def SingleParticleDerivativeVector(self,kstate,particle,t):
if self.interaction_type == "ClassicalNBody":
rad = farts.xy2rad(kstate[particle],
self.SingleParticleNewtonianForce(particle,
2,
2))
elif self.interaction_type == None:
rad = farts.xy2rad(self.state[particle],(0,0))
elif self.interaction_type == "ClassicalElastic":
raise ValueError("ClassicalElastic collisions not implemented yet")
r = rad[0,0]
phi = rad[0,1]
if(r > 999 or r < self.event_horizon):
if particle not in self.cleanup:
self.cleanup.append(particle)
f = np.array(([rad[0,0],rad[1,0]],[rad[0,1],rad[1,1]]))
G=np.array([[f[0,1],
-(1/f[0,0]**4)*(self.a(t)**2-2*self.M*f[0,0]+(f[0,0]**2))*((self.M*(f[0,0]**4)*f[0,1]**2)/(self.a(t)**2-2*self.M*f[0,0]+(f[0,0]**2))**2-((f[0,0]**5)*(f[0,1]**2))/((self.a(t)**2)-2*self.M*f[0,0]+(f[0,0]**2))**2+self.M*(-1+self.a(t)*f[1,1])**2+(f[0,0]**3)*((f[0,1]**2)/((self.a(t)**2)-2*self.M*f[0,0]+(f[0,0]**2))-(f[1,1]**2)))+rad[2,0]],
[f[1,1],
-((2*f[0,1]*(self.a(t)*self.M+(-(self.a(t)**2)*self.M+f[0,0]**3)*f[1,1]))/(f[0,0]*(2*(self.a(t)**2)*self.M+(self.a(t)**2)*f[0,0]+(f[0,0]**3))))+rad[2,1]]])
return(farts.G2xy(G,r,phi))
def SingleParticleDerivativeVector(self, kstate, particle, t):
#print("\n\n\nInput XYZ state: ", self.state)
if self.interaction == False:
rad = farts.xy2rad(kstate[particle])
elif self.interaction == 'ClassicalNBody':
rad = farts.xy2rad(kstate[particle],
self.SingleParticleNewtonianForce(particle, 100, self.cr))
elif self.interation == True:
raise ValueError('Ambiguous interaction specification')
r = rad[0,0]
theta = rad[0,1]
phi = rad[0,2]
if(r > 999 or r < self.event_horizon+0.2):
if particle not in self.cleanup:
self.cleanup.append(particle)
f = np.array(([rad[0,0],rad[1,0]],
[rad[0,1],rad[1,1]],
[rad[0,2],rad[1,2]]))
#print("\nInput RTP state: ", f)
rdd = (-4*pow(self.M,3) + f[0,0]*(4*pow(self.M,2) + f[0,0]*(-self.M + self.M*pow(f[0,1],2) + f[0,0]*pow(-2*self.M + f[0,0],2)*(pow(f[1,1],2) + pow(f[2,1],2)*pow(np.sin(f[1,0]),2)))))/(pow(f[0,0],3)*(-2*self.M + f[0,0]))
Tdd = (-2*f[0,1]*f[1,1])/f[0,0] + np.cos(f[1,0])*pow(f[2,1],2)*np.sin(f[1,0])
Pdd = (-2*(f[0,1] + (np.cos(f[1,0])/np.sin(f[1,0]))*f[0,0]*f[1,1])*f[2,1])/f[0,0]
# The Kerr metric
G = np.array([[f[0,1],rdd],
[f[1,1],Tdd],
[f[2,1],Pdd]])
#print("\nRTP G: ",G)
#print("G: \n", G)
xyG = farts.G2xy(G,r,theta,phi)
#print("\nXYZ G: ",xyG)
#print("\nxyG: \n",xyG)
return(xyG)
def SingleParticleDerivativeVector(self, kstate, particle, t):
#print("\n\n\nInput XY state: ", self.state)
if self.interaction == False:
rad = farts.xy2rad(kstate[particle],(0,0))
elif self.interaction == 'ClassicalNBody':
rad = farts.xy2rad(kstate[particle],
self.SingleParticleNewtonianForce(particle, 100, self.cr))
elif self.interation == True:
raise ValueError('Ambiguous interaction specification')
r = rad[0,0]
phi = rad[0,1]
if(r > 999 or r < self.event_horizon-0.2):
if particle not in self.cleanup:
self.cleanup.append(particle)
f = np.array(([rad[0,0],rad[1,0]],
[rad[0,1],rad[1,1]]))
#print("\nInput RP state: ", f)
# The Kerr metric
G=np.array([[f[0,1],
(-(self.M*pow(pow(self.a(t),2) - 2*self.M*f[0,0] + pow(f[0,0],2),2)) + self.a(t)*self.M*pow(pow(self.a(t),2) - 2*self.M*f[0,0] + pow(f[0,0],2),2)*f[1,1] + pow(pow(self.a(t),2) - 2*self.M*f[0,0] + pow(f[0,0],2),2)*f[1,1]*(self.a(t)*self.M + (-(pow(self.a(t),2)*self.M) + pow(f[0,0],3))*f[1,1]) + pow(f[0,0],3)*(-pow(self.a(t),2) + self.M*f[0,0])*pow(f[0,1],2))/(pow(f[0,0],4)*(pow(self.a(t),2) - 2*self.M*f[0,0] + pow(f[0,0],2)))],
[f[1,1],
