Generated Code

# Size of variable arrays:
sizeAlgebraic = 16
sizeStates = 6
sizeConstants = 11
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] = "RT in component main (J_per_mol)"
    legend_states[0] = "q_1 in component main (mole)"
    legend_states[1] = "q_2 in component main (mole)"
    legend_states[2] = "q_3 in component main (mole)"
    legend_states[3] = "q_4 in component main (mole)"
    legend_states[4] = "q_e0 in component main (mole)"
    legend_states[5] = "q_e1 in component main (mole)"
    legend_algebraic[14] = "v_1 in component main (mol_per_s)"
    legend_algebraic[15] = "v_2 in component main (mol_per_s)"
    legend_algebraic[0] = "u_1 in component main (J_per_mol)"
    legend_algebraic[2] = "u_2 in component main (J_per_mol)"
    legend_algebraic[4] = "u_3 in component main (J_per_mol)"
    legend_algebraic[6] = "u_4 in component main (J_per_mol)"
    legend_algebraic[8] = "u_e0 in component main (J_per_mol)"
    legend_algebraic[11] = "u_e1 in component main (J_per_mol)"
    legend_algebraic[9] = "u_f_1 in component main (J_per_mol)"
    legend_algebraic[12] = "u_r_1 in component main (J_per_mol)"
    legend_algebraic[13] = "u_f_2 in component main (J_per_mol)"
    legend_algebraic[10] = "u_r_2 in component main (J_per_mol)"
    legend_constants[1] = "K_q_1 in component main (per_mol)"
    legend_constants[2] = "K_q_2 in component main (per_mol)"
    legend_constants[3] = "K_q_3 in component main (per_mol)"
    legend_constants[4] = "K_q_4 in component main (per_mol)"
    legend_constants[5] = "K_q_e0 in component main (per_mol)"
    legend_constants[6] = "K_q_e1 in component main (per_mol)"
    legend_constants[7] = "kappa_1 in component main (mol_per_s)"
    legend_constants[8] = "kappa_2 in component main (mol_per_s)"
    legend_algebraic[1] = "q_e_tot in component main (mole)"
    legend_algebraic[3] = "A_f in component main (per_mol3_per_s)"
    legend_algebraic[5] = "A_r in component main (per_mol3_per_s)"
    legend_constants[9] = "B_f in component main (per_mol3)"
    legend_constants[10] = "B_r in component main (per_mol3)"
    legend_algebraic[7] = "v_SS in component main (mol_per_s)"
    legend_rates[0] = "d/dt q_1 in component main (mole)"
    legend_rates[1] = "d/dt q_2 in component main (mole)"
    legend_rates[2] = "d/dt q_3 in component main (mole)"
    legend_rates[3] = "d/dt q_4 in component main (mole)"
    legend_rates[4] = "d/dt q_e0 in component main (mole)"
    legend_rates[5] = "d/dt q_e1 in component main (mole)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 2578.73058
    states[0] = 3
    states[1] = 1
    states[2] = 0
    states[3] = 0
    states[4] = 1
    states[5] = 1
    constants[1] = 2
    constants[2] = 2
    constants[3] = 2
    constants[4] = 2
    constants[5] = 2
    constants[6] = 2
    constants[7] = 0.20
    constants[8] = 0.1
    constants[9] = (((constants[5]/constants[6])*constants[7])/(constants[7]+constants[8]))*constants[1]*(power(constants[2], 2.00000))
    constants[10] = (((constants[5]/constants[6])*constants[7])/(constants[7]+constants[8]))*constants[3]*(power(constants[4], 2.00000))
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = constants[0]*log(constants[1]*states[0])
    algebraic[2] = constants[0]*log(constants[2]*states[1])
    algebraic[8] = constants[0]*log(constants[5]*states[4])
    algebraic[9] = algebraic[0]+2.00000*algebraic[2]+algebraic[8]
    algebraic[11] = constants[0]*log(constants[6]*states[5])
    algebraic[12] = algebraic[11]
    algebraic[14] = constants[7]*(exp(algebraic[9]/constants[0])-exp(algebraic[12]/constants[0]))
    rates[0] = -algebraic[14]
    rates[1] = -2.00000*algebraic[14]
    algebraic[13] = algebraic[11]
    algebraic[4] = constants[0]*log(constants[3]*states[2])
    algebraic[6] = constants[0]*log(constants[4]*states[3])
    algebraic[10] = algebraic[4]+2.00000*algebraic[6]+algebraic[8]
    algebraic[15] = constants[8]*(exp(algebraic[13]/constants[0])-exp(algebraic[10]/constants[0]))
    rates[2] = algebraic[15]
    rates[3] = 2.00000*algebraic[15]
    rates[4] = algebraic[15]-algebraic[14]
    rates[5] = algebraic[14]-algebraic[15]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = constants[0]*log(constants[1]*states[0])
    algebraic[2] = constants[0]*log(constants[2]*states[1])
    algebraic[8] = constants[0]*log(constants[5]*states[4])
    algebraic[9] = algebraic[0]+2.00000*algebraic[2]+algebraic[8]
    algebraic[11] = constants[0]*log(constants[6]*states[5])
    algebraic[12] = algebraic[11]
    algebraic[14] = constants[7]*(exp(algebraic[9]/constants[0])-exp(algebraic[12]/constants[0]))
    algebraic[13] = algebraic[11]
    algebraic[4] = constants[0]*log(constants[3]*states[2])
    algebraic[6] = constants[0]*log(constants[4]*states[3])
    algebraic[10] = algebraic[4]+2.00000*algebraic[6]+algebraic[8]
    algebraic[15] = constants[8]*(exp(algebraic[13]/constants[0])-exp(algebraic[10]/constants[0]))
    algebraic[1] = states[4]+states[5]
    algebraic[3] = ((algebraic[1]*constants[5]*constants[7]*constants[8])/(constants[7]+constants[8]))*constants[1]*(power(constants[2], 2.00000))
    algebraic[5] = ((algebraic[1]*constants[5]*constants[7]*constants[8])/(constants[7]+constants[8]))*constants[3]*(power(constants[4], 2.00000))
    algebraic[7] = (algebraic[3]*states[0]*(power(states[1], 2.00000))-algebraic[5]*states[2]*(power(states[3], 2.00000)))/(1.00000+constants[9]*states[0]*(power(states[1], 2.00000))+constants[10]*states[2]*(power(states[3], 2.00000)))
    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)