Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 12
sizeStates = 3
sizeConstants = 19
from math import *
from numpy import *
def createLegends():
legend_states = [""] * sizeStates
legend_rates = [""] * sizeStates
legend_algebraic = [""] * sizeAlgebraic
legend_voi = ""
legend_constants = [""] * sizeConstants
legend_voi = "time in component environment (dimensionless)"
legend_states[0] = "C in component C (dimensionless)"
legend_constants[0] = "gamma in component C (dimensionless)"
legend_algebraic[5] = "Vs in component Vs (dimensionless)"
legend_algebraic[0] = "V1 in component V1 (dimensionless)"
legend_algebraic[10] = "V2 in component V2 (dimensionless)"
legend_algebraic[6] = "Vd in component Vd (dimensionless)"
legend_states[1] = "K in component K (dimensionless)"
legend_states[2] = "RP in component RP (dimensionless)"
legend_algebraic[11] = "V3 in component V3 (dimensionless)"
legend_algebraic[1] = "V4 in component V4 (dimensionless)"
legend_algebraic[2] = "E in component E (dimensionless)"
legend_constants[1] = "sigma in component E (dimensionless)"
legend_algebraic[3] = "RE in component RE (dimensionless)"
legend_algebraic[7] = "KP in component KP (dimensionless)"
legend_algebraic[8] = "KPI in component KPI (dimensionless)"
legend_constants[2] = "thetaI in component KPI (dimensionless)"
legend_algebraic[9] = "I in component I (dimensionless)"
legend_constants[3] = "lambda in component I (dimensionless)"
legend_constants[4] = "thetaE in component RE (dimensionless)"
legend_algebraic[4] = "R in component R (dimensionless)"
legend_constants[5] = "VCs in component Vs (dimensionless)"
legend_constants[6] = "Vsm in component Vs (dimensionless)"
legend_constants[7] = "KsE in component Vs (dimensionless)"
legend_constants[8] = "V1m in component V1 (dimensionless)"
legend_constants[9] = "K1C in component V1 (dimensionless)"
legend_constants[10] = "K1 in component V1 (dimensionless)"
legend_constants[11] = "V2m in component V2 (dimensionless)"
legend_constants[12] = "K2 in component V2 (dimensionless)"
legend_constants[13] = "V3m in component V3 (dimensionless)"
legend_constants[14] = "K3 in component V3 (dimensionless)"
legend_constants[15] = "V4m in component V4 (dimensionless)"
legend_constants[16] = "K4 in component V4 (dimensionless)"
legend_constants[17] = "VdEm in component Vd (dimensionless)"
legend_constants[18] = "KdC in component Vd (dimensionless)"
legend_rates[0] = "d/dt C in component C (dimensionless)"
legend_rates[1] = "d/dt K in component K (dimensionless)"
legend_rates[2] = "d/dt RP in component RP (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 0.38
constants[0] = 1.0
states[1] = 0.1
states[2] = 1.0
constants[1] = 10
constants[2] = 1.0
constants[3] = 1.0
constants[4] = 0.01
constants[5] = 1.0
constants[6] = 1.0
constants[7] = 0.1
constants[8] = 50.0
constants[9] = 0.1
constants[10] = 0.0001
constants[11] = 40
constants[12] = 0.0001
constants[13] = 3000
constants[14] = 0.0001
constants[15] = 3.0
constants[16] = 0.0001
constants[17] = 1000.0
constants[18] = 0.005
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rootfind_0(voi, constants, rates, states, algebraic)
algebraic[5] = constants[5]+constants[6]*(algebraic[2]/(constants[7]+algebraic[2]))
algebraic[0] = constants[8]*(states[0]/(constants[9]+states[0]))*(states[1]/(constants[10]+states[1]))
rootfind_1(voi, constants, rates, states, algebraic)
algebraic[10] = constants[11]*(algebraic[7]/(constants[12]+algebraic[7]))
algebraic[6] = states[0]+constants[17]*algebraic[2]*(states[0]/(constants[18]+states[0]))
rates[0] = (algebraic[5]+constants[0]*algebraic[10])-(constants[0]*algebraic[0]+algebraic[6])
rates[1] = algebraic[10]-algebraic[0]
algebraic[11] = constants[13]*algebraic[7]*(algebraic[3]/(constants[14]+algebraic[3]))
algebraic[1] = constants[15]*(states[2]/(constants[16]+states[2]))
rates[2] = algebraic[11]-algebraic[1]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[5] = constants[5]+constants[6]*(algebraic[2]/(constants[7]+algebraic[2]))
algebraic[0] = constants[8]*(states[0]/(constants[9]+states[0]))*(states[1]/(constants[10]+states[1]))
algebraic[10] = constants[11]*(algebraic[7]/(constants[12]+algebraic[7]))
algebraic[6] = states[0]+constants[17]*algebraic[2]*(states[0]/(constants[18]+states[0]))
algebraic[11] = constants[13]*algebraic[7]*(algebraic[3]/(constants[14]+algebraic[3]))
algebraic[1] = constants[15]*(states[2]/(constants[16]+states[2]))
return algebraic
initialGuess0 = None
def rootfind_0(voi, constants, rates, states, algebraic):
"""Calculate values of algebraic variables for DAE"""
from scipy.optimize import fsolve
global initialGuess0
if initialGuess0 is None: initialGuess0 = ones(3)*0.1
if not iterable(voi):
soln = fsolve(residualSN_0, initialGuess0, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
initialGuess0 = soln
algebraic[2] = soln[0]
algebraic[3] = soln[1]
algebraic[4] = soln[2]
else:
for (i,t) in enumerate(voi):
soln = fsolve(residualSN_0, initialGuess0, args=(algebraic[:,i], voi[i], constants, rates[:i], states[:,i]), xtol=1E-6)
initialGuess0 = soln
algebraic[2][i] = soln[0]
algebraic[3][i] = soln[1]
algebraic[4][i] = soln[2]
def residualSN_0(algebraicCandidate, algebraic, voi, constants, rates, states):
resid = array([0.0] * 3)
algebraic[2] = algebraicCandidate[0]
algebraic[3] = algebraicCandidate[1]
algebraic[4] = algebraicCandidate[2]
resid[0] = (algebraic[2]-(1.00000-constants[1]*algebraic[3]))
resid[1] = (algebraic[3]-constants[4]*algebraic[4]*algebraic[2])
resid[2] = (algebraic[4]-(1.00000-(states[2]+algebraic[3])))
return resid
initialGuess1 = None
def rootfind_1(voi, constants, rates, states, algebraic):
"""Calculate values of algebraic variables for DAE"""
from scipy.optimize import fsolve
global initialGuess1
if initialGuess1 is None: initialGuess1 = ones(3)*0.1
if not iterable(voi):
soln = fsolve(residualSN_1, initialGuess1, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
initialGuess1 = soln
algebraic[7] = soln[0]
algebraic[8] = soln[1]
algebraic[9] = soln[2]
else:
for (i,t) in enumerate(voi):
soln = fsolve(residualSN_1, initialGuess1, args=(algebraic[:,i], voi[i], constants, rates[:i], states[:,i]), xtol=1E-6)
initialGuess1 = soln
algebraic[7][i] = soln[0]
algebraic[8][i] = soln[1]
algebraic[9][i] = soln[2]
def residualSN_1(algebraicCandidate, algebraic, voi, constants, rates, states):
resid = array([0.0] * 3)
algebraic[7] = algebraicCandidate[0]
algebraic[8] = algebraicCandidate[1]
algebraic[9] = algebraicCandidate[2]
resid[0] = (algebraic[7]-(1.00000-(algebraic[8]+states[1])))
resid[1] = (algebraic[8]-constants[2]*algebraic[7]*algebraic[9])
resid[2] = (algebraic[9]-(1.00000-constants[3]*algebraic[8]))
return resid
def solve_model():
"""Solve model with ODE solver"""
from scipy.integrate import ode
# Initialise constants and state variables
(init_states, constants) = initConsts()
# Set timespan to solve over
voi = linspace(0, 10, 500)
# Construct ODE object to solve
r = ode(computeRates)
r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1)
r.set_initial_value(init_states, voi[0])
r.set_f_params(constants)
# Solve model
states = array([[0.0] * len(voi)] * sizeStates)
states[:,0] = init_states
for (i,t) in enumerate(voi[1:]):
if r.successful():
r.integrate(t)
states[:,i+1] = r.y
else:
break
# Compute algebraic variables
algebraic = computeAlgebraic(constants, states, voi)
return (voi, states, algebraic)
def plot_model(voi, states, algebraic):
"""Plot variables against variable of integration"""
import pylab
(legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends()
pylab.figure(1)
pylab.plot(voi,vstack((states,algebraic)).T)
pylab.xlabel(legend_voi)
pylab.legend(legend_states + legend_algebraic, loc='best')
pylab.show()
if __name__ == "__main__":
(voi, states, algebraic) = solve_model()
plot_model(voi, states, algebraic)