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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Removing particles from the simulation
Let's set up a simple simulation with 10 bodies, and have the simulation assign them unique hashes so we can keep track of them (see UniquelyIdentifyingParticles.ipynb).
Step1:  We could also add custom names to particles
Step2:  Now let's do a simple example where we do a short initial integration to isolate the particles that interest us for a longer simulation
Step3:  At this stage, we might be interested in particles that remained within some semimajor axis range, particles that were in resonance with a particular planet, etc.  Let's imagine a simple (albeit arbitrary) case where we only want to keep particles that had $x < 0$ at the end of the preliminary integration. Let's first print out the particle hashes and x positions.
Step4:  4066125545 is the hash corresponding to the string "Saturn" we added above.  Next, let's use the remove() function to filter out particlse. As an argument, we pass the corresponding index in the particles array.
Step5:  By default, the remove() function removes the i-th particle from the particles array, and shifts all particles with higher indices down by 1.  This ensures that the original order in the particles array is preserved (e.g., to help with output).
By running through the planets in reverse order above, we are guaranteed that when a particle with index i gets removed, the particle replacing it doesn't need to also be removed (we already checked it).
If you have many particles and many removals (or you don't care about the ordering), you can save the reshuffling of all particles with higher indices with the flag keepSorted=0
Step6:  We see that the particles array is no longer sorted by hash.  Note that the default keepSorted=1 only keeps things sorted (i.e., if they were sorted by hash to start with).  If you custom-assign hashes with strings (or manually) the default will simply preserve the original order.
Because in general particles can change positions in the particles array, a more robust way of referring to them (rather than with their index) is through their hash, which won't change.  You can pass sim.remove either the hash directly, or if you pass a string, it will be automatically converted to its corresponding hash
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Python Code:
import rebound
import numpy as np
sim = rebound.Simulation()
sim.add(m=1.)
sim.particles[0].hash = sim.generate_unique_hash()
for i in range(1,10):
    sim.add(a=i)
    sim.particles[i].hash = sim.generate_unique_hash()
sim.move_to_com()
print("Particle hashes:{0}".format([sim.particles[i].hash for i in range(sim.N)]))
Explanation: Removing particles from the simulation
Let's set up a simple simulation with 10 bodies, and have the simulation assign them unique hashes so we can keep track of them (see UniquelyIdentifyingParticles.ipynb).
End of explanation
sim.add(a=10, hash="Saturn")
print("Particle hashes:{0}".format([sim.particles[i].hash for i in range(sim.N)]))
Explanation: We could also add custom names to particles:
End of explanation
Noutputs = 1000
xs = np.zeros((sim.N, Noutputs))
ys = np.zeros((sim.N, Noutputs))
times = np.linspace(0.,50*2.*np.pi, Noutputs, endpoint=False)
for i, time in enumerate(times):
    sim.integrate(time)
    xs[:,i] = [sim.particles[j].x for j in range(sim.N)]
    ys[:,i] = [sim.particles[j].y for j in range(sim.N)]
%matplotlib inline
import matplotlib.pyplot as plt
fig,ax = plt.subplots(figsize=(15,5))
for i in range(sim.N):
    plt.plot(xs[i,:], ys[i,:])
ax.set_aspect('equal')
Explanation: Now let's do a simple example where we do a short initial integration to isolate the particles that interest us for a longer simulation:
End of explanation
print("Hash\tx")
for i in range(sim.N):
    print("{0}\t{1}".format(sim.particles[i].hash, xs[i,-1]))
Explanation: At this stage, we might be interested in particles that remained within some semimajor axis range, particles that were in resonance with a particular planet, etc.  Let's imagine a simple (albeit arbitrary) case where we only want to keep particles that had $x < 0$ at the end of the preliminary integration. Let's first print out the particle hashes and x positions.
End of explanation
for i in reversed(range(1,sim.N)):
    if xs[i,-1] > 0:
        sim.remove(i)
print("Number of particles after cut = {0}".format(sim.N))
print("Hashes of remaining particles = {0}".format([p.hash for p in sim.particles]))
Explanation: 4066125545 is the hash corresponding to the string "Saturn" we added above.  Next, let's use the remove() function to filter out particlse. As an argument, we pass the corresponding index in the particles array.
End of explanation
sim.remove(2, keepSorted=0)
print("Number of particles after cut = {0}".format(sim.N))
print("Hashes of remaining particles = {0}".format([p.hash for p in sim.particles]))
Explanation: By default, the remove() function removes the i-th particle from the particles array, and shifts all particles with higher indices down by 1.  This ensures that the original order in the particles array is preserved (e.g., to help with output).
By running through the planets in reverse order above, we are guaranteed that when a particle with index i gets removed, the particle replacing it doesn't need to also be removed (we already checked it).
If you have many particles and many removals (or you don't care about the ordering), you can save the reshuffling of all particles with higher indices with the flag keepSorted=0:
End of explanation
sim.remove(hash="Saturn")
print("Number of particles after cut = {0}".format(sim.N))
print("Hashes of remaining particles = {0}".format([p.hash for p in sim.particles]))
Explanation: We see that the particles array is no longer sorted by hash.  Note that the default keepSorted=1 only keeps things sorted (i.e., if they were sorted by hash to start with).  If you custom-assign hashes with strings (or manually) the default will simply preserve the original order.
Because in general particles can change positions in the particles array, a more robust way of referring to them (rather than with their index) is through their hash, which won't change.  You can pass sim.remove either the hash directly, or if you pass a string, it will be automatically converted to its corresponding hash:
End of explanation
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