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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:
 4. How to Run a Simulation
In sections 2 and 3, we explained the way to build a model and to setup the intial state. Now, it is the time to run a simulation. Corresponding to World classes, six Simulator classes are there
Step1:  4.1. How to Setup a Simulator
Except for the initialization (so-called constructor function) with arguments specific to the algorithm, all Simulators have the same APIs.
Step2:  Before constructing a Simulator, parepare a Model and a World corresponding to the type of Simulator.
Step3:  Simulator requires both Model and World in this order at the construction.
Step4:  If you bind the Model to the World, you need only the World to create a Simulator.
Step5:  Of course, the Model and World bound to a Simulator can be drawn from Simulator in the way below
Step6:  After updating the World by yourself, you must initialize the internal state of a Simulator before running simulation.
Step7:  For algorithms with a fixed step interval, the Simulator also requires dt.
Step8:  4.2. Running Simulations
For running simulations, Simulator provides two APIs, step and run.
step() advances a simulation for the time that the Simulator expects, next_time().
Step9:  last_reactions() returns a list of pairs of ReactionRule and ReactionInfo which occurs at the last step. Each algorithm have its own implementation of ReactionInfo. See help(module.ReactionInfo) for details.
Step10:  step(upto) advances a simulation for next_time if next_time is less than upto, or for upto otherwise. step(upto) returns whether the time does NOT reach the limit, upto.
Step11:  To run a simulation just until the time, upto, call step(upto) while it returns True.
Step12:  This is just what run does. run(tau) advances a simulation upto t()+tau.
Step13:  num_steps returns the number of steps during the simulation.
Step14:  4.3. Capsulizing Algorithm into a Factory Class
Owing to the portability of a Model and consistent APIs of Worlds and Simulators, it is very easy to write a script common in algorithms. However, when switching the algorithm, still we have to rewrite the name of classes in the code, one by one.
To avoid the trouble, E-Cell4 also provides a Factory class for each algorithm. Factory encapsulates World and Simulator with their arguments needed for the construction. By using Factory class, your script could be portable and robust agaist changes in the algorithm.
Factory just provides two functions, world and simulator.
Step15:  singlerun above is free from the algorithm. Thus, by just switching Factory, you can easily compare the results.
Step16:  When you need to provide several parameters to initialize World or Simulator, run_simulation also accepts Factory instead of solver.
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Python Code:
from ecell4_base.core import *
Explanation: 4. How to Run a Simulation
In sections 2 and 3, we explained the way to build a model and to setup the intial state. Now, it is the time to run a simulation. Corresponding to World classes, six Simulator classes are there: spatiocyte.SpatiocyteSimulator, egfrd.EGFRDSimulator, bd.BDSimulator, meso.MesoscopicSimulator, gillespie.GillespieSimulator, and ode.ODESimulator. Each Simulator class only accepts the corresponding type of World, but all of them allow the same Model.
End of explanation
from ecell4_base import *
Explanation: 4.1. How to Setup a Simulator
Except for the initialization (so-called constructor function) with arguments specific to the algorithm, all Simulators have the same APIs.
End of explanation
from ecell4 import species_attributes, reaction_rules, get_model
with species_attributes():
    A | B | C | {'D': 1, 'radius': 0.005}
with reaction_rules():
    A + B == C | (0.01, 0.3)
m = get_model()
w1 = gillespie.World()
w2 = ode.World()
w3 = spatiocyte.World()
w4 = bd.World()
w5 = meso.World()
w6 = egfrd.World()
Explanation: Before constructing a Simulator, parepare a Model and a World corresponding to the type of Simulator.
End of explanation
sim1 = gillespie.Simulator(w1, m)
sim2 = ode.Simulator(w2, m)
sim3 = spatiocyte.Simulator(w3, m)
sim4 = bd.Simulator(w4, m)
sim5 = meso.Simulator(w5, m)
sim6 = egfrd.Simulator(w6, m)
Explanation: Simulator requires both Model and World in this order at the construction.
End of explanation
w1.bind_to(m)
w2.bind_to(m)
w3.bind_to(m)
w4.bind_to(m)
w5.bind_to(m)
w6.bind_to(m)
sim1 = gillespie.Simulator(w1)
sim2 = ode.Simulator(w2)
sim3 = spatiocyte.Simulator(w3)
sim4 = bd.Simulator(w4)
sim5 = meso.Simulator(w5)
sim6 = egfrd.Simulator(w6)
Explanation: If you bind the Model to the World, you need only the World to create a Simulator.
End of explanation
print(sim1.model(), sim1.world())
print(sim2.model(), sim2.world())
print(sim3.model(), sim3.world())
print(sim4.model(), sim4.world())
print(sim5.model(), sim5.world())
print(sim6.model(), sim6.world())
Explanation: Of course, the Model and World bound to a Simulator can be drawn from Simulator in the way below:
End of explanation
w1.add_molecules(Species('C'), 60)
w2.add_molecules(Species('C'), 60)
w3.add_molecules(Species('C'), 60)
w4.add_molecules(Species('C'), 60)
w5.add_molecules(Species('C'), 60)
w6.add_molecules(Species('C'), 60)
sim1.initialize()
sim2.initialize()
sim3.initialize()
sim4.initialize()
sim5.initialize()
sim6.initialize()
Explanation: After updating the World by yourself, you must initialize the internal state of a Simulator before running simulation.
