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pam-fi |
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************************************************************************ |
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* |
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* subroutine to evaluate the vector alfa (AL) |
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* which minimizes CHI^2 |
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* |
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* - modified from mini.f in order to call differente chi^2 routine. |
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* The new one includes also single clusters: in this case |
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* the residual is defined as the distance between the track and the |
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* segment AB associated to the single cluster. |
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* |
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* |
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************************************************************************ |
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SUBROUTINE MINI_2(ISTEP,IFAIL) |
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IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
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include '../common/commontracker.f' !tracker general common |
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include '../common/common_mini_2.f' !common for the tracking procedure |
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logical DEBUG |
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common/dbg/DEBUG |
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parameter (inf=1.e8) !just a huge number... |
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c------------------------------------------------------------------------ |
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c variables used in the tracking procedure (mini and its subroutines) |
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c |
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c N.B.: in mini & C. (and in the following block of variables too) |
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c the plane ordering is reversed in respect of normal |
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c ordering, but they maintain their Z coordinates. so plane number 1 is |
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c the first one that a particle meets, and its Z coordinate is > 0 |
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c------------------------------------------------------------------------ |
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DATA ZINI/23.5/ !z coordinate of the reference plane |
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DATA XGOOD,YGOOD/nplanes*1.,nplanes*1./ !planes to be used in the tracking |
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DATA STEPAL/5*1.d-7/ !alpha vector step |
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DATA ISTEPMAX/100/ !maximum number of steps in the chi^2 minimization |
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DATA TOLL/1.d-8/ !tolerance in reaching the next plane during |
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* !the tracking procedure |
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DATA STEPMAX/100./ !maximum number of steps in the trackin gprocess |
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c DATA ALMAX/inf,inf,inf,inf,0.25e2/ !limits on alpha vector components |
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c DATA ALMIN/-inf,-inf,-inf,-inf,-0.25e2/ !" |
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DATA ALMAX/inf,inf,1.,inf,0.25e2/ !limits on alpha vector components |
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DATA ALMIN/-inf,-inf,-1.,-inf,-0.25e2/ !" |
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DIMENSION DAL(5) !increment of vector alfa |
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INTEGER IFLAG |
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c-------------------------------------------------------- |
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c IFLAG =1 ---- chi2 derivatives computed by using |
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c incremental ratios and posxyz.f |
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c IFLAG =2 ---- the approximation of Golden is used |
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c (see chisq.f) |
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c |
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c NB: the two metods gives equivalent results BUT |
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c method 2 is faster!! |
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c-------------------------------------------------------- |
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DATA IFLAG/2/ |
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* ---------------------------------------------------------- |
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* define ALTOL(5) ---> tolerances on state vector |
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* |
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* ---------------------------------------------------------- |
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FACT=10. !scale factor to define |
