Generated Code

# Size of variable arrays:
sizeAlgebraic = 15
sizeStates = 5
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 environment (second)"
    legend_constants[0] = "R in component environment (J_per_K_per_mol)"
    legend_constants[1] = "T in component environment (kelvin)"
    legend_constants[2] = "F in component environment (C_per_mol)"
    legend_constants[3] = "C_m in component environment (fF)"
    legend_states[0] = "q_K_o in component environment (fmol)"
    legend_states[1] = "q_K_i in component environment (fmol)"
    legend_states[2] = "q_C_Kp in component environment (fmol)"
    legend_states[3] = "q_O_Kp in component environment (fmol)"
    legend_algebraic[11] = "v_Kp in component Kp (fmol_per_sec)"
    legend_states[4] = "q_mem in component environment (fC)"
    legend_algebraic[13] = "I_mem_Kp in component Kp (fA)"
    legend_constants[4] = "K_C_Kp in component Kp_parameters (per_fmol)"
    legend_constants[5] = "K_K_o in component Kp_parameters (per_fmol)"
    legend_constants[6] = "K_K_i in component Kp_parameters (per_fmol)"
    legend_constants[7] = "K_O_Kp in component Kp_parameters (per_fmol)"
    legend_constants[8] = "kappa_Kp in component Kp_parameters (fmol_per_sec)"
    legend_constants[9] = "kappa_gKp in component Kp_parameters (fmol_per_sec)"
    legend_constants[10] = "zK in component Kp_parameters (dimensionless)"
    legend_constants[11] = "z_f_Kp in component Kp_parameters (dimensionless)"
    legend_constants[12] = "z_r_Kp in component Kp_parameters (dimensionless)"
    legend_algebraic[2] = "mu_K_o in component Kp (J_per_mol)"
    legend_algebraic[3] = "mu_K_i in component Kp (J_per_mol)"
    legend_algebraic[1] = "mu_C_Kp in component Kp (J_per_mol)"
    legend_algebraic[4] = "mu_O_Kp in component Kp (J_per_mol)"
    legend_algebraic[7] = "Am_Kp in component Kp (J_per_mol)"
    legend_algebraic[5] = "Af_Kp in component Kp (J_per_mol)"
    legend_algebraic[8] = "Ar_Kp in component Kp (J_per_mol)"
    legend_algebraic[6] = "Af_gKp in component Kp (J_per_mol)"
    legend_algebraic[9] = "Ar_gKp in component Kp (J_per_mol)"
    legend_algebraic[10] = "v_gKp in component Kp (fmol_per_sec)"
    legend_algebraic[12] = "v_C_Kp in component Kp (fmol_per_sec)"
    legend_algebraic[14] = "v_O_Kp in component Kp (fmol_per_sec)"
    legend_algebraic[0] = "V_mem in component Kp (volt)"
    legend_rates[0] = "d/dt q_K_o in component environment (fmol)"
    legend_rates[1] = "d/dt q_K_i in component environment (fmol)"
    legend_rates[4] = "d/dt q_mem in component environment (fC)"
    legend_rates[2] = "d/dt q_C_Kp in component environment (fmol)"
    legend_rates[3] = "d/dt q_O_Kp in component environment (fmol)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 8.314
    constants[1] = 310
    constants[2] = 96485
    constants[3] = 153400
    states[0] = 27.9828
    states[1] = 5510
    states[2] = 1.3813E-07
    states[3] = 3.45317E-08
    states[4] = -13039
    constants[4] = 41.6265
    constants[5] = 0.059344
    constants[6] = 0.0080926
    constants[7] = 145.607
    constants[8] = 252.3419
    constants[9] = 24.0195
    constants[10] = 1
    constants[11] = 0
    constants[12] = -4.4669
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = states[4]/constants[3]
    algebraic[7] = constants[10]*constants[2]*algebraic[0]
    algebraic[3] = constants[0]*constants[1]*log(constants[6]*states[1])
    algebraic[4] = constants[0]*constants[1]*log(constants[7]*states[3])
    algebraic[5] = algebraic[3]+constants[10]*constants[2]*algebraic[0]+algebraic[4]
    algebraic[2] = constants[0]*constants[1]*log(constants[5]*states[0])
    algebraic[8] = algebraic[2]+algebraic[4]
    algebraic[11] = custom_piecewise([equal(algebraic[7] , 0.00000), constants[8]*(exp(algebraic[5]/(constants[0]*constants[1]))-exp(algebraic[8]/(constants[0]*constants[1]))) , True, (((constants[8]*algebraic[7])/(constants[0]*constants[1]))/(exp(algebraic[7]/(constants[0]*constants[1]))-1.00000))*(exp(algebraic[5]/(constants[0]*constants[1]))-exp(algebraic[8]/(constants[0]*constants[1])))])
    rates[0] = algebraic[11]
    rates[1] = -algebraic[11]
    algebraic[6] = constants[0]*constants[1]*log(constants[4]*states[2])+constants[11]*constants[2]*algebraic[0]
    algebraic[9] = constants[0]*constants[1]*log(constants[7]*states[3])+constants[12]*constants[2]*algebraic[0]
    algebraic[10] = constants[9]*(exp(algebraic[6]/(constants[0]*constants[1]))-exp(algebraic[9]/(constants[0]*constants[1])))
    algebraic[12] = -algebraic[10]
    rates[2] = algebraic[12]
    algebraic[13] = constants[2]*((-constants[10]*algebraic[11]+constants[12]*algebraic[10])-constants[11]*algebraic[10])
    rates[4] = algebraic[13]
    algebraic[14] = algebraic[10]-(algebraic[11]-algebraic[11])
    rates[3] = algebraic[14]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = states[4]/constants[3]
    algebraic[7] = constants[10]*constants[2]*algebraic[0]
    algebraic[3] = constants[0]*constants[1]*log(constants[6]*states[1])
    algebraic[4] = constants[0]*constants[1]*log(constants[7]*states[3])
    algebraic[5] = algebraic[3]+constants[10]*constants[2]*algebraic[0]+algebraic[4]
    algebraic[2] = constants[0]*constants[1]*log(constants[5]*states[0])
    algebraic[8] = algebraic[2]+algebraic[4]
    algebraic[11] = custom_piecewise([equal(algebraic[7] , 0.00000), constants[8]*(exp(algebraic[5]/(constants[0]*constants[1]))-exp(algebraic[8]/(constants[0]*constants[1]))) , True, (((constants[8]*algebraic[7])/(constants[0]*constants[1]))/(exp(algebraic[7]/(constants[0]*constants[1]))-1.00000))*(exp(algebraic[5]/(constants[0]*constants[1]))-exp(algebraic[8]/(constants[0]*constants[1])))])
    algebraic[6] = constants[0]*constants[1]*log(constants[4]*states[2])+constants[11]*constants[2]*algebraic[0]
    algebraic[9] = constants[0]*constants[1]*log(constants[7]*states[3])+constants[12]*constants[2]*algebraic[0]
    algebraic[10] = constants[9]*(exp(algebraic[6]/(constants[0]*constants[1]))-exp(algebraic[9]/(constants[0]*constants[1])))
    algebraic[12] = -algebraic[10]
    algebraic[13] = constants[2]*((-constants[10]*algebraic[11]+constants[12]*algebraic[10])-constants[11]*algebraic[10])
    algebraic[14] = algebraic[10]-(algebraic[11]-algebraic[11])
    algebraic[1] = constants[0]*constants[1]*log(constants[4]*states[2])
    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)