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AR-SLOWD.f
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c THIS CODE USES THE ALGORITHMIC REGULARIZATION i.e. no coordinate transformation, only time transformation + leapfrog + extrapolation method
! NearFinalVersionOf_ARC.f
subroutine ARCparams_Dot_CH_is_here ! This subroutine is not used, but the content is simply what is supposed to be in the file ARCparams.CH.
! If you do not have that file, create it and copy the content of this,
! without the 'end' statement, into it! Then you can compile this code.
! ARCparams.CH =filename
IMPLICIT REAL*8 (A-H,M,O-Z)
PARAMETER (NMX=200,NMX2=2*NMX,NMX3=3*NMX,NMX4=4*NMX,
& NMX8=8*NMX,NMXm=NMX*(NMX-1)/2)
COMMON/DataForRoutines1/X(NMX3),V(NMX3),WTTL,M(NMX),
& XC(NMX3),WC(NMX3),MC(NMX)
& ,XI(NMX3),VI(NMX3),MASS,RINV(NMXm),RSUM,INAME(NMX),N
COMMON/DataForChainRoutinesTwo/MMIJ,CMX(3),CMV(3)
& ,ENERGY,Energr,CHTIME
common/softening/ee,cmethod(3),Clight,NofBH
common/TIMECOMMON/Taika,timecomparison,steppi
common/spincommon/spin(3)! the relative spin of M(1) !Spin=spin*G*M^2/c
common/tolerancecommon/EPS
common/slowi/aat(nmx),rix(nmx),rsch(nmx),OK(nmx,-1:1)
common/rajahairio/tiny_pertu
end
! The following publications contain info needed for understanding this code
! \bibitem[Hellstr{\"o}m and Mikkola(2010)]{2010CeMDA.106..143H} Hellstr{\"o}m, C., Mikkola, S.\ 2010.\ Explicit algorithmic regularization in the few-body problem for velocity-dependent perturbations.\ Celestial Mechanics and Dynamical Astronomy 106, 143-156.
! \bibitem[Mikkola and Merritt(2008)]{2008AJ....135.2398M} Mikkola, S., Merritt, D.\ 2008.\ Implementing Few-Body Algorithmic Regularization with Post-Newtonian Terms.\ The Astronomical Journal 135, 2398-2405.
! \bibitem[Mikkola and Merritt(2006)]{2006MNRAS.372..219M} Mikkola, S., Merritt, D.\ 2006.\ Algorithmic regularization with velocity-dependent forces.\ Monthly Notices of the Royal Astronomical Society 372, 219-223.
! \bibitem[Mikkola and Aarseth(2002)]{2002CeMDA..84..343M} Mikkola, S., Aarseth, S.\ 2002.\ A Time-Transformed Leapfrog Scheme.\ Celestial Mechanics and Dynamical Astronomy 84, 343-354.
! \bibitem[Mikkola and Aarseth(1996)]{1996CeMDA..64..197M} Mikkola, S., Aarseth, S.~J.\ 1996.\ A Slow-down Treatment for Close Binaries.\ Celestial Mechanics and Dynamical Astronomy 64, 197-208.
! \bibitem[Mikkola and Aarseth(1993)]{1993CeMDA..57..439M} Mikkola, S., Aarseth, S.~J.\ 1993.\ An implementation of N-body chain regularization.\ Celestial Mechanics and Dynamical Astronomy 57, 439-459.
! \bibitem[Mikkola and Tanikawa(2013)]{2013NewA...20...38M} Mikkola, S., Tanikawa, K.\ 2013.\ Implementation of an efficient logarithmic-Hamiltonian three-body code.\ New Astronomy 20, 38-41.
! \bibitem[Mikkola and Tanikawa(2013)]{2013MNRAS.430.2822M} Mikkola, S., Tanikawa, K.\ 2013.\ Regularizing dynamical problems with the symplectic logarithmic Hamiltonian leapfrog.\ Monthly Notices of the Royal Astronomical Society 430, 2822-2827.
! \bibitem[Mikkola and Tanikawa(1999)]{1999MNRAS.310..745M} Mikkola, S., Tanikawa, K.\ 1999.\ Algorithmic regularization of the few-body problem.\ Monthly Notices of the Royal Astronomical Society 310, 745-749.
Program ARCcode ! This is the main program, not subroutine.
! IMPLICIT REAL*8 (A-H,M,O-Z) ! this is in 'ARCparams.CH'
include 'ARCparams.CH'
COMMON/DIAGNOSTICS/GAMMA,H,IWR
common/justforfun/Tkin,Upot,dSkin,dSpot ! used in diagno
common/outputindex/index4output(200),N_ini
!REAL*8 G0(3),G(3),xw(3),vw(3)
REAL*8 cmet(3),xwr(NMX3)!,dum(3) !& ,ai(NMX),ei(NMX),inc(NMX),Omi(NMX),ooi(NMX)
& ,cmxx(3),cmvx(3)
LOGICAL NEWREG
CHARACTER*22 outfile
common/vindex/ivelocity
common/collision/icollision,ione,itwo,iwarning
! common/slowi/aat(nmx),rix(nmx),rsch(nmx),OK(nmx,-1:1)
! common/rajahairio/tiny_pertu
! UNITS: I use G=1 (all other things are up to the user)
! BUT: I always use M_sun=1, lenght unit= 1AU.
