Cassini MIMI Investigation at Fundamental Technologies

Numerical Computation of Energy-Dependent Geometric Factors of E and F Electron Detectors of CASSINI/MIMI/LEMMS

Technical Report by Xiaodong Hong and Thomas P. Armstrong, May 10, 1997

*			PROGRAM TRAJRT3BDET.FOR		   *

*******************************************************************************
*                                  TRAJRT1BDET                                *
* THIS SUBROUTINE SHOULD BE LINKED WITH TRAJ2PT.  IT NOT ONLY INCLUDES        *
* TRAJRT2DET, BUT ALSO THE DIFFERENTIAL EQUATION SOLVER TDHPCG.               *
*******************************************************************************

      	SUBROUTINE DHPCG(PRMT,PV,DERY,NDIM,IHLF,FCT,OUTP,AUX)

      	implicit none
      	REAL*8 PRMT(5),X,H,Z,DELT,PV(6),DERY(6),AUX(16,6)
      	INTEGER NHIT,wscatter,scatter,i,n,istep,imod,ihlf,
     &		ihlf1,isw,ndim
      	common /nhit/nhit,/wscatter/wscatter,/scatter/scatter

      integer startnsurf,ape
      logical firstcheck,secondcheck    
      common /startnsurf/startnsurf,/ape/ape
      common /firstcheck/firstcheck,/secondcheck/secondcheck

