def potential_energies_barnes_hut(
result): # return potential energy in each frame
frames = result.numpy()
return np.array([
cs.getEnergiesC(cs.BodyList3(frame), thetamax=0.7, G=sc.G)
for frame in frames
])
def gen_galaxy(pos, DM_pos, m, mDM, mBH, v, vDM):
"""Generate a galaxy (Bodylist) of a massive black hole M and n stars, with initial positions, velocities and masses randomly distributed"""
posarray = pos
n = len(pos)
nDM = len(DM_pos)
massarray = m
velarray = v
bodies = [cs.Body3(pos=np.zeros(3), vel=np.zeros(3), mass=mBH)]
for i in range(n):
bodies.append(
cs.Body3(pos=posarray[i], vel=velarray[i], mass=massarray[i]))
posarrayDM = DM_pos
massarrayDM = mDM
bodiesDM = []
velarrayDM = vDM
for i in range(0, nDM):
bodiesDM.append(
cs.Body3(pos=posarrayDM[i],
vel=velarrayDM[i],
mass=massarrayDM[i],
dark_matter=True))
allbodies = np.concatenate((bodies, bodiesDM))
return cs.BodyList3(np.array(allbodies))
def zip_to_bodylist(pos_list, vel_list, m_list, dark_matter_list=None):
"""Constructs a BodyList3 from iterables of positions, velocities and masses.
Accepts native python & numpy objects"""
if dark_matter_list is None:
dark_matter_list = np.full(len(pos_list), False)
bodies = [
make_body(pos, vel, m, dark_matter=dm) for pos, vel, m, dm in zip(
pos_list, vel_list, m_list, dark_matter_list)
]
return cs.BodyList3(np.array(bodies))
def genDMG(n, M=sc.Msgra, R=1, RD=sc.RDmw/sc.RCmw, spherical=False, nDM=0, rho0=1, Rs=10, c=12):
"""Generate a galaxy (Bodylist) of a massive black hole M and n stars, with initial positions, velocities and masses randomly distributed"""
theta = np.random.uniform(0, 2 * np.pi, n)
if spherical == True:
phi = np.pi/2 - np.random.normal(0,0.1,n)
else:
phi = np.pi/2
r = rd.radSample(R,RD,n)
x = r * np.cos(theta) * np.sin(phi)
y = r * np.sin(theta) * np.sin(phi)
z = r * np.cos(phi)
posarray = np.column_stack((x, y, z))
v = np.sqrt(sc.G*M*(1/r))
v_x = -np.sin(theta) * v
v_y = np.cos(theta) * v
v_z = np.zeros(n)
velarray = np.column_stack((v_x, v_y, v_z))
massarray = md.massSample(n)
bodies = [cs.Body3(pos=np.zeros(3), vel=np.zeros(3), mass=M)]
for i in range(1,n):
bodies.append(cs.Body3(pos=posarray[i], vel=velarray[i], mass=massarray[i]))
thetaDM = np.random.uniform(0,2*np.pi,nDM)
phiDM = np.random.uniform(0,np.pi,nDM)
rDM = DMrd.DMradSample(nDM, rho0, Rs, c)
xDM = rDM * np.cos(thetaDM) * np.sin(phiDM)
yDM = rDM * np.sin(thetaDM) * np.sin(phiDM)
zDM = rDM * np.cos(phiDM)
posarrayDM = np.column_stack((xDM, yDM, zDM))
vDM = np.sqrt(sc.G*M*(1/rDM))
v_xDM = -np.sin(thetaDM) * vDM
v_yDM = np.cos(thetaDM) * vDM
v_zDM = np.zeros(nDM)
velarrayDM = np.column_stack((v_xDM, v_yDM, v_zDM))
massarrayDM = 100*md.massSample(nDM)
bodiesDM = []
for i in range(0, nDM):
bodiesDM.append(cs.Body3(pos=posarrayDM[i], vel=velarrayDM[i], mass=massarrayDM[i]))
allbodies = np.concatenate((bodies,bodiesDM))
print(len(allbodies))
return cs.BodyList3(np.array(allbodies))
def genEGalaxy(n,M=sc.Msgra,R=1,RD=sc.RDmw/sc.RCmw,space=False,elliptical=False,spiralarms=1):
"""Generate a galaxy (Bodylist) of a massive black hole M and n stars, with initial positions, velocities and masses randomly distributed"""
massarray = md.massSample(n)
if space == True:
phi = np.pi/2 - np.random.normal(0,0.1,n)
else:
phi = np.pi/2
if elliptical == True:
spiral = 1
e = 0.5*np.ones(n)+np.random.normal(0,0.005,n)
else:
spiral = 0
e = np.zeros(n)
r = rd.radSample(n,R,RD)
for i in range(len(r)):
if r[i] <= sc.RCmw:
theta = np.random.uniform(0,2*np.pi,n)
else:
theta = (1-spiral) * np.random.uniform(0, 2 * np.pi, n) + spiral * (-2*np.pi*r/np.amax(r)+np.pi/10*np.random.normal(0,1,n)+np.pi*np.random.randint(0,2,n))
a = r/(1+e)
x = r * np.cos(theta) * np.sin(phi)
y = r * np.sin(theta) * np.sin(phi)
z = r * np.cos(phi)
posarray = np.column_stack((x, y, z))
plt.scatter(x,y)
plt.show()
v = np.sqrt(sc.G*(M+massarray)*(2/r-1/a))
v_x = -np.sin(theta) * v
v_y = np.cos(theta) * v
v_z = np.zeros(n)
velarray = np.column_stack((v_x, v_y, v_z))
plt.scatter(v_x, v_y)
plt.show()
bodies = [cs.Body3(pos=np.zeros(3), vel=np.zeros(3), mass=M)]
for i in range(1,n):
bodies.append(cs.Body3(pos=posarray[i], vel=velarray[i], mass=massarray[i]))
return cs.BodyList3(np.array(bodies))
def extract_last_bodylist_from_result(result):
last = result[-1, :]
bl = cs.BodyList3(last)
return bl
# m = np.array([1e6, 1, 10000, 10], dtype=np.double)
# bodylist = utils.zip_to_bodylist(r0, v0, m)
# N = len(bodylist)
# ---mini-galaxy: bodies arranged in rings around a black hole---
m_BH = 100000 # mass of black hole
galaxy_bodies = [utils.make_body(np.zeros(3), np.zeros(3), m_BH)] # black hole
for r in np.arange(1, 10) * 25: # add stars
for theta in np.linspace(0, 2 * np.pi, int(3 * r / 25))[:-1]:
pos = np.array([r * np.sin(theta), r * np.cos(theta), 0],
dtype=np.double)
v = np.array([np.cos(theta), -np.sin(theta), 0],
dtype=np.double) * np.sqrt(G * m_BH / r)
m = np.double(10)
galaxy_bodies.append(cs.Body3(pos, v, m))
bodylist = cs.BodyList3(np.array(galaxy_bodies))
n_steps = 3000 # int(30/1e-4)
begin = time.time()
result = cs.LeapFrogSaveC(bodylist, 1e-1, n_steps, thetamax, G)
end = time.time()
print("Simulation finished after", end - begin, "s")
s = utils.get_positions(result)
large_limits = {
"xlim": (-1000, 1000),
"ylim": (-1000, 1000),
"zlim": (-1000, 1000)
}
medium_limits = {"xlim": (-300, 300), "ylim": (-300, 300), "zlim": (-300, 300)}