! IN SUCH A SYSTEM: time is such that 1 year = 2*Pi
! C (vel. of light) is approximately = 10,000. (c=299792458 m / s, AU=149597870.7km ==> c=10065.1 au/t1)
666 CONTINUE ! jump here to start a new simulation in the same run.
icollision=0
iopen=0
TIME=0 ! initialization
SP0=0
DELTAT=1 ! something (but read below)
IWR=1 ! write some info ( set -1 to not to get that..), read below
! Initial values, UNITS: G=1
TINY_PERTU=1.e-6 ! should be read
READ(5,*,err=999)IWR,N,DELTAT,TMAX,stepr,soft,cmet,Clight,!
& outfile,Ixc,Nbh ,spin,EPS,ivelocity,KSMX,tiny_pertu
! stepr is now obsolete
! Look the example cdr* file. It contains some info about the data read here.
! (look to the end part of the data file!)
DO I=1,N-1
rsch(i)=1.d0
END DO ! I
if(N.lt.2)STOP ! if N<2 this code is not needed
ee=soft**2 ! square of softening lenght (often zero, but can be used)
open(66,file=outfile) ! output file
open(67,file='merge.dat') ! output for merger info
MASS=0
DO I=1,N
L=3*(I-1)
READ(5,*)M(I),(X(L+K),K=1,3),(V(L+K),K=1,3) ! Read masses, coordinates anf velocities
MASS=MASS+M(I) ! determine total mass
index4output(i)=i ! initialize output index (to be modified in case of mergers)
test=M(I)+cdot(x(L+1),X(L+1))+cdot(V(L+1),V(L+1))
if(test.eq.0.0)go to 2
END DO
2 N=I-1
!write(6,*)I,N,' = I N'
N_ini=N
call Reduce2cm(x,m,N,cmxx) ! x->cm-system, in this version output is in cm anyway
call Reduce2cm(v,m,N,cmvx) ! v->cm-system
do k=1,3
! cmxx(k)=0 ! cm coords ->0
! cmvx(k)=0 ! cm vels ->0
end do
ENER0=0
NEWREG=.TRUE. ! Now we are starting a new regularized integration
!KSMX=10 000 ! only this many steps without return, KSMX is actually read, normally big value recommended
goto 200 ! Go to write initial quantities (i.e. at time=0), after which code returns to statement 100
c
100 CONTINUE
call ARC !
& (N,X,V,M,TIME,DELTAT,EPS,NEWREG,KSMX,soft,cmet,clight,Ixc,NBH,
& spin,CMXX,CMVX) ! Here you get cm-coords (=Xa) aind cm-vels (=V). CMXX and CMCX are position and velocity of the centre-of-mass
! At this point U can do your own analysis/output etc....
200 CONTINUE
call Diagnostic output(time,xwr,cmxx) ! write errors and coords to the given outputfile (name read to variable 'outfile')
! some more coords are written in the routine MERGE_I1_I2 in case whén a BH swollows an other body
if(iwr.ge.0) call Write Elements(time,iopen) ! with respect to M(1), to files aexes.dat, eccs.dat, incs.dat, Omes.dat,omes.dat,
if(iwr.gt.1)call FIND BINARIES(time) ! this is usually unimportant, but may give info about binary formation
234 format(1x,f18.6,1p,600g13.5)
! rs=2*m(1)/clight**2 ! Radius of event horizon of M1
IF(TIME.LT.TMAX)then ! continue if not yet at maximum time
GOTO 100
else
goto 666 ! go read data for the next experiment (to stop set a line of zeros into the data file)
end if
999 END
subroutine Diagnostic output(time,xwr,cmxx)
include 'ARCparams.CH'
COMMON/DIAGNOSTICS/GAMMA,H,IWR
common/justforfun/Tkin,Upot,dSkin,dSpot ! used in diagno
common/outputindex/index4output(200),N_ini
REAL*8 G0(3),G(3),xwr(NMX3),CMXX(3)!,CMVX(3)
common/vindex/ivelocity
common/collision/icollision,ione,itwo,iwarning
save
if(time.eq.0.0)then
iENER0=0
goto 200
END IF
c Diagnostics !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
call CONSTANTS OF MOTION(ENER1,G,AL)
IF(ENER0.eq.0.0)THEN
c This CONTANTS OF MOTION works only after first cal of ARC ! Therefore this is here
ENER0=ENER1
g0(1)=g(1)
g0(2)=g(2)
g0(3)=g(3)
cangmo=mass**2.5d0*sqrt(Al)/abs(Ener0)
end if
am_error=sqrt(square(g,g0))/cangmo ! in case of perturbations this is not necessarily error but just a measure of change
WRITE(6,123)TIME!
& ,log((Tkin-ENERGY)/Upot),log(dSkin/dSpot),am_error
& ,ENERGY,ENERGR!logH = the primary constant (=0!)