	scatter=0
      NHIT=0
      N=1  
      IHLF1=0
      IHLF=0
      X=PRMT(1)
      H=PRMT(3)
      PRMT(5)=0.D0 
      DO I=1,NDIM  
         AUX(16,I)=0.D0 
         AUX(15,I)=DERY(I)  
         AUX(1,I)=PV(I)  
      END DO
C     ERROR RETURNS
      IF ((H*PRMT(2)).LT.X*H) THEN
         IHLF=13
      ELSE IF ((H*PRMT(2)).EQ.X*H) THEN
         IHLF=12
      END IF
      ISW=0
C     ****************************************************************
C
C     COMPUTATION OF DERY FOR STARTING VALUES  
C     BLOCK 1   VS OLD LABELS 4_20
C
C     ***************************************************************
      DO WHILE (ISW.NE.4)
         IF(ISW.EQ.0) THEN
            IHLF1=0
            CALL FCT(X,PV,DERY)
C           RECORDING OF STARTING VALUES  
           CALL OUTP(X,PV,DERY,IHLF,NDIM,PRMT,NHIT)
            IF (NHIT.NE.0) then
D              write(6,*) 'nhit is not zero', nhit
            RETURN
                end if
            IF(PRMT(5).NE.0.) THEN
D        write(6,*)'prmt(5) is not zero', prmt(5)
               RETURN
            END IF
            DO I=1,NDIM  
               AUX(8,I)=DERY(I) 
            END DO
C           COMPUTATION OF AUX(2,I)  
            ISW=1
         ELSE  IF (ISW.EQ.1) THEN
            IF (IHLF1.NE.1) THEN
               X=X+H
               DO I=1,NDIM 
                  AUX(2,I)=PV(I)  
               END DO
            END IF
            IHLF1=0
C           INCREMENT IS TESTED BY MEANS OF BISECTION  
            IHLF=IHLF+1  
            X=X-H
            DO I=1,NDIM 
               AUX(4,I)=AUX(2,I)  
            END DO
            H=.5D0*H 
            N=1  
            ISW=2
         ELSE IF (ISW.EQ.2) THEN
            X=X+H
            CALL FCT(X,PV,DERY)
            N=2  
            DO  I=1,NDIM 
               AUX(2,I)=PV(I)  
               AUX(9,I)=DERY(I) 
            ENDDO
            ISW=3
         ELSE IF (ISW.EQ.3) THEN
C           COMPUTATION OF TEST VALUE DELT 
            DELT=0.D0
            DO  I=1,NDIM 
               DELT=DELT+AUX(15,I)*DABS(PV(I)-AUX(4,I))  
            ENDDO
            DELT=.66666666667D-1*DELT  
	    if (delt.le.prmt(4)) then   
c            IF (DELE.LE.PRMT(4)) THEN
               ISW=5
            ELSE
               IF (IHLF.GE.10) THEN
                  IHLF=11
                  X=X+H
                  ISW=0
                  IHLF1=2
               ELSE
C                 NO SATISFACTORY ACCURACY AFTER 10 BISECTIONS. ERROR MESSAGE. 
                  IHLF1=1
                  ISW=1
               ENDIF
            ENDIF
         ELSE IF (ISW.EQ.5) THEN
C           THERE IS SATISFACTORY ACCURACY AFTER LESS THAN 11 BISECTIONS.  
            X=X+H
            CALL FCT(X,PV,DERY)
            DO I=1,NDIM 
               AUX(3,I)=PV(I)  
               AUX(10,I)=DERY(I)  
            ENDDO
            N=3  
            ISW=4
         ENDIF
C        *******************************************************************
C
C        THE FOLLOWING PART OF SUBROUTINE HPCG COMPUTES BY MEANS OF 
C        RUNGE-KUTTA METHOD STARTING VALUES FOR THE NOT SELF-STARTING 
C        PREDICTOR-CORRECTOR METHOD.
C        BLOCK 2   VS OLD LABELS 100_104 
C
C        *******************************************************************
         IF (ISW.NE.5.AND.IHLF1.EQ.0) THEN
            DO I=1,NDIM  
               Z=H*AUX(N+7,I) 
               AUX(5,I)=Z
               PV(I)=AUX(N,I)+.4D0*Z 
            ENDDO
C           Z IS AN AUXILIARY STORAGE LOCATION 
            Z=X+.4D0*H
            CALL FCT(X,PV,DERY)
            DO I=1,NDIM  
               Z=H*DERY(I)  
               AUX(6,I)=Z
               PV(I)=AUX(N,I)+.29697760925D0*AUX(5,I)+.15875964497D0*Z 
            ENDDO
            Z=X+.45573725422D0*H 
            CALL FCT(X,PV,DERY)
            DO I=1,NDIM  
               Z=H*DERY(I)  
               AUX(7,I)=Z
       PV(I)=AUX(N,I)+0.21810038823D0*AUX(5,I)-3.0509651487D0*AUX(6,I)  
     *        + 3.8328647605D0*Z  
            ENDDO
            Z=X+H
            CALL FCT(X,PV,DERY)
            DO I=1,NDIM  
          PV(I)=AUX(N,I)+.17476028223D0*AUX(5,I)-.55148066288D0*AUX(6,I)  
