          IWORK( P+1 ) = M + 1
          IF( IWORK( P ).EQ.IWORK( P+1 ) )
         $   P = P - 1
    *
    *     Determine block structure of B
    *
          Q = P + 1
          J = 1
       60 CONTINUE
          IF( J.GT.N )
         $   GO TO 70
          Q = Q + 1
          IWORK( Q ) = J
          J = J + NB
          IF( J.GE.N )
         $   GO TO 70
          IF( B( J, J-1 ).NE.ZERO )
         $   J = J + 1
          GO TO 60
       70 CONTINUE
    *
          IWORK( Q+1 ) = N + 1
          IF( IWORK( Q ).EQ.IWORK( Q+1 ) )
         $   Q = Q - 1
    *
          IF( NOTRAN ) THEN
    *
             DO 150 IROUND = 1, ISOLVE
    *
    *           Solve (I, J)-subsystem
    *               A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J)
    *               D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J)
    *           for I = P, P - 1,..., 1; J = 1, 2,..., Q
    *
                DSCALE = ZERO
                DSUM = ONE
                PQ = 0
                SCALE = ONE
                DO 130 J = P + 2, Q
                   JS = IWORK( J )
                   JE = IWORK( J+1 ) - 1
                   NB = JE - JS + 1
                   DO 120 I = P, 1, -1
                      IS = IWORK( I )
                      IE = IWORK( I+1 ) - 1
                      MB = IE - IS + 1
                      PPQQ = 0
                      CALL DTGSY2( TRANS, IFUNC, MB, NB, A( IS, IS ), LDA,
         $                         B( JS, JS ), LDB, C( IS, JS ), LDC,
         $                         D( IS, IS ), LDD, E( JS, JS ), LDE,
         $                         F( IS, JS ), LDF, SCALOC, DSUM, DSCALE,
         $                         IWORK( Q+2 ), PPQQ, LINFO )
                      IF( LINFO.GT.0 )
         $               INFO = LINFO
    *
                      PQ = PQ + PPQQ
                      IF( SCALOC.NE.ONE ) THEN
                         DO 80 K = 1, JS - 1
                            CALL DSCAL( M, SCALOC, C( 1, K ), 1 )
                            CALL DSCAL( M, SCALOC, F( 1, K ), 1 )
       80                CONTINUE
                         DO 90 K = JS, JE
                            CALL DSCAL( IS-1, SCALOC, C( 1, K ), 1 )
                            CALL DSCAL( IS-1, SCALOC, F( 1, K ), 1 )
       90                CONTINUE
                         DO 100 K = JS, JE
                            CALL DSCAL( M-IE, SCALOC, C( IE+1, K ), 1 )
                            CALL DSCAL( M-IE, SCALOC, F( IE+1, K ), 1 )
      100                CONTINUE
                         DO 110 K = JE + 1, N
                            CALL DSCAL( M, SCALOC, C( 1, K ), 1 )
                            CALL DSCAL( M, SCALOC, F( 1, K ), 1 )
      110                CONTINUE
                         SCALE = SCALE*SCALOC
                      END IF
    *
    *                 Substitute R(I, J) and L(I, J) into remaining
    *                 equation.