! ENERGY and EnerGR (=Relativistic change of ENERGY) are integrated (due to possible external perturbations)
& ,N ! print time, logH, N (of bodies left)
call flush(6)
123 FORMAT(1x,'T: ',1p,g20.6,' log((T-E)/U)=',1p,g10.2,
& ' log(dSdot/sdotU)=',1p,g10.2,
& ' d(RxV)/Am=',1p,3g15.7,
& ' Nb=',0p,1x,i3)
200 continue
if(iwr.gt.-2)then
do i=1,3*N_ini
xwr(i)=1.d9 ! put all outside
end do
do i=1,N
j=index4output(i) ! take still existing particles 2 correct indicies
j0=3*j-3
i0=3*i-3
do k=1,3
xwr(j0+k)=x(i0+k)+cmxx(k) ! add centre-of-mass (remove cmxx if U need cm coords)
! or replace cmxx(k) by -x(k) if U want M1 to be
! origin (se also subroutine MERGE_I1_I2)
end do ! k
end do !i
write(66,234)time,(xwr(k),k=1,3*n_ini)
c & (xwr(k)-xwr(1),xwr(k+1)-xwr(2),xwr(k+2)-xwr(3),k=1,3*n_ini,3) ! Write coords to 66,
! in case of a collision write more in Merge_i1_i2
! this is just for figs and/or movies
call flush(66)
end if ! iwr.gt.-2
234 format(1x,f18.6,1p,600g13.5)
return
end
subroutine Write Elements(time,iopen) ! with respect to M(1)
! IMPLICIT REAL*8 (A-H,M,O-Z) ! this is in 'ARCparams.CH'
include 'ARCparams.CH'
COMMON/DIAGNOSTICS/GAMMA,H,IWR
common/justforfun/Tkin,Upot,dSkin,dSpot ! used in diagno
common/outputindex/index4output(200),N_ini
REAL*8 !G0(3),G(3), cmet(3),
& xw(3),vw(3)!,xwr(NMX3)!,dum(3)
& ,ai(NMX),ei(NMX),inc(NMX),Omi(NMX),ooi(NMX)!,cmxx(3),cmvx(3)
!LOGICAL NEWREG
!CHARACTER*22 outfile
common/vindex/ivelocity
common/collision/icollision,ione,itwo,iwarning
save
do j=2,N_ini! Needed if N_ini>N
ai(j)=0
ei(j)=0
inc(j)=0
Omi(j)=0
ooi(j)=0
end do
do i=2,N
i0=3*i-3
do k=1,3
xw(k)=x(i0+k)-x(k)
vw(k)=v(i0+k)-v(k)
end do
mw=m(1)+m(i)
! Orbital elements with respect to the central body evaluated here.
j=index4output(i)
call elmnts
& (xw,vw,mw,ai(j),ei(j),moi,inc(j),Omi(j),ooi(j),alfai,qi,tqi)
end do ! i=2,N
! in case of a collision write more in Merge_i1_i2
! this is just for figs and/or movies
if(iopen.eq.0 )then
iopen=1
open(71,file='axes.dat')
open(72,file='eccs.dat')
open(73,file='incs.dat')
open(74,file='Omes.dat')
open(75,file='omes.dat')
open(76,file='spin.dat')
end if
!
!Write Keplerian orbital elements (with respect to M1)
write(71,171)time,(ai(k),k=2,N_ini) ! a
write(72,171)time,(ei(k),k=2,N_ini) ! e
write(73,171)time,(inc(k),k=2,N_ini) ! i
write(74,171)time,(Omi(k),k=2,N_ini) ! \Omega
write(75,171)time,(ooi(k),k=2,N_ini) ! \omega
spa=sqrt(cdot(spin,spin))
if(sp0.eq.0)sp0=spa
dsp=spa-sp0
write(76,*)time,spin,dsp ! spin(k), k=1,3 of M1 (|spin|<1),
! dsp is error in the length of the spin vector
171 format(1x,f12.3,201g18.10)
call flush(71)
call flush(72)
call flush(73)
call flush(74)
call flush(75)
call flush(76)
return
end
Subroutine MERGE_I1_I2(time)!Merge the colliding body with the BH, ('time' is here only for write(66....)
include 'ARCparams.CH'
REAL*8 SM(NMX),XR(NMX3),XDR(NMX3),xwr(nmx3),ywr(nmx3)
COMMON/collision/icollision,Ione,Itwo,iwarning
common/outputindex/index4output(200),N_ini
COMMON/DIAGNOSTICS/GAMMA,H,IWR
save
! --------------------------------------------4 MOVIE -------------------------
if(iwr.gt.-2)then ! Set IWR=-2 if you do not want this output
do i=1,3*N_ini
xwr(i)=1.d9
end do
do i=1,N
j=index4output(i)
j0=3*j-3
i0=3*i-3
do k=1,3
xwr(j0+k)=x(i0+k)+cmx(k)
ywr(j0+k)=xwr(j0+k)
if(i.gt.3 .and. (i.eq.ione .or. i.eq.itwo))ywr(j0+k)=1.d9 ! this moves the body out of movie screen(?)
