def simulation(par):
anom, dt, e, integrator = par
e = 1. - pow(10., e)
dt = pow(10., dt) * torb
rebound.reset()
rebound.integrator = integrator
rebound.force_is_velocitydependent = 0
rebound.dt = dt
rebound.add(m=1.)
rebound.add(m=0., x=(1. - e), vy=np.sqrt((1. + e) / (1. - e)))
particles = rebound.particles
Ei = -1. / np.sqrt(particles[1].x * particles[1].x + particles[1].y *
particles[1].y + particles[1].z * particles[1].z
) + 0.5 * (particles[1].vx * particles[1].vx +
particles[1].vy * particles[1].vy +
particles[1].vz * particles[1].vz)
rebound.integrate(tmax, exactFinishTime=0, keepSynchronized=1)
Ef = -1. / np.sqrt(particles[1].x * particles[1].x + particles[1].y *
particles[1].y + particles[1].z * particles[1].z
) + 0.5 * (particles[1].vx * particles[1].vx +
particles[1].vy * particles[1].vy +
particles[1].vz * particles[1].vz)
return [
float(rebound.iter) / rebound.t * dt,
np.fabs((Ef - Ei) / Ei) + 1e-16,
rebound.timing / rebound.t * dt * 1e6 / 2., (Ef - Ei) / Ei
]
def simulation(par):
saturn_a, saturn_e = par
rebound.reset()
rebound.integrator = "whfast-nocor"
rebound.min_dt = 5.
rebound.dt = 1.
# These parameters are only approximately those of Jupiter and Saturn.
sun = rebound.Particle(m=1.)
rebound.add(sun)
jupiter = rebound.add(primary=sun,
m=0.000954,
a=5.204,
anom=0.600,
omega=0.257,
e=0.048)
saturn = rebound.add(primary=sun,
m=0.000285,
a=saturn_a,
anom=0.871,
omega=1.616,
e=saturn_e)
rebound.move_to_com()
rebound.init_megno(1e-16)
rebound.integrate(1e3 * 2. * np.pi)
return [
rebound.calculate_megno(),
1. / (rebound.calculate_lyapunov() * 2. * np.pi)
] # returns MEGNO and Lypunov timescale in years
def simulation(par):
saturn_a, saturn_e = par
rebound.reset()
rebound.integrator = "whfast-nocor"
rebound.dt = 5.
# These parameters are only approximately those of Jupiter and Saturn.
rebound.add(m=1.)
rebound.add(m=0.000954, a=5.204, anom=0.600, omega=0.257, e=0.048)
rebound.add(m=0.000285, a=saturn_a, anom=0.871, omega=1.616, e=saturn_e)
rebound.move_to_com()
rebound.init_megno(1e-16)
rebound.integrate(5e2*2.*np.pi) # integrator for 500 years
return [rebound.calculate_megno(),1./(rebound.calculat_lyapunov()*2.*np.pi)] # returns MEGNO and Lypunov timescale in years
def simulation(par):
saturn_a, saturn_e = par
rebound.reset()
rebound.set_min_dt(0.1)
# These parameters are only approximately those of Jupiter and Saturn.
sun = rebound.Particle(m=1.)
rebound.particle_add(sun)
jupiter = rebound.particle_add(primary=sun,m=0.000954, a=5.204, anom=0.600, omega=0.257, e=0.048)
saturn = rebound.particle_add(primary=sun,m=0.000285, a=saturn_a, anom=0.871, omega=1.616, e=saturn_e)
rebound.move_to_center_of_momentum()
rebound.megno_init(1e-16)
rebound.integrate(1e4*2.*np.pi)
return [rebound.get_megno(),1./(rebound.get_lyapunov()*2.*np.pi)] # returns MEGNO and Lypunov timescale in years
def simulation(integrator):
print("Running "+integrator)
with open(integrator+".txt","w") as f:
rebound.reset()
rebound.set_integrator(integrator)
rebound.set_dt(0.2)
rebound.add_particle(m=1.)
rebound.add_particle(m=0.01, a=1,e=0.1)
rebound.add_particle(m=0.01, a=2.)
