Generated Code

# Size of variable arrays:
sizeAlgebraic = 18
sizeStates = 4
sizeConstants = 14
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 (second)"
    legend_states[0] = "HCO3_int in component concentrations (mM)"
    legend_states[1] = "HCO3_ext in component concentrations (mM)"
    legend_states[2] = "Cl_int in component concentrations (mM)"
    legend_states[3] = "Cl_ext in component concentrations (mM)"
    legend_algebraic[12] = "J_AE1_HCO3 in component AE1 (mM_per_s)"
    legend_algebraic[17] = "J_AE1_Cl in component AE1 (mM_per_s)"
    legend_algebraic[13] = "J_HCO3_influx in component AE1 (mM_per_s)"
    legend_algebraic[14] = "J_Cl_influx in component AE1 (mM_per_s)"
    legend_constants[0] = "K_HCO3_ext in component AE1 (mM)"
    legend_constants[1] = "K_HCO3_int in component AE1 (mM)"
    legend_constants[2] = "K_Cl_ext in component AE1 (mM)"
    legend_constants[3] = "K_Cl_int in component AE1 (mM)"
    legend_constants[4] = "P_HCO3_ext in component AE1 (per_s)"
    legend_constants[5] = "P_HCO3_int in component AE1 (per_s)"
    legend_constants[6] = "P_Cl_ext in component AE1 (per_s)"
    legend_constants[7] = "P_Cl_int in component AE1 (per_s)"
    legend_algebraic[1] = "beta_ext in component AE1 (dimensionless)"
    legend_algebraic[8] = "beta_int in component AE1 (dimensionless)"
    legend_algebraic[9] = "gamma_ext in component AE1 (dimensionless)"
    legend_algebraic[10] = "gamma_int in component AE1 (dimensionless)"
    legend_algebraic[11] = "sigma in component AE1 (per_s)"
    legend_constants[8] = "x_Tmax in component AE1 (mM)"
    legend_constants[9] = "K_I in component AE1 (mM)"
    legend_algebraic[0] = "x_T in component AE1 (mM)"
    legend_algebraic[15] = "x_ext in component AE1 (mM)"
    legend_algebraic[16] = "x_int in component AE1 (mM)"
    legend_algebraic[2] = "Jo_bm in component AE1 (mM_per_s)"
    legend_algebraic[3] = "Ji_bm in component AE1 (mM_per_s)"
    legend_algebraic[4] = "Js_bm in component AE1 (mM_per_s)"
    legend_algebraic[5] = "Jo_cm in component AE1 (mM_per_s)"
    legend_algebraic[6] = "Ji_cm in component AE1 (mM_per_s)"
    legend_algebraic[7] = "Js_cm in component AE1 (mM_per_s)"
    legend_rates[0] = "d/dt HCO3_int in component concentrations (mM)"
    legend_rates[1] = "d/dt HCO3_ext in component concentrations (mM)"
    legend_rates[2] = "d/dt Cl_int in component concentrations (mM)"
    legend_rates[3] = "d/dt Cl_ext in component concentrations (mM)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 50.0
    states[1] = 0.0
    states[2] = 0.0
    states[3] = 0.0
    constants[0] = 198
    constants[1] = 198
    constants[2] = 50
    constants[3] = 50
    constants[4] = 1247
    constants[5] = 135
    constants[6] = 562
    constants[7] = 61
    constants[8] = 1
    constants[9] = 172
    constants[10] = 0.00000
    constants[11] = 1.00000
    constants[12] = 0.00000
    constants[13] = 0.00000
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[0] = constants[10]
    rates[1] = constants[11]
    rates[2] = constants[12]
    rates[3] = constants[13]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = constants[8]/(1.00000+states[0]/constants[9])
    algebraic[1] = states[1]/constants[0]
    algebraic[2] = power((1.00000/algebraic[0])*(1.00000/constants[4]+1.00000/constants[5]+constants[1]/(constants[5]*states[0])), -1.00000)
    algebraic[3] = power((1.00000/algebraic[0])*(1.00000/constants[4]+1.00000/constants[5]+constants[0]/(constants[4]*states[1])), -1.00000)
    algebraic[4] = power((1.00000/algebraic[0])*(1.00000/constants[4]+1.00000/constants[5]), -1.00000)
    algebraic[5] = power((1.00000/algebraic[0])*(1.00000/constants[6]+1.00000/constants[7]+constants[3]/(constants[7]*states[2])), -1.00000)
    algebraic[6] = power((1.00000/algebraic[0])*(1.00000/constants[6]+1.00000/constants[7]+constants[2]/(constants[6]*states[3])), -1.00000)
    algebraic[7] = power((1.00000/algebraic[0])*(1.00000/constants[6]+1.00000/constants[7]), -1.00000)
    algebraic[8] = states[0]/constants[1]
    algebraic[9] = states[3]/constants[2]
    algebraic[10] = states[2]/constants[3]
    algebraic[11] = (1.00000+algebraic[1]+algebraic[9])*(constants[5]*algebraic[8]+constants[7]*algebraic[10])+(1.00000+algebraic[8]+algebraic[10])*(constants[4]*algebraic[1]+constants[6]*algebraic[9])
    algebraic[12] = (algebraic[0]/algebraic[11])*(constants[5]*algebraic[8]*constants[6]*algebraic[9]-constants[4]*algebraic[1]*constants[7]*algebraic[10])
    algebraic[13] = (algebraic[0]/algebraic[11])*constants[4]*algebraic[1]*(constants[5]*algebraic[8]+constants[7]*algebraic[10])
    algebraic[14] = (algebraic[0]/algebraic[11])*constants[6]*algebraic[9]*(constants[5]*algebraic[8]+constants[7]*algebraic[10])
    algebraic[15] = (algebraic[0]*(constants[5]*algebraic[8]+constants[7]*algebraic[10]))/algebraic[11]
    algebraic[16] = (algebraic[0]*(constants[4]*algebraic[1]+constants[6]*algebraic[9]))/algebraic[11]
    algebraic[17] = -algebraic[12]
    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)