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Sc_euclidean.f90
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Sc_euclidean.f90
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!The Polymorphic Tracking Code
!Copyright (C) Etienne Forest and CERN
module S_euclidean
use S_extend_poly
implicit none
public
PRIVATE transr,transp !,TRANSP_P
PRIVATE ROT_XZR,ROT_XZP !,ROT_XZP_P
PRIVATE ROT_YZR,ROT_YZP !,ROT_YZP_P
PRIVATE ROT_XYR,ROT_XYP !,ROT_XYP_P
private zero_r_z,zero_r_xy,zero_T_XYZ,zero_E_GENERAL,zero_E_GENERAL_s
INTERFACE TRANS
MODULE PROCEDURE transR
MODULE PROCEDURE transp
! MODULE PROCEDURE TRANSP_P ! New stuff
! MODULE PROCEDURE transS
! MODULE PROCEDURE TRANSS_S ! New stuff
END INTERFACE
INTERFACE ROT_XZ
MODULE PROCEDURE ROT_XZR
MODULE PROCEDURE ROT_XZP
! MODULE PROCEDURE ROT_XZP_P
! MODULE PROCEDURE ROT_XZS
! MODULE PROCEDURE ROT_XZS_S
END INTERFACE
INTERFACE ROT_YZ
MODULE PROCEDURE ROT_YZR
MODULE PROCEDURE ROT_YZP
! MODULE PROCEDURE ROT_YZP_P
! MODULE PROCEDURE ROT_YZS
! MODULE PROCEDURE ROT_YZS_S
END INTERFACE
INTERFACE ROT_XY
MODULE PROCEDURE ROT_XYR
MODULE PROCEDURE ROT_XYP
! MODULE PROCEDURE ROT_XYP_P
! MODULE PROCEDURE ROT_XYS
! MODULE PROCEDURE ROT_XYS_S
END INTERFACE
TYPE R_XY
REAL(DP) A(2)
END TYPE R_XY
TYPE R_Z
REAL(DP) A
END TYPE R_Z
TYPE T_XYZ
LOGICAL(LP) SIXTRACK
REAL(DP) L_DESIGN,DL_SIXTRACK
REAL(DP) D(3),DL
END TYPE T_XYZ
TYPE E_GENERAL
INTEGER KIND
TYPE(R_XY) T1
TYPE(R_Z) T2
TYPE(T_XYZ) T3
END TYPE E_GENERAL
INTERFACE init
MODULE PROCEDURE zero_r_xy
MODULE PROCEDURE zero_r_z
MODULE PROCEDURE zero_T_XYZ
MODULE PROCEDURE zero_E_GENERAL
MODULE PROCEDURE zero_E_GENERAL_s
END INTERFACE
CONTAINS
subroutine print_e_general(e,mf)
IMPLICIT NONE
type(e_general) e
integer mf
if(e%kind==1) then
write(mf,*) " kind 1: x and y angle "
write(mf,*) e%t1%a
endif
if(e%kind==2) then
write(mf,*) " kind 2 : y angle "
write(mf,*) e%t2%a
endif
if(e%kind==3) then
write(mf,*) " kind 3 : dx,dy,dz "
write(mf,*) e%t3%d
write(mf,*) " coeff of (1+delta) "
write(mf,*) e%t3%dl
if(e%t3%SIXTRACK ) then
write(mf,*) " L_DESIGN, DL_SIXTRACK "
write(mf,*) e%t3%L_DESIGN , e%t3%DL_SIXTRACK
else
write(mf,*) " L_DESIGN "
write(mf,*) e%t3%L_DESIGN
endif
endif
end subroutine print_e_general
subroutine zero_r_xy(t)
implicit none
TYPE(R_XY) t
t%a=0
end subroutine zero_r_xy
subroutine zero_r_z(t)
implicit none
TYPE(R_Z) t
t%a=0
end subroutine zero_r_z
subroutine zero_T_XYZ(t)
implicit none
TYPE(T_XYZ) t
t%SIXTRACK=.false.