rebound.move_to_center_of_momentum()
rebound.init_megno(1e-10)
particles = rebound.get_particles()
times = np.logspace(2,5,num=1000)
for t in times:
rebound.integrate(t,0)
print("%e %e %e %e %e %e %e %e\n" %(rebound.get_t(), rebound.get_megno(), particles[0].x, particles[1].x, particles[2].x, particles[3].x, particles[4].x, particles[5].x),file=f)
def simulation(integrator):
print("Running "+integrator)
with open(integrator+".txt","w") as f:
rebound.reset()
rebound.integrator = integrator
rebound.dt = 0.2
rebound.add(m=1.)
rebound.add(m=0.01, a=1,e=0.1)
rebound.add(m=0.01, a=2.)
rebound.move_to_com()
rebound.init_megno(1e-10)
particles = rebound.particles
times = np.logspace(2,5,num=1000)
for t in times:
rebound.integrate(t,0)
print("%e %e %e %e %e %e %e %e\n" %(rebound.t, rebound.calculate_megno(), particles[0].x, particles[1].x, particles[2].x, particles[3].x, particles[4].x, particles[5].x),file=f)
def simulation(par):
saturn_a, saturn_e = par
rebound.reset()
rebound.integrator = "whfast-nocor"
rebound.min_dt = 5.
rebound.dt = 1.
# These parameters are only approximately those of Jupiter and Saturn.
sun = rebound.Particle(m=1.)
rebound.add(sun)
jupiter = rebound.add(primary=sun,m=0.000954, a=5.204, anom=0.600, omega=0.257, e=0.048)
saturn = rebound.add(primary=sun,m=0.000285, a=saturn_a, anom=0.871, omega=1.616, e=saturn_e)
rebound.move_to_com()
rebound.init_megno(1e-16)
rebound.integrate(1e3*2.*np.pi)
return [rebound.calculate_megno(),1./(rebound.calculate_lyapunov()*2.*np.pi)] # returns MEGNO and Lypunov timescale in years
def simulation(par):
saturn_a, saturn_e = par
rebound.reset()
rebound.integrator = "whfast-nocor"
rebound.dt = 5.
# These parameters are only approximately those of Jupiter and Saturn.
rebound.add(m=1.)
rebound.add(m=0.000954, a=5.204, anom=0.600, omega=0.257, e=0.048)
rebound.add(m=0.000285, a=saturn_a, anom=0.871, omega=1.616, e=saturn_e)
rebound.move_to_com()
rebound.init_megno(1e-16)
rebound.integrate(5e2 * 2. * np.pi) # integrator for 500 years
return [
rebound.calculate_megno(),
1. / (rebound.calculat_lyapunov() * 2. * np.pi)
] # returns MEGNO and Lypunov timescale in years
def simulation(par):
anom, dt, e, integrator = par
e = 1.-pow(10.,e)
dt = pow(10.,dt)*torb
rebound.reset()
rebound.set_integrator(integrator)
rebound.set_force_is_velocitydependent(0)
rebound.set_dt(dt)
rebound.add_particle(m=1.)
rebound.add_particle(m=0., x=(1.-e), vy=np.sqrt((1.+e)/(1.-e)))
particles = rebound.get_particles()
Ei = -1./np.sqrt(particles[1].x*particles[1].x+particles[1].y*particles[1].y+particles[1].z*particles[1].z) + 0.5 * (particles[1].vx*particles[1].vx+particles[1].vy*particles[1].vy+particles[1].vz*particles[1].vz)
rebound.integrate(tmax,exactFinishTime=0,keepSynchronized=1)
Ef = -1./np.sqrt(particles[1].x*particles[1].x+particles[1].y*particles[1].y+particles[1].z*particles[1].z) + 0.5 * (particles[1].vx*particles[1].vx+particles[1].vy*particles[1].vy+particles[1].vz*particles[1].vz)
return [float(rebound.get_iter())/rebound.get_t()*dt, np.fabs((Ef-Ei)/Ei)+1e-16, rebound.get_timing()/rebound.get_t()*dt*1e6/2., (Ef-Ei)/Ei]
def simulation(par):
anom, dt, e, integrator = par
e = 1.-pow(10.,e)
dt = pow(10.,dt)*torb
rebound.reset()
rebound.integrator = integrator
rebound.force_is_velocitydependent = 0
rebound.dt = dt
rebound.add(m=1.)
