Generated Code
The following is python code generated by the CellML API from this CellML file. (Back to language selection)
The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 15
sizeStates = 5
sizeConstants = 24
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] = "y0 in component y0 (dimensionless)"
legend_algebraic[10] = "g0 in component y0 (dimensionless)"
legend_algebraic[5] = "r0 in component y0 (dimensionless)"
legend_algebraic[0] = "h0 in component y0 (dimensionless)"
legend_constants[0] = "S0 in component y0 (dimensionless)"
legend_states[1] = "y2 in component y2 (dimensionless)"
legend_constants[1] = "a00 in component model_parameters (dimensionless)"
legend_constants[2] = "a02 in component model_parameters (dimensionless)"
legend_constants[3] = "c0 in component model_parameters (first_order_rate_constant)"
legend_constants[4] = "e0 in component model_parameters (first_order_rate_constant)"
legend_constants[5] = "epsilon in component model_parameters (dimensionless)"
legend_states[2] = "y1 in component y1 (dimensionless)"
legend_algebraic[11] = "g1 in component y1 (dimensionless)"
legend_algebraic[6] = "r1 in component y1 (dimensionless)"
legend_algebraic[1] = "h1 in component y1 (dimensionless)"
legend_constants[6] = "S1 in component y1 (dimensionless)"
legend_constants[7] = "a10 in component model_parameters (dimensionless)"
legend_constants[8] = "a12 in component model_parameters (dimensionless)"
legend_constants[9] = "a11 in component model_parameters (dimensionless)"
legend_constants[10] = "e1 in component model_parameters (first_order_rate_constant)"
legend_algebraic[12] = "g2 in component y2 (dimensionless)"
legend_algebraic[7] = "r2 in component y2 (dimensionless)"
legend_algebraic[2] = "h2 in component y2 (dimensionless)"
legend_constants[11] = "S2 in component y2 (dimensionless)"
legend_states[3] = "y3 in component y3 (dimensionless)"
legend_states[4] = "y4 in component y4 (dimensionless)"
legend_constants[12] = "a23 in component model_parameters (dimensionless)"
legend_constants[13] = "a24 in component model_parameters (dimensionless)"
legend_constants[14] = "a20 in component model_parameters (dimensionless)"
legend_constants[15] = "a21 in component model_parameters (dimensionless)"
legend_constants[16] = "a22 in component model_parameters (dimensionless)"
legend_constants[17] = "e2 in component model_parameters (first_order_rate_constant)"
legend_algebraic[13] = "g3 in component y3 (dimensionless)"
legend_algebraic[8] = "r3 in component y3 (dimensionless)"
legend_algebraic[3] = "h3 in component y3 (dimensionless)"
legend_constants[18] = "S3 in component y3 (dimensionless)"
legend_constants[19] = "a32 in component model_parameters (dimensionless)"
legend_constants[20] = "a33 in component model_parameters (dimensionless)"
legend_algebraic[14] = "g4 in component y4 (dimensionless)"
legend_algebraic[9] = "r4 in component y4 (dimensionless)"
legend_algebraic[4] = "h4 in component y4 (dimensionless)"
legend_constants[21] = "S4 in component y4 (dimensionless)"
legend_constants[22] = "a42 in component model_parameters (dimensionless)"
legend_constants[23] = "a44 in component model_parameters (dimensionless)"
legend_rates[0] = "d/dt y0 in component y0 (dimensionless)"
legend_rates[2] = "d/dt y1 in component y1 (dimensionless)"
legend_rates[1] = "d/dt y2 in component y2 (dimensionless)"
legend_rates[3] = "d/dt y3 in component y3 (dimensionless)"
legend_rates[4] = "d/dt y4 in component y4 (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 0.4
constants[0] = 0.010
states[1] = 1.17
constants[1] = -0.00843
constants[2] = -0.440
constants[3] = 0.443
constants[4] = 0.0
constants[5] = 0.50
states[2] = 1.4
constants[6] = 0.010
constants[7] = 0.082
constants[8] = -0.0668
constants[9] = -0.0040
constants[10] = 0.0
constants[11] = 0.010
states[3] = 0.95
states[4] = 0.65
constants[12] = 0.0576
constants[13] = 3.25E-4
constants[14] = 0.0
constants[15] = 0.0310
constants[16] = -0.0957
constants[17] = 0.0
constants[18] = 0.010
constants[19] = 0.00869
constants[20] = -0.00857
constants[21] = 0.010
constants[22] = 1.39E-4
constants[23] = -1.43E-4