(2*(-(self.a(t)*self.M) + (pow(self.a(t),2)*self.M + 2*self.M*pow(f[0,0],2) - pow(f[0,0],3))*f[1,1])*f[0,1])/(pow(f[0,0],2)*(pow(self.a(t),2) - 2*self.M*f[0,0] + pow(f[0,0],2)))]])
#print("\nRTP G: ",G)
#G = np.array([[f[0,1],rad[2,0]],
# [f[1,1],rad[2,1]]])
xyG = farts.G2xy(G,r,phi)
#print("\nXY G: ",xyG)
return(xyG)
def __init__(self,
Nparticles,
M=1,
a = None,
dt=0.01,
interaction = False,
collisions = 'elastic',
masses = None,
init_state = None,
cr = 0.001,
save_dir = "./output"):
self.start_particles = Nparticles
self.Nparticles = Nparticles
self.interaction = interaction
self.M = M
self.dt = dt
self.a = a
self.cr = cr
self.event_horizon = 0
self.cleanup = []
if init_state is not None:
self.use_state = np.copy(init_state)
else:
self.use_state = None
self.save_dir = save_dir
self.init_state = np.copy(init_state)
self.state = np.copy(init_state)
self.collision_dict = {}
self.collisions=collisions
self.collided_particles = np.array([])
self.fname_list = []
self.dirname = ""
self.plotdata = 0
self.skip_mkdir=False
self.nsteps = 0
self.old_collisions = []
if self.Nparticles == None and self.init_state is not None:
self.Nparticles = len(self.init_state)
if self.a == None:
self.a = farts.a0
if init_state is not None:
if init_state.shape == (Nparticles,2,3):
self.init_state = init_state
else:
raise ValueError("Initial state not the right shape: ",init_state.shape,
"\nShould be ",(Nparticles,2,3))
if masses == None:
self.masses = np.zeros(Nparticles)+0.0001
else:
if len(masses) == Nparticles:
self.masses = masses
else:
raise ValueError("Mass list must be of length ", Nparticles,
"\nGiven length:", len(masses))
self.collision_radius = .05
def UpdateStateVectorRK4(self,t):
self.event_horizon = self.get_event_horizon(t)
new_state = np.ndarray((self.Nparticles,2,3))
for particle in xrange(self.Nparticles):
kstate = np.copy(self.state)
k1 = self.dt * self.SingleParticleDerivativeVector(kstate,particle, t)
kstate[particle] = np.copy(self.state[particle]) + k1/2
k2 = self.dt * self.SingleParticleDerivativeVector(kstate,particle,t+(self.dt/2))
kstate[particle] = np.copy(self.state[particle]) + k2/2
k3 = self.dt * self.SingleParticleDerivativeVector(kstate,particle,t+(self.dt/2))
kstate[particle] = np.copy(self.state[particle]) + k3
k4 = self.dt * self.SingleParticleDerivativeVector(kstate,particle,t+self.dt)
new_state[particle] = np.copy(self.state[particle]) + (1/3)*(k1/2 + k2 + k3 + k4/2)
#Get rid of gobbled or ejected particles
if self.cleanup != []:
new_state = np.delete(new_state,self.cleanup,axis=0)
self.remove_particle(particle)
for particle in self.cleanup:
print("\n***particle {} shit the bed at step {}***".format(particle,int(t/self.dt)))
print("***particle {} removed***".format(particle))
self.cleanup.remove(particle)
if self.cleanup == []:
print("***cleanup completed***")
self.cleanup = []
big_particle_list = []
big_vector_list = []
new_masses_list = []
#Cleanup collided particles
if self.collisions == "inelastic":
if self.collision_dict != {}:
for key in self.collision_dict:
particles = self.collision_dict[key][1]
m = 0
x = self.collision_dict[key][0][0]
y = self.collision_dict[key][0][1]
mvx = 0
mvy = 0
for particle in particles:
m += self.masses[particle]
for particle in particles:
mvx += (self.state[particle][1][0]*self.masses[particle])
mvy += (self.state[particle][1][1]*self.masses[particle])
big_particle_list.append(particle)
new_masses_list.append(m)
new_particle = [[x,y],[mvx/m,mvy/m]]
big_vector_list.append(new_particle)
self.masses = np.delete(self.masses,big_particle_list,axis=0)
self.masses = np.append(self.masses,np.array(new_masses_list),axis = 0)
