Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 8
sizeStates = 5
sizeConstants = 22
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_states[0] = "R in component R (nanomolar)"
legend_constants[0] = "delta_R in component R (first_order_rate_constant)"
legend_algebraic[0] = "logR in component R (dimensionless)"
legend_algebraic[1] = "f1 in component f1 (flux)"
legend_states[1] = "U in component U (nanomolar)"
legend_constants[1] = "delta_U in component U (first_order_rate_constant)"
legend_algebraic[2] = "logU in component U (dimensionless)"
legend_constants[2] = "alpha0 in component model_parameters (per_nanomolar_day)"
legend_constants[3] = "alpha1 in component model_parameters (per_nanomolar_day)"
legend_constants[4] = "d01 in component model_parameters (first_order_rate_constant)"
legend_constants[5] = "d12 in component model_parameters (first_order_rate_constant)"
legend_states[2] = "B1 in component B1 (nanomolar)"
legend_states[3] = "B2 in component B2 (nanomolar)"
legend_algebraic[6] = "P in component P (nanomolar)"
legend_algebraic[7] = "f2 in component f2 (flux)"
legend_constants[6] = "delta_b1 in component B1 (first_order_rate_constant)"
legend_algebraic[4] = "logB1 in component B1 (dimensionless)"
legend_constants[7] = "delta_b2 in component B2 (first_order_rate_constant)"
legend_algebraic[5] = "logB2 in component B2 (dimensionless)"
legend_constants[8] = "PE in component P (nanomolar)"
legend_algebraic[3] = "q in component P (dimensionless)"
legend_constants[9] = "G in component P (first_order_rate_constant)"
legend_constants[10] = "ti in component P (day)"
legend_constants[11] = "T in component P (day)"
legend_constants[12] = "P0 in component model_parameters (nanomolar)"
legend_constants[13] = "a in component f1 (flux)"
legend_constants[14] = "a0 in component f1 (flux)"
legend_constants[15] = "b in component f1 (nanomolar)"
legend_constants[16] = "b0 in component f1 (nanomolar)"
legend_states[4] = "x in component x (flux)"
legend_constants[17] = "P1 in component x (nanomolar)"
legend_constants[18] = "s in component x (nanomolar_day2)"
legend_constants[19] = "delta_x in component x (first_order_rate_constant)"
legend_constants[20] = "kappa in component f2 (flux)"
legend_constants[21] = "kappa0 in component f2 (nanomolar)"
legend_rates[0] = "d/dt R in component R (nanomolar)"
legend_rates[1] = "d/dt U in component U (nanomolar)"
legend_rates[2] = "d/dt B1 in component B1 (nanomolar)"
legend_rates[3] = "d/dt B2 in component B2 (nanomolar)"
legend_rates[4] = "d/dt x in component x (flux)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 1.0
constants[0] = 1.905
states[1] = 1.0
constants[1] = 7.5
constants[2] = 4.15
constants[3] = 3.02
constants[4] = 13.0
constants[5] = 4.72E3
states[2] = 1.0
states[3] = 1.0
constants[6] = 7.5
constants[7] = 50.0
constants[8] = 20.55
constants[9] = 35.6
constants[10] = 1.0
constants[11] = 9.0
constants[12] = 0.25
constants[13] = 3.58E5
constants[14] = 2.33E4
constants[15] = 100.0
constants[16] = 263.0
states[4] = 0.0
constants[17] = 20.0
constants[18] = 3.71E5
constants[19] = 0.207
constants[20] = 2.4E5
constants[21] = 6.55E3
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[3] = constants[3]*states[2]*states[1]-(constants[5]*states[3]+constants[7]*states[3])
algebraic[1] = constants[14]*(1.00000-states[3]/(constants[15]+states[3]))+(states[4]*(1.00000-exp(-states[4]/constants[13]))*states[3])/(constants[16]+states[3])
rates[0] = algebraic[1]-constants[0]*states[0]
algebraic[3] = custom_piecewise([less(voi , constants[10]), 0.00000 , less(voi , constants[11]+constants[10]) & greater_equal(voi , constants[10]), 1.00000-exp(-constants[9]*(voi-constants[10])) , True, exp(constants[9]*constants[11]-1.00000)*exp(constants[9]*(voi-constants[10]))])
algebraic[6] = constants[12]+constants[8]*algebraic[3]
rates[2] = (constants[2]*algebraic[6]*states[1]+constants[5]*states[3])-(constants[4]*states[2]+constants[6]*states[2]+constants[3]*states[2]*states[1])
rates[4] = (constants[18]*(algebraic[6]-constants[12]))/(algebraic[6]+constants[17])-constants[19]*states[4]
algebraic[7] = (constants[20]*states[0])/(constants[21]+states[0])
rates[1] = (algebraic[7]+constants[4]*states[2]+constants[5]*states[3])-(constants[1]*states[1]+constants[2]*algebraic[6]*states[1]+constants[3]*states[2]*states[1])
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[1] = constants[14]*(1.00000-states[3]/(constants[15]+states[3]))+(states[4]*(1.00000-exp(-states[4]/constants[13]))*states[3])/(constants[16]+states[3])
algebraic[3] = custom_piecewise([less(voi , constants[10]), 0.00000 , less(voi , constants[11]+constants[10]) & greater_equal(voi , constants[10]), 1.00000-exp(-constants[9]*(voi-constants[10])) , True, exp(constants[9]*constants[11]-1.00000)*exp(constants[9]*(voi-constants[10]))])
algebraic[6] = constants[12]+constants[8]*algebraic[3]
algebraic[7] = (constants[20]*states[0])/(constants[21]+states[0])
algebraic[0] = log(states[0], 10)
algebraic[2] = log(states[1], 10)
algebraic[4] = log(states[2], 10)
algebraic[5] = log(states[3], 10)
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)