Generated Code

# Size of variable arrays:
sizeAlgebraic = 9
sizeStates = 2
sizeConstants = 13
from math import *
from numpy import *

def createLegends():
    legend_states = [""] * sizeStates
    legend_rates = [""] * sizeStates
    legend_algebraic = [""] * sizeAlgebraic
    legend_voi = ""
    legend_constants = [""] * sizeConstants
    legend_voi = "t in component main (second)"
    legend_constants[0] = "V_m in component main (J_per_C)"
    legend_constants[1] = "RTF in component main (J_per_C)"
    legend_constants[10] = "epsilon in component main (dimensionless)"
    legend_states[0] = "TA_i in component main (mol_per_m3)"
    legend_algebraic[0] = "CO2_o in component main (mol_per_m3)"
    legend_algebraic[5] = "CO2_i in component main (mol_per_m3)"
    legend_algebraic[7] = "HCO3_i in component main (mol_per_m3)"
    legend_algebraic[1] = "HCO3_o in component main (mol_per_m3)"
    legend_states[1] = "H_i in component main (mol_per_m3)"
    legend_constants[2] = "H_o in component main (mol_per_m3)"
    legend_constants[3] = "H_Lim in component main (mol_per_m3)"
    legend_algebraic[6] = "M_CO2 in component main (mol_per_m2_s)"
    legend_algebraic[8] = "M_HCO3 in component main (mol_per_m2_s)"
    legend_algebraic[3] = "M_H in component main (mol_per_m2_s)"
    legend_algebraic[2] = "pH_i in component main (dimensionless)"
    legend_constants[11] = "pH_o in component main (dimensionless)"
    legend_constants[12] = "pH_Lim in component main (dimensionless)"
    legend_constants[4] = "P_CO2 in component main (m_per_s)"
    legend_constants[5] = "P_HCO3 in component main (m_per_s)"
    legend_constants[6] = "k in component main (m_per_s)"
    legend_constants[7] = "K_A in component main (mol_per_m3)"
    legend_constants[8] = "rho in component main (per_m)"
    legend_algebraic[4] = "alpha_i in component main (dimensionless)"
    legend_constants[9] = "beta in component main (mol_per_m3)"
    legend_rates[0] = "d/dt TA_i in component main (mol_per_m3)"
    legend_rates[1] = "d/dt H_i in component main (mol_per_m3)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = -0.057
    constants[1] = 0.0256796
    states[0] = 0.0
    states[1] = 3.981071705534970e-05
    constants[2] = 1.995262314968879e-05
    constants[3] = 3.981071705534970e-05
    constants[4] = 6e-5
    constants[5] = 5e-9
    constants[6] = 0.0375
    constants[7] = 1e-3
    constants[8] = 8000
    constants[9] = -26
    constants[10] = exp(-constants[0]/constants[1])
    constants[11] = -log(0.00100000*constants[2], 10)
    constants[12] = -log(0.00100000*constants[3], 10)
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = custom_piecewise([less(voi , 100.000), 0.00000 , less(voi , 2800.00), 1.18770 , True, 0.00000])
    algebraic[4] = states[1]/(states[1]+constants[7])
    algebraic[5] = algebraic[4]*states[0]
    algebraic[6] = constants[4]*(algebraic[0]-algebraic[5])
    algebraic[7] = (1.00000-algebraic[4])*states[0]
    algebraic[1] = (constants[7]*algebraic[0])/constants[2]
    algebraic[8] = (((constants[5]*constants[0])/constants[1])*(algebraic[1]-algebraic[7]*constants[10]))/(1.00000-constants[10])
    rates[0] = constants[8]*(algebraic[6]+algebraic[8])
    algebraic[2] = -log(0.00100000*states[1], 10)
    algebraic[3] = custom_piecewise([less(algebraic[2] , constants[12]), constants[6]*(states[1]-constants[3]) , True, 0.00000])
    rates[1] = ((-2.30300*states[1])/constants[9])*constants[8]*(((1.00000-algebraic[4])*algebraic[6]-algebraic[4]*algebraic[8])-algebraic[3])
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = custom_piecewise([less(voi , 100.000), 0.00000 , less(voi , 2800.00), 1.18770 , True, 0.00000])
    algebraic[4] = states[1]/(states[1]+constants[7])
    algebraic[5] = algebraic[4]*states[0]
    algebraic[6] = constants[4]*(algebraic[0]-algebraic[5])
    algebraic[7] = (1.00000-algebraic[4])*states[0]
    algebraic[1] = (constants[7]*algebraic[0])/constants[2]
    algebraic[8] = (((constants[5]*constants[0])/constants[1])*(algebraic[1]-algebraic[7]*constants[10]))/(1.00000-constants[10])
    algebraic[2] = -log(0.00100000*states[1], 10)
    algebraic[3] = custom_piecewise([less(algebraic[2] , constants[12]), constants[6]*(states[1]-constants[3]) , True, 0.00000])
    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)