     *     +1.2055355994D0*AUX(7,I)+.17118478122D0*H*DERY(I)  
            ENDDO
         ENDIF
      ENDDO
C     *******************************************************************
C
C     BLOCK 3   VS OLD LABELS 21_22
C
C     *******************************************************************
      N=1  
      X=X+H
      CALL FCT(X,PV,DERY)
      X=PRMT(1)
      DO I=1,NDIM 
         AUX(11,I)=DERY(I)  
         PV(I)=AUX(1,I)+H*(.375D0*AUX(8,I)+.79166666667D0*AUX(9,I) 
     *   -.20833333333D0*AUX(10,I)+.41666666667D-1*DERY(I)) 
      ENDDO
C     *********************************************************************
C
C     BLOCK 4   VS OLD LABELS 23_30
C
C     *********************************************************************
      DO WHILE (N.LT.4)
         X=X+H
         N=N+1
         CALL FCT(X,PV,DERY) 
         CALL OUTP(X,PV,DERY,IHLF,NDIM,PRMT,NHIT)
         IF (NHIT.NE.0) then
        write (6,*) 'nhit is not zero', nhit
        RETURN
                end if
            IF(PRMT(5).NE.0.) THEN
D        write(6,*)'prmt(5) is not zero', prmt(5)
            RETURN
         ELSE IF((N-4).LT.0) THEN
            DO I=1,NDIM 
               AUX(N,I)=PV(I)  
               AUX(N+7,I)=DERY(I) 
            ENDDO
            IF (N.LT.3) THEN
               DO I=1,NDIM 
                  DELT=AUX(9,I)+AUX(9,I) 
                  DELT=DELT+DELT 
               PV(I)=AUX(1,I)+.33333333333D0*H*(AUX(8,I)+DELT+AUX(10,I)) 
               ENDDO
            ELSE 
               DO I=1,NDIM 
                  DELT=AUX(9,I)+AUX(10,I)
                  DELT=DELT+DELT+DELT  
                  PV(I)=AUX(1,I)+.375D0*H*(AUX(8,I)+DELT+AUX(11,I)) 
               ENDDO
            ENDIF
         ENDIF
      ENDDO
      ISW=6
C     ******************************************************************
C
C     POSSIBLE BREAK POINT FOR LINKAGE
C     STARTING VALUES ARE COMPUTED
C     NOW START HAMMINGS MODIFIED PREDICTOR-CORRECTOR METHOD.  
C     BLOCK 5   VS OLD LABELS 200_226
C
C     ******************************************************************
      ISTEP=3  
      DO WHILE (ISW.GE.6)
         IF (ISW.EQ.6) THEN
            IF (N.EQ.8) THEN
C              N=8 CAUSES THE ROWS OF AUX TO CHANGE THEIR STORAGE LOCATIONS 
               DO N=2,7 
                  DO I=1,NDIM  
                     AUX(N-1,I)=AUX(N,I)  
                     AUX(N+6,I)=AUX(N+7,I)  
                  ENDDO
               ENDDO
               N=7  
            ENDIF
C           N LESS THAN 8 CAUSES N+1 TO GET N  
            N=N+1
C           COMPUTATION OF NEXT VECTOR PV
            DO I=1,NDIM  
               AUX(N-1,I)=PV(I)  
               AUX(N+6,I)=DERY(I) 
            ENDDO
            X=X+H
            ISW=7
         ELSE IF (ISW.EQ.7) THEN
            ISTEP=ISTEP+1  
            DO I=1,NDIM  
               DELT=AUX(N-4,I)+1.3333333333D0*H*(AUX(N+6,I)+AUX(N+6,I)
     *         -AUX(N+5,I)+AUX(N+4,I)+AUX(N+4,I))
               PV(I)=DELT-.92561983471D0*AUX(16,I) 
               AUX(16,I)=DELT 
            ENDDO
C           PREDICTOR IS NOW GENERATED IN ROW 16 OF AUX, MODIFIED PREDICTOR
C           IS GENERATED I PV.  DELT MEANS AN AUXILIARY STORAGE.  
            CALL FCT(X,PV,DERY)
C           DERIVATIVE OF MODIFIED PREDICTOR IS GENERATED IN DERY  
            DO I=1,NDIM  
               DELT=.125D0*(9.D0*AUX(N-1,I)-AUX(N-3,I)+3.D0*H*(DERY(I)
     *         +AUX(N+6,I)+AUX(N+6,I)-AUX(N+5,I)))
               AUX(16,I)=AUX(16,I)-DELT
               PV(I)=DELT+.7438016529D-1*AUX(16,I) 
            ENDDO
C           TEST WHETHER H MUST BE HALVED OR DOUBLED 
            DELT=0.D0
            DO I=1,NDIM  
               DELT=DELT+AUX(15,I)*DABS(AUX(16,I))  
            ENDDO
            ISW=8
         ELSE IF (ISW.EQ.8) THEN
            IF(DELT.LT.PRMT(4).OR.IHLF1.EQ.5) THEN
               IHLF1=0
C              H MUST NOT BE HALVED.  THAT MEANS PV(I) ARE GOOD. 
               CALL FCT(X,PV,DERY)
               CALL OUTP(X,PV,DERY,IHLF,NDIM,PRMT,NHIT)
               IF (NHIT.NE.0) then
                   write (6,*) 'nhit is not zero', nhit
                   RETURN
               end if

