      SUBROUTINE CTGEVC( SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL,
     $                   LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      CHARACTER          HOWMNY, SIDE
      INTEGER            INFO, LDA, LDB, LDVL, LDVR, M, MM, N
*     ..
*     .. Array Arguments ..
      LOGICAL            SELECT( * )
      REAL               RWORK( * )
      COMPLEX            A( LDA, * ), B( LDB, * ), VL( LDVL, * ),
     $                   VR( LDVR, * ), WORK( * )
*     ..
*
*
*  Purpose
*  =======
*
*  CTGEVC computes some or all of the right and/or left generalized
*  eigenvectors of a pair of complex upper triangular matrices (A,B).
*
*  The right generalized eigenvector x and the left generalized
*  eigenvector y of (A,B) corresponding to a generalized eigenvalue
*  w are defined by:
*
*          (A - wB) * x = 0  and  y**H * (A - wB) = 0
*
*  where y**H denotes the conjugate tranpose of y.
*
*  If an eigenvalue w is determined by zero diagonal elements of both A
*  and B, a unit vector is returned as the corresponding eigenvector.
*
*  If all eigenvectors are requested, the routine may either return
*  the matrices X and/or Y of right or left eigenvectors of (A,B), or
*  the products Z*X and/or Q*Y, where Z and Q are input unitary
*  matrices.  If (A,B) was obtained from the generalized Schur
*  factorization of an original pair of matrices
*     (A0,B0) = (Q*A*Z**H,Q*B*Z**H),
*  then Z*X and Q*Y are the matrices of right or left eigenvectors of
*  A.
*
*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'R': compute right eigenvectors only;
*          = 'L': compute left eigenvectors only;
*          = 'B': compute both right and left eigenvectors.
*
*  HOWMNY  (input) CHARACTER*1
*          = 'A': compute all right and/or left eigenvectors;
*          = 'B': compute all right and/or left eigenvectors, and
*                 backtransform them using the input matrices supplied
*                 in VR and/or VL;
*          = 'S': compute selected right and/or left eigenvectors,
*                 specified by the logical array SELECT.
*
*  SELECT  (input) LOGICAL array, dimension (N)
*          If HOWMNY='S', SELECT specifies the eigenvectors to be
*          computed.
*          If HOWMNY='A' or 'B', SELECT is not referenced.
*          To select the eigenvector corresponding to the j-th
*          eigenvalue, SELECT(j) must be set to .TRUE..
*
*  N       (input) INTEGER
*          The order of the matrices A and B.  N >= 0.
*
*  A       (input) COMPLEX array, dimension (LDA,N)
*          The upper triangular matrix A.
*
*  LDA     (input) INTEGER
*          The leading dimension of array A.  LDA >= max(1,N).
*
*  B       (input) COMPLEX array, dimension (LDB,N)
*          The upper triangular matrix B.  B must have real diagonal
*          elements.
*
*  LDB     (input) INTEGER
*          The leading dimension of array B.  LDB >= max(1,N).
*
*  VL      (input/output) COMPLEX array, dimension (LDVL,MM)
*          On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must
*          contain an N-by-N matrix Q (usually the unitary matrix Q
*          of left Schur vectors returned by CHGEQZ).
*          On exit, if SIDE = 'L' or 'B', VL contains:
*          if HOWMNY = 'A', the matrix Y of left eigenvectors of (A,B);
*          if HOWMNY = 'B', the matrix Q*Y;
*          if HOWMNY = 'S', the left eigenvectors of (A,B) specified by
*                      SELECT, stored consecutively in the columns of
*                      VL, in the same order as their eigenvalues.
*          If SIDE = 'R', VL is not referenced.
*
*  LDVL    (input) INTEGER
*          The leading dimension of array VL.
*          LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
*
*  VR      (input/output) COMPLEX array, dimension (LDVR,MM)
*          On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
*          contain an N-by-N matrix Q (usually the unitary matrix Z
*          of right Schur vectors returned by CHGEQZ).