end do ! k
end do !i
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
do i_delay=1,33!Make the movie FLASH in case of a MERGER. (thefore 33 outputs, each other time out of he movie frame)
write(66,234)time,
& (xwr(k)-xwr(1),xwr(k+1)-xwr(2),xwr(k+2)-xwr(3),k=1,3*n_ini,3)
write(66,234)time,
& (ywr(k)-ywr(1),ywr(k+1)-ywr(2),ywr(k+2)-ywr(3),k=1,3*n_ini,3)
234 format(1x,f18.6,1p,600g13.5)
end do
call flush(66)
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
end if ! iwr.gt.-2
!--------------------------------------------------------------------------------
DO I=1,ione-1
SM(I)=M(I)
DO K=1,3
XR(3*I-3+K)=X(3*I-3+K)
XDR(3*I-3+K)=V(3*I-3+K)
end do
end do
Myks=M(ione)
Mkax=M(itwo)
SM(Ione)=M(Ione)+M(Itwo)
DO 6 K=1,3
XR(3*Ione-3+K)=(M(Ione)*X((Ione-1)*3+K)
& +M(Itwo)*X((Itwo-1)*3+K))/SM(Ione)
XDR(3*Ione-3+K)=(M(Ione)*V((Ione-1)*3+K)
& +M(Itwo)*V((Itwo-1)*3+K))/SM(Ione)
6 CONTINUE
DO I=Ione+1,Itwo-1
sm(i)=m(i)
do k=1,3
XR(3*I-3+K)=X(3*I-3+k)
XDR(3*I-3+K)=V(3*I-3+k)
end do
end do
do i=Itwo,N-1
index4output(i)=index4output(i+1)
end do
DO I=Itwo+1,N
sm(i-1)=m(i)
do k=1,3
XR(3*I-6+K)=X(3*I-3+k)
XDR(3*I-6+K)=V(3*I-3+k)
end do
end do
! MOVE THE REDUCED SYSTEM TO M,X,V
! New value of the number of bodies.
N=N-1
if(Itwo.le.NofBH)NofBH=NofBH-1 ! # of BH's reduced!
DO 8 I=1,N
M(I)=SM(I)
DO 7 K=1,3
X(3*i-3+k)=XR(3*i-3+k)
V(3*i-3+k)=XDR(3*i-3+k)
7 CONTINUE
8 CONTINUE
icollision=0
i1wr=index4output(ione)
i2wr=index4output(itwo) !?? wrong ?? because already changed (above)
write(6,*)' Merge:',i1wr,i2wr-1,' (N, NBH=) (',N,' , ',NofBH, ') '
& ,' masses ',(M(k),k=1,n),Myks,Mkax
write(67,*)' At time ',time,' bodies number ',ione,
&' and ',itwo ,' with masses ',Myks,Mkax,' merge '
call flush(67)
ione=0
itwo=0
if(N.eq.1)then
write(6,*)' Only one body left!'
STOP
end if
RETURN
END
! * * *
SUBROUTINE ARC ! This is the original Alforithmic Regularization Chain code.
& (NN,XX,VX,MX,TIME,DELTAT,TOL,NEWREG,KSMX,soft,cmet,cl,Ixc,NBH,
& spini,CMXX,CMVX)
! BETTER TO USE CM-coords & vels for XX & VX and CMXX CMVX
! FOR CM-position (needed in the Perturbations routine).
!-----------------------------------------------------------------
! NOTE: some variables (eg. Energy and EnerGR are only in the
! common. The internal NB-energy = ENERGY (should be)
! Energy= integrated E-value (excluding grav.radiation)
! EnerGr= Energy radiated away (grav.radiation if Clight.ne.0.0)
! CHAIN INTEGRATION. Perturbations & CM-motion included (in principle).
! NN=# of bodies; XX=(cm)coords, VX=(cm)vels, MX=masses,
!c CMXX=coords of CM, CMVX=vels of CM ! removed
! TIME=time, dettaT=time interval
! STEP=stepsize (set=0 initially)
! NEWREG=.true. iff chain membership has changed
! KSMX=max # of steps without return (use some large # )
! soft =optional softening( U=1/sqrt(r**2+soft**2) )
! cmet= 3-d vector that determines the method:
! (1,0,0) =logH, (0,1,0)=TTL,(0,0,1)=DIFSY2 without t-tranformation
!
! cl=speed of light
! NOTE: cl=0 => no relativistic terms !!!
! Ixc = 2 =>iteration to excat time, 1 => approximate exact time, =0 no exact time but return after CHTIME>DELTAT
! often IXC =0 is fastest, IXC=1 second fastest, IXC=2 can be slow (but usually accurate output time).