End of explanation
sim2.set_dt(1e-6)  # ode.Simulator. This is optional
sim4.set_dt(1e-6)  # bd.Simulator
Explanation: For algorithms with a fixed step interval, the Simulator also requires dt.
End of explanation
print(sim1.t(), sim1.next_time(), sim1.dt())
print(sim2.t(), sim2.next_time(), sim2.dt())  # => (0.0, 1e-6, 1e-6)
print(sim3.t(), sim3.next_time(), sim3.dt())
print(sim4.t(), sim4.next_time(), sim4.dt())  # => (0.0, 1e-6, 1e-6)
print(sim5.t(), sim5.next_time(), sim5.dt())
print(sim6.t(), sim6.next_time(), sim6.dt())  # => (0.0, 0.0, 0.0)
sim1.step()
sim2.step()
sim3.step()
sim4.step()
sim5.step()
sim6.step()
print(sim1.t())
print(sim2.t())  # => 1e-6
print(sim3.t())
print(sim4.t())  # => 1e-6
print(sim5.t())
print(sim6.t())  # => 0.0
Explanation: 4.2. Running Simulations
For running simulations, Simulator provides two APIs, step and run.
step() advances a simulation for the time that the Simulator expects, next_time().
End of explanation
print(sim1.last_reactions())
# print(sim2.last_reactions())
print(sim3.last_reactions())
print(sim4.last_reactions())
print(sim5.last_reactions())
print(sim6.last_reactions())
Explanation: last_reactions() returns a list of pairs of ReactionRule and ReactionInfo which occurs at the last step. Each algorithm have its own implementation of ReactionInfo. See help(module.ReactionInfo) for details.
End of explanation
print(sim1.step(1.0), sim1.t())
print(sim2.step(1.0), sim2.t())
print(sim3.step(1.0), sim3.t())
print(sim4.step(1.0), sim4.t())
print(sim5.step(1.0), sim5.t())
print(sim6.step(1.0), sim6.t())
Explanation: step(upto) advances a simulation for next_time if next_time is less than upto, or for upto otherwise. step(upto) returns whether the time does NOT reach the limit, upto.
End of explanation
while sim1.step(1.0): pass
while sim2.step(0.001): pass
while sim3.step(0.001): pass
while sim4.step(0.001): pass
while sim5.step(1.0): pass
while sim6.step(0.001): pass
print(sim1.t())  # => 1.0
print(sim2.t())  # => 0.001
print(sim3.t())  # => 0.001
print(sim4.t())  # => 0.001
print(sim5.t())  # => 1.0
print(sim6.t())  # => 0.001
Explanation: To run a simulation just until the time, upto, call step(upto) while it returns True.
End of explanation
sim1.run(1.0)
sim2.run(0.001)
sim3.run(0.001)
sim4.run(0.001)
sim5.run(1.0)
sim6.run(0.001)
print(sim1.t())  # => 2.0
print(sim2.t())  # => 0.002
print(sim3.t())  # => 0.002
print(sim4.t())  # => 0.002
print(sim5.t())  # => 2.0
print(sim6.t())  # => 0.02
Explanation: This is just what run does. run(tau) advances a simulation upto t()+tau.
End of explanation
print(sim1.num_steps())
print(sim2.num_steps())
print(sim3.num_steps())
print(sim4.num_steps())
print(sim5.num_steps())
print(sim6.num_steps())
Explanation: num_steps returns the number of steps during the simulation.
End of explanation
def singlerun(f, m):
    w = f.world(Real3(1, 1, 1))
    w.bind_to(m)
    w.add_molecules(Species('C'), 60)
    
    sim = f.simulator(w)
    sim.run(0.01)
    print(sim.t(), w.num_molecules(Species('C')))
Explanation: 4.3. Capsulizing Algorithm into a Factory Class
Owing to the portability of a Model and consistent APIs of Worlds and Simulators, it is very easy to write a script common in algorithms. However, when switching the algorithm, still we have to rewrite the name of classes in the code, one by one.
To avoid the trouble, E-Cell4 also provides a Factory class for each algorithm. Factory encapsulates World and Simulator with their arguments needed for the construction. By using Factory class, your script could be portable and robust agaist changes in the algorithm.
Factory just provides two functions, world and simulator.
End of explanation
singlerun(gillespie.Factory(), m)
singlerun(ode.Factory(), m)
singlerun(spatiocyte.Factory(), m)
singlerun(bd.Factory(bd_dt_factor=1), m)
singlerun(meso.Factory(), m)
singlerun(egfrd.Factory(), m)
Explanation: singlerun above is free from the algorithm. Thus, by just switching Factory, you can easily compare the results.
End of explanation
from ecell4.util import run_simulation
print(run_simulation(0.01, model=m, y0={'C': 60}, return_type='array', solver=gillespie.Factory())[-1])
print(run_simulation(0.01, model=m, y0={'C': 60}, return_type='array', solver=ode.Factory())[-1])
print(run_simulation(0.01, model=m, y0={'C': 60}, return_type='array', solver=spatiocyte.Factory())[-1])
print(run_simulation(0.01, model=m, y0={'C': 60}, return_type='array', solver=bd.Factory(bd_dt_factor=1))[-1])
print(run_simulation(0.01, model=m, y0={'C': 60}, return_type='array', solver=meso.Factory())[-1])
print(run_simulation(0.01, model=m, y0={'C': 60}, return_type='array', solver=egfrd.Factory())[-1])
Explanation: When you need to provide several parameters to initialize World or Simulator, run_simulation also accepts Factory instead of solver.
End of explanation
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