t%L_DESIGN=0
t%DL_SIXTRACK=0
t%DL=0
t%D=0
end subroutine zero_T_XYZ
subroutine zero_E_GENERAL(t,i)
implicit none
TYPE(E_GENERAL) t
integer i
t%kind=i
call init(t%t1)
call init(t%t2)
call init(t%t3)
end subroutine zero_E_GENERAL
subroutine zero_E_GENERAL_s(t)
implicit none
TYPE(E_GENERAL) t(:)
integer i
do i=1,size(t)
call init(t(i),0)
enddo
end subroutine zero_E_GENERAL_s
SUBROUTINE TRANS_dl(A,dl,LD,X,b,ctime,DL_SIXTRACK,SIXTRACK) ! for sixtrack recombination
IMPLICIT NONE
real(dp),INTENT(INOUT):: X(6)
real(dp) PZ
real(dp),INTENT(IN):: A(3),b,dl,LD,DL_SIXTRACK
LOGICAL(lp),INTENT(IN):: ctime,SIXTRACK
X(1)=X(1)-A(1)
X(3)=X(3)-A(2)
if(ctime) then ! THIS IS SIXTRACK HERE
PZ=sqrt(1.0_dp+2.0_dp*X(5)/b+x(5)**2)
X(1)=X(1)+A(3)*X(2)/pz
X(3)=X(3)+A(3)*X(4)/pz
IF(SIXTRACK) THEN
X(6)=X(6)+((X(2)*X(2)+X(4)*X(4))/2.0_dp/pz**2+1.0_dp)*(1.0_dp/b+x(5))*A(3)/pz-A(3)/B ! SIXTRACK DRIFT b=beta0
X(6)=X(6)+ dl*(1.0_dp/b+x(5))/pz + DL_SIXTRACK/B ! EXTRA
ELSE
X(6)=X(6)+((X(2)*X(2)+X(4)*X(4))/2.0_dp/pz**2+1.0_dp)*(1.0_dp/b+x(5))*A(3)/pz+ dl*(1.0_dp/b+x(5))/pz-LD/B
ENDIF
else
X(1)=X(1)+A(3)*X(2)/(1.0_dp+X(5))
X(3)=X(3)+A(3)*X(4)/(1.0_dp+X(5))
IF(SIXTRACK) THEN
X(6)=X(6)+(A(3)/(1.0_dp+X(5)))*(X(2)*X(2)+X(4)*X(4))/2.0_dp/(1.0_dp+X(5))
X(6)=X(6)+dl + DL_SIXTRACK
ELSE
X(6)=X(6)+(A(3)/(1.0_dp+X(5)))*(X(2)*X(2)+X(4)*X(4))/2.0_dp/(1.0_dp+X(5))+a(3)+ dl-LD
ENDIF
endif
END SUBROUTINE TRANS_dl
SUBROUTINE track_e_general_s(E,X,b,ctime)
IMPLICIT NONE
real(dp),INTENT(INOUT):: X(6)
real(dp),INTENT(IN):: b
LOGICAL(lp),INTENT(IN):: ctime
TYPE(E_GENERAL),INTENT(IN):: E(:)
integer i
do i=1,size(e)
call track_e_general(E(i),X,b,ctime)
enddo
END SUBROUTINE track_e_general_s
SUBROUTINE track_e_general(E,X,b,ctime)
IMPLICIT NONE
real(dp),INTENT(INOUT):: X(6)
real(dp),INTENT(IN):: b
LOGICAL(lp),INTENT(IN):: ctime
TYPE(E_GENERAL),INTENT(IN):: E
IF(E%KIND==1) THEN
CALL ROT_YZ(E%T1%A(2),X,b,my_FALSE,ctime) ! inverted
CALL ROT_XZ(E%T1%A(1),X,b,my_FALSE,ctime)
ELSEIF(E%KIND==2) THEN
CALL ROT_XY(E%T2%A,X)