               IF(PRMT(5).NE.0.OR.IHLF.GE.11.OR.(H*(X-PRMT(2))).GE.0
     *         .OR.DABS(X-PRMT(2)).LT.0.1D0*DABS(H)) THEN
 1150             FORMAT(I5)
D                 write(6,*)'Something else is wrong', prmt(5), IHLF
                  RETURN
               ELSE
                  IF (DELT.LE..2D-1*PRMT(4).AND.IHLF.GT.0
     *              .AND.N.GE.7.AND.ISTEP.GE.4) THEN
C     H COULD BE DOUBLED IF ALL NECESSARY PRECEEDING VALUES ARE AVAILABLE
                     IMOD=ISTEP/2 
                     IF ((ISTEP-IMOD-IMOD).EQ.0) THEN
                        H=H+H
                        IHLF=IHLF-1  
                        ISTEP=0  
                        DO I=1,NDIM  
                           AUX(N-1,I)=AUX(N-2,I)  
                           AUX(N-2,I)=AUX(N-4,I)  
                           AUX(N-3,I)=AUX(N-6,I)  
                           AUX(N+6,I)=AUX(N+5,I)  
                           AUX(N+5,I)=AUX(N+3,I)  
                           AUX(N+4,I)=AUX(N+1,I)  
                           DELT=AUX(N+6,I)+AUX(N+5,I) 
                           DELT=DELT+DELT+DELT  
             AUX(16,I)=8.962962963D0*(PV(I)-AUX(N-3,I))-3.361111111D0*H* 
     *                     (DERY(I)+DELT+AUX(N+4,I))  
                        ENDDO
                        ISW=6
                     ELSE
                        ISW=6
                     ENDIF
                  ELSE
                     ISW=6
                  ENDIF
               ENDIF
               ISW=6
            ELSE
               ISW=9
            ENDIF
         ELSE IF (ISW.EQ.9) THEN
C           H MUST BE HALVED 
            IHLF=IHLF+1  
            IF (IHLF.LE.10) THEN
               ISW=10
            ELSE
               ISW=8
               IHLF1=5
            ENDIF
         ELSE IF (ISW.EQ.10) THEN
            H=.5D0*H 
            ISTEP=0  
            DO I=1,NDIM  
               PV(I)=.390625D-2*(8.D1*AUX(N-1,I)+135.D0*AUX(N-2,I)
     *        + 4.D1*AUX(N-1,I)+AUX(N-4,I))-.1171875D0*(AUX(N+6,I)
     *        -  6.D0*AUX(N+5,I)-AUX(N+4,I))*H
           AUX(N-4,I)=.390625D-2*(12.D0*AUX(N-1,I)+135.D0*AUX(N-2,I)+ 
     *         08.D0*AUX(N-3,I)+AUX(N-4,I))-.234375D-1*(AUX(N+6,I)+  
     *         8.D0*AUX(N+5,I)-9.D0*AUX(N+4,I))*H  
               AUX(N-3,I)=AUX(N-2,I)  
               AUX(N+4,I)=AUX(N+5,I)  
            ENDDO
            X=X-H
            DELT=X-(H+H) 
            CALL FCT(X,PV,DERY)
            DO I=1,NDIM  
               AUX(N-2,I)=PV(I)  
               AUX(N+5,I)=DERY(I) 
               PV(I)=AUX(N-4,I)  
            ENDDO
            DELT=DELT-(H+H)  
            CALL FCT(X,PV,DERY)
            DO I=1,NDIM  
               DELT=AUX(N+5,I)+AUX(N+4,I) 
               DELT=DELT+DELT+DELT  
               AUX(16,I)=8.9629696296D0*(AUX(N-1,I)-PV(I))
     *       -  3.3611111111D0*H*(AUX(N+6,I)+DELT+DERY(I))  
               AUX(N+3,I)=DERY(I) 
            ENDDO
            ISW=7
         ENDIF
      ENDDO

