Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 0
sizeStates = 5
sizeConstants = 36
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 (minute)"
legend_states[0] = "x1 in component x1 (microg_l)"
legend_constants[0] = "lambda_1 in component model_parameters (first_order_rate_constant)"
legend_states[1] = "x3 in component x3 (microg_l)"
legend_constants[1] = "a1 in component model_parameters (flux)"
legend_constants[2] = "a2 in component model_parameters (flux)"
legend_constants[3] = "a3 in component model_parameters (first_order_rate_constant)"
legend_constants[4] = "a4 in component model_parameters (second_order_rate_constant)"
legend_constants[5] = "a5 in component model_parameters (per_microg_l)"
legend_constants[6] = "a6 in component model_parameters (per_microg_l2)"
legend_constants[7] = "a7 in component model_parameters (per_microg_l)"
legend_constants[8] = "a8 in component model_parameters (per_microg_l2)"
legend_states[2] = "x2 in component x2 (microg_l)"
legend_constants[9] = "lambda_2 in component model_parameters (first_order_rate_constant)"
legend_constants[10] = "a9 in component model_parameters (flux)"
legend_constants[11] = "a10 in component model_parameters (first_order_rate_constant)"
legend_constants[12] = "a11 in component model_parameters (second_order_rate_constant)"
legend_constants[13] = "a12 in component model_parameters (per_microg_l)"
legend_constants[14] = "a13 in component model_parameters (per_microg_l2)"
legend_constants[15] = "a14 in component model_parameters (per_microg_l)"
legend_constants[16] = "a15 in component model_parameters (per_microg_l2)"
legend_constants[33] = "lambda_3_ in component model_parameters (first_order_rate_constant)"
legend_states[3] = "x4 in component x4 (microg_l)"
legend_states[4] = "x5 in component x5 (microg_l)"
legend_constants[17] = "a16 in component model_parameters (flux)"
legend_constants[18] = "a17 in component model_parameters (first_order_rate_constant)"
legend_constants[19] = "a18 in component model_parameters (second_order_rate_constant)"
legend_constants[20] = "a19 in component model_parameters (first_order_rate_constant)"
legend_constants[21] = "a20 in component model_parameters (second_order_rate_constant)"
legend_constants[22] = "a21 in component model_parameters (per_microg_l)"
legend_constants[23] = "a22 in component model_parameters (per_microg_l2)"
legend_constants[24] = "a23 in component model_parameters (per_microg_l)"
legend_constants[25] = "a24 in component model_parameters (per_microg_l2)"
legend_constants[26] = "a25 in component model_parameters (first_order_rate_constant)"
legend_constants[27] = "a26 in component model_parameters (first_order_rate_constant)"
legend_constants[34] = "lambda_4_ in component model_parameters (first_order_rate_constant)"
legend_constants[28] = "a27 in component model_parameters (first_order_rate_constant)"
legend_constants[35] = "lambda_5_ in component model_parameters (first_order_rate_constant)"
legend_constants[29] = "a28 in component model_parameters (first_order_rate_constant)"
legend_constants[30] = "lambda_3 in component model_parameters (first_order_rate_constant)"
legend_constants[31] = "lambda_4 in component model_parameters (first_order_rate_constant)"
legend_constants[32] = "lambda_5 in component model_parameters (first_order_rate_constant)"
legend_rates[0] = "d/dt x1 in component x1 (microg_l)"
legend_rates[2] = "d/dt x2 in component x2 (microg_l)"
legend_rates[1] = "d/dt x3 in component x3 (microg_l)"
legend_rates[3] = "d/dt x4 in component x4 (microg_l)"
legend_rates[4] = "d/dt x5 in component x5 (microg_l)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 0.01067
constants[0] = 0.059
states[1] = 6.51
constants[1] = 0.000017
constants[2] = 0.0023
constants[3] = 0.6
constants[4] = 45
constants[5] = 36
constants[6] = 216
constants[7] = 0.28
constants[8] = 0.36
states[2] = 0.04665
constants[9] = 0.028
constants[10] = 0.0003
constants[11] = 0.18
constants[12] = 150
constants[13] = 18
constants[14] = 460
constants[15] = 0.46
constants[16] = 0.1
states[3] = 60.61
states[4] = 12.61
constants[17] = 0.04
constants[18] = 150
constants[19] = 3800
constants[20] = 57
constants[21] = 2600
constants[22] = 200
constants[23] = 9400
constants[24] = 10
constants[25] = 320
constants[26] = 0.04
constants[27] = 0.00097
constants[28] = 0.57
constants[29] = 0.0017
constants[30] = 0.0986
constants[31] = 0.024
constants[32] = 3e-5
constants[33] = constants[30]+constants[28]+constants[29]
constants[34] = constants[31]+constants[26]
constants[35] = constants[32]+constants[27]
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[0] = (constants[1]+(constants[2]+constants[3]*states[0]+constants[4]*(power(states[0], 2.00000)))/(1.00000+constants[5]*states[0]+constants[6]*(power(states[0], 2.00000))+constants[7]*states[1]+constants[8]*(power(states[1], 2.00000))))-constants[0]*states[0]
rates[2] = (constants[10]+constants[11]*states[0]+constants[12]*(power(states[0], 2.00000)))/(1.00000+constants[13]*states[0]+constants[14]*(power(states[0], 2.00000))+constants[15]*states[1]+constants[16]*(power(states[1], 2.00000)))-constants[9]*states[2]
rates[1] = (constants[17]+(constants[18]*states[0]+constants[19]*(power(states[0], 2.00000))+constants[20]*states[2]+constants[21]*(power(states[2], 2.00000)))/(1.00000+constants[22]*states[0]+constants[23]*(power(states[0], 2.00000))+constants[24]*states[2]+constants[25]*(power(states[2], 2.00000)))+constants[26]*states[3]+constants[27]*states[4])-constants[33]*states[1]
rates[3] = constants[28]*states[1]-constants[34]*states[3]
rates[4] = constants[29]*states[1]-constants[35]*states[4]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
return algebraic
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)