ELSE
CALL TRANS_dl(E%T3%D,E%T3%dl,E%T3%L_DESIGN,X,b,ctime,E%T3%DL_SIXTRACK,E%T3%SIXTRACK)
ENDIF
END SUBROUTINE track_e_general
SUBROUTINE recombine(S,E)
IMPLICIT NONE
TYPE(E_GENERAL),INTENT(INout):: S(:)
TYPE(E_GENERAL),INTENT(INout)::E(3)
integer i,j,K
do j=1,size(s)
do i=1,size(s)
if(s(i)%kind==3) then
do k=i,size(s)-1
call commute_e(s(k),s(k+1))
enddo
endif
enddo
enddo
do j=1,size(s)
do i=1,size(s)
if(s(i)%kind==2) then
do k=i,size(s)-1
if(s(k+1)%kind==3) exit
call commute_e(s(k),s(k+1))
enddo
endif
enddo
enddo
do i=1,size(s)
write(6,*) s(i)%kind
enddo
E(1)%kind=1
E(2)%kind=2
E(3)%kind=3
E(1)%T1%A=0.0_dp
E(2)%T2%A=0.0_dp
E(3)%T3%D=0.0_dp
E(3)%T3%DL=0.0_dp
E(3)%T3%DL_SIXTRACK=0.0_dp
E(3)%T3%L_DESIGN=0.0_dp
do i=1,size(s)
if(S(I)%KIND==1) THEN
E(1)%T1%A=E(1)%T1%A+S(I)%T1%A
ENDIF
if(S(I)%KIND==2) THEN
E(2)%T2%A=E(2)%T2%A+S(I)%T2%A
ENDIF
if(S(I)%KIND==3) THEN
E(3)%T3%D=E(3)%T3%D+S(I)%T3%D
E(3)%T3%DL=E(3)%T3%DL+S(I)%T3%DL
E(3)%T3%L_DESIGN=E(3)%T3%L_DESIGN+S(I)%T3%L_DESIGN
ENDIF
enddo
E(3)%T3%DL_SIXTRACK=-E(3)%T3%L_DESIGN+E(3)%T3%D(3)
END SUBROUTINE recombine
SUBROUTINE COMMUTE_E(E1,E2)
IMPLICIT NONE
TYPE(E_GENERAL),INTENT(INOUT):: E1,E2
TYPE(E_GENERAL) ET
real(dp) D(2),A
IF(E1%KIND==1) THEN
IF(E2%KIND==1) THEN
ET=E1
E1=E2
E2=ET
ELSEIF(E2%KIND==2) THEN
ET=E1
A=E2%T2%A
D(1)=COS(A)*E1%T1%A(1)+SIN(A)*E1%T1%A(2)
D(2)=COS(A)*E1%T1%A(2)-SIN(A)*E1%T1%A(1)
E1=E2
E2=ET
E2%T1%A=D
ELSEIF(E2%KIND==3) THEN
ET=E1
E2%T3%DL=E2%T3%DL+E2%T3%D(1)*E1%T1%A(1)+E2%T3%D(2)*E1%T1%A(2)
E2%T3%DL=E2%T3%DL-E2%T3%D(3)*(E1%T1%A(1)**2+E1%T1%A(2)**2)/2.D0
E2%T3%D(1:2)=E2%T3%D(1:2)-E2%T3%D(3)*E1%T1%A
E1=E2
E2=ET
ENDIF
return
ENDIF
IF(E1%KIND==2) THEN
IF(E2%KIND==1) THEN
ET=E2
A=E1%T2%A
D(1)=COS(A)*E2%T1%A(1)-SIN(A)*E2%T1%A(2)
D(2)=COS(A)*E2%T1%A(2)+SIN(A)*E2%T1%A(1)
E2=E1
E1=ET
E1%T1%A=D
ELSEIF(E2%KIND==2) THEN
ET=E1
E1=E2
E2=ET
ELSEIF(E2%KIND==3) THEN
ET=E2
A=E1%T2%A
D(1)=COS(A)*E2%T3%D(1)-SIN(A)*E2%T3%D(2)
D(2)=COS(A)*E2%T3%D(2)+SIN(A)*E2%T3%D(1)
ET%T3%D(1:2)=D
E2=E1
E1=ET
ENDIF
return
ENDIF