*          On exit, if SIDE = 'R' or 'B', VR contains:
*          if HOWMNY = 'A', the matrix X of right eigenvectors of (A,B);
*          if HOWMNY = 'B', the matrix Z*X;
*          if HOWMNY = 'S', the right eigenvectors of (A,B) specified by
*                      SELECT, stored consecutively in the columns of
*                      VR, in the same order as their eigenvalues.
*          If SIDE = 'L', VR is not referenced.
*
*  LDVR    (input) INTEGER
*          The leading dimension of the array VR.
*          LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
*
*  MM      (input) INTEGER
*          The number of columns in the arrays VL and/or VR. MM >= M.
*
*  M       (output) INTEGER
*          The number of columns in the arrays VL and/or VR actually
*          used to store the eigenvectors.  If HOWMNY = 'A' or 'B', M
*          is set to N.  Each selected eigenvector occupies one column.
*
*  WORK    (workspace) COMPLEX array, dimension (2*N)
*
*  RWORK   (workspace) REAL array, dimension (2*N)
*
*  INFO    (output) INTEGER
*          = 0:  successful exit.
*          < 0:  if INFO = -i, the i-th argument had an illegal value.
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
      COMPLEX            CZERO, CONE
      PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ),
     $                   CONE = ( 1.0E+0, 0.0E+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            COMPL, COMPR, ILALL, ILBACK, ILBBAD, ILCOMP,
     $                   LSA, LSB
      INTEGER            I, IBEG, IEIG, IEND, IHWMNY, IM, ISIDE, ISRC,
     $                   J, JE, JR
      REAL               ACOEFA, ACOEFF, ANORM, ASCALE, BCOEFA, BIG,
     $                   BIGNUM, BNORM, BSCALE, DMIN, SAFMIN, SBETA,
     $                   SCALE, SMALL, TEMP, ULP, XMAX
      COMPLEX            BCOEFF, CA, CB, D, SALPHA, SUM, SUMA, SUMB, X
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               SLAMCH
      COMPLEX            CLADIV
      EXTERNAL           LSAME, SLAMCH, CLADIV
*     ..
*     .. External Subroutines ..
      EXTERNAL           CGEMV, SLABAD, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, AIMAG, CMPLX, CONJG, MAX, MIN, REAL
*     ..
*     .. Statement Functions ..
      REAL               ABS1
*     ..
*     .. Statement Function definitions ..
      ABS1( X ) = ABS( REAL( X ) ) + ABS( AIMAG( X ) )
*     ..
*     .. Executable Statements ..
*
*     Decode and Test the input parameters
*
      IF( LSAME( HOWMNY, 'A' ) ) THEN
         IHWMNY = 1
         ILALL = .TRUE.
         ILBACK = .FALSE.
      ELSE IF( LSAME( HOWMNY, 'S' ) ) THEN
         IHWMNY = 2
         ILALL = .FALSE.
         ILBACK = .FALSE.
      ELSE IF( LSAME( HOWMNY, 'B' ) .OR. LSAME( HOWMNY, 'T' ) ) THEN
         IHWMNY = 3
         ILALL = .TRUE.
         ILBACK = .TRUE.
      ELSE
         IHWMNY = -1
      END IF
*
      IF( LSAME( SIDE, 'R' ) ) THEN
         ISIDE = 1
         COMPL = .FALSE.
         COMPR = .TRUE.
      ELSE IF( LSAME( SIDE, 'L' ) ) THEN
         ISIDE = 2
         COMPL = .TRUE.
         COMPR = .FALSE.
      ELSE IF( LSAME( SIDE, 'B' ) ) THEN
         ISIDE = 3
         COMPL = .TRUE.
         COMPR = .TRUE.