      return

      END  

C-----------------------------------------------------------------------
C-----------------------------------------------------------------------
C THIS IS A FILE OF ROUTINES THAT HAVE BEEN DECLARED EXTERNAL IN THE 
C MAIN PROGRAM & WHICH ARE PASSED INTO THE ROUTINE DHPCG THAT SOLVES THE
C SYSTEM OF DIFFERENTIAL EQUATIONS.

      SUBROUTINE FCT(X,Y,DERY)
 

      IMPLICIT NONE
      INTEGER NDIM
      PARAMETER (NDIM=6)
      REAL*8 BX,BY,BZ,DERY(NDIM),FAC,QMC,X,X00,Y(NDIM),Y00,Z00
      COMMON /QMC/QMC
C     COMMON /BX/BX,BY,BZ,/X00/X00,Y00,Z00
      PARAMETER (FAC=1.0D-2)
C SUBROUTINE TO COMPUTE THE RIGHT HAND SIDE DERY OF THE SYSTEM AT THE 
C GIVEN VALUES OF X & Y.
 

      X00 = Y(1)/FAC
      Y00 = Y(2)/FAC
      Z00 = Y(3)/FAC
      CALL FDMOD(X00,Y00,Z00,BX,BY,BZ)
D     PRINT *,' QMC ',QMC
D     PRINT *,' X00 ',X00,' Y00 ',Y00,' Z00 ',Z00
D     PRINT *,' BX ',BX,' BY ',BY,' BZ ',BZ
      DERY(1) = Y(4)
      DERY(2) = Y(5)
      DERY(3) = Y(6)
      DERY(4) = QMC * (Y(5)*BZ - Y(6)*BY)
      DERY(5) = QMC * (Y(6)*BX - Y(4)*BZ)
      DERY(6) = QMC * (Y(4)*BY - Y(5)*BX)
      

      RETURN
      END
C--------------------------------------------------------------------
C---------------------------------------------------------------------
      	SUBROUTINE OUTP(X,Y,DERY,IHLF,NDIM,PRMT,HIT)

C PURPOSE : THIS IS A ROUTINE THAT IS DECLARED EXTERNAL IN THE MAIN
C ROUTINE. IT PRINTS THE OUTPUT VALUES OBTAINED FROM THE ROUTINE
C DHPCG - WHICH SOLVES THE SYSTEM OF DIFF. EQUATIONS.

      	IMPLICIT NONE
      	CHARACTER*72 FNAME
      	INTEGER HIT,I,IHLF,MULC,MULC1,NCOUNT,NDIM,NSURF,NU,NTRAJ
     & 		,wscatter,scatter,Nscatter,npas
      	REAL*8 DERY(NDIM),PRMT(5),X,Y(NDIM),TLN(2,3),TOTV,BX,BY,BZ,B,
     &   X00,Y00,Z00,FAC,x01(3),x02(3),aux(16,6),sect(3),c1(4)
	real*8 theta,phi,nsurf1
	real*8 fphi,dist,x1,y1,z1
      	PARAMETER (FAC=1.0D-2)
      integer startnsurf,ape
      logical firstcheck,secondcheck    
      common /startnsurf/startnsurf,/ape/ape
      common /firstcheck/firstcheck,/secondcheck/secondcheck

	common /wscatter/wscatter,/scatter/scatter,/sect/sect,/c1/c1
	common /Nscatter/Nscatter,/nsurf1/nsurf1,/theta/theta,/phi/phi
      	COMMON /NCOUNT/NCOUNT,/FNAME/FNAME
C     	COMMON /BX/BX,BY,BZ,/X00/X00,Y00,Z00
      	COMMON /TLN/TLN,/NU/NU
      	DATA MULC/40/,MULC1/5/
	INCLUDE 'pass.cmn'
	external fct
c,outp1

C     	OPEN(UNIT=3,FILE='TRAJ.DAT',ACCESS='SEQUENTIAL',STATUS='OLD')
      	OPEN(UNIT=4,FILE=FNAME,ACCESS='SEQUENTIAL',STATUS='OLD')
c      	OPEN(UNIT=7,FILE='TRAJSH.DAT',ACCESS='SEQUENTIAL',STATUS='OLD')
C     	OPEN(UNIT=8,FILE='PASS.DAT',ACCESS='SEQUENTIAL',STATUS='OLD')

      	TOTV=DSQRT(Y(4)*Y(4) + Y(5)*Y(5) + Y(6)*Y(6))

      	IF (NCOUNT .EQ. 0) THEN
c       	    WRITE(7,15) X,(Y(I),I=1,NDIM),TOTV
       	    WRITE(4,20) (Y(I)/FAC,I=1,3)
      	END IF

      	NCOUNT = NCOUNT + 1
      	IF (MOD(NCOUNT,MULC) .EQ. 0) THEN
c            WRITE(7,15) X,(Y(I),I=1,NDIM),TOTV
      	END IF

      	IF (MOD(NCOUNT,MULC1) .EQ. 0) THEN
            WRITE(4,20) (Y(I)/FAC,I=1,3)
      	END IF

D     	B = DSQRT(BX*BX + BY*BY + BZ*BZ)