IF(E1%KIND==3) THEN
IF(E2%KIND==1) THEN
ET=E2
E1%T3%DL=E1%T3%DL-E1%T3%D(1)*E2%T1%A(1)-E1%T3%D(2)*E2%T1%A(2)
E1%T3%DL=E1%T3%DL-E1%T3%D(3)*(E2%T1%A(1)**2+E2%T1%A(2)**2)/2.D0
E1%T3%D(1:2)=E1%T3%D(1:2)+E1%T3%D(3)*E2%T1%A
E2=E1
E1=ET
ELSEIF(E2%KIND==2) THEN
ET=E1
A=E2%T2%A
D(1)=COS(A)*E1%T3%D(1)+SIN(A)*E1%T3%D(2)
D(2)=COS(A)*E1%T3%D(2)-SIN(A)*E1%T3%D(1)
ET%T3%D(1:2)=D
E1=E2
E2=ET
ELSEIF(E2%KIND==3) THEN
ET=E1
E1=E2
E2=ET
ENDIF
return
ENDIF
END SUBROUTINE COMMUTE_E
SUBROUTINE ROT_YZR(A,X,b,EXACT,ctime)
IMPLICIT NONE
real(dp),INTENT(INOUT):: X(6)
real(dp) XN(6)
real(dp),INTENT(IN):: A,b
LOGICAL(lp),INTENT(IN):: EXACT,ctime
XN(1)=X(3)
XN(2)=X(4)
XN(3)=X(1) ! Using a relabelling i.e. a symmetry with respect to plane z
XN(4)=X(2) ! Could have used an x-y rotation of angle 90 degrees (AIMIN)
XN(5)=X(5)
XN(6)=X(6)
CALL ROT_XZ(A,XN,b,EXACT,ctime)
X(1)=XN(3)
X(2)=XN(4)
X(3)=XN(1)
X(4)=XN(2)
X(5)=XN(5)
X(6)=XN(6)
END SUBROUTINE ROT_YZR
SUBROUTINE ROT_YZP(A,X,b,EXACT,ctime)
IMPLICIT NONE
TYPE(REAL_8),INTENT(INOUT):: X(6)
TYPE(REAL_8) XN(6)
real(dp),INTENT(IN):: A,b
LOGICAL(lp),INTENT(IN):: EXACT,ctime
CALL ALLOC(XN,6)
XN(1)=X(3)
XN(2)=X(4)
XN(3)=X(1)
XN(4)=X(2)
XN(5)=X(5)
XN(6)=X(6)
CALL ROT_XZ(A,XN,b,EXACT,ctime)
X(1)=XN(3)
X(2)=XN(4)
X(3)=XN(1)
X(4)=XN(2)
X(5)=XN(5)
X(6)=XN(6)
CALL KILL(XN,6)
END SUBROUTINE ROT_YZP
SUBROUTINE TRANSR(A,X,b,EXACT,ctime)
IMPLICIT NONE
real(dp),INTENT(INOUT):: X(6)
real(dp) PZ
real(dp),INTENT(IN):: A(3),b
LOGICAL(lp),INTENT(IN):: EXACT,ctime
X(1)=X(1)-A(1)
X(3)=X(3)-A(2)
IF(EXACT) THEN
if(ctime) then
PZ=ROOT(1.0_dp+2.0_dp*X(5)/b+x(5)**2-X(2)**2-X(4)**2)
X(1)=X(1)+A(3)*X(2)/PZ
X(3)=X(3)+A(3)*X(4)/PZ
X(6)=X(6)+A(3)*(1.0_dp/b+X(5))/PZ
else
PZ=ROOT((1.0_dp+X(5))**2-X(2)**2-X(4)**2)
X(1)=X(1)+A(3)*X(2)/PZ
X(3)=X(3)+A(3)*X(4)/PZ
X(6)=X(6)+A(3)*(1.0_dp+X(5))/PZ
endif
ELSE
if(ctime) then ! THIS IS SIXTRACK HERE
PZ=sqrt(1.0_dp+2.0_dp*X(5)/b+x(5)**2)
X(1)=X(1)+A(3)*X(2)/pz
X(3)=X(3)+A(3)*X(4)/pz
X(6)=X(6)+((X(2)*X(2)+X(4)*X(4))/2.0_dp/pz**2+1.0_dp)*(1.0_dp/b+x(5))*A(3)/pz