INCLUDE 'ARCparams.CH'
COMMON/DerOfTime/GTIME
COMMON/DIAGNOSTICS/GAMMA,H,IWR
common/omegacoefficients/OMEC(NMX,NMX)
common/collision/icollision,ione,itwo,iwarning
common/itemaxcommon/aitemax,itemax,itemax_used
common/turhia/rw,fr,frm,akiih(3)
REAL*8 G0(3),XX(*),VX(*),MX(*),cmet(3),spini(3),CMXX(3),CMVX(3)
REAL*8 Y(1500),SY(1500),Yold(1500)
LOGICAL MUSTSWITCH,NEWREG
data ntrue,nfalse,nwritten/3*0/
save
! Initial constants of motion
10 CONTINUE !
tnext0=time+deltat
knx=tnext0/deltat+0.1d0
tnext=knx*deltat
tstep=tnext-time
if(newreg)then
ntrue=ntrue+1
else
nfalse=nfalse+1
end if
if(ntrue.gt.nfalse+10 .and. nwritten.eq.0)then
nwritten=1
write(6,*)char(7),char(7)
write(6,*)' NEWREG should be set .TRUE. only'
write(6,*)' in the very beginning of a new simulation'
write(6,*)' NOT at every step!! (May reduce accuracy!!)'
write(6,*)' even if it may look like the contrary.'
end if
if(NN.gt.NMX)then
write(6,*)' THIS CODE CAN HANDLE ONLY ',NMX,' BODIES '
write(6,*)' Yuo are trying to use N=',NN
write(6,*)' Try increasing NMX in ARCparams.CH '
write(6,*)' and increase some (large) dimensions elsewhere'
write(6,*)' in the same proportion. STOPPING'
STOP
end if
! if(cmet(1).eq.0.0 .and. cmet(2).ne.0.0)then
! write(6,*)' In this version cmethod(1) should not be zero'
! write(6,*)' if cmethod(2).ne.0.0 '
! write(6,*)cmet,' = cmethod(k),k=1,3 '
! write(6,*)' STOPPING '
! STOP
! end if
if(deltat.eq.0 .and. Ixc .eq.1)then
write(6,*)' You cannot use DELTA=0 and Ixc=1 '
write(6,*)' since then every output will be at time=0 '
write(6,*)' STOPPING '
STOP
end if
if(cmet(1)+cmet(2)+cmet(3).eq.0)then
write(6,*)' You have not defined the time-transformation'
write(6,*)cmet,' = cmethod(k),k=1,3 '
write(6,*)' STOPPING '
STOP
end if
CHTIME=0.D0
icollision=0
Taika=TIME ! to common
NofBH=NBH ! - " -
IF(NEWREG)THEN
step=0
iwarning=0
itemax=12
itemax_used=0
ee=soft**2 ! to common
do k=1,3
spin(k)=spini(k) ! 2 common
cmethod(k)=cmet(k) ! 2 common
end do
clight=cl ! -"-
N=NN
mass=0
DO I=1,N
M(I)=MX(I)
mass=mass+m(i)
END DO
MMIJ=0.D0
DO I=1,N-1
DO J=I+1,N
MMIJ=MMIJ+M(I)*M(J)
END DO
END DO
MMIJ=MMIJ/(N*(N-1)/2.d0) !mean mass product
IF(MMIJ.eq.0.0.and.cmethod(2).ne.0.0)MMIJ=1
DO I=1,3*N
X(I)=XX(I)
V(I)=VX(I)
END DO
IF(MMIJ.eq.0)THEN
write(6,*)'You have at most one non-zero mass => t''=1/0 and'
write(6,*)'this does not work'
STOP
END IF
call FIND CHAIN INDICES ! necessary 4 forming the chain
IF(IWR.GT.0)WRITE(6,1232)time,(INAME(KW),KW=1,N)
call INITIALIZE XC and WC
call CONSTANTS OF MOTION(ENERGY,G0,ALAG)
EnerGr=0 ! Energy change due to relativisstic PN-terms
gtime=1/ALAG
do K=1,3
CMX(K)=CMXX(K)
CMV(K)=CMVX(K)
end do
call omegacoef
STIME=0.D0
NEWREG=.FALSE.
WTTL=Wfunction()
mmss=0
do i=1,n-1
do j=i+1,n
mmss=mmss+m(i)*m(j)
end do
end do
call Take Y from XC WC (Y,Nvar)
do i=1,Nvar
SY(i)=0.1 ! arbitrary assumption for the order of magnitude of quantities
end do
if(step.eq.0)then
step=1.e-3
!call Initial Stepsize(X,V,M,N,ee,step) ! New initial step determination
call Estimate Stepsize(tstep,step) !
end if
EPS=TOL
END IF ! NEWREG
KSTEPS=0
stimex=0
777 KSTEPS=KSTEPS+1
call Take Y from XC WC (Y,Nvar)
call Obtain Order of Y(SY,Y)
stime=0
f1=chtime-tstep!deltaT ! for exact time iteration
d1=gtime
call take y from XC WC(Yold,Nvar)
call on off slow binaries
steppi=step ! to common
call DIFSYAB(Nvar,EPS,SY,step,stime,Y)
I_switch=1
call Put Y to XC WC (Y,Nvar) ! move parameters in Y to CHAIN variables
if(step.eq.0)stop
call CHECK SWITCHING CONDITIONS(MUST SWITCH) ! is it necessary to find new CHAIN?