      	IF (NU .EQ. 1) THEN
            DO I=1,3
            	TLN(2,I)=Y(I)/FAC
       	    END DO
      	ELSE
       	    DO I=1,3
            	TLN(1,I)=TLN(2,I)
            	TLN(2,I)=Y(I)/FAC
            END DO

	    do 31 i=1,3
	    	x01(i)=tln(1,i)
	    	x02(i)=tln(2,i)
31	    end do

       if ( (x02(1).gt.7.0).or.(x02(1).lt.0.0).or.(x02(2).gt.4)
     & .or.(x02(2).lt.1.0).or.(x02(3).gt.1.0).or.
     & (x02(3).lt.-1.0) ) then
c       if ( (((x02(1).gt.7.0).or.(x02(1).lt.0.0)).or.((x02(2).gt.4)
c     & .or.(x02(2).lt.1.8))).or.((x02(3).gt.0.6).or.
c     & (x02(3).lt.-0.6)) ) then
           hit = 1
c        write(6,*)'Special case, trajectory has run out of assembly'	
c       else
c  	   hit = 0	
       end if
c           if (secondcheck) then       
c                 write(6,*)'-----',startnsurf,ape
c           end if

            CALL CHECKHIT(HIT,NSURF)
                        !HIT=0 :CONTINUE WITH TRAJECTORY CALCULATION
                        !   =1 :HIT THE NSURF(NTH SURFACE), LOST
                        !   =2 :SUCCESSFULLY ESCAPED FROM THE SENSOR 

       	    IF (HIT .EQ. 1) THEN
         	WRITE(4,20) (Y(I)/FAC,I=1,3)
D        	WRITE(6,*) 'HIT',HIT,'SURFACE NO.',NSURF-1 
D        	WRITE(4,*) 'HIT',HIT,'SURFACE NO.',NSURF-1
       	    ELSE 
         	IF (HIT .EQ. 2) THEN
          	    WRITE(4,20) (Y(I)/FAC,I=1,3)
D         	    WRITE(6,*) 'ESCAPED'
D         	    WRITE(4,*) 'ESCAPED'
          	    NPAS=NPAS+1
	            X1=TLN(2,1)-TLN(1,1)
  	    	    Y1=TLN(2,2)-TLN(1,2)
	    	    Z1=TLN(2,3)-TLN(1,3)
		    DIST=DSQRT(X1*X1 + Y1*Y1 + Z1*Z1)
		    pas(npas,1)=theta
		    pas(npas,2)=phi
		    PAS(NPAS,3)=DACOS(Z1/DIST)
		    PAS(NPAS,4)=FPHI(X1,Y1)
		    pas(npas,11)=1
C		    PASVEL(NPAS,1)=DACOS(Y(6)/TOTV)
C		    PASVEL(NPAS,2)=FPHI(Y(4),Y(5))
		    DO I=1,6
	  	     	PAS(NPAS,I+4)=Y(I)
		    END DO
         	END IF                                 	
       	    END IF 	

c	    if ((hit.eq.0).and.(scatter.eq.1)) then
c	    	if (wscatter.eq.1) then
c		    call SCATTERSUB(HIT,sect,X01,X02,C1,y)
c		    nsurf1=nsurf-1
c		    if (hit.eq.0) then	
c	       	    	call fct(x,y,dery)	
c	    	    	call DHPCG1(PRMT,Y,DERY,NDIM,IHLF,FCT,OUTP1,AUX)
c		    end if
c	        end if
c	    	if (wscatter.eq.2) then
c	    	    do i=1,nscatter
c		    	call SCATTERSUB(HIT,sect,X01,X02,C1,y)
c			nsurf1=nsurf-1
c		    	if (hit.eq.0) then
c	       	    	    call fct(x,y,dery)	
c	    	    	    call DHPCG1(PRMT,Y,DERY,NDIM,IHLF,
c     &					FCT,OUTP1,AUX)
C------------------------------------------------------------------------
C   	Here is a modification to restrict only one diffuse scattering
C	   occurs during the process, Be careful with this modification
C	   need more testing for this.

c			        if (hit.eq.2) then	
c				    nu=nu+1
c				    return
c			    	end if
C------------------------------------------------------------------------
c		    	end if
c		    end do	
c	    	end if
c		hit=1
c	    end if

      	END IF 
      	NU=NU+1      

C     	WRITE(3,15) X,(Y(I),I=1,NDIM),TOTV
C15   	FORMAT (1X,D14.7,6(1X,D14.7),1X,D14.7,1X,F10.3)
 15   	FORMAT (1X,D14.7,6(1X,D15.8),1X,D21.14)
 20   	FORMAT(3(X,F9.6))
      	RETURN
      	END

****************************************************************************

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