Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 19
sizeStates = 17
sizeConstants = 18
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] = "A in component differentials (molar)"
legend_states[1] = "G in component differentials (molar)"
legend_states[2] = "GA in component differentials (molar)"
legend_states[3] = "T in component differentials (molar)"
legend_states[4] = "R in component differentials (molar)"
legend_states[5] = "GT in component differentials (molar)"
legend_states[6] = "GD in component differentials (molar)"
legend_states[7] = "Pi_ in component differentials (molar)"
legend_states[8] = "D in component differentials (molar)"
legend_states[9] = "RG in component differentials (molar)"
legend_states[10] = "RGT in component differentials (molar)"
legend_states[11] = "GAT in component differentials (molar)"
legend_states[12] = "GAD in component differentials (molar)"
legend_states[13] = "RGD in component differentials (molar)"
legend_states[14] = "RGA in component differentials (molar)"
legend_states[15] = "RGAT in component differentials (molar)"
legend_states[16] = "RGAD in component differentials (molar)"
legend_algebraic[7] = "A2 in component A2 (molar_per_second)"
legend_algebraic[8] = "A3 in component A3 (molar_per_second)"
legend_algebraic[16] = "A5 in component A5 (molar_per_second)"
legend_algebraic[6] = "R2 in component R2 (molar_per_second)"
legend_algebraic[9] = "R3 in component R3 (molar_per_second)"
legend_algebraic[14] = "R4 in component R4 (molar_per_second)"
legend_algebraic[0] = "T1 in component T1 (molar_per_second)"
legend_algebraic[5] = "T3 in component T3 (molar_per_second)"
legend_algebraic[15] = "T4 in component T4 (molar_per_second)"
legend_algebraic[3] = "P1 in component P1 (molar_per_second)"
legend_algebraic[12] = "P2 in component P2 (molar_per_second)"
legend_algebraic[10] = "P3 in component P3 (molar_per_second)"
legend_algebraic[17] = "P4 in component P4 (molar_per_second)"
legend_algebraic[4] = "D1 in component D1 (molar_per_second)"
legend_algebraic[13] = "D2 in component D2 (molar_per_second)"
legend_algebraic[11] = "D3 in component D3 (molar_per_second)"
legend_algebraic[18] = "D4 in component D4 (molar_per_second)"
legend_algebraic[1] = "Z in component output (dimensionless)"
legend_algebraic[2] = "v in component output (per_second)"
legend_constants[0] = "G_tot in component output (molar)"
legend_constants[1] = "k1 in component P1 (per_second)"
legend_constants[2] = "k1 in component P2 (per_second)"
legend_constants[3] = "k1 in component P3 (per_second)"
legend_constants[4] = "k1 in component P4 (per_second)"
legend_constants[5] = "k1 in component T1 (per_molar_per_second)"
legend_constants[6] = "k1 in component D1 (per_second)"
legend_constants[7] = "k1 in component T3 (per_molar_per_second)"
legend_constants[8] = "k2 in component R2 (per_second)"
legend_constants[9] = "k1 in component A2 (per_molar_per_second)"
legend_constants[10] = "k2 in component A3 (per_second)"
legend_constants[11] = "k1 in component R3 (per_molar_per_second)"
legend_constants[12] = "k1 in component D3 (per_second)"
legend_constants[13] = "k1 in component D2 (per_second)"
legend_constants[14] = "k1 in component R4 (per_molar_per_second)"
legend_constants[15] = "k1 in component T4 (per_molar_per_second)"
legend_constants[16] = "k1 in component A5 (per_molar_per_second)"
legend_constants[17] = "k1 in component D4 (per_second)"
legend_rates[0] = "d/dt A in component differentials (molar)"
legend_rates[1] = "d/dt G in component differentials (molar)"
legend_rates[2] = "d/dt GA in component differentials (molar)"
legend_rates[3] = "d/dt T in component differentials (molar)"
legend_rates[4] = "d/dt R in component differentials (molar)"
legend_rates[5] = "d/dt GT in component differentials (molar)"
legend_rates[6] = "d/dt GD in component differentials (molar)"
legend_rates[7] = "d/dt Pi_ in component differentials (molar)"
legend_rates[8] = "d/dt D in component differentials (molar)"
