Generated Code

# Size of variable arrays:
sizeAlgebraic = 15
sizeStates = 1
sizeConstants = 17
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_i in component Concentrations (mM)"
    legend_constants[0] = "HCO3_e in component Concentrations (mM)"
    legend_constants[1] = "Cl_i in component Concentrations (mM)"
    legend_constants[2] = "Cl_e in component Concentrations (mM)"
    legend_constants[3] = "x_Tmax in component Concentrations (nmol_per_cm2)"
    legend_algebraic[0] = "x_T in component Concentrations (nmol_per_cm2)"
    legend_constants[4] = "K_I in component AE1_rate_constants (mM)"
    legend_constants[5] = "Kc_p in component AE1_rate_constants (mM)"
    legend_constants[6] = "Kc_pp in component AE1_rate_constants (mM)"
    legend_constants[7] = "Kb_p in component AE1_rate_constants (mM)"
    legend_constants[8] = "Kb_pp in component AