x0 = [1,1.27e-6,0]
# params
paramEval = [('b',0.5), ('k',1.0/3.0)]
# initialize the model
ode = modelDef.SIR().setParameters(paramEval).setInitialValue(x0,t0)
# set the time sequence that we would like to observe
t = numpy.linspace(1, 150, 100)
numStep = len(t)
# Standard. Find the solution.
solution = ode.integrate(t)
y = solution[1::,1:2]
theta = [0.4,1.0/2.0]
objSIR = odeLossFunc.squareLoss(theta,ode,x0,t0,t,y,['I','R'])
lb = numpy.array([0.,0.],float)
ub = numpy.array([2.,2.],float)
pyOptimUtil.gradient.simplexGradient
beta,h,adjustedStepSize,info = pyOptimUtil.gradient.simplexGradient.linear(objSIR.cost, theta, h = 0.1, S=None, lb=lb, ub=ub)
info['S'].dot(beta)
numpy.arccos(info['S'].dot(betaNorm))
numpy.arccos(info['S'].dot([0.5,0.5]/numpy.linalg.norm([0.5,0.5])))
numpy.degrees(numpy.arccos(info['S'].dot([0.5,0.5]/numpy.linalg.norm([0.5,0.5]))))
10.0,9.6,5.0,2.0, ### the omega
7.0,0.81,0.80, ### alpha, delta, theta
0.1,1.0]) ### kappa,intervention time
theta3 = [ 2.47063919e-02, 8.34896582e-01, 2.00000000e+00,
6.52250983e+01, 8.88857685e+01, 7.62593478e+00,
3.51943235e+01, 2.77555756e-17, 8.14831909e-01,
3.46944695e-18, 3.73088898e+02, 1.03377245e+01]
theta4 = [ 2.31507228e-02, 1.99997489e+00, 1.45839939e+00,
1.00000000e+02, 1.00000000e+02, 9.87598235e+01,
1.53450124e+01, 1.00000000e-08, 7.10575971e-01,
9.99999990e-01, 3.29899411e+02, 1.28215876e+01]
objLegrand = odeLossFunc.squareLoss(theta,ode,x0,t0,t[1::],y[1::,:],['I','R'],[1175e4,1175e4])
objLegrand.cost(theta)
objLegrand.cost(theta1)
objLegrand.sensitivity(theta,intName='ivode')
objLegrand.sensitivity(theta,intName='lsoda')
ode.Jacobian(x0,t0)
scipy.linalg.eig(ode.Jacobian(x0,t0))[0]
S = solution[:,0]
E = solution[:,1]
I = solution[:,2]
H = solution[:,3]
F = solution[:,4]
R = solution[:,5]
5.0 / 7.0,
2.0 / 7.0, ### the omega
7.0 / 7.0,
0.81,
0.80, ### alpha, delta, theta
300,
12.0
]) ### kappa,intervention time
# starting value
y = numpy.reshape(numpy.append(numpy.array(yCase), numpy.array(yDeath)),
(len(yCase), 2), 'F') / 1175e4
x0 = [1, 49.0 / 1175e4, 0.0, 0.0, 0.0, 29.0 / 1175e4]
t0 = 0
objLegrand = odeLossFunc.squareLoss(theta, ode, x0, t0, t[1::], y[1::, :],
['I', 'R'], [1175e4, 1175e4])
boxBounds = [(0.0, 2.0), (0.0, 2.0), (0.0, 2.0), (0.0, 100.0), (0.0, 100.0),
(0.0, 100.0), (0.0, 100.0), (0.0, 100.0), (0.0, 1.0), (0.0, 1.0),
(0.0, 1000.0), (0.0, 218.0)]
cons = ({
'type': 'ineq',
'fun': lambda x: numpy.array([x[3] - x[5], x[4] - x[5]])
})
npBox = numpy.array(boxBounds)
lb = npBox[:, 0]
ub = npBox[:, 1]
1.0
]) ### kappa,intervention time
