if norm > 1:
s /= norm
i /= norm
s.label = 'Susceptible'
i.label = 'Infected'
# create recovered field
r = ScalarField(s.grid, data=1 - s - i, label='Recovered')
return FieldCollection([s, i, r])
def evolution_rate(self, state, t=0):
s, i, r = state
diff = self.diffusivity
ds_dt = diff * s.laplace(self.bc) - self.beta * i * s
di_dt = diff * i.laplace(self.bc) + self.beta * i * s - self.gamma * i
dr_dt = diff * r.laplace(self.bc) + self.gamma * i
return FieldCollection([ds_dt, di_dt, dr_dt])
eq = SIRPDE(beta=2, gamma=0.1)
# initialize state
grid = UnitGrid([32, 32])
s = ScalarField(grid, 1)
i = ScalarField(grid, 0)
i.data[0, 0] = 1
state = eq.get_state(s, i)
# simulate the pde
tracker = PlotTracker(interval=10, plot_args={'vmin': 0, 'vmax': 1})
sol = eq.solve(state, t_range=50, dt=1e-2, tracker=['progress', tracker])
s /= norm
i /= norm
s.label = "Susceptible"
i.label = "Infected"
# create recovered field
r = ScalarField(s.grid, data=1 - s - i, label="Recovered")
return FieldCollection([s, i, r])
def evolution_rate(self, state, t=0):
s, i, r = state
diff = self.diffusivity
ds_dt = diff * s.laplace(self.bc) - self.beta * i * s
di_dt = diff * i.laplace(self.bc) + self.beta * i * s - self.gamma * i
dr_dt = diff * r.laplace(self.bc) + self.gamma * i
return FieldCollection([ds_dt, di_dt, dr_dt])
eq = SIRPDE(beta=2, gamma=0.1)
# initialize state
grid = UnitGrid([32, 32])
s = ScalarField(grid, 1)
i = ScalarField(grid, 0)
i.data[0, 0] = 1
state = eq.get_state(s, i)
# simulate the pde
tracker = PlotTracker(interval=10, plot_args={"vmin": 0, "vmax": 1})
sol = eq.solve(state, t_range=50, dt=1e-2, tracker=["progress", tracker])
#!/usr/bin/env python3
from pde import (DiffusionPDE, UnitGrid, ScalarField, MemoryStorage,
PlotTracker, PrintTracker, RealtimeIntervals)
eq = DiffusionPDE() # define the pde
grid = UnitGrid([16, 16]) # generate grid
state = ScalarField.random_uniform(grid, 0.2,
0.3) # generate initial condition
storage = MemoryStorage()
trackers = [
'progress', # show progress bar during simulation
'steady_state', # abort when steady state is reached
storage.tracker(interval=1), # store data every simulation time unit
PlotTracker(show=True), # show images during simulation
# print some output every 5 real seconds:
PrintTracker(interval=RealtimeIntervals(duration=5))
]
eq.solve(state, 10, dt=0.1, tracker=trackers)
storage[0].plot(show=True)
"""
Create a movie live
===================
This example shows how to create a movie while running the simulation. Making movies
requires that `ffmpeg` is installed in a standard location.
"""
from pde import DiffusionPDE, PlotTracker, ScalarField, UnitGrid
grid = UnitGrid([16, 16]) # generate grid
state = ScalarField.random_uniform(grid, 0.2,
0.3) # generate initial condition
tracker = PlotTracker(movie="diffusion.mov") # create movie tracker
eq = DiffusionPDE() # define the physics
eq.solve(state, t_range=2, dt=0.005, tracker=tracker)