rebound.add(m=0., x=(1.-e), vy=np.sqrt((1.+e)/(1.-e)))
particles = rebound.particles
Ei = -1./np.sqrt(particles[1].x*particles[1].x+particles[1].y*particles[1].y+particles[1].z*particles[1].z) + 0.5 * (particles[1].vx*particles[1].vx+particles[1].vy*particles[1].vy+particles[1].vz*particles[1].vz)
rebound.integrate(tmax,exactFinishTime=0,keepSynchronized=1)
Ef = -1./np.sqrt(particles[1].x*particles[1].x+particles[1].y*particles[1].y+particles[1].z*particles[1].z) + 0.5 * (particles[1].vx*particles[1].vx+particles[1].vy*particles[1].vy+particles[1].vz*particles[1].vz)
return [float(rebound.iter)/rebound.t*dt, np.fabs((Ef-Ei)/Ei)+1e-16, rebound.timing/rebound.t*dt*1e6/2., (Ef-Ei)/Ei]
def simulation(integrator):
print("Running " + integrator)
with open(integrator + ".txt", "w") as f:
rebound.reset()
rebound.integrator = integrator
rebound.dt = 0.2
rebound.add(m=1.)
rebound.add(m=0.01, a=1, e=0.1)
rebound.add(m=0.01, a=2.)
rebound.move_to_com()
rebound.init_megno(1e-10)
particles = rebound.particles
times = np.logspace(2, 5, num=1000)
for t in times:
rebound.integrate(t, 0)
print("%e %e %e %e %e %e %e %e\n" %
(rebound.t, rebound.calculate_megno(), particles[0].x,
particles[1].x, particles[2].x, particles[3].x,
particles[4].x, particles[5].x),
file=f)
def simulation(par):
S, dt,e0 = par
rebound.reset()
rebound.set_integrator("wh")
#rebound.set_integrator("whfast")
rebound.set_dt(dt)
rebound.particle_add(m=1.)
rebound.particle_add(m=0.,a=1.,e=e0)
#rebound.move_to_center_of_momentum()
#rebound.megno_init(1.e-16)
particles = rebound.particles_get()
def starkforce(): # need to put inside simulation(par) to have access to S and particles
particles[1].ax += -S
rebound.set_additional_forces(starkforce)
rebound.integrate(50000.*np.pi)
return [rebound.get_megno(), rebound.get_t()]
# Import the rebound module
import sys; sys.path.append('../')
import rebound
from rebound import Particle
import numpy as np
from interruptible_pool import InterruptiblePool
for i in np.linspace(-2.*np.pi,2.*np.pi,1000):
rebound.reset()
rebound.set_integrator("whfast-nocor")
rebound.set_dt(0.01*2.*np.pi)
try:
rebound.particle_add(m=1.)
rebound.particle_add(m=0., a=1., e=1.01, anom=i)
particles = rebound.particles_get()
print particles[1].x, particles[1].y, i
#rebound.step()
#print particles[1].x, particles[1].y, i
except:
pass
def simulation(par):
integrator = par
rebound.reset()
k = 0.01720209895
G = k*k
rebound.set_G(G)
rebound.set_dt(dt)
rebound.set_integrator(integrator)
rebound.add_particle(m=1.00000597682, x=-4.06428567034226e-3, y=-6.08813756435987e-3, z=-1.66162304225834e-6, vx=+6.69048890636161e-6, vy=-6.33922479583593e-6, vz=-3.13202145590767e-9) # Sun
rebound.add_particle(m=1./1047.355, x=+3.40546614227466e+0, y=+3.62978190075864e+0, z=+3.42386261766577e-2, vx=-5.59797969310664e-3, vy=+5.51815399480116e-3, vz=-2.66711392865591e-6) # Jupiter
# rebound.add_particle(m=1./3501.6, x=+6.60801554403466e+0, y=+6.38084674585064e+0, z=-1.36145963724542e-1, vx=-4.17354020307064e-3, vy=+3.99723751748116e-3, vz=+1.67206320571441e-5) # Saturn
# rebound.add_particle(m=1./22869., x=+1.11636331405597e+1, y=+1.60373479057256e+1, z=+3.61783279369958e-1, vx=-3.25884806151064e-3, vy=+2.06438412905916e-3, vz=-2.17699042180559e-5) # Uranus
# rebound.add_particle(m=1./19314., x=-3.01777243405203e+1, y=+1.91155314998064e+0, z=-1.53887595621042e-1, vx=-2.17471785045538e-4, vy=-3.11361111025884e-3, vz=+3.58344705491441e-5) # Neptune
# rebound.add_particle(m=0, x=-2.13858977531573e+1, y=+3.20719104739886e+1, z=+2.49245689556096e+0, vx=-1.76936577252484e-3, vy=-2.06720938381724e-3, vz=+6.58091931493844e-4) # Pluto
N = rebound.get_N()
def move_to_heliocentric():
particles = rebound.get_particles()
for i in xrange(1,N):
particles[i].x -= particles[0].x
particles[i].y -= particles[0].y
particles[i].z -= particles[0].z
particles[i].vx -= particles[0].vx
particles[i].vy -= particles[0].vy
particles[i].vz -= particles[0].vz
particles[0].x = 0.