      ELSE
         ISIDE = -1
      END IF
*
      INFO = 0
      IF( ISIDE.LT.0 ) THEN
         INFO = -1
      ELSE IF( IHWMNY.LT.0 ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -6
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -8
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'CTGEVC', -INFO )
         RETURN
      END IF
*
*     Count the number of eigenvectors
*
      IF( .NOT.ILALL ) THEN
         IM = 0
         DO 10 J = 1, N
            IF( SELECT( J ) )
     $         IM = IM + 1
   10    CONTINUE
      ELSE
         IM = N
      END IF
*
*     Check diagonal of B
*
      ILBBAD = .FALSE.
      DO 20 J = 1, N
         IF( AIMAG( B( J, J ) ).NE.ZERO )
     $      ILBBAD = .TRUE.
   20 CONTINUE
*
      IF( ILBBAD ) THEN
         INFO = -7
      ELSE IF( COMPL .AND. LDVL.LT.N .OR. LDVL.LT.1 ) THEN
         INFO = -10
      ELSE IF( COMPR .AND. LDVR.LT.N .OR. LDVR.LT.1 ) THEN
         INFO = -12
      ELSE IF( MM.LT.IM ) THEN
         INFO = -13
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'CTGEVC', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      M = IM
      IF( N.EQ.0 )
     $   RETURN
*
*     Machine Constants
*
      SAFMIN = SLAMCH( 'Safe minimum' )
      BIG = ONE / SAFMIN
      CALL SLABAD( SAFMIN, BIG )
      ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
      SMALL = SAFMIN*N / ULP
      BIG = ONE / SMALL
      BIGNUM = ONE / ( SAFMIN*N )
*
*     Compute the 1-norm of each column of the strictly upper triangular
*     part of A and B to check for possible overflow in the triangular
*     solver.
*
      ANORM = ABS1( A( 1, 1 ) )
      BNORM = ABS1( B( 1, 1 ) )
      RWORK( 1 ) = ZERO
      RWORK( N+1 ) = ZERO
      DO 40 J = 2, N
         RWORK( J ) = ZERO
         RWORK( N+J ) = ZERO
         DO 30 I = 1, J - 1
            RWORK( J ) = RWORK( J ) + ABS1( A( I, J ) )
            RWORK( N+J ) = RWORK( N+J ) + ABS1( B( I, J ) )
   30    CONTINUE
         ANORM = MAX( ANORM, RWORK( J )+ABS1( A( J, J ) ) )
         BNORM = MAX( BNORM, RWORK( N+J )+ABS1( B( J, J ) ) )
   40 CONTINUE
*
      ASCALE = ONE / MAX( ANORM, SAFMIN )
      BSCALE = ONE / MAX( BNORM, SAFMIN )
*
*     Left eigenvectors
*
      IF( COMPL ) THEN
         IEIG = 0
*
*        Main loop over eigenvalues
*
         DO 140 JE = 1, N
            IF( ILALL ) THEN
               ILCOMP = .TRUE.
            ELSE
               ILCOMP = SELECT( JE )
            END IF
            IF( ILCOMP ) THEN
               IEIG = IEIG + 1
*
               IF( ABS1( A( JE, JE ) ).LE.SAFMIN .AND.
     $             ABS( REAL( B( JE, JE ) ) ).LE.SAFMIN ) THEN
*
*                 Singular matrix pencil -- return unit eigenvector
*
                  DO 50 JR = 1, N
                     VL( JR, IEIG ) = CZERO
   50             CONTINUE
                  VL( IEIG, IEIG ) = CONE
                  GO TO 140
               END IF
*
*              Non-singular eigenvalue:
*              Compute coefficients  a  and  b  in
*                   H
*                 y  ( a A - b B ) = 0
*
               TEMP = ONE / MAX( ABS1( A( JE, JE ) )*ASCALE,
     $                ABS( REAL( B( JE, JE ) ) )*BSCALE, SAFMIN )
               SALPHA = ( TEMP*A( JE, JE ) )*ASCALE
               SBETA = ( TEMP*REAL( B( JE, JE ) ) )*BSCALE
               ACOEFF = SBETA*ASCALE
               BCOEFF = SALPHA*BSCALE
*
*              Scale to avoid underflow
*
               LSA = ABS( SBETA ).GE.SAFMIN .AND. ABS( ACOEFF ).LT.SMALL
               LSB = ABS1( SALPHA ).GE.SAFMIN .AND. ABS1( BCOEFF ).LT.