legend_rates[9] = "d/dt RG in component differentials (molar)"
legend_rates[10] = "d/dt RGT in component differentials (molar)"
legend_rates[11] = "d/dt GAT in component differentials (molar)"
legend_rates[12] = "d/dt GAD in component differentials (molar)"
legend_rates[13] = "d/dt RGD in component differentials (molar)"
legend_rates[14] = "d/dt RGA in component differentials (molar)"
legend_rates[15] = "d/dt RGAT in component differentials (molar)"
legend_rates[16] = "d/dt RGAD in component differentials (molar)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 0
states[1] = 0
states[2] = 0
states[3] = 0.000468
states[4] = 0
states[5] = 0
states[6] = 1e-8
states[7] = 0.0044
states[8] = 0.000149
states[9] = 0
states[10] = 0
states[11] = 0
states[12] = 0
states[13] = 0
states[14] = 0
states[15] = 0
states[16] = 0
constants[0] = 1e-8
constants[1] = 0.013
constants[2] = 25
constants[3] = 0.013
constants[4] = 25
constants[5] = 529000
constants[6] = 0.0001
constants[7] = 853000
constants[8] = 1.28
constants[9] = 386000
constants[10] = 0.95
constants[11] = 94700000
constants[12] = 2
constants[13] = 0.0001
constants[14] = 22800000
constants[15] = 1620000
constants[16] = 6300000
constants[17] = 2.75
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[0] = constants[5]*states[1]*states[3]
algebraic[4] = constants[6]*states[6]
rates[1] = algebraic[4]-algebraic[0]
algebraic[7] = constants[9]*states[5]*states[0]
algebraic[6] = -constants[8]*states[10]
algebraic[3] = constants[1]*states[5]
rates[5] = ((algebraic[0]-algebraic[3])-algebraic[6])-algebraic[7]
algebraic[8] = -constants[10]*states[12]
algebraic[9] = constants[11]*states[6]*states[4]
rates[6] = ((algebraic[3]-algebraic[4])-algebraic[8])-algebraic[9]
algebraic[5] = constants[7]*states[9]*states[3]
algebraic[11] = constants[12]*states[13]
rates[9] = -algebraic[5]+algebraic[11]
algebraic[10] = constants[3]*states[10]
rates[13] = (algebraic[9]+algebraic[10])-algebraic[11]
algebraic[12] = constants[2]*states[11]
rates[11] = algebraic[7]-algebraic[12]
algebraic[13] = constants[13]*states[12]
rates[12] = (algebraic[8]+algebraic[12])-algebraic[13]
algebraic[14] = constants[14]*states[2]*states[4]
rates[2] = algebraic[13]-algebraic[14]
rates[4] = -(algebraic[6]+algebraic[9]+algebraic[14])
algebraic[15] = constants[15]*states[14]*states[3]
rates[3] = -(algebraic[0]+algebraic[5]+algebraic[15])
algebraic[16] = constants[16]*states[10]*states[0]
rates[0] = -(algebraic[7]+algebraic[8]+algebraic[16])
rates[10] = ((algebraic[5]+algebraic[6])-algebraic[10])-algebraic[16]
algebraic[17] = constants[4]*states[15]
rates[7] = algebraic[3]+algebraic[10]+algebraic[12]+algebraic[17]
rates[15] = (algebraic[15]+algebraic[16])-algebraic[17]
algebraic[18] = constants[17]*states[16]
rates[8] = algebraic[4]+algebraic[11]+algebraic[13]+algebraic[18]
rates[14] = (algebraic[14]-algebraic[15])+algebraic[18]
rates[16] = algebraic[17]-algebraic[18]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = constants[5]*states[1]*states[3]
algebraic[4] = constants[6]*states[6]
algebraic[7] = constants[9]*states[5]*states[0]
algebraic[6] = -constants[8]*states[10]
algebraic[3] = constants[1]*states[5]
algebraic[8] = -constants[10]*states[12]
algebraic[9] = constants[11]*states[6]*states[4]
algebraic[5] = constants[7]*states[9]*states[3]
algebraic[11] = constants[12]*states[13]
algebraic[10] = constants[3]*states[10]
algebraic[12] = constants[2]*states[11]
algebraic[13] = constants[13]*states[12]
algebraic[14] = constants[14]*states[2]*states[4]
algebraic[15] = constants[15]*states[14]*states[3]
algebraic[16] = constants[16]*states[10]*states[0]
algebraic[17] = constants[4]*states[15]
algebraic[18] = constants[17]*states[16]
algebraic[1] = (states[5]+states[10]+states[15]+states[11])/constants[0]
algebraic[2] = (constants[4]*states[15]+constants[2]*states[11]+constants[3]*states[10]+constants[1]*states[5])/constants[0]
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)