Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 12
sizeStates = 4
sizeConstants = 20
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 (day)"
legend_algebraic[6] = "rel_LH_E2_P4_RP_LH in component RP_LH (microg_day)"
legend_states[0] = "RP_LH in component RP_LH (microg)"
legend_algebraic[10] = "syn_LH_E2_P4 in component RP_LH (microg_day)"
legend_constants[0] = "V0_LH in component RP_LH (microg_day)"
legend_constants[1] = "V1_LH in component RP_LH (microg_day)"
legend_constants[2] = "h in component RP_LH (dimensionless)"
legend_constants[3] = "Km_LH in component RP_LH (ng_L)"
legend_constants[4] = "Ki_LHP in component RP_LH (nmol_L)"
legend_constants[5] = "kLH_rel in component RP_LH (first_order_rate_constant)"
legend_constants[6] = "CLH_P in component RP_LH (L_nmol)"
legend_constants[7] = "CLH_E in component RP_LH (L_ng)"
legend_algebraic[3] = "E2 in component E2 (ng_L)"
legend_algebraic[4] = "E2_dE in component E2_dE (ng_L)"
legend_algebraic[5] = "P4 in component P4 (nmol_L)"
legend_algebraic[8] = "P4_dP in component P4_dP (nmol_L)"
legend_states[1] = "LH in component LH (microg_l)"
legend_constants[8] = "v_dit in component LH (litre)"
legend_algebraic[0] = "clear_LH in component LH (microg_l_day)"
legend_constants[9] = "kLH_cl in component LH (first_order_rate_constant)"
legend_algebraic[7] = "rel_FSH_E2_P4_RP_FSH in component RP_FSH (microg_day)"
legend_states[2] = "RP_FSH in component RP_FSH (microg)"
legend_algebraic[11] = "syn_FSH_Ih in component RP_FSH (microg_day)"
legend_constants[10] = "V_FSH in component RP_FSH (microg_day)"
legend_constants[11] = "Ki_FSH_Ih in component RP_FSH (U_L)"
legend_constants[12] = "kFSH_rel in component RP_FSH (first_order_rate_constant)"
legend_constants[13] = "CFSH_P in component RP_FSH (L_nmol)"
legend_constants[14] = "CFSH_E in component RP_FSH (L_ng2)"
legend_algebraic[9] = "Ih_dIh in component Ih_dIh (U_L)"
legend_states[3] = "FSH in component FSH (microg_l)"
legend_constants[15] = "v_dis in component FSH (litre)"
legend_algebraic[2] = "clear_FSH in component FSH (microg_l_day)"
legend_constants[16] = "kFSH_cl in component FSH (first_order_rate_constant)"
legend_constants[17] = "dE in component E2_dE (day)"
legend_constants[18] = "dP in component P4_dP (day)"
legend_algebraic[1] = "Ih in component Ih (U_L)"
legend_constants[19] = "dIh in component Ih_dIh (day)"
legend_rates[0] = "d/dt RP_LH in component RP_LH (microg)"
legend_rates[1] = "d/dt LH in component LH (microg_l)"
legend_rates[2] = "d/dt RP_FSH in component RP_FSH (microg)"
legend_rates[3] = "d/dt FSH in component FSH (microg_l)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 467.0
constants[0] = 1400.0
constants[1] = 95900.0
constants[2] = 8.0
constants[3] = 360.0
constants[4] = 26.0
constants[5] = 3.0
constants[6] = 0.024
constants[7] = 0.008
states[1] = 40.0
constants[8] = 2.5
constants[9] = 14.0
states[2] = 0.0
constants[10] = 4400.0
constants[11] = 1176.5
constants[12] = 45.0
constants[13] = 3.0
constants[14] = 0.005
states[3] = 150.0
constants[15] = 2.5
constants[16] = 8.21
constants[17] = 0.42
constants[18] = 2.9
constants[19] = 2.0
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[3] = (300.000-(240.000*(power(voi+1.00000, 2.00000)))/(3.00000+power(voi+1.00000, 2.00000)))+90.0000*exp(-((power(voi-8.00000, 2.00000))/10.0000))
algebraic[5] = 52.0000*exp(-((power(voi-7.00000, 2.00000))/18.0000))
algebraic[6] = (constants[5]*(1.00000+constants[6]*algebraic[5])*states[0])/(1.00000+constants[7]*algebraic[3])
algebraic[0] = constants[9]*states[1]
rates[1] = algebraic[6]/constants[8]-algebraic[0]
algebraic[7] = (constants[12]*(1.00000+constants[13]*algebraic[5])*states[2])/(1.00000+constants[14]*(power(algebraic[3], 2.00000)))
algebraic[2] = constants[16]*states[3]
rates[3] = algebraic[7]/constants[15]-algebraic[2]
algebraic[4] = (300.000-(240.000*(power((voi+1.00000)-constants[17], 2.00000)))/(3.00000+power((voi+1.00000)-constants[17], 2.00000)))+90.0000*exp(-((power(voi-(constants[17]+8.00000), 2.00000))/10.0000))
algebraic[8] = 52.0000*exp(-((power(voi-(constants[18]+7.00000), 2.00000))/18.0000))
algebraic[10] = (constants[0]+(constants[1]*(power(algebraic[4], constants[2])))/(power(constants[3], constants[2])+power(algebraic[4], constants[2])))/(1.00000+algebraic[8]/constants[4])
rates[0] = algebraic[10]-algebraic[6]
algebraic[9] = 300.000+1330.00*exp(-((power(voi-(7.00000+constants[19]), 2.00000))/19.0000))
algebraic[11] = constants[10]/(1.00000+algebraic[9]/constants[11])
rates[2] = algebraic[11]-algebraic[7]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[3] = (300.000-(240.000*(power(voi+1.00000, 2.00000)))/(3.00000+power(voi+1.00000, 2.00000)))+90.0000*exp(-((power(voi-8.00000, 2.00000))/10.0000))
algebraic[5] = 52.0000*exp(-((power(voi-7.00000, 2.00000))/18.0000))
algebraic[6] = (constants[5]*(1.00000+constants[6]*algebraic[5])*states[0])/(1.00000+constants[7]*algebraic[3])
algebraic[0] = constants[9]*states[1]
algebraic[7] = (constants[12]*(1.00000+constants[13]*algebraic[5])*states[2])/(1.00000+constants[14]*(power(algebraic[3], 2.00000)))
algebraic[2] = constants[16]*states[3]
algebraic[4] = (300.000-(240.000*(power((voi+1.00000)-constants[17], 2.00000)))/(3.00000+power((voi+1.00000)-constants[17], 2.00000)))+90.0000*exp(-((power(voi-(constants[17]+8.00000), 2.00000))/10.0000))
algebraic[8] = 52.0000*exp(-((power(voi-(constants[18]+7.00000), 2.00000))/18.0000))
algebraic[10] = (constants[0]+(constants[1]*(power(algebraic[4], constants[2])))/(power(constants[3], constants[2])+power(algebraic[4], constants[2])))/(1.00000+algebraic[8]/constants[4])
algebraic[9] = 300.000+1330.00*exp(-((power(voi-(7.00000+constants[19]), 2.00000))/19.0000))
algebraic[11] = constants[10]/(1.00000+algebraic[9]/constants[11])
algebraic[1] = 300.000+1330.00*exp(-((power(voi-7.00000, 2.00000))/19.0000))
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)