IF(MUST SWITCH)THEN
I_switch=0
call Chain Transformation ! Here the new CHAIN is formed
WTTL=Wfunction() ! this may not be necessary, but probably OK.
call Take Y from XC WC(Y,Nvar) ! CHAIN variables to Y vector
!IF(IWR.GT.0) WRITE(6,1232)time+chtime,(INAME(KW),KW=1,N) !for checking what is going on
1232 FORMAT(1X,g12.4,' I-CHAIN',20I3)
END IF ! MUST SWITCH
f2=chtime-tstep!deltaT ! for exact time iteration
d2=gtime
x1=-stime
x2=0
IF(CHTIME.LT.tstep.and.(KSTEPS.lt.KSMX)
& .and.(icollision.eq.0))goto 777
c------------------------------------------------------------------------------------------
IF (icollision.NE.0) THEN ! handle a collison
nmerger = nmerger + 1
CALL Merge_i1_i2(time) ! MERGE the two particles
newreg=.TRUE. ! chain has changed=> restart needed
NN=N ! copy new chain
DO i=1,NN
MX(i)=M(i)
DO k=1,3
xx(3*i-3+k)=x(3*i-3+k)
vx(3*i-3+k)=v(3*i-3+k)
ENDDO
ENDDO ! done copying new chain
tstep=tnext-time ! set time step to continue
! chain integration
c write(16,*)time, tstep,' GOTO 10 '
IF ((abs(tstep).GT.1.d-6*deltat).AND.(NN.GT.1)) GOTO 10 ! continue if necessary (and if there are at least 2 bodies)
ENDIF
c..........................................................................................
if(KSTEPS.lt.KSMX .and.Ixc.gt.0.and.icollision.eq.0)then
! Integrate TO approximate EXACT OUTPUTTIME
IF(Ixc.eq.1)then ! approx outputtime with Stumpff-Weiss-priciple
if(abs(f1).lt.abs(f2)*I_switch)then ! I_switch prevents use of f1 if just SWITCHed
call put y to xc wc (yold,nvar)
call obtain order of y(sy,y)
1001 call Estimate Stepsize(-f1,step2) !lengt of s-step to get nearly exact output time
!write(6,*)' STEPPI2 ',step2
call DIFSYAB(Nvar,EPS,SY,step2,stime,Yold)
call Put Y to XC WC (Yold,Nvar)
else
call Estimate Stepsize(-f2,step2)
call obtain order of y (sy,y)
!write(6,*)' Steppi2 ',step2
call DIFSYAB(Nvar,EPS,SY,step2,stime,Y)
call Put Y to XC WC (Y,Nvar)
end if
stimex=stimex+stime! 4 estimating max next step
elseif(Ixc.eq.2)then ! Iteration to exact time
call Iterate2ExactTime(Y,Nvar,deltaT,f1,d1,f2,d2,x1,x2)
end if
end if
if(stimex.eq.0)stimex=step
call update x and v
DO I=1,3*N
XX(I)=X(I)
VX(I)=V(I)
END DO
DO I=1,3
spini(I)=spin(I)
CMXX(I)=CMX(I)
CMVX(I)=CMV(I)
END DO
TIME=TIME+CHTIME
if(chtime.lt.0.D0)write(6,*)time,chtime, ' t cht <0!'
!write(16,*)time,tstep,chtime,deltat,' t tstep chtime deltat '
RETURN
END
subroutine Iterate2ExactTime(Y0,Nvar,deltaT,f1,d1,f2,d2,x1,x2)
INCLUDE 'ARCparams.CH'
COMMON/DerOfTime/GTIME
COMMON/collision/icollision,Ione,Itwo,iwarning
REAL*8 Y(1500),SY(1500),Y0(*)
data tiny/1.d-6/
save
! This a quite slow iteration to exact time. Can also fail but that is rear.
iskeleita=0
it=0
hs=abs(x1-x2)
1111 CONTINUE
it=it+1
do i=1,nvar
y(i)=y0(i)
end do
stime=0
dx1=-f1/d1
dx2=-f2/d2
if(abs(dx1).lt.abs(dx2))then
xnew=x1+dx1
else
xnew=x2+dx2
end if
!
test=(x1-xnew)*(xnew-x2)
if(test.lt.(-tiny*hs).or.(it+1).eq.(it+1)/5*5)then
xnew=(x1+x2)/2 ! bisect if out of interval
end if
sfinal=xnew
call Put Y to XC WC (Y,Nvar)
!--------------------------------------------------------------------------
call Obtain Order of Y(SY,y)
do k=1,5
step=sfinal-stime
if(abs(step).gt.1.d-6*abs(hs).or.k.eq.1)then !!!!
