Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 13
sizeStates = 6
sizeConstants = 13
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 (second)"
legend_states[0] = "D in component equations (dimensionless)"
legend_states[1] = "A_1 in component equations (dimensionless)"
legend_states[2] = "A_2 in component equations (dimensionless)"
legend_algebraic[0] = "R_off in component equations (dimensionless)"
legend_constants[0] = "x_0 in component equations (dimensionless)"
legend_states[3] = "x_1 in component equations (dimensionless)"
legend_states[4] = "x_2 in component equations (dimensionless)"
legend_algebraic[7] = "g in component equations (per_second)"
legend_algebraic[11] = "f in component equations (per_second)"
legend_algebraic[8] = "h in component equations (per_second)"
legend_algebraic[3] = "lambda_A1 in component equations (dimensionless)"
legend_algebraic[5] = "lambda_A2 in component equations (dimensionless)"
legend_algebraic[4] = "F_t in component equations (dimensionless)"
legend_algebraic[1] = "E_1 in component equations (dimensionless)"
legend_algebraic[2] = "E_2 in component equations (dimensionless)"
legend_algebraic[12] = "dSL_dt in component equations (per_second)"
legend_states[5] = "SL in component equations (dimensionless)"
legend_constants[1] = "k_on in component equations (per_second)"
legend_constants[2] = "k_off in component equations (per_second)"
legend_constants[3] = "f_r in component equations (per_second)"
legend_algebraic[9] = "f_prime in component equations (per_second)"
legend_constants[4] = "f_prime_0 in component equations (per_second)"
legend_constants[5] = "h_0 in component equations (per_second)"
legend_algebraic[10] = "h_prime in component equations (per_second)"
legend_constants[6] = "h_prime_0 in component equations (per_second)"
legend_constants[7] = "g_0 in component equations (per_second)"
legend_constants[8] = "nu in component equations (dimensionless)"
legend_algebraic[6] = "sigma in component equations (dimensionless)"
legend_constants[9] = "sigma_minus in component equations (dimensionless)"
legend_constants[10] = "sigma_plus in component equations (dimensionless)"
legend_constants[11] = "R_T in component equations (dimensionless)"
legend_constants[12] = "e_cb in component equations (dimensionless)"
legend_rates[0] = "d/dt D in component equations (dimensionless)"
legend_rates[1] = "d/dt A_1 in component equations (dimensionless)"
legend_rates[2] = "d/dt A_2 in component equations (dimensionless)"
legend_rates[4] = "d/dt x_2 in component equations (dimensionless)"
legend_rates[3] = "d/dt x_1 in component equations (dimensionless)"
legend_rates[5] = "d/dt SL in component equations (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 0.005
states[1] = 0.005
states[2] = 0.005
constants[0] = 1e-16
states[3] = 1e-16
states[4] = 1e-16
states[5] = 2
constants[1] = 120
constants[2] = 50
constants[3] = 50
constants[4] = 400
constants[5] = 8
constants[6] = 6
constants[7] = 4
constants[8] = 3
constants[9] = 1
constants[10] = 8
constants[11] = 1
constants[12] = 1.5
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[6] = custom_piecewise([greater(states[4] , constants[0]), constants[10] , less(states[4] , constants[0]), constants[9] , True, 0.00000])
algebraic[7] = constants[7]*exp(algebraic[6]*(power(states[4]-constants[0], 2.00000)))
algebraic[8] = constants[5]*exp(algebraic[6]*(power(states[3], 2.00000)))
algebraic[10] = constants[6]*exp(algebraic[6]*(power(states[4], 2.00000)-power(states[3], 2.00000)))
rates[2] = algebraic[8]*states[1]-(algebraic[10]+algebraic[7])*states[2]
algebraic[0] = ((constants[11]-states[0])-states[1])-states[2]
algebraic[3] = states[1]/constants[11]
algebraic[5] = states[2]/constants[11]
algebraic[11] = constants[3]*(power(1.00000+algebraic[3]*(exp((states[3]/constants[0])*(constants[8]-1.00000))-1.00000)+algebraic[5]*(exp((states[4]/constants[0])*(constants[8]-1.00000))-1.00000), 2.00000))
algebraic[9] = constants[4]*exp(algebraic[6]*(power(states[3], 2.00000)))
rates[0] = (constants[1]*algebraic[0]+algebraic[9]*states[1]+algebraic[7]*states[2])-(constants[2]+algebraic[11])*states[0]
rates[1] = (algebraic[11]*states[0]+algebraic[10]*states[2])-(algebraic[9]+algebraic[8])*states[1]
algebraic[12] = custom_piecewise([greater(voi , 0.00100000) & less(voi , 0.00200000), 21.2000 , True, 0.00000])
rates[4] = custom_piecewise([equal(states[2] , 0.00000), algebraic[12] , True, ((-algebraic[8]*states[1])/states[2])*(states[4]-constants[0])+algebraic[12]])
rates[3] = custom_piecewise([equal(states[1] , 0.00000), algebraic[12] , True, -((algebraic[11]*states[0])/states[1]+(algebraic[10]*states[2])/states[1])*states[3]+algebraic[12]])
rates[5] = algebraic[12]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[6] = custom_piecewise([greater(states[4] , constants[0]), constants[10] , less(states[4] , constants[0]), constants[9] , True, 0.00000])
algebraic[7] = constants[7]*exp(algebraic[6]*(power(states[4]-constants[0], 2.00000)))
algebraic[8] = constants[5]*exp(algebraic[6]*(power(states[3], 2.00000)))
algebraic[10] = constants[6]*exp(algebraic[6]*(power(states[4], 2.00000)-power(states[3], 2.00000)))
algebraic[0] = ((constants[11]-states[0])-states[1])-states[2]
algebraic[3] = states[1]/constants[11]
algebraic[5] = states[2]/constants[11]
algebraic[11] = constants[3]*(power(1.00000+algebraic[3]*(exp((states[3]/constants[0])*(constants[8]-1.00000))-1.00000)+algebraic[5]*(exp((states[4]/constants[0])*(constants[8]-1.00000))-1.00000), 2.00000))
algebraic[9] = constants[4]*exp(algebraic[6]*(power(states[3], 2.00000)))
algebraic[12] = custom_piecewise([greater(voi , 0.00100000) & less(voi , 0.00200000), 21.2000 , True, 0.00000])
algebraic[1] = constants[12]*states[1]
algebraic[2] = constants[12]*states[2]
algebraic[4] = algebraic[1]*states[3]+algebraic[2]*states[4]
return algebraic
def custom_piecewise(cases):
"""Compute result of a piecewise function"""
return select(cases[0::2],cases[1::2])
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)