particles[0].y = 0.
particles[0].z = 0.
particles[0].vx = 0.
particles[0].vy = 0.
particles[0].vz = 0.
def energy():
if integrator=="wh":
rebound.move_to_center_of_momentum()
particles = rebound.get_particles()
E_kin = 0.
E_pot = 0.
for i in xrange(N):
E_kin += 0.5*particles[i].m*(particles[i].vx*particles[i].vx + particles[i].vy*particles[i].vy + particles[i].vz*particles[i].vz)
for j in xrange(i+1,N):
dx = particles[i].x-particles[j].x
dy = particles[i].y-particles[j].y
dz = particles[i].z-particles[j].z
r2 = dx*dx + dy*dy + dz*dz
E_pot -= G*particles[i].m*particles[j].m/np.sqrt(r2)
if integrator=="wh":
move_to_heliocentric()
return E_kin+E_pot
rebound.move_to_center_of_momentum()
es = []
ei = energy()
for time in xrange(Nsteps):
rebound.step()
ef = energy()
e = (ei-ef)
es.append(e)
ei = ef
es = np.array(es)
print integrator + " done."
return [es]
def simulation(par):
integrator, run, trial = par
rebound.reset()
k = 0.01720209895
Gfac = 1./k
rebound.set_dt(dt)
rebound.set_integrator(integrator)
rebound.set_force_is_velocitydependent(0)
massfac = 1.
rebound.add_particle(m=1.00000597682, x=-4.06428567034226e-3, y=-6.08813756435987e-3, z=-1.66162304225834e-6, vx=+6.69048890636161e-6*Gfac, vy=-6.33922479583593e-6*Gfac, vz=-3.13202145590767e-9*Gfac) # Sun
rebound.add_particle(m=massfac/1407.355, x=+3.40546614227466e+0, y=+3.62978190075864e+0, z=+3.42386261766577e-2, vx=-5.59797969310664e-3*Gfac, vy=+5.51815399480116e-3*Gfac, vz=-2.66711392865591e-6*Gfac) # Jupiter
rebound.add_particle(m=massfac/3501.6, x=+6.60801554403466e+0, y=+6.38084674585064e+0, z=-1.36145963724542e-1, vx=-4.17354020307064e-3*Gfac, vy=+3.99723751748116e-3*Gfac, vz=+1.67206320571441e-5*Gfac) # Saturn
rebound.add_particle(m=massfac/22869., x=+1.11636331405597e+1, y=+1.60373479057256e+1, z=+3.61783279369958e-1, vx=-3.25884806151064e-3*Gfac, vy=+2.06438412905916e-3*Gfac, vz=-2.17699042180559e-5*Gfac) # Uranus
rebound.add_particle(m=massfac/19314., x=-3.01777243405203e+1, y=+1.91155314998064e+0, z=-1.53887595621042e-1, vx=-2.17471785045538e-4*Gfac, vy=-3.11361111025884e-3*Gfac, vz=+3.58344705491441e-5*Gfac) # Neptune
N = rebound.get_N()
particles = rebound.get_particles()
np.random.seed(run)
for i in xrange(N):
particles[i].m *= 1.+1e-3*np.random.rand()
particles[i].x *= 1.+1e-3*np.random.rand()
particles[i].y *= 1.+1e-3*np.random.rand()
particles[i].z *= 1.+1e-3*np.random.rand()
particles[i].vx *= 1.+1e-3*np.random.rand()
particles[i].vy *= 1.+1e-3*np.random.rand()
particles[i].vz *= 1.+1e-3*np.random.rand()
def move_to_heliocentric():
particles = rebound.get_particles()
particles[0].x = 0.