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[5] = custom_piecewise([less(states[0] , constants[5]) & less(constants[1]*states[0]+constants[2]*states[1] , 0.00000), 1.00000-exp((constants[0]*(power(states[0], 2.00000)))/((constants[1]*states[0]+constants[2]*states[1])*(power(constants[5]-states[0], 2.00000)))) , True, 1.00000])
algebraic[0] = custom_piecewise([greater(constants[1]*states[0]+constants[2]*states[1] , 0.00000), (constants[1]*states[0]+constants[2]*states[1])/(1.00000+((constants[1]*states[0]+constants[2]*states[1])/constants[0])*(1.00000-exp(-((constants[1]*states[0]+constants[2]*states[1])/constants[0])))) , less_equal(constants[1]*states[0]+constants[2]*states[1] , 0.00000), constants[1]*states[0]+constants[2]*states[1] , True, float('nan')])
algebraic[10] = algebraic[0]*algebraic[5]
rates[0] = 1.00000*algebraic[10]+constants[3]+constants[4]
algebraic[6] = custom_piecewise([less(states[2] , constants[5]) & less(constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1] , 0.00000), 1.00000-exp((constants[6]*(power(states[2], 2.00000)))/((constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1])*(power(constants[5]-states[2], 2.00000)))) , True, 1.00000])
algebraic[1] = custom_piecewise([greater(constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1] , 0.00000), (constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1])/(1.00000+((constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1])/constants[6])*(1.00000-exp(-((constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1])/constants[6])))) , less_equal(constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1] , 0.00000), constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1] , True, float('nan')])
algebraic[11] = algebraic[1]*algebraic[6]
rates[2] = 1.00000*algebraic[11]+constants[10]
algebraic[7] = custom_piecewise([less(states[1] , constants[5]) & less(constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4] , 0.00000), 1.00000-exp((constants[11]*(power(states[1], 2.00000)))/((constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4])*(power(constants[5]-states[1], 2.00000)))) , True, 1.00000])
algebraic[2] = custom_piecewise([greater(constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4] , 0.00000), (constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4])/(1.00000+((constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4])/constants[11])*(1.00000-exp(-((constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4])/constants[11])))) , less_equal(constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4] , 0.00000), constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4] , True, float('nan')])
algebraic[12] = algebraic[2]*algebraic[7]
rates[1] = 1.00000*algebraic[12]+constants[17]
algebraic[8] = custom_piecewise([less(states[3] , constants[5]) & less(constants[19]*states[1]+constants[20]*states[3] , 0.00000), 1.00000-exp((constants[18]*(power(states[3], 2.00000)))/((constants[19]*states[1]+constants[20]*states[3])*(power(constants[5]-states[3], 2.00000)))) , True, 1.00000])
algebraic[3] = custom_piecewise([greater(constants[19]*states[1]+constants[20]*states[3] , 0.00000), (constants[19]*states[1]+constants[20]*states[3])/(1.00000+((constants[19]*states[1]+constants[20]*states[3])/constants[18])*(1.00000-exp(-((constants[19]*states[1]+constants[20]*states[3])/constants[18])))) , less_equal(constants[19]*states[1]+constants[20]*states[3] , 0.00000), constants[19]*states[1]+constants[20]*states[3] , True, float('nan')])
algebraic[13] = algebraic[3]*algebraic[8]
rates[3] = 1.00000*algebraic[13]
algebraic[9] = custom_piecewise([less(states[4] , constants[5]) & less(constants[22]*states[1]+constants[23]*states[4] , 0.00000), 1.00000-exp((constants[21]*(power(states[4], 2.00000)))/((constants[22]*states[1]+constants[23]*states[4])*(power(constants[5]-states[4], 2.00000)))) , True, 1.00000])
algebraic[4] = custom_piecewise([greater(constants[22]*states[1]+constants[23]*states[4] , 0.00000), (constants[22]*states[1]+constants[23]*states[4])/(1.00000+((constants[22]*states[1]+constants[23]*states[4])/constants[21])*(1.00000-exp(-((constants[22]*states[1]+constants[23]*states[4])/constants[21])))) , less_equal(constants[22]*states[1]+constants[23]*states[4] , 0.00000), constants[22]*states[1]+constants[23]*states[4] , True, float('nan')])
algebraic[14] = algebraic[4]*algebraic[9]