     $               SMALL
*
               SCALE = ONE
               IF( LSA )
     $            SCALE = ( SMALL / ABS( SBETA ) )*MIN( ANORM, BIG )
               IF( LSB )
     $            SCALE = MAX( SCALE, ( SMALL / ABS1( SALPHA ) )*
     $                    MIN( BNORM, BIG ) )
               IF( LSA .OR. LSB ) THEN
                  SCALE = MIN( SCALE, ONE /
     $                    ( SAFMIN*MAX( ONE, ABS( ACOEFF ),
     $                    ABS1( BCOEFF ) ) ) )
                  IF( LSA ) THEN
                     ACOEFF = ASCALE*( SCALE*SBETA )
                  ELSE
                     ACOEFF = SCALE*ACOEFF
                  END IF
                  IF( LSB ) THEN
                     BCOEFF = BSCALE*( SCALE*SALPHA )
                  ELSE
                     BCOEFF = SCALE*BCOEFF
                  END IF
               END IF
*
               ACOEFA = ABS( ACOEFF )
               BCOEFA = ABS1( BCOEFF )
               XMAX = ONE
               DO 60 JR = 1, N
                  WORK( JR ) = CZERO
   60          CONTINUE
               WORK( JE ) = CONE
               DMIN = MAX( ULP*ACOEFA*ANORM, ULP*BCOEFA*BNORM, SAFMIN )
*
*                                              H
*              Triangular solve of  (a A - b B)  y = 0
*
*                                      H
*              (rowwise in  (a A - b B) , or columnwise in a A - b B)
*
               DO 100 J = JE + 1, N
*
*                 Compute
*                       j-1
*                 SUM = sum  conjg( a*A(k,j) - b*B(k,j) )*x(k)
*                       k=je
*                 (Scale if necessary)
*
                  TEMP = ONE / XMAX
                  IF( ACOEFA*RWORK( J )+BCOEFA*RWORK( N+J ).GT.BIGNUM*
     $                TEMP ) THEN
                     DO 70 JR = JE, J - 1
                        WORK( JR ) = TEMP*WORK( JR )
   70                CONTINUE
                     XMAX = ONE
                  END IF
                  SUMA = CZERO
                  SUMB = CZERO
*
                  DO 80 JR = JE, J - 1
                     SUMA = SUMA + CONJG( A( JR, J ) )*WORK( JR )
                     SUMB = SUMB + CONJG( B( JR, J ) )*WORK( JR )
   80             CONTINUE
                  SUM = ACOEFF*SUMA - CONJG( BCOEFF )*SUMB
*
*                 Form x(j) = - SUM / conjg( a*A(j,j) - b*B(j,j) )
*
*                 with scaling and perturbation of the denominator
*
                  D = CONJG( ACOEFF*A( J, J )-BCOEFF*B( J, J ) )
                  IF( ABS1( D ).LE.DMIN )
     $               D = CMPLX( DMIN )
*
                  IF( ABS1( D ).LT.ONE ) THEN
                     IF( ABS1( SUM ).GE.BIGNUM*ABS1( D ) ) THEN
                        TEMP = ONE / ABS1( SUM )
                        DO 90 JR = JE, J - 1
                           WORK( JR ) = TEMP*WORK( JR )
   90                   CONTINUE
                        XMAX = TEMP*XMAX
                        SUM = TEMP*SUM
                     END IF
                  END IF
                  WORK( J ) = CLADIV( -SUM, D )
                  XMAX = MAX( XMAX, ABS1( WORK( J ) ) )
  100          CONTINUE
*
*              Back transform eigenvector if HOWMNY='B'.