particles[0].y = 0.
particles[0].z = 0.
particles[0].vx = 0.
particles[0].vy = 0.
particles[0].vz = 0.
def energy():
particles = rebound.get_particles()
com_vx = 0.
com_vy = 0.
com_vz = 0.
if integrator=="wh" or integrator=="mercury" or integrator[0:7]=="swifter":
mtot = 0.
for i in xrange(0,N):
com_vx += particles[i].vx*particles[i].m
com_vy += particles[i].vy*particles[i].m
com_vz += particles[i].vz*particles[i].m
mtot += particles[i].m
com_vx /= mtot
com_vy /= mtot
com_vz /= mtot
E_kin = 0.
E_pot = 0.
for i in xrange(N):
dvx = particles[i].vx - com_vx
dvy = particles[i].vy - com_vy
dvz = particles[i].vz - com_vz
E_kin += 0.5*particles[i].m*(dvx*dvx + dvy*dvy + dvz*dvz)
for j in xrange(i+1,N):
dx = particles[i].x-particles[j].x
dy = particles[i].y-particles[j].y
dz = particles[i].z-particles[j].z
r2 = dx*dx + dy*dy + dz*dz
E_pot -= particles[i].m*particles[j].m/np.sqrt(r2)
return E_kin+E_pot
times = np.logspace(np.log10(orbit),np.log10(tmax),Ngrid)
if integrator=="wh" or integrator=="mercury" or integrator[0:7]=="swifter":
move_to_heliocentric()
else:
rebound.move_to_center_of_momentum()
ei = energy()
es = []
runtime = 0.
for t in times:
rebound.integrate(t,exactFinishTime=0,keepSynchronized=0)
ef = energy()
e = np.fabs((ei-ef)/ei)+1.1e-16
es.append(e)
runtime += rebound.get_timing()
integrator, run, trial = par
print integrator.ljust(13) + " %9.5fs"%(runtime) + "\t Error: %e" %( e)
es = np.array(es)
return [times, es]
def simulation(par):
import rebound
integrator, dt, run = par
rebound.reset()
k = 0.01720209895
G = k * k
rebound.G = G
rebound.dt = dt
rebound.integrator = integrator
rebound.force_is_velocitydependent = 0
rebound.add(m=1.00000597682,
x=-4.06428567034226e-3,
y=-6.08813756435987e-3,
z=-1.66162304225834e-6,
vx=+6.69048890636161e-6,
vy=-6.33922479583593e-6,
vz=-3.13202145590767e-9) # Sun
rebound.add(m=1. / 1407.355,
x=+3.40546614227466e+0,
y=+3.62978190075864e+0,
z=+3.42386261766577e-2,
vx=-5.59797969310664e-3,
vy=+5.51815399480116e-3,
vz=-2.66711392865591e-6) # Jupiter
rebound.add(m=1. / 3501.6,
x=+6.60801554403466e+0,
y=+6.38084674585064e+0,
z=-1.36145963724542e-1,
vx=-4.17354020307064e-3,
vy=+3.99723751748116e-3,
vz=+1.67206320571441e-5) # Saturn
rebound.add(m=1. / 22869.,
x=+1.11636331405597e+1,
y=+1.60373479057256e+1,
z=+3.61783279369958e-1,
vx=-3.25884806151064e-3,
vy=+2.06438412905916e-3,
vz=-2.17699042180559e-5) # Uranus
rebound.add(m=1. / 19314.,
x=-3.01777243405203e+1,
y=+1.91155314998064e+0,
z=-1.53887595621042e-1,
vx=-2.17471785045538e-4,
vy=-3.11361111025884e-3,
vz=+3.58344705491441e-5) # Neptune
N = rebound.N
particles = rebound.particles
np.random.seed(run)
for i in xrange(N):
particles[i].m *= 1. + 1e-3 * np.random.rand()
particles[i].x *= 1. + 1e-3 * np.random.rand()
particles[i].y *= 1. + 1e-3 * np.random.rand()
particles[i].z *= 1. + 1e-3 * np.random.rand()
particles[i].vx *= 1. + 1e-3 * np.random.rand()
particles[i].vy *= 1. + 1e-3 * np.random.rand()
particles[i].vz *= 1. + 1e-3 * np.random.rand()
def move_to_heliocentric():
particles[0].x = 0.
particles[0].y = 0.
particles[0].z = 0.
particles[0].vx = 0.
particles[0].vy = 0.
particles[0].vz = 0.
def energy():
com_vx = 0.
com_vy = 0.
com_vz = 0.
if integrator == "wh" or integrator == "mercury" or integrator[
0:7] == "swifter":
mtot = 0.
for i in xrange(0, N):
com_vx += particles[i].vx * particles[i].m
com_vy += particles[i].vy * particles[i].m
com_vz += particles[i].vz * particles[i].m
mtot += particles[i].m
com_vx /= mtot
com_vy /= mtot
com_vz /= mtot
E_kin = 0.
E_pot = 0.
for i in xrange(N):
dvx = particles[i].vx - com_vx
dvy = particles[i].vy - com_vy
dvz = particles[i].vz - com_vz
E_kin += 0.5 * particles[i].m * (dvx * dvx + dvy * dvy + dvz * dvz)
for j in xrange(i + 1, N):
dx = particles[i].x - particles[j].x
dy = particles[i].y - particles[j].y
dz = particles[i].z - particles[j].z
r2 = dx * dx + dy * dy + dz * dz
E_pot -= G * particles[i].m * particles[j].m / np.sqrt(r2)
return E_kin + E_pot
if integrator == "wh" or integrator == "mercury" or integrator[
0:7] == "swifter":
move_to_heliocentric()
else:
rebound.move_to_com()
ei = energy()
runtime = 0.
rebound.integrate(tmax, exactFinishTime=0)
ef = energy()
e = np.fabs((ei - ef) / ei) + 1.1e-16
runtime += rebound.timing
integrator, dt, run = par
print integrator.ljust(13) + " %9.5fs" % (runtime) + "\t Error: %e" % (e)
return [runtime, e]
def simulation(par):
integrator, mass = par
rebound.reset()
mass = pow(10., mass)
k = 0.01720209895
G = k * k
rebound.G = G
rebound.dt = 0.
rebound.integrator = integrator
rebound.add(m=1.00000597682,
x=-4.06428567034226e-3,
y=-6.08813756435987e-3,
z=-1.66162304225834e-6,
vx=+6.69048890636161e-6,
vy=-6.33922479583593e-6,
vz=-3.13202145590767e-9) # Sun
rebound.add(m=mass,
x=+3.40546614227466e+0,
y=+3.62978190075864e+0,
z=+3.42386261766577e-2,
vx=-5.59797969310664e-3,
vy=+5.51815399480116e-3,
vz=-2.66711392865591e-6) # Jupiter
rebound.add(m=mass,
x=+6.60801554403466e+0,
y=+6.38084674585064e+0,
z=-1.36145963724542e-1,
vx=-4.17354020307064e-3,
vy=+3.99723751748116e-3,
vz=+1.67206320571441e-5) # Saturn
rebound.add(m=mass,
x=+1.11636331405597e+1,
y=+1.60373479057256e+1,
z=+3.61783279369958e-1,
vx=-3.25884806151064e-3,
vy=+2.06438412905916e-3,
vz=-2.17699042180559e-5) # Uranus
rebound.add(m=mass,
x=-3.01777243405203e+1,
y=+1.91155314998064e+0,
z=-1.53887595621042e-1,
vx=-2.17471785045538e-4,
vy=-3.11361111025884e-3,
vz=+3.58344705491441e-5) # Neptune
N = rebound.N
def move_to_heliocentric():
particles = rebound.particles
for i in xrange(1, N):
particles[i].x -= particles[0].x
particles[i].y -= particles[0].y
particles[i].z -= particles[0].z
particles[i].vx -= particles[0].vx
particles[i].vy -= particles[0].vy
particles[i].vz -= particles[0].vz
particles[0].x = 0.
particles[0].y = 0.
particles[0].z = 0.
particles[0].vx = 0.
particles[0].vy = 0.
particles[0].vz = 0.
def energy():
if integrator == "wh":
rebound.move_to_com()
particles = rebound.particles
E_kin = 0.
E_pot = 0.
for i in xrange(N):
E_kin += 0.5 * particles[i].m * (
particles[i].vx * particles[i].vx + particles[i].vy *
particles[i].vy + particles[i].vz * particles[i].vz)
for j in xrange(i + 1, N):
dx = particles[i].x - particles[j].x
dy = particles[i].y - particles[j].y
dz = particles[i].z - particles[j].z
r2 = dx * dx + dy * dy + dz * dz
E_pot -= G * particles[i].m * particles[j].m / np.sqrt(r2)
if integrator == "wh":
move_to_heliocentric()
return E_kin + E_pot
rebound.move_to_com()
ei = energy()
es = 1e-20
for s in xrange(1000):
rebound.step()
ef = energy()
e = np.fabs((ei - ef) / ei)
es = max(es, e)
return es
def simulation(par):
integrator, mass = par
rebound.reset()
mass = pow(10.,mass)
k = 0.01720209895
G = k*k
rebound.G = G
rebound.dt = 0.
rebound.integrator = integrator
rebound.add(m=1.00000597682, x=-4.06428567034226e-3, y=-6.08813756435987e-3, z=-1.66162304225834e-6, vx=+6.69048890636161e-6, vy=-6.33922479583593e-6, vz=-3.13202145590767e-9) # Sun
rebound.add(m=mass, x=+3.40546614227466e+0, y=+3.62978190075864e+0, z=+3.42386261766577e-2, vx=-5.59797969310664e-3, vy=+5.51815399480116e-3, vz=-2.66711392865591e-6) # Jupiter
rebound.add(m=mass, x=+6.60801554403466e+0, y=+6.38084674585064e+0, z=-1.36145963724542e-1, vx=-4.17354020307064e-3, vy=+3.99723751748116e-3, vz=+1.67206320571441e-5) # Saturn
rebound.add(m=mass, x=+1.11636331405597e+1, y=+1.60373479057256e+1, z=+3.61783279369958e-1, vx=-3.25884806151064e-3, vy=+2.06438412905916e-3, vz=-2.17699042180559e-5) # Uranus
rebound.add(m=mass, x=-3.01777243405203e+1, y=+1.91155314998064e+0, z=-1.53887595621042e-1, vx=-2.17471785045538e-4, vy=-3.11361111025884e-3, vz=+3.58344705491441e-5) # Neptune
N = rebound.N
def move_to_heliocentric():
particles = rebound.particles
for i in xrange(1,N):
particles[i].x -= particles[0].x
particles[i].y -= particles[0].y
particles[i].z -= particles[0].z
particles[i].vx -= particles[0].vx
particles[i].vy -= particles[0].vy
particles[i].vz -= particles[0].vz
particles[0].x = 0.
particles[0].y = 0.
particles[0].z = 0.
particles[0].vx = 0.
particles[0].vy = 0.
particles[0].vz = 0.
def energy():
if integrator=="wh":
rebound.move_to_com()
particles = rebound.particles
E_kin = 0.
E_pot = 0.
for i in xrange(N):
E_kin += 0.5*particles[i].m*(particles[i].vx*particles[i].vx + particles[i].vy*particles[i].vy + particles[i].vz*particles[i].vz)
for j in xrange(i+1,N):
dx = particles[i].x-particles[j].x
dy = particles[i].y-particles[j].y
dz = particles[i].z-particles[j].z
r2 = dx*dx + dy*dy + dz*dz
E_pot -= G*particles[i].m*particles[j].m/np.sqrt(r2)
if integrator=="wh":
move_to_heliocentric()
return E_kin+E_pot
rebound.move_to_com()
ei = energy()
es = 1e-20
for s in xrange(1000):
rebound.step()
ef = energy()
e = np.fabs((ei-ef)/ei)
es = max(es,e)
return es
def simulation(par):
import rebound
integrator, dt, run = par
rebound.reset()
k = 0.01720209895
G = k*k
rebound.G = G
rebound.dt = dt
if integrator == "whfast-nocor":
integrator = "whfast"
else:
rebound.integrator_whfast_corrector = 11
rebound.integrator = integrator
rebound.force_is_velocitydependent = 0
rebound.add(m=1.00000597682, x=-4.06428567034226e-3, y=-6.08813756435987e-3, z=-1.66162304225834e-6, vx=+6.69048890636161e-6, vy=-6.33922479583593e-6, vz=-3.13202145590767e-9) # Sun
rebound.add(m=1./1407.355, x=+3.40546614227466e+0, y=+3.62978190075864e+0, z=+3.42386261766577e-2, vx=-5.59797969310664e-3, vy=+5.51815399480116e-3, vz=-2.66711392865591e-6) # Jupiter
rebound.add(m=1./3501.6, x=+6.60801554403466e+0, y=+6.38084674585064e+0, z=-1.36145963724542e-1, vx=-4.17354020307064e-3, vy=+3.99723751748116e-3, vz=+1.67206320571441e-5) # Saturn
rebound.add(m=1./22869., x=+1.11636331405597e+1, y=+1.60373479057256e+1, z=+3.61783279369958e-1, vx=-3.25884806151064e-3, vy=+2.06438412905916e-3, vz=-2.17699042180559e-5) # Uranus
rebound.add(m=1./19314., x=-3.01777243405203e+1, y=+1.91155314998064e+0, z=-1.53887595621042e-1, vx=-2.17471785045538e-4, vy=-3.11361111025884e-3, vz=+3.58344705491441e-5) # Neptune
N = rebound.N
particles = rebound.particles
np.random.seed(run)
for i in xrange(N):
particles[i].m *= 1.+1e-3*np.random.rand()
particles[i].x *= 1.+1e-3*np.random.rand()
particles[i].y *= 1.+1e-3*np.random.rand()
particles[i].z *= 1.+1e-3*np.random.rand()
particles[i].vx *= 1.+1e-3*np.random.rand()
particles[i].vy *= 1.+1e-3*np.random.rand()
particles[i].vz *= 1.+1e-3*np.random.rand()
def move_to_heliocentric():
particles[0].x = 0.
particles[0].y = 0.
particles[0].z = 0.
particles[0].vx = 0.
particles[0].vy = 0.
particles[0].vz = 0.
def energy():
com_vx = 0.
com_vy = 0.
com_vz = 0.
if integrator=="wh" or integrator=="mercury" or integrator[0:7]=="swifter":
mtot = 0.
for i in xrange(0,N):
com_vx += particles[i].vx*particles[i].m
com_vy += particles[i].vy*particles[i].m
com_vz += particles[i].vz*particles[i].m
mtot += particles[i].m
com_vx /= mtot
com_vy /= mtot
com_vz /= mtot
E_kin = 0.
E_pot = 0.
for i in xrange(N):
dvx = particles[i].vx - com_vx
dvy = particles[i].vy - com_vy
dvz = particles[i].vz - com_vz
E_kin += 0.5*particles[i].m*(dvx*dvx + dvy*dvy + dvz*dvz)
for j in xrange(i+1,N):
dx = particles[i].x-particles[j].x
dy = particles[i].y-particles[j].y
dz = particles[i].z-particles[j].z
r2 = dx*dx + dy*dy + dz*dz
E_pot -= G*particles[i].m*particles[j].m/np.sqrt(r2)
return E_kin+E_pot
if integrator=="wh" or integrator=="mercury" or integrator[0:7]=="swifter":
move_to_heliocentric()
else:
rebound.move_to_com()
ei = energy()
runtime = 0.
rebound.integrate(tmax,exact_finish_time=0)
ef = energy()
e = np.fabs((ei-ef)/ei)+1.1e-16
runtime += rebound.timing
integrator, dt, run = par
print integrator.ljust(13) + " %9.5fs"%(runtime) + "\t Error: %e" %( e)
return [runtime, e]