rates[4] = 1.00000*algebraic[14]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[5] = custom_piecewise([less(states[0] , constants[5]) & less(constants[1]*states[0]+constants[2]*states[1] , 0.00000), 1.00000-exp((constants[0]*(power(states[0], 2.00000)))/((constants[1]*states[0]+constants[2]*states[1])*(power(constants[5]-states[0], 2.00000)))) , True, 1.00000])
algebraic[0] = custom_piecewise([greater(constants[1]*states[0]+constants[2]*states[1] , 0.00000), (constants[1]*states[0]+constants[2]*states[1])/(1.00000+((constants[1]*states[0]+constants[2]*states[1])/constants[0])*(1.00000-exp(-((constants[1]*states[0]+constants[2]*states[1])/constants[0])))) , less_equal(constants[1]*states[0]+constants[2]*states[1] , 0.00000), constants[1]*states[0]+constants[2]*states[1] , True, float('nan')])
algebraic[10] = algebraic[0]*algebraic[5]
algebraic[6] = custom_piecewise([less(states[2] , constants[5]) & less(constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1] , 0.00000), 1.00000-exp((constants[6]*(power(states[2], 2.00000)))/((constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1])*(power(constants[5]-states[2], 2.00000)))) , True, 1.00000])
algebraic[1] = custom_piecewise([greater(constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1] , 0.00000), (constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1])/(1.00000+((constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1])/constants[6])*(1.00000-exp(-((constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1])/constants[6])))) , less_equal(constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1] , 0.00000), constants[7]*states[0]+constants[9]*states[2]+constants[8]*states[1] , True, float('nan')])
algebraic[11] = algebraic[1]*algebraic[6]
algebraic[7] = custom_piecewise([less(states[1] , constants[5]) & less(constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4] , 0.00000), 1.00000-exp((constants[11]*(power(states[1], 2.00000)))/((constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4])*(power(constants[5]-states[1], 2.00000)))) , True, 1.00000])
algebraic[2] = custom_piecewise([greater(constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4] , 0.00000), (constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4])/(1.00000+((constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4])/constants[11])*(1.00000-exp(-((constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4])/constants[11])))) , less_equal(constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4] , 0.00000), constants[14]*states[0]+constants[15]*states[2]+constants[16]*states[1]+constants[12]*states[3]+constants[13]*states[4] , True, float('nan')])
algebraic[12] = algebraic[2]*algebraic[7]
algebraic[8] = custom_piecewise([less(states[3] , constants[5]) & less(constants[19]*states[1]+constants[20]*states[3] , 0.00000), 1.00000-exp((constants[18]*(power(states[3], 2.00000)))/((constants[19]*states[1]+constants[20]*states[3])*(power(constants[5]-states[3], 2.00000)))) , True, 1.00000])
algebraic[3] = custom_piecewise([greater(constants[19]*states[1]+constants[20]*states[3] , 0.00000), (constants[19]*states[1]+constants[20]*states[3])/(1.00000+((constants[19]*states[1]+constants[20]*states[3])/constants[18])*(1.00000-exp(-((constants[19]*states[1]+constants[20]*states[3])/constants[18])))) , less_equal(constants[19]*states[1]+constants[20]*states[3] , 0.00000), constants[19]*states[1]+constants[20]*states[3] , True, float('nan')])
algebraic[13] = algebraic[3]*algebraic[8]
algebraic[9] = custom_piecewise([less(states[4] , constants[5]) & less(constants[22]*states[1]+constants[23]*states[4] , 0.00000), 1.00000-exp((constants[21]*(power(states[4], 2.00000)))/((constants[22]*states[1]+constants[23]*states[4])*(power(constants[5]-states[4], 2.00000)))) , True, 1.00000])
algebraic[4] = custom_piecewise([greater(constants[22]*states[1]+constants[23]*states[4] , 0.00000), (constants[22]*states[1]+constants[23]*states[4])/(1.00000+((constants[22]*states[1]+constants[23]*states[4])/constants[21])*(1.00000-exp(-((constants[22]*states[1]+constants[23]*states[4])/constants[21])))) , less_equal(constants[22]*states[1]+constants[23]*states[4] , 0.00000), constants[22]*states[1]+constants[23]*states[4] , True, float('nan')])
algebraic[14] = algebraic[4]*algebraic[9]
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)