call DIFSYAB(Nvar,EPS,SY,step,stime,Y)
iskeleita=iskeleita+1
! it=it+1
else
goto 222
end if
end do
222 continue
call Put Y to XC WC (Y,Nvar)
call UPDATE X AND V
fnew=chtime-deltaT
dfnew=gtime
! keep it bracketed
if(f1*fnew.le.0.D0)then
f2=fnew
d2=dfnew
x2=xnew
else
f1=fnew
d1=dfnew
x1=xnew
end if
if((abs(deltaT-chtime).gt.1.d-6*deltat).and.(it.lt.100))
& goto 1111
! ONE FINAL STEP SHOULD BE HERE (if above not-so-accurate test)
!--------------------------------------------------------------------
do i=1,Nvar
y0(i)=y(i)
end do
call Put Y to XC WC (Y,Nvar)
call UPDATE X AND V
return
end
subroutine LEAPFROG(STEP,Leaps,stime) !Leapfroging steps for the Bulirsch-Stoer extrapolation
implicit real*8 (a-h,M,o-z)
save
CALL PUT V 2 W
hs=step
h2=hs/2
call XCmotion(h2)
stime=stime+h2
do k=1,Leaps-1
call WCmotion(hs)
call XCmotion(hs)
stime=stime+hs
end do
call WCmotion(hs)
call XCmotion(h2)
stime=stime+h2
return
end
function Wfunction() ! evaluate the TTL-function for time tranformation ! eioo subroutine
INCLUDE 'ARCparams.CH'
common/omegacoefficients/OMEC(NMX,NMX)
save
OMEGA=0.0d0
DO I=1,N-1
DO J=I+1,N
if(omec(i,j).ne.0.D0)then
RIJ=SQRT(SQUARE(X(3*I-2),X(3*J-2)))
OMEGA=OMEGA+omec(i,j)/RIJ
end if
END DO
END DO
Wfunction=OMEGA
RETURN
END
subroutine omegacoef ! coefficients in \Omega=sum omec(i,j)/r_{ij}
INCLUDE 'ARCparams.CH'
common/omegacoefficients/OMEC(NMX,NMX)
SAVE
icount=0
do i=1,N-1
do j=i+1,N
! if both masses are=0, then they do not interact (and omec can be set =0)
if(m(i)+m(j).gt.0.D0 .and. cmethod(2).ne.0.D0)then
OMEC(I,J)=mmij
OMEC(J,I)=mmij
icount=icount+1
else
OMEC(I,J)=0
OMEC(J,I)=0
end if
end do
end do
if(icount.eq.0)cmethod(2)=0 ! all terms zero anyway (for some different settings of omec)
return
end
SUBROUTINE XCMOTION(hs) ! movement of coordinates
INCLUDE 'ARCparams.CH'
COMMON/IncrementCommon/WTTLinc,XCinc(NMX3),WCinc(NMX3),
& CMXinc(3),CMVinc(3),ENERGYinc,Energrinc,CHTIMEinc,spin inc(3)
COMMON/DerOfTime/G
COMMON/DIAGNOSTICS/GAMMA,H,IWR
save
Te=-ENERGY
if(cmethod(1).ne.0.0d0)then
call EVALUATE V(V,WC)
do I=1,N
I0=3*I-3
Te=Te+M(I)*(V(I0+1)**2+V(I0+2)**2+V(I0+3)**2)/2 ! Kinetic energyi-Energy
end do
end if ! cmethod(1).ne.0.0d0
G=1/(Te*cmethod(1)+WTTL*cmethod(2)+cmethod(3)) ! time transformation = t'
if(G.lt.0.D0.and.iwr.gt.0)then
write(6,*)1/G,' tdot <0 ! '
return ! this was seriously wrong, but may work because this step (likely) gets rejected
end if
dT= hs*G
DO I=1,N-1
L=3*(I-1)
DO K=1,3
XCinc(L+K)=XCinc(L+k)+WC(L+K)*dT ! incerements of coords
XC(L+K)=XC(L+K)+WC(L+K)*dT ! the new coords are needed anyway
END DO
END DO
CHTIMEinc=CHTIMEinc+dT ! time increment (time is a coordinate)
CHTIME=CHTIME+dT ! new time value
do k=1,3
CMXinc(k)=CMXinc(k)+dt*cmv(k) ! center of mass increment
cmx(k)=cmx(k)+dt*cmv(k) ! new cm-coordinates
end do
RETURN
END
subroutine PUT V 2 W ! these parameters are needed if there are v-ependent forces
include 'ARCparams.CH'
common/vwcommon/Ww(nmx3),WTTLw,cmvw(3),spinw(3)
save
do i=1,3*(N-1)
Ww(i)=WC(I)
end do
WTTLw=WTTL
do k=1,3
spinw(k)=spin(k)
cmvw(k)=cmv(k)
end do
return
end
subroutine Velocity Dependent Perturbations ! This name tells what this is!
& (dT,Va,spina,acc,dcmv,df,dfGR,dspin)
INCLUDE 'ARCparams.CH'
common/vindex/ivelocity
real*8 df(*),Va(*),dcmv(3),dfGR(*),dfR(nmx3),acc(nmx3)
real*8 dspin(3),spina(3)
save
! v-dependent perturbations are evaluated here
do i=1,3*n
dfr(i)=0
dfgr(i)=0
end do
do k=1,3
dspin(k)=0
end do
if(Clight.ne.0)then ! include only if Clight set >0
call Relativistic ACCELERATIONS(dfr,dfGR,Va,spina,dspin)
end if
if(ivelocity.gt.0)then ! USED ONLY IF ivelcity.gt.0
call Non relativistic v_dependent perturbations(dfr)! add v-dependent to dfr(), (e.g. friction)
end if
do i=1,3*n
df(i)=acc(i)+dfr(i)
end do
call reduce 2 cm(df,m,n,dcmv)
return
end
SUBROUTINE CHECK SWITCHING CONDITIONS(MUSTSWITCH)! Is it necessary to construct a new CHAIN?