else
X(1)=X(1)+A(3)*X(2)/(1.0_dp+X(5))
X(3)=X(3)+A(3)*X(4)/(1.0_dp+X(5))
X(6)=X(6)+(A(3)/(1.0_dp+X(5)))*(X(2)*X(2)+X(4)*X(4))/2.0_dp/(1.0_dp+X(5))+a(3)
endif
ENDIF
END SUBROUTINE TRANSR
SUBROUTINE TRANSP(A,X,b,EXACT,ctime)
IMPLICIT NONE
TYPE(REAL_8),INTENT(INOUT):: X(6)
TYPE(REAL_8) PZ
real(dp),INTENT(IN):: A(3),b
LOGICAL(lp),INTENT(IN):: EXACT,ctime
X(1)=X(1)-A(1)
X(3)=X(3)-A(2)
IF(EXACT) THEN
CALL ALLOC(PZ)
if(ctime) then
PZ=SQRT(1.0_dp+2.0_dp*X(5)/b+x(5)**2-X(2)**2-X(4)**2)
X(1)=X(1)+A(3)*X(2)/PZ
X(3)=X(3)+A(3)*X(4)/PZ
X(6)=X(6)+A(3)*(1.0_dp/b+X(5))/PZ
else
PZ=SQRT((1.0_dp+X(5))**2-X(2)**2-X(4)**2)
X(1)=X(1)+A(3)*X(2)/PZ
X(3)=X(3)+A(3)*X(4)/PZ
X(6)=X(6)+A(3)*(1.0_dp+X(5))/PZ
endif
CALL KILL(PZ)
ELSE
if(ctime) then
PZ=SQRT(1.0_dp+2.0_dp*X(5)/b+x(5)**2)
X(1)=X(1)+A(3)*X(2)/pz
X(3)=X(3)+A(3)*X(4)/pz
X(6)=X(6)+((X(2)*X(2)+X(4)*X(4))/2.0_dp/pz**2+1.0_dp)*(1.0_dp/b+x(5))*A(3)/pz
else
X(1)=X(1)+A(3)*X(2)/(1.0_dp+X(5))
X(3)=X(3)+A(3)*X(4)/(1.0_dp+X(5))
X(6)=X(6)+(A(3)/(1.0_dp+X(5)))*(X(2)*X(2)+X(4)*X(4))/2.0_dp/(1.0_dp+X(5))+a(3)
endif
ENDIF
END SUBROUTINE TRANSP
SUBROUTINE ROT_XYR(A,X)
IMPLICIT NONE
real(dp),INTENT(INOUT):: X(6)
real(dp) XN(4)
real(dp),INTENT(IN):: A
real(dp) :: cosa, sina
cosa = COS(A)
sina = SIN(A)
! IF(EXACT) THEN
XN(1)=COSA*X(1)+SINA*X(3)
XN(3)=COSA*X(3)-SINA*X(1)
XN(2)=COSA*X(2)+SINA*X(4)
XN(4)=COSA*X(4)-SINA*X(2)
X(1)=XN(1)
X(2)=XN(2)
X(3)=XN(3)
X(4)=XN(4)
! ELSE
! X(1)=X(1)+A*X(3)
! X(4)=X(4)-A*X(2)
! X(2)=X(2)+A*X(4)
! X(3)=X(3)-A*X(1)
! ENDIF
END SUBROUTINE ROT_XYR
SUBROUTINE ROT_XYP(A,X)
IMPLICIT NONE
TYPE(REAL_8),INTENT(INOUT):: X(6)
TYPE(REAL_8) XN(4)
real(dp),INTENT(IN):: A
real(dp) :: cosa, sina
cosa = COS(A)
sina = SIN(A)
! IF(EXACT) THEN
CALL ALLOC(XN,4)
XN(1)=COSA*X(1)+SINA*X(3)
XN(3)=COSA*X(3)-SINA*X(1)
XN(2)=COSA*X(2)+SINA*X(4)
XN(4)=COSA*X(4)-SINA*X(2)
X(1)=XN(1)
X(2)=XN(2)
X(3)=XN(3)
X(4)=XN(4)
CALL KILL(XN,4)
! ELSE
! X(1)=X(1)+A*X(3)
! X(4)=X(4)-A*X(2)
! X(2)=X(2)+A*X(4)
! X(3)=X(3)-A*X(1)