*
               IF( ILBACK ) THEN
                  CALL CGEMV( 'N', N, N+1-JE, CONE, VL( 1, JE ), LDVL,
     $                        WORK( JE ), 1, CZERO, WORK( N+1 ), 1 )
                  ISRC = 2
                  IBEG = 1
               ELSE
                  ISRC = 1
                  IBEG = JE
               END IF
*
*              Copy and scale eigenvector into column of VL
*
               XMAX = ZERO
               DO 110 JR = IBEG, N
                  XMAX = MAX( XMAX, ABS1( WORK( ( ISRC-1 )*N+JR ) ) )
  110          CONTINUE
*
               IF( XMAX.GT.SAFMIN ) THEN
                  TEMP = ONE / XMAX
                  DO 120 JR = IBEG, N
                     VL( JR, IEIG ) = TEMP*WORK( ( ISRC-1 )*N+JR )
  120             CONTINUE
               ELSE
                  IBEG = N + 1
               END IF
*
               DO 130 JR = 1, IBEG - 1
                  VL( JR, IEIG ) = CZERO
  130          CONTINUE
*
            END IF
  140    CONTINUE
      END IF
*
*     Right eigenvectors
*
      IF( COMPR ) THEN
         IEIG = IM + 1
*
*        Main loop over eigenvalues
*
         DO 250 JE = N, 1, -1
            IF( ILALL ) THEN
               ILCOMP = .TRUE.
            ELSE
               ILCOMP = SELECT( JE )
            END IF
            IF( ILCOMP ) THEN
               IEIG = IEIG - 1
*
               IF( ABS1( A( JE, JE ) ).LE.SAFMIN .AND.
     $             ABS( REAL( B( JE, JE ) ) ).LE.SAFMIN ) THEN
*
*                 Singular matrix pencil -- return unit eigenvector
*
                  DO 150 JR = 1, N
                     VR( JR, IEIG ) = CZERO
  150             CONTINUE
                  VR( IEIG, IEIG ) = CONE
                  GO TO 250
               END IF
*
*              Non-singular eigenvalue:
*              Compute coefficients  a  and  b  in
*
*              ( a A - b B ) x  = 0
*
               TEMP = ONE / MAX( ABS1( A( JE, JE ) )*ASCALE,
     $                ABS( REAL( B( JE, JE ) ) )*BSCALE, SAFMIN )
               SALPHA = ( TEMP*A( JE, JE ) )*ASCALE
               SBETA = ( TEMP*REAL( B( JE, JE ) ) )*BSCALE
               ACOEFF = SBETA*ASCALE
               BCOEFF = SALPHA*BSCALE
*
*              Scale to avoid underflow
*
               LSA = ABS( SBETA ).GE.SAFMIN .AND. ABS( ACOEFF ).LT.SMALL
               LSB = ABS1( SALPHA ).GE.SAFMIN .AND. ABS1( BCOEFF ).LT.