new_state = np.delete(new_state,big_particle_list,axis=0)
new_state = np.append(new_state,np.array(big_vector_list),axis = 0)
self.Nparticles = len(new_state)
self.collision_dict = {}
self.collided_particles = np.array([])
elif self.collisions == 'elastic':
distances = squareform(pdist(self.state[:,0,:]))
ind1, ind2 = np.where(distances < 2 * self.collision_radius)
unique = (ind1 < ind2)
ind1 = ind1[unique]
ind2 = ind2[unique]
new_collisions = zip(ind1,ind2)
for i in new_collisions:
if i not in self.old_collisions:
i1 = i[0]
i2 = i[1]
m1 = self.masses[i1]
m2 = self.masses[i2]
x1 = new_state[i1,0,0]
y1 = new_state[i1,0,1]
z1 = new_state[i2,0,3]
x2 = new_state[i2,0,0]
y2 = new_state[i2,0,1]
z2 = new_state[i2,0,2]
x1d = new_state[i1,1,0]
y1d = new_state[i1,1,1]
z1d = new_state[i1,1,2]
x2d = new_state[i2,1,0]
y2d = new_state[i2,1,1]
z2d = new_state[i2,1,2]
new_state[i1, 1] = [(x1d*(m1-m2) + 2*m2*x2d)/(m1+m2),
(y1d*(m1-m2) + 2*m2*y2d)/(m1+m2),
(z1d*(m1-m2) + 2*m2*z2d)/(m1+m2)]
new_state[i2, 1] = [(x2d*(m2-m1) + 2*m1*x1d)/(m1+m2),
(y2d*(m2-m1) + 2*m1*y1d)/(m1+m2),
(z2d*(m2-m1) + 2*m1*z1d)/(m1+m2)]
self.old_collisions = new_collisions
return(new_state)
def SingleParticleNewtonianForce(self, i, soi_radius, collision_radius):
forces = np.zeros([self.Nparticles,2])
x1 = self.state[i,0,0]
y1 = self.state[i,0,1]
m1 = self.masses[i]
collided1 = 0
if self.interaction=='ClassicalNBody':
xmin = x1-soi_radius
xmax = x1+soi_radius
ymin = y1-soi_radius
ymax = y1+soi_radius
sliced_indices_x = np.where(np.logical_and(self.state[:,0,0]>xmin,self.state[:,0,0]<xmax))
sliced_indices_y = np.where(np.logical_and(self.state[:,0,1]>ymin,self.state[:,0,1]<ymax))
sliced_indices = np.intersect1d(sliced_indices_x,sliced_indices_y)
sliced_arr = self.state[sliced_indices]
no_i_indices = np.where(np.logical_and(sliced_arr[:,0,0] == x1,sliced_arr[:,0,1]==y1))
sliced_arr = np.delete(sliced_arr,no_i_indices,axis=0)
sliced_masses = self.masses[sliced_indices]
sliced_masses = np.delete(sliced_masses,no_i_indices,axis=0)
distances2 = np.array(np.transpose(np.matrix((sliced_arr[:,0,0]-x1)**2+(sliced_arr[:,0,1]-y1)**2)))
jforce = np.array(np.transpose(np.matrix(sliced_masses)))/distances2
jforcedir = np.array(np.transpose(np.matrix([sliced_arr[:,0,0]-x1,sliced_arr[:,0,1]-y1])))/np.sqrt(distances2)
forces = jforce*jforcedir
for particle_num in xrange(self.Nparticles):
if particle_num != i:
collided2 = 0
m2 = self.masses[particle_num]
x2 = self.state[particle_num,0,0]
y2 = self.state[particle_num,0,1]
distance2 = ((x2-x1)**2+(y2-y1)**2)
"""
if the collision dict is empty, put in the two particles being evaluated.
if it's not empty, first search to see if the main particle is in there
if the main particle is in there, move on to the secondary
if the secondary particle is not in there, put it in the entry with the main particle
"""
if self.Nparticles == 2:
if distance2>500000:
print('\n',distance2)
print(self.state)
raise ValueError("it f****d the duck")
elif self.Nparticles == 1:
raise ValueError("it shit the bed")
if self.collisions != False and i not in self.cleanup and particle_num not in self.cleanup:
if distance2 < collision_radius:
if self.collision_dict == {}:
self.collision_dict[0] = [(x1,y1),[i,particle_num]]
else:
i_val = farts.dict_check(self.collision_dict, i)
keynum = max(self.collision_dict)+1
if i_val == -1:
self.collision_dict[keynum] = [(x1,y1),[i]]
i_val = keynum
elif farts.dict_check(self.collision_dict, particle_num) == -1:
self.collision_dict[i_val][1].append(particle_num)
return(np.sum(forces,axis=0))