! ENDIF
END SUBROUTINE ROT_XYP
SUBROUTINE ROT_XZR(A,X,b,EXACT,ctime)
IMPLICIT NONE
real(dp),INTENT(INOUT):: X(6)
real(dp) XN(6),PZ,PT
real(dp),INTENT(IN):: A,b
real(dp) sina, cosa, tana
LOGICAL(lp),INTENT(IN):: EXACT,ctime
IF(EXACT) THEN
COSA = COS(A)
SINA = SIN(A)
TANA = TAN(A)
if(ctime) then
PZ=ROOT(1.0_dp+2.0_dp*x(5)/b+X(5)**2-X(2)**2-X(4)**2)
PT=1.0_dp-X(2)*TANA/PZ
XN(1)=X(1)/COSA/PT
XN(2)=X(2)*COSA+SINA*PZ
XN(3)=X(3)+X(4)*X(1)*TANA/PZ/PT
XN(6)=X(6)+X(1)*TANA/PZ/PT*(1.0_dp/b+x(5))
else
PZ=ROOT((1.0_dp+X(5))**2-X(2)**2-X(4)**2)
PT=1.0_dp-X(2)*TANA/PZ
XN(1)=X(1)/COSA/PT
XN(2)=X(2)*COSA+SINA*PZ
XN(3)=X(3)+X(4)*X(1)*TANA/PZ/PT
XN(6)=X(6)+(1.0_dp+X(5))*X(1)*TANA/PZ/PT
endif
X(1)=XN(1)
X(2)=XN(2)
X(3)=XN(3)
X(6)=XN(6)
ELSE
if(ctime) then ! SIXTRACK
PZ=sqrt(1.0_dp+2.0_dp*x(5)/b+X(5)**2)
X(2)=X(2)+A*PZ
X(6)=X(6)+A*X(1)*(1.0_dp/b+x(5))/PZ
else
X(2)=X(2)+A*(1.0_dp+X(5))
X(6)=X(6)+A*X(1)
endif
ENDIF
! CALL CHECK_STABILITY(X)
END SUBROUTINE ROT_XZR
SUBROUTINE ROT_XZP(A,X,b,EXACT,ctime)
IMPLICIT NONE
TYPE(REAL_8),INTENT(INOUT):: X(6)
TYPE(REAL_8) XN(6),PZ,PT
real(dp),INTENT(IN):: A,b
real(dp) sina, cosa, tana
LOGICAL(lp),INTENT(IN):: EXACT,ctime
IF(EXACT) THEN
COSA = COS(A)
SINA = SIN(A)
TANA = TAN(A)
CALL ALLOC(XN,6)
CALL ALLOC(PZ)
CALL ALLOC(PT)
if(ctime) then
PZ=SQRT(1.0_dp+2.0_dp*x(5)/b+X(5)**2-X(2)**2-X(4)**2)
PT=1.0_dp-X(2)*TANA/PZ
XN(1)=X(1)/COSA/PT
XN(2)=X(2)*COSA+SINA*PZ
XN(3)=X(3)+X(4)*X(1)*TANA/PZ/PT
XN(6)=X(6)+X(1)*TANA/PZ/PT*(1.0_dp/b+x(5))
else
PZ=SQRT((1.0_dp+X(5))**2-X(2)**2-X(4)**2)
PT=1.0_dp-X(2)*TANA/PZ
XN(1)=X(1)/COSA/PT
XN(2)=X(2)*COSA+SINA*PZ
XN(3)=X(3)+X(4)*X(1)*TANA/PZ/PT
XN(6)=X(6)+(1.0_dp+X(5))*X(1)*TANA/PZ/PT
endif
X(1)=XN(1)
X(2)=XN(2)
X(3)=XN(3)
X(6)=XN(6)
CALL KILL(XN,6)
CALL KILL(PZ)
CALL KILL(PT)
ELSE
if(ctime) then
CALL ALLOC(PZ)
PZ=SQRT(1.0_dp+2.0_dp*x(5)/b+X(5)**2)
X(2)=X(2)+A*PZ
X(6)=X(6)+A*X(1)*(1.0_dp/b+x(5))/PZ
CALL KILL(PZ)
else
X(2)=X(2)+A*(1.0_dp+X(5))
X(6)=X(6)+A*X(1)
endif
ENDIF
END SUBROUTINE ROT_XZP
end module S_euclidean