     $               SMALL
*
               SCALE = ONE
               IF( LSA )
     $            SCALE = ( SMALL / ABS( SBETA ) )*MIN( ANORM, BIG )
               IF( LSB )
     $            SCALE = MAX( SCALE, ( SMALL / ABS1( SALPHA ) )*
     $                    MIN( BNORM, BIG ) )
               IF( LSA .OR. LSB ) THEN
                  SCALE = MIN( SCALE, ONE /
     $                    ( SAFMIN*MAX( ONE, ABS( ACOEFF ),
     $                    ABS1( BCOEFF ) ) ) )
                  IF( LSA ) THEN
                     ACOEFF = ASCALE*( SCALE*SBETA )
                  ELSE
                     ACOEFF = SCALE*ACOEFF
                  END IF
                  IF( LSB ) THEN
                     BCOEFF = BSCALE*( SCALE*SALPHA )
                  ELSE
                     BCOEFF = SCALE*BCOEFF
                  END IF
               END IF
*
               ACOEFA = ABS( ACOEFF )
               BCOEFA = ABS1( BCOEFF )
               XMAX = ONE
               DO 160 JR = 1, N
                  WORK( JR ) = CZERO
  160          CONTINUE
               WORK( JE ) = CONE
               DMIN = MAX( ULP*ACOEFA*ANORM, ULP*BCOEFA*BNORM, SAFMIN )
*
*              Triangular solve of  (a A - b B) x = 0  (columnwise)
*
*              WORK(1:j-1) contains sums w,
*              WORK(j+1:JE) contains x
*
               DO 170 JR = 1, JE - 1
                  WORK( JR ) = ACOEFF*A( JR, JE ) - BCOEFF*B( JR, JE )
  170          CONTINUE
               WORK( JE ) = CONE
*
               DO 210 J = JE - 1, 1, -1
*
*                 Form x(j) := - w(j) / d
*                 with scaling and perturbation of the denominator
*
                  D = ACOEFF*A( J, J ) - BCOEFF*B( J, J )
                  IF( ABS1( D ).LE.DMIN )
     $               D = CMPLX( DMIN )
*
                  IF( ABS1( D ).LT.ONE ) THEN
                     IF( ABS1( WORK( J ) ).GE.BIGNUM*ABS1( D ) ) THEN
                        TEMP = ONE / ABS1( WORK( J ) )
                        DO 180 JR = 1, JE
                           WORK( JR ) = TEMP*WORK( JR )
  180                   CONTINUE
                     END IF
                  END IF
*
                  WORK( J ) = CLADIV( -WORK( J ), D )
*
                  IF( J.GT.1 ) THEN
*
*                    w = w + x(j)*(a A(*,j) - b B(*,j) ) with scaling
*
                     IF( ABS1( WORK( J ) ).GT.ONE ) THEN
                        TEMP = ONE / ABS1( WORK( J ) )
                        IF( ACOEFA*RWORK( J )+BCOEFA*RWORK( N+J ).GE.
     $                      BIGNUM*TEMP ) THEN
                           DO 190 JR = 1, JE
                              WORK( JR ) = TEMP*WORK( JR )
  190                      CONTINUE
                        END IF
                     END IF
*
                     CA = ACOEFF*WORK( J )
                     CB = BCOEFF*WORK( J )
                     DO 200 JR = 1, J - 1
                        WORK( JR ) = WORK( JR ) + CA*A( JR, J ) -
     $                               CB*B( JR, J )
  200                CONTINUE
                  END IF
  210          CONTINUE
*
*              Back transform eigenvector if HOWMNY='B'.
*
               IF( ILBACK ) THEN
                  CALL CGEMV( 'N', N, JE, CONE, VR, LDVR, WORK, 1,
     $                        CZERO, WORK( N+1 ), 1 )
                  ISRC = 2
                  IEND = N
               ELSE
                  ISRC = 1
                  IEND = JE
               END IF
*
*              Copy and scale eigenvector into column of VR
*
               XMAX = ZERO
               DO 220 JR = 1, IEND
                  XMAX = MAX( XMAX, ABS1( WORK( ( ISRC-1 )*N+JR ) ) )
  220          CONTINUE
*
               IF( XMAX.GT.SAFMIN ) THEN
                  TEMP = ONE / XMAX
                  DO 230 JR = 1, IEND
                     VR( JR, IEIG ) = TEMP*WORK( ( ISRC-1 )*N+JR )
  230             CONTINUE
               ELSE
                  IEND = 0
               END IF
*
               DO 240 JR = IEND + 1, N
                  VR( JR, IEIG ) = CZERO
  240          CONTINUE
*
            END IF
  250    CONTINUE
      END IF
*
      RETURN
*
*     End of CTGEVC
*
      END
