Generated Code

# Size of variable arrays:
sizeAlgebraic = 5
sizeStates = 3
sizeConstants = 25
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 (picomolar)"
    legend_constants[0] = "DR in component model_parameters (flux)"
    legend_algebraic[0] = "pi_C in component model_parameters (dimensionless)"
    legend_constants[22] = "DB in component model_parameters (first_order_rate_constant)"
    legend_states[1] = "B in component B (picomolar)"
    legend_constants[1] = "kB in component model_parameters (first_order_rate_constant)"
    legend_states[2] = "C in component C (picomolar)"
    legend_constants[2] = "DC in component model_parameters (flux)"
    legend_algebraic[4] = "pi_L in component pi_L (dimensionless)"
    legend_constants[3] = "DA in component model_parameters (first_order_rate_constant)"
    legend_constants[4] = "k1 in component pi_L (second_order_rate_constant)"
    legend_constants[5] = "k2 in component pi_L (first_order_rate_constant)"
    legend_constants[6] = "k3 in component pi_L (second_order_rate_constant)"
    legend_constants[7] = "k4 in component pi_L (first_order_rate_constant)"
    legend_constants[8] = "K in component pi_L (picomolar)"
    legend_constants[9] = "ko in component pi_L (first_order_rate_constant)"
    legend_constants[10] = "Io in component pi_L (flux)"
    legend_constants[11] = "IL in component pi_L (flux)"
    legend_constants[12] = "rL in component pi_L (flux)"
    legend_constants[13] = "KOP in component pi_L (picomole_day_picomole_cells)"
    legend_constants[14] = "KLP in component pi_L (picomole_picomole_cells)"
    legend_algebraic[3] = "pi_P in component model_parameters (dimensionless)"
    legend_constants[15] = "f0 in component model_parameters (dimensionless)"
    legend_constants[16] = "dB in component model_parameters (first_order_rate_constant)"
    legend_algebraic[1] = "IP in component model_parameters (flux)"
    legend_constants[17] = "kP in component model_parameters (first_order_rate_constant)"
    legend_algebraic[2] = "P in component model_parameters (picomolar)"
    legend_constants[23] = "P_0 in component model_parameters (picomolar)"
    legend_constants[24] = "P_s in component model_parameters (picomolar)"
    legend_constants[18] = "C_s in component model_parameters (picomolar)"
    legend_constants[19] = "SP in component model_parameters (flux)"
    legend_constants[20] = "k5 in component model_parameters (second_order_rate_constant)"
    legend_constants[21] = "k6 in component model_parameters (first_order_rate_constant)"
    legend_rates[0] = "d/dt R in component R (picomolar)"
    legend_rates[1] = "d/dt B in component B (picomolar)"
    legend_rates[2] = "d/dt C in component C (picomolar)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 0.00
    constants[0] = 7E-4
    states[1] = 0.00
    constants[1] = 0.189
    states[2] = 0.00
    constants[2] = 2.1E-3
    constants[3] = 0.7
    constants[4] = 1E-2
    constants[5] = 10.0
    constants[6] = 5.8E-4
    constants[7] = 1.7E-2
    constants[8] = 10.0
    constants[9] = 0.35
    constants[10] = 0.0
    constants[11] = 0.0
    constants[12] = 1E3
    constants[13] = 2E5
    constants[14] = 3E6
    constants[15] = 0.05
    constants[16] = 0.7
    constants[17] = 86.0
    constants[18] = 5E-3
    constants[19] = 250.0
    constants[20] = 0.02
    constants[21] = 3.0
    constants[22] = constants[15]*constants[16]
    constants[23] = constants[19]/constants[17]
    constants[24] = constants[21]/constants[20]
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = (states[2]+constants[15]*constants[18])/(states[2]+constants[18])
    rates[0] = constants[0]*algebraic[0]-(constants[22]/algebraic[0])*states[0]
    rates[1] = (constants[22]/algebraic[0])*states[0]-constants[1]*states[1]
    algebraic[1] = custom_piecewise([greater(voi , 20.0000) & less_equal(voi , 80.0000), 1000.00 , True, 0.00000])
    algebraic[2] = algebraic[1]/constants[17]
    algebraic[3] = (algebraic[2]+constants[23])/(algebraic[2]+constants[24])
    algebraic[4] = (constants[6]/constants[7])*((constants[14]*algebraic[3]*states[1])/(1.00000+(constants[6]*constants[8])/constants[7]+(constants[4]/(constants[5]*constants[9]))*((constants[13]/algebraic[3])*states[0]+constants[10])))*(1.00000+constants[11]/constants[12])
    rates[2] = constants[2]*algebraic[4]-constants[3]*algebraic[0]*states[2]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = (states[2]+constants[15]*constants[18])/(states[2]+constants[18])
    algebraic[1] = custom_piecewise([greater(voi , 20.0000) & less_equal(voi , 80.0000), 1000.00 , True, 0.00000])
    algebraic[2] = algebraic[1]/constants[17]
    algebraic[3] = (algebraic[2]+constants[23])/(algebraic[2]+constants[24])
    algebraic[4] = (constants[6]/constants[7])*((constants[14]*algebraic[3]*states[1])/(1.00000+(constants[6]*constants[8])/constants[7]+(constants[4]/(constants[5]*constants[9]))*((constants[13]/algebraic[3])*states[0]+constants[10])))*(1.00000+constants[11]/constants[12])
    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)