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!tolerance on alfa |
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ALTOL(1)=RESX(1)/FACT !al(1) = x |
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ALTOL(2)=RESY(1)/FACT !al(2) = y |
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ALTOL(3)=DSQRT(RESX(1)**2 !al(3)=sin(theta) |
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$ +RESY(1)**2)/44.51/FACT |
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ALTOL(4)=ALTOL(3) !al(4)=phi |
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c deflection error (see PDG) |
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DELETA1=0.01*RESX(1)/0.3/0.4/0.4451**2*SQRT(720./(6.+4.)) |
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DELETA2=0.016/0.3/0.4/0.4451*SQRT(0.4451/9.36) |
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* ---------------------------------------------------------- |
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* |
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ISTEP=0 !num. steps to minimize chi^2 |
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JFAIL=0 !error flag |
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CALL CHISQ(IFLAG,JFAIL) !chi^2 and its derivatives |
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IF(JFAIL.NE.0) THEN |
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IFAIL=1 |
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if(DEBUG) |
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$ PRINT *,'mini_2 ===> error on CHISQ computation !!!' |
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RETURN |
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ENDIF |
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* |
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* ----------------------- |
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* START MINIMIZATION LOOP |
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* ----------------------- |
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10 ISTEP=ISTEP+1 !<<<<<<<<<<<<<< NEW STEP !! |
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CHI2_P=CHI2 |
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c print*,'@@@@@ ',istep,' - ',al |
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cost=1e-7 |
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DO I=1,5 |
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DO J=1,5 |
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CHI2DD(I,J)=CHI2DD(I,J)*COST |
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ENDDO |
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CHI2D(I)=CHI2D(I)*COST |
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ENDDO |
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*------------------------------------------------------------* |
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* track fitting with FREE deflection |
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*------------------------------------------------------------* |
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CALL DSFACT(5,CHI2DD,5,IFA,DET,JFA) !CHI2DD matrix determinant |
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IF(IFA.NE.0) THEN !not positive-defined |
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if(DEBUG)then |
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PRINT *, |
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$ 'MINI_HOUGH ==> '// |
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$ '** ERROR ** on matrix inversion (not positive-defined)!!!' |
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$ ,DET |
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endif |
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IFAIL=1 |
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RETURN |
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ENDIF |
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CALL DSFINV(5,CHI2DD,5) !CHI2DD matrix inversion |
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* ******************************************* |
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* find new value of AL-pha !* |
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* !* |
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DO I=1,5 !* |
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DAL(I)=0. !* |
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DO J=1,5 !* |
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DAL(I)=DAL(I)-CHI2DD(I,J)*CHI2D(J) !* |
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COV(I,J)=CHI2DD(I,J) !* |
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ENDDO !* |
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ENDDO !* |
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DO I=1,5 !* |
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AL(I)=AL(I)+DAL(I) !* |
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ENDDO !* |
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* ******************************************* |
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* check parameter bounds: |
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DO I=1,5 |
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IF(AL(I).GT.ALMAX(I).OR.AL(I).LT.ALMIN(I))THEN |
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if(DEBUG)then |
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PRINT*,' **WARNING** ' |
