def test_SimulateCTMC(self):
'''
Stochastic ode under the interpretation that we have a continuous
time Markov chain as the underlying process
'''
#x0 = [1,1.27e-6,0] # original
x0 = [2362206.0, 3.0, 0.0]
t = numpy.linspace(0, 250, 50)
stateList = ['S', 'I', 'R']
paramList = ['beta', 'gamma', 'N']
transitionList = [
Transition(origState='S',
destState='I',
equation='beta*S*I/N',
transitionType=TransitionType.T),
Transition(origState='I',
destState='R',
equation='gamma*I',
transitionType=TransitionType.T)
]
# initialize the model
odeS = SimulateOdeModel(stateList,
paramList,
transitionList=transitionList)
odeS.setParameters([0.5, 1.0 / 3.0, x0[0]]).setInitialValue(x0, t[0])
solution = odeS.integrate(t[1::])
odeS.transitionMean(x0, t[0])
odeS.transitionVar(x0, t[0])
odeS.transitionMean(solution[10, :], t[10])
odeS.transitionVar(solution[10, :], t[10])
simX, simT = odeS.simulateJump(250, 3, full_output=True)
def test_stochastic(self):
# Tests the following system simulating jumps
# A + A -> C
# A + B -> D
# \emptyset -> A
# \emptyset -> B
stateList = ['A', 'B', 'C', 'D']
paramList = ['k1', 'k2', 'k3', 'k4']
transitionList = [
Transition(origState=('A','A'), destState='C', equation='A * (A - 1) * k1',
transitionType=TransitionType.T),
Transition(origState=('A','B'), destState='D', equation='A * B * k2',
transitionType=TransitionType.T)
]
# our birth and deaths
birthDeathList = [
Transition(origState='A', equation='k3', transitionType=TransitionType.B),
Transition(origState='B', equation='k4', transitionType=TransitionType.B)
]
ode = SimulateOdeModel(stateList,
paramList,
birthDeathList=birthDeathList,
transitionList=transitionList)
x0 = [0,0,0,0]
t = numpy.linspace(0, 100, 100)
ode.setParameters(paramEval).setInitialValue(x0, t[0])
simX, simT = ode.simulateJump(t, 5, full_output=True)
def test_SimulateCTMC(self):
'''
Stochastic ode under the interpretation that we have a continuous
time Markov chain as the underlying process
'''
#x0 = [1,1.27e-6,0] # original
x0 = [2362206.0, 3.0, 0.0]
t = numpy.linspace(0, 250, 50)
stateList = ['S','I','R']
paramList = ['beta','gamma','N']
transitionList = [
Transition(origState='S',destState='I',equation='beta * S * I/N',transitionType=TransitionType.T),
Transition(origState='I',destState='R',equation='gamma * I',transitionType=TransitionType.T)
]
# initialize the model
odeS = SimulateOdeModel(stateList,
paramList,
transitionList=transitionList)
odeS.setParameters([0.5, 1.0/3.0, x0[0]]).setInitialValue(x0, t[0])
solution = odeS.integrate(t[1::])
odeS.transitionMean(x0,t[0])
odeS.transitionVar(x0,t[0])
odeS.transitionMean(solution[10,:],t[10])
odeS.transitionVar(solution[10,:],t[10])
simX,simT = odeS.simulateJump(250, 3, full_output=True)
def test_simulateParam2(self):
'''
Stochastic ode under the interpretation that the parameters follow
some sort of distribution. In this case, a function handle which
has the same name as R
'''
t0 = 0
# the initial state, normalized to zero one
x0 = [1, 1.27e-6, 0]
# set the time sequence that we would like to observe
t = numpy.linspace(0, 150, 100)
# Standard. Find the solution.
ode = common_models.SIR()
ode.setParameters([0.5, 1.0 / 3.0])
ode.setInitialValue(x0, t0)
solutionReference = ode.integrate(t[1::], full_output=False)
# now we need to define our ode explicitly
stateList = ['S', 'I', 'R']
paramList = ['beta', 'gamma']
transitionList = [
Transition(origState='S',
destState='I',
equation='beta*S*I',
transitionType=TransitionType.T),
Transition(origState='I',
destState='R',
equation='gamma*I',
transitionType=TransitionType.T)
]
# our stochastic version
odeS = SimulateOdeModel(stateList,
paramList,
transitionList=transitionList)
# define our parameters in terms of two gamma distributions
# where the expected values are the same as before [0.5,1.0/3.0]
d = dict()
d['beta'] = (rgamma, {'shape': 100.0, 'rate': 200.0})
d['gamma'] = (rgamma, (100.0, 300.0))
odeS.setParameters(d).setInitialValue(x0, t0)
# now we generate the solutions
solutionDiff = odeS.simulateParam(t[1::], 1000) - solutionReference
# test :)
if numpy.any(abs(solutionDiff) >= 0.2):
raise Exception("Possible problem with simulating the parameters")
def test_simulateParam2(self):
'''
Stochastic ode under the interpretation that the parameters follow
some sort of distribution. In this case, a function handle which
has the same name as R
'''
t0 = 0
# the initial state, normalized to zero one
x0 = [1,1.27e-6,0]
# set the time sequence that we would like to observe
t = numpy.linspace(0, 150, 100)
# Standard. Find the solution.
ode = common_models.SIR()
ode.setParameters([0.5,1.0/3.0])
ode.setInitialValue(x0,t0)
solutionReference = ode.integrate(t[1::],full_output=False)
# now we need to define our ode explicitly
stateList = ['S','I','R']
paramList = ['beta','gamma']
transitionList = [
Transition(origState='S',destState='I',equation='beta * S * I',transitionType=TransitionType.T),
Transition(origState='I',destState='R',equation='gamma * I',transitionType=TransitionType.T)
]
# our stochastic version
odeS = SimulateOdeModel(stateList,
paramList,
transitionList=transitionList)
# define our parameters in terms of two gamma distributions
# where the expected values are the same as before [0.5,1.0/3.0]
d = dict()
d['beta'] = (rgamma,{'shape':100.0,'rate':200.0})
d['gamma'] = (rgamma,(100.0,300.0))
odeS.setParameters(d).setInitialValue(x0,t0)
# now we generate the solutions
solutionDiff = odeS.simulateParam(t[1::],1000) - solutionReference
# test :)
if numpy.any(abs(solutionDiff)>=0.2):
raise Exception("Possible problem with simulating the parameters")
def test_stochastic(self):
# Tests the following system simulating jumps
# A + A -> C
# A + B -> D
# \emptyset -> A
# \emptyset -> B
stateList = ['A', 'B', 'C', 'D']
paramList = ['k1', 'k2', 'k3', 'k4']
transitionList = [
Transition(origState=('A', 'A'),
destState='C',
equation='A * (A - 1) * k1',
transitionType=TransitionType.T),
Transition(origState=('A', 'B'),
destState='D',
equation='A * B * k2',
transitionType=TransitionType.T)
]
# our birth and deaths
birthDeathList = [
Transition(origState='A',
equation='k3',
transitionType=TransitionType.B),
Transition(origState='B',
equation='k4',
transitionType=TransitionType.B)
]
ode = SimulateOdeModel(stateList,
paramList,
birthDeathList=birthDeathList,
transitionList=transitionList)
x0 = [0, 0, 0, 0]
t = numpy.linspace(0, 100, 100)
ode.setParameters(paramEval).setInitialValue(x0, t[0])
simX, simT = ode.simulateJump(t, 5, full_output=True)