theta3 = [
2.47063919e-02, 8.34896582e-01, 2.00000000e+00, 6.52250983e+01,
8.88857685e+01, 7.62593478e+00, 3.51943235e+01, 2.77555756e-17,
8.14831909e-01, 3.46944695e-18, 3.73088898e+02, 1.03377245e+01
]
theta4 = [
2.31507228e-02, 1.99997489e+00, 1.45839939e+00, 1.00000000e+02,
1.00000000e+02, 9.87598235e+01, 1.53450124e+01, 1.00000000e-08,
7.10575971e-01, 9.99999990e-01, 3.29899411e+02, 1.28215876e+01
]
objLegrand = odeLossFunc.squareLoss(theta, ode, x0, t0, t[1::], y[1::, :],
['I', 'R'], [1175e4, 1175e4])
objLegrand.cost()
ode.setParameters(theta).setInitialValue(x0, t0)
objLegrand.cost()
s, o = objLegrand.sensitivity(full_output=True)
j, o = objLegrand.jac(full_output=True)
j1, o1 = objLegrand.jacIV(full_output=True)
s1, o1 = objLegrand.sensitivityIV(full_output=True)
objLegrand.adjointInterpolate()
objLegrand.adjointInterpolate1()
objLegrand.adjointInterpolate2()
10.0,9.6,5.0,2.0, ### the omega
7.0,0.81,0.80, ### alpha, delta, theta
0.1,1.0]) ### kappa,intervention time
theta3 = [ 2.47063919e-02, 8.34896582e-01, 2.00000000e+00,
6.52250983e+01, 8.88857685e+01, 7.62593478e+00,
3.51943235e+01, 2.77555756e-17, 8.14831909e-01,
3.46944695e-18, 3.73088898e+02, 1.03377245e+01]
theta4 = [ 2.31507228e-02, 1.99997489e+00, 1.45839939e+00,
1.00000000e+02, 1.00000000e+02, 9.87598235e+01,
1.53450124e+01, 1.00000000e-08, 7.10575971e-01,
9.99999990e-01, 3.29899411e+02, 1.28215876e+01]
objLegrand = odeLossFunc.squareLoss(theta,ode,x0,t0,t[1::],y[1::,:],['I','R'],[1175e4,1175e4])
objLegrand.cost()
ode.setParameters(theta).setInitialValue(x0,t0)
objLegrand.cost()
s,o = objLegrand.sensitivity(full_output=True)
j,o = objLegrand.jac(full_output=True)
j1,o1 = objLegrand.jacIV(full_output=True)
s1,o1 = objLegrand.sensitivityIV(full_output=True)
objLegrand.adjointInterpolate()
objLegrand.adjointInterpolate1()
objLegrand.adjointInterpolate2()
t = numpy.linspace(0, 150, 100)
numStep = len(t)
# Standard. Find the solution.
ode = modelDef.SIR()
ode.setParameters([0.5,1.0/3.0])
ode.setInitialValue(x0,t0)
solution = ode.integrate(t[1::],full_output=False)
theta = [0.2,0.2]
# y = copy.copy(solution[:,1:2])
# y[1::] = y[1::] + numpy.random.normal(loc=0.0,scale=0.1,size=numStep-1)
# odeSIR = odeLossFunc.squareLoss([0.5,1.0/3.0] ,ode,x0,t0,t[1:len(t)],y[1:len(t)],'R')
objSIR = odeLossFunc.squareLoss(theta,ode,x0,t0,t[1::],solution[1::,1:3],['I','R'])
box = [(0.,2.),(0.,2.)]
npBox = numpy.array(box)
lb = npBox[:,0]
ub = npBox[:,1]
solvers = [
'ralg',
'lincher',
'gsubg',
'scipy_slsqp',
'scipy_cobyla',
'interalg',
'auglag',
'ptn',