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PRINT*,'MINI_2 ==> AL(',I,') out of range' |
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PRINT*,' value: ',AL(I), |
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$ ' limits: ',ALMIN(I),ALMAX(I) |
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print*,'istep ',istep |
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endif |
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IFAIL=1 |
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RETURN |
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ENDIF |
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ENDDO |
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* new estimate of chi^2: |
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JFAIL=0 !error flag |
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CALL CHISQ(IFLAG,JFAIL) !chi^2 and its derivatives |
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IF(JFAIL.NE.0) THEN |
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IFAIL=1 |
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if(DEBUG) |
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$ PRINT *,'mini_2: ===> error on CHISQ computation !!!' |
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RETURN |
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ENDIF |
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* check number of steps: |
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IF(ISTEP.gt.ISTEPMAX) then |
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IFAIL=1 |
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if(DEBUG) |
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$ PRINT *,'mini_2: WARNING ===> ISTEP.GT.ISTEPMAX=',ISTEPMAX |
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goto 11 |
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endif |
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* --------------------------------------------- |
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* evaluate deflection tolerance on the basis of |
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* estimated deflection |
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* --------------------------------------------- |
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ALTOL(5)=DSQRT(DELETA1**2+DELETA2**2*AL(5)**2)/FACT |
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*---- check tolerances: |
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DO I=1,5 |
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IF(ABS(DAL(I)).GT.ALTOL(I))GOTO 10 !>>>> new step! |
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ENDDO |
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* ------------------------------------ |
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* Number of Degree Of Freedom |
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ndof=0 |
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do ip=1,nplanes |
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ndof=ndof |
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$ +int(xgood(ip)) |
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$ +int(ygood(ip)) |
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enddo |
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ndof=ndof-5 |
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* ------------------------------------ |
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* Reduced chi^2 |
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CHI2 = CHI2/dble(ndof) |
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11 CONTINUE |
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101 CONTINUE |
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c print*,'END MINI' |
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RETURN |
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END |
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****************************************************************************** |
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* |
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* routine to compute chi^2 and its derivatives |
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* |
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* |
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* (modified in respect to the previous one in order to include |
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* single clusters. In this case the residual is evaluated by |
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* calculating the distance between the track intersection and the |
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* segment AB associated to the single cluster) |
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* |
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****************************************************************************** |
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SUBROUTINE CHISQ(IFLAG,IFAIL) |
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IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
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include '../common/commontracker.f' !tracker general common |
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include '../common/common_mini_2.f' !common for the tracking procedure |
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DIMENSION XV2(nplanes),YV2(nplanes),XV1(nplanes),YV1(nplanes) |
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$ ,XV0(nplanes),YV0(nplanes) |