    *
                      IF( I.GT.1 ) THEN
                         CALL DGEMM( 'N', 'N', IS-1, NB, MB, -ONE,
         $                           A( 1, IS ), LDA, C( IS, JS ), LDC, ONE,
         $                           C( 1, JS ), LDC )
                         CALL DGEMM( 'N', 'N', IS-1, NB, MB, -ONE,
         $                           D( 1, IS ), LDD, C( IS, JS ), LDC, ONE,
         $                           F( 1, JS ), LDF )
                      END IF
                      IF( J.LT.Q ) THEN
                         CALL DGEMM( 'N', 'N', MB, N-JE, NB, ONE,
         $                           F( IS, JS ), LDF, B( JS, JE+1 ), LDB,
         $                           ONE, C( IS, JE+1 ), LDC )
                         CALL DGEMM( 'N', 'N', MB, N-JE, NB, ONE,
         $                           F( IS, JS ), LDF, E( JS, JE+1 ), LDE,
         $                           ONE, F( IS, JE+1 ), LDF )
                      END IF
      120          CONTINUE
      130       CONTINUE
                IF( DSCALE.NE.ZERO ) THEN
                   IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN
                      DIF = SQRT( DBLE( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) )
                   ELSE
                      DIF = SQRT( DBLE( PQ ) ) / ( DSCALE*SQRT( DSUM ) )
                   END IF
                END IF
                IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN
                   IF( NOTRAN ) THEN
                      IFUNC = IJOB
                   END IF
                   SCALE2 = SCALE
                   CALL DLACPY( 'F', M, N, C, LDC, WORK, M )
                   CALL DLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M )
                   CALL DLASET( 'F', M, N, ZERO, ZERO, C, LDC )
                   CALL DLASET( 'F', M, N, ZERO, ZERO, F, LDF )
                ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN
                   CALL DLACPY( 'F', M, N, WORK, M, C, LDC )
                   CALL DLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF )
                   SCALE = SCALE2
                END IF
      150    CONTINUE
    *
          ELSE
    *
    *        Solve transposed (I, J)-subsystem
    *             A(I, I)' * R(I, J)  + D(I, I)' * L(I, J)  =  C(I, J)
    *             R(I, J)  * B(J, J)' + L(I, J)  * E(J, J)' = -F(I, J)
    *        for I = 1,2,..., P; J = Q, Q-1,..., 1
    *
             SCALE = ONE
             DO 210 I = 1, P
                IS = IWORK( I )
                IE = IWORK( I+1 ) - 1
                MB = IE - IS + 1
                DO 200 J = Q, P + 2, -1
                   JS = IWORK( J )
                   JE = IWORK( J+1 ) - 1
                   NB = JE - JS + 1
                   CALL DTGSY2( TRANS, IFUNC, MB, NB, A( IS, IS ), LDA,
         $                      B( JS, JS ), LDB, C( IS, JS ), LDC,
         $                      D( IS, IS ), LDD, E( JS, JS ), LDE,
         $                      F( IS, JS ), LDF, SCALOC, DSUM, DSCALE,
         $                      IWORK( Q+2 ), PPQQ, LINFO )
                   IF( LINFO.GT.0 )
         $            INFO = LINFO
                   IF( SCALOC.NE.ONE ) THEN
                      DO 160 K = 1, JS - 1
                         CALL DSCAL( M, SCALOC, C( 1, K ), 1 )
                         CALL DSCAL( M, SCALOC, F( 1, K ), 1 )
      160             CONTINUE
                      DO 170 K = JS, JE
                         CALL DSCAL( IS-1, SCALOC, C( 1, K ), 1 )
                         CALL DSCAL( IS-1, SCALOC, F( 1, K ), 1 )
      170             CONTINUE
                      DO 180 K = JS, JE
                         CALL DSCAL( M-IE, SCALOC, C( IE+1, K ), 1 )
                         CALL DSCAL( M-IE, SCALOC, F( IE+1, K ), 1 )
      180             CONTINUE
                      DO 190 K = JE + 1, N
                         CALL DSCAL( M, SCALOC, C( 1, K ), 1 )
                         CALL DSCAL( M, SCALOC, F( 1, K ), 1 )
      190             CONTINUE
                      SCALE = SCALE*SCALOC
                   END IF
    *
    *              Substitute R(I, J) and L(I, J) into remaining equation.
    *
                   IF( J.GT.P+2 ) THEN
                      CALL DGEMM( 'N', 'T', MB, JS-1, NB, ONE, C( IS, JS ),
         $                        LDC, B( 1, JS ), LDB, ONE, F( IS, 1 ),
         $                        LDF )
                      CALL DGEMM( 'N', 'T', MB, JS-1, NB, ONE, F( IS, JS ),
         $                        LDF, E( 1, JS ), LDE, ONE, F( IS, 1 ),
         $                        LDF )
                   END IF
                   IF( I.LT.P ) THEN
                      CALL DGEMM( 'T', 'N', M-IE, NB, MB, -ONE,
         $                        A( IS, IE+1 ), LDA, C( IS, JS ), LDC, ONE,
         $                        C( IE+1, JS ), LDC )
                      CALL DGEMM( 'T', 'N', M-IE, NB, MB, -ONE,
         $                        D( IS, IE+1 ), LDD, F( IS, JS ), LDF, ONE,
         $                        C( IE+1, JS ), LDC )
                   END IF
      200       CONTINUE
      210    CONTINUE
    *
          END IF
    *
          WORK( 1 ) = LWMIN
    *
          RETURN
    *
    *     End of DTGSYL
    *
          END