INCLUDE 'ARCparams.CH'
LOGICAL MUSTSWITCH
DATA Ncall,NSWITCH/0,200000000/
save
MUST SWITCH=.FALSE.
Ncall=Ncall+1
! Switch anyway after every NSWITCHth step.
IF(Ncall.GE.NSWITCH)THEN
Ncall=0
MUST SWITCH=.TRUE.
RETURN
END IF
! Inspect the structure of the chain.
! NOTE: Inverse values 1/r are used instead of r itself.
ADISTI=0.5*(N-1)/RSUM
LRI=N-1
DO I=1,N-2
DO J=I+2,N
LRI=LRI+1
! Do not inspect if 1/r is small.
IF(RINV(LRI).GT.ADISTI)THEN
IF(J-I.GT.2)THEN
! Check for a dangerous long loop.
! RINVMX=MAX(RINV(I-1),RINV(I),RINV(J-1),RINV(J))
IF(I.GT.1)THEN
RINVMX=MAX(RINV(I-1),RINV(I))
ELSE
RINVMX=RINV(1)
END IF
RINVMX=MAX(RINVMX,RINV(J-1))
IF(J.LT.N)RINVMX=MAX(RINVMX,RINV(J))
IF(RINV(LRI).GT.RINVMX)THEN ! 0.7*RINVMX may be more careful
MUST SWITCH=.TRUE.
Ncall=0
RETURN
END IF
ELSE
! Is this a triangle with smallest size not regularised?
IF( RINV(LRI).GT.MAX(RINV(I),RINV(I+1)))THEN
MUST SWITCH=.TRUE.
Ncall=0
RETURN
END IF
END IF
END IF
END DO
END DO
RETURN
END
SUBROUTINE FIND CHAIN INDICES ! Here the new indecies along the new CHAIN are obtained
INCLUDE 'ARCparams.CH'
REAL*8 RIJ2(NMXM)
INTEGER IC(NMX2),IJ(NMXM,2),IND(NMXM)
LOGICAL USED(NMXM),SUC,LOOP
save
L=0
DO I=1,N-1
DO J=I+1,N
L=L+1
RIJ2(L)=SQUARE(X(3*I-2),X(3*J-2))
IJ(L,1)=I
IJ(L,2)=J
USED(L)=.FALSE.
END DO
END DO
call ARRANGE(L,RIJ2,IND)
LMIN=1+NMX
LMAX=2+NMX
IC(LMIN)=IJ(IND(1),1)
IC(LMAX)=IJ(IND(1),2)
USED(IND(1))=.TRUE.
1 DO I=2,L
LI=IND(I)
IF( .NOT.USED(LI))THEN
call CHECK CONNECTION(IC,LMIN,LMAX,IJ,LI,SUC,LOOP)
IF(SUC)THEN
USED(LI)=.TRUE.
GOTO 2
ELSE
USED(LI)=LOOP
END IF
END IF
END DO
2 IF(LMAX-LMIN+1.LT.N)GO TO 1
L=0
DO I=LMIN,LMAX
L=L+1
INAME(L)=IC(I)
END DO
RETURN
END
SUBROUTINE CHECK CONNECTION(IC,LMIN,LMAX,IJ,LI,SUC,LOOP) ! Loops in CHAIN are not allowed
INCLUDE 'ARCparams.CH'
INTEGER IC(*),ICC(2),IJ(NMXM,2)
LOGICAL SUC,LOOP
save
SUC=.FALSE.
LOOP=.FALSE.
ICC(1)=IC(LMIN)
ICC(2)=IC(LMAX)
DO I=1,2
DO J=1,2
IF(ICC(I).EQ.IJ(LI,J))THEN
JC=3-J
LOOP=.TRUE.
DO L=LMIN,LMAX
IF(IC(L).EQ.IJ(LI,JC))RETURN
END DO
SUC=.TRUE.
LOOP=.FALSE.
IF(I.EQ.1)THEN
LMIN=LMIN-1
IC(LMIN)=IJ(LI,JC)
RETURN
ELSE
LMAX=LMAX+1
IC(LMAX)=IJ(LI,JC)
RETURN
END IF
END IF
END DO
END DO
RETURN
END
SUBROUTINE ARRANGE(N,Array,Indx) ! this is a sorting routine (needed in CHAIN construction)
implicit real*8 (a-h,o-z)
dimension Array(*),Indx(*)
save
do 11 j=1,N
Indx(j)=J
11 continue
if(N.lt.2)RETURN
l=N/2+1
ir=N
10 CONTINUE
IF(l.gt.1)THEN
l=l-1
Indxt=Indx(l)
q=Array(Indxt)
ELSE
Indxt=Indx(ir)
q=Array(Indxt)
Indx(ir)=Indx(1)
ir=ir-1
IF(ir.eq.1)THEN
Indx(1)=Indxt
RETURN
END IF
END IF
i=l
j=l+l
20 IF(j.le.ir)THEN
IF(j.lt.ir)THEN
IF(Array(Indx(j)).lt.Array(Indx(j+1)))j=j+1
END IF
IF(q.lt.Array(Indx(j)))THEN
Indx(i)=Indx(j)