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DIMENSION AL_P(5) |
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* |
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* chi^2 computation |
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* |
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DO I=1,5 |
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AL_P(I)=AL(I) |
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ENDDO |
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JFAIL=0 !error flag |
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CALL POSXYZ(AL_P,JFAIL) !track intersection with tracking planes |
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IF(JFAIL.NE.0) THEN |
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PRINT *,'CHISQ ==> error from tracking routine POSXYZ !!' |
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IFAIL=1 |
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RETURN |
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ENDIF |
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DO I=1,nplanes |
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XV0(I)=XV(I) |
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YV0(I)=YV(I) |
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ENDDO |
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* ------------------------------------------------ |
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c$$$ CHI2=0. |
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c$$$ DO I=1,nplanes |
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c$$$ CHI2=CHI2 |
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c$$$ + +(XV(I)-XM(I))**2/RESX(i)**2 *XGOOD(I)*YGOOD(I) |
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c$$$ + +(YV(I)-YM(I))**2/RESY(i)**2 *YGOOD(I)*XGOOD(I) |
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c$$$ ENDDO |
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* --------------------------------------------------------- |
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* For planes with only a X or Y-cl included, instead of |
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* a X-Y couple, the residual for chi^2 calculation is |
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* evaluated by finding the point x-y, along the segment AB, |
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* closest to the track. |
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* The X or Y coordinate, respectivelly for X and Y-cl, is |
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* then assigned to XM or YM, which is then considered the |
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* measured position of the cluster. |
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* --------------------------------------------------------- |
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CHI2=0. |
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DO I=1,nplanes |
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IF(XGOOD(I).EQ.1.AND.YGOOD(I).EQ.0)THEN !X-cl |
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BETA = (XM_B(I)-XM_A(I))/(YM_B(I)-YM_A(I)) |
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ALFA = XM_A(I) - BETA * YM_A(I) |
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YM(I) = ( YV(I) + BETA*XV(I) - BETA*ALFA )/(1+BETA**2) |
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if(YM(I).lt.dmin1(YM_A(I),YM_B(I))) |
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$ YM(I)=dmin1(YM_A(I),YM_B(I)) |
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if(YM(I).gt.dmax1(YM_A(I),YM_B(I))) |
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$ YM(I)=dmax1(YM_A(I),YM_B(I)) |
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XM(I) = ALFA + BETA * YM(I) !<<<< measured coordinates |
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ELSEIF(XGOOD(I).EQ.0.AND.YGOOD(I).EQ.1)THEN !Y-cl |
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BETA = (YM_B(I)-YM_A(I))/(XM_B(I)-XM_A(I)) |
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ALFA = YM_A(I) - BETA * XM_A(I) |
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XM(I) = ( XV(I) + BETA*YV(I) - BETA*ALFA )/(1+BETA**2) |
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if(XM(I).lt.dmin1(XM_A(I),XM_B(I))) |
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$ XM(I)=dmin1(XM_A(I),XM_B(I)) |
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if(XM(I).gt.dmax1(XM_A(I),XM_B(I))) |
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$ XM(I)=dmax1(XM_A(I),XM_B(I)) |
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YM(I) = ALFA + BETA * XM(I) !<<<< measured coordinates |
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ENDIF |
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CHI2=CHI2 |
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+ +(XV(I)-XM(I))**2/RESX(i)**2 *( XGOOD(I)*YGOOD(I) ) |
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+ +(YV(I)-YM(I))**2/RESY(i)**2 *( YGOOD(I)*XGOOD(I) ) |
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+ +((XV(I)-XM(I))**2+(YV(I)-YM(I))**2)/RESX(i)**2 |
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+ *( XGOOD(I)*(1-YGOOD(I)) ) |
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+ +((XV(I)-XM(I))**2+(YV(I)-YM(I))**2)/RESY(i)**2 |
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+ *( (1-XGOOD(I))*YGOOD(I) ) |
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ENDDO |
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* ------------------------------------------------ |
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* |
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* calculation of derivatives (dX/dAL_fa and dY/dAL_fa) |
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* |
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* ////////////////////////////////////////////////// |
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* METHOD 1 -- incremental ratios |
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* ////////////////////////////////////////////////// |
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IF(IFLAG.EQ.1) THEN |
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DO J=1,5 |
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DO JJ=1,5 |
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AL_P(JJ)=AL(JJ) |
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ENDDO |
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AL_P(J)=AL_P(J)+STEPAL(J)/2. |
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JFAIL=0 |
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CALL POSXYZ(AL_P,JFAIL) |
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IF(JFAIL.NE.0) THEN |
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PRINT *,'CHISQ ==> error from tracking routine POSXYZ !!' |
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IFAIL=1 |
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RETURN |
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ENDIF |
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DO I=1,nplanes |
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XV2(I)=XV(I) |
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YV2(I)=YV(I) |
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ENDDO |
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AL_P(J)=AL_P(J)-STEPAL(J) |
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JFAIL=0 |
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CALL POSXYZ(AL_P,JFAIL) |
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IF(JFAIL.NE.0) THEN |
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PRINT *,'CHISQ ==> error from tracking routine POSXYZ !!' |
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IFAIL=1 |
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RETURN |
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ENDIF |
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DO I=1,nplanes |
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XV1(I)=XV(I) |
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YV1(I)=YV(I) |
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ENDDO |
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DO I=1,nplanes |
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DXDAL(I,J)=(XV2(I)-XV1(I))/STEPAL(J) |
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DYDAL(I,J)=(YV2(I)-YV1(I))/STEPAL(J) |
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ENDDO |
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ENDDO |
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ENDIF |
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* ////////////////////////////////////////////////// |
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* METHOD 2 -- Bob Golden |
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* ////////////////////////////////////////////////// |
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IF(IFLAG.EQ.2) THEN |
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DO I=1,nplanes |
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DXDAL(I,1)=1. |
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DYDAL(I,1)=0. |
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DXDAL(I,2)=0. |
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DYDAL(I,2)=1. |
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COSTHE=DSQRT(1.-AL(3)**2) |
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IF(COSTHE.EQ.0.) THEN |
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PRINT *,'=== WARNING ===> COSTHE=0' |
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STOP |
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ENDIF |
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DXDAL(I,3)=(ZINI-ZM(I))*DCOS(AL(4))/COSTHE**3 |
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DYDAL(I,3)=(ZINI-ZM(I))*DSIN(AL(4))/COSTHE**3 |
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DXDAL(I,4)=-AL(3)*(ZINI-ZM(I))*DSIN(AL(4))/COSTHE |
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DYDAL(I,4)=AL(3)*(ZINI-ZM(I))*DCOS(AL(4))/COSTHE |
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IF(AL(5).NE.0.) THEN |
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DXDAL(I,5)= |
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+ (XV(I)-(AL(1)+AL(3)/COSTHE*(ZINI-ZM(I)) |
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+ *DCOS(AL(4))))/AL(5) |
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DYDAL(I,5)= |
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+ (YV(I)-(AL(2)+AL(3)/COSTHE*(ZINI-ZM(I)) |
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+ *DSIN(AL(4))))/AL(5) |
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ELSE |
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DXDAL(I,5)=100.*( 0.25 *0.3*0.4*(0.01*(ZINI-ZM(I)))**2 ) |
362 |
|
|
DYDAL(I,5)=0. |
363 |
|
|
ENDIF |
364 |
|
|
|
365 |
|
|
ENDDO |
366 |
|
|
ENDIF |
367 |
|
|
* |
368 |
|
|
* x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x |
369 |
|
|
* >>> CHI2D evaluation |
370 |
|
|
* |
371 |
|
|
DO J=1,5 |
372 |
|
|
CHI2D(J)=0. |
373 |
|
|
DO I=1,nplanes |
374 |
|
|
CHI2D(J)=CHI2D(J) |
375 |
|
|
+ +2.*(XV0(I)-XM(I))/RESX(i)**2*DXDAL(I,J) *XGOOD(I) |
376 |
|
|
+ +2.*(YV0(I)-YM(I))/RESY(i)**2*DYDAL(I,J) *YGOOD(I) |
377 |
|
|
ENDDO |
378 |
|
|
ENDDO |
379 |
|
|
* |
380 |
|
|
* >>> CHI2DD evaluation |
381 |
|
|
* |
382 |
|
|
DO I=1,5 |
383 |
|
|
DO J=1,5 |
384 |
|
|
CHI2DD(I,J)=0. |
385 |
|
|
DO K=1,nplanes |
386 |
|
|
CHI2DD(I,J)=CHI2DD(I,J) |
387 |
|
|
+ +2.*DXDAL(K,I)*DXDAL(K,J)/RESX(k)**2 *XGOOD(K) |
388 |
|
|
+ +2.*DYDAL(K,I)*DYDAL(K,J)/RESY(k)**2 *YGOOD(K) |
389 |
|
|
ENDDO |
390 |
|
|
ENDDO |
391 |
|
|
ENDDO |
392 |
|
|
* x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x |
393 |
|
|
|
394 |
|
|
RETURN |
395 |
|
|
END |
396 |
|
|
|
397 |
|
|
|
398 |
|
|
***************************************************************** |
399 |
|
|
* |
400 |
|
|
* Routine to compute the track intersection points |
401 |
|
|
* on the tracking-system planes, given the track parameters |
402 |
|
|
* |
403 |
|
|
* The routine is based on GRKUTA, which computes the |
404 |
|
|
* trajectory of a charged particle in a magnetic field |
405 |
|
|
* by solving the equatins of motion with Runge-Kuta method. |
406 |
|
|
* |
407 |
|
|
* Variables that have to be assigned when the subroutine |
408 |
|
|
* is called are: |
409 |
|
|
* |
410 |
|
|
* ZM(1,NPLANES) ----> z coordinates of the planes |
411 |
|
|
* AL_P(1,5) ----> track-parameter vector |
412 |
|
|
* |
413 |
|
|
* ----------------------------------------------------------- |
414 |
|
|
* NB !!! |
415 |
|
|
* The routine works properly only if the |
416 |
|
|
* planes are numbered in descending order starting from the |
417 |
|
|
* reference plane (ZINI) |
418 |
|
|
* ----------------------------------------------------------- |
419 |
|
|
* |
420 |
|
|
***************************************************************** |
421 |
|
|
|
422 |
|
|
SUBROUTINE POSXYZ(AL_P,IFAIL) |
423 |
|
|
|
424 |
|
|
IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
425 |
|
|
|
426 |
|
|
include '../common/commontracker.f' !tracker general common |
427 |
|
|
include '../common/common_mini_2.f' !common for the tracking procedure |
428 |
|
|
c |
429 |
|
|
DIMENSION AL_P(5) |
430 |
|
|
* |
431 |
|
|
DO I=1,nplanes |
432 |
|
|
ZV(I)=ZM(I) ! |
433 |
|
|
ENDDO |
434 |
|
|
* |
435 |
|
|
* set parameters for GRKUTA |
436 |
|
|
* |
437 |
|
|
IF(AL_P(5).NE.0) CHARGE=AL_P(5)/DABS(AL_P(5)) |
438 |
|
|
IF(AL_P(5).EQ.0) CHARGE=1. |
439 |
|
|
VOUT(1)=AL_P(1) |
440 |
|
|
VOUT(2)=AL_P(2) |
441 |
|
|
VOUT(3)=ZINI ! DBLE(Z0)-DBLE(ZSPEC) |
442 |
|
|
VOUT(4)=AL_P(3)*DCOS(AL_P(4)) |
443 |
|
|
VOUT(5)=AL_P(3)*DSIN(AL_P(4)) |
444 |
|
|
VOUT(6)=-1.*DSQRT(1.-AL_P(3)**2) |
445 |
|
|
IF(AL_P(5).NE.0.) VOUT(7)=DABS(1./AL_P(5)) |
446 |
|
|
IF(AL_P(5).EQ.0.) VOUT(7)=1.E8 |
447 |
|
|
DO I=1,nplanes |
448 |
|
|
step=vout(3)-zv(i) |
449 |
|
|
10 DO J=1,7 |
450 |
|
|
VECT(J)=VOUT(J) |
451 |
|
|
VECTINI(J)=VOUT(J) |
452 |
|
|
ENDDO |
453 |
|
|
11 continue |
454 |
|
|
CALL GRKUTA(CHARGE,STEP,VECT,VOUT) |
455 |
|
|
IF(VOUT(3).GT.VECT(3)) THEN |
456 |
|
|
IFAIL=1 |
457 |
|
|
PRINT *,'posxy (grkuta): WARNING ===> backward track!!' |
458 |
|
|
print*,'charge',charge |
459 |
|
|
print*,'vect',vect |
460 |
|
|
print*,'vout',vout |
461 |
|
|
print*,'step',step |
462 |
|
|
RETURN |
463 |
|
|
ENDIF |
464 |
|
|
Z=VOUT(3) |
465 |
|
|
IF(Z.LE.ZM(I)+TOLL.AND.Z.GE.ZM(I)-TOLL) GOTO 100 |
466 |
|
|
IF(Z.GT.ZM(I)+TOLL) GOTO 10 |
467 |
|
|
IF(Z.LE.ZM(I)-TOLL) THEN |
468 |
|
|
STEP=STEP*(ZM(I)-VECT(3))/(Z-VECT(3)) |
469 |
|
|
DO J=1,7 |
470 |
|
|
VECT(J)=VECTINI(J) |
471 |
|
|
ENDDO |
472 |
|
|
GOTO 11 |
473 |
|
|
ENDIF |
474 |
|
|
|
475 |
|
|
* ----------------------------------------------- |
476 |
|
|
* evaluate track coordinates |
477 |
|
|
100 XV(I)=VOUT(1) |
478 |
|
|
YV(I)=VOUT(2) |
479 |
|
|
ZV(I)=VOUT(3) |
480 |
|
|
AXV(I)=DATAN(VOUT(4)/VOUT(6))*180./ACOS(-1.) |
481 |
|
|
AYV(I)=DATAN(VOUT(5)/VOUT(6))*180./ACOS(-1.) |
482 |
|
|
* ----------------------------------------------- |
483 |
|
|
|
484 |
|
|
ENDDO |
485 |
|
|
|
486 |
|
|
RETURN |
487 |
|
|
END |
488 |
|
|
|
489 |
|
|
|
490 |
|
|
|
491 |
|
|
|
492 |
|
|
|
493 |
|
|
* ********************************************************** |
494 |
|
|
* Some initialization routines |
495 |
|
|
* ********************************************************** |
496 |
|
|
|
497 |
|
|
* ---------------------------------------------------------- |
498 |
|
|
* Routine to initialize COMMON/TRACK/ |
499 |
|
|
* |
500 |
|
|
subroutine track_init |
501 |
|
|
|
502 |
|
|
IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
503 |
|
|
|
504 |
|
|
include '../common/commontracker.f' !tracker general common |
505 |
|
|
include '../common/common_mini_2.f' !common for the tracking procedure |
506 |
|
|
include '../common/common_mech.f' |
507 |
|
|
|
508 |
|
|
do i=1,5 |
509 |
|
|
AL(i) = 0. |
510 |
|
|
enddo |
511 |
|
|
|
512 |
|
|
do ip=1,NPLANES |
513 |
|
|
ZM(IP) = fitz(nplanes-ip+1) !init to mech. position |
514 |
|
|
XM(IP) = -100. !0. |
515 |
|
|
YM(IP) = -100. !0. |
516 |
|
|
XM_A(IP) = -100. !0. |
517 |
|
|
YM_A(IP) = -100. !0. |
518 |
|
|
c ZM_A(IP) = 0 |
519 |
|
|
XM_B(IP) = -100. !0. |
520 |
|
|
YM_B(IP) = -100. !0. |
521 |
|
|
c ZM_B(IP) = 0 |
522 |
|
|
RESX(IP) = 1000. !3.d-4 |
523 |
|
|
RESY(IP) = 1000. !12.d-4 |
524 |
|
|
XGOOD(IP) = 0 |
525 |
|
|
YGOOD(IP) = 0 |
526 |
|
|
enddo |
527 |
|
|
|
528 |
|
|
return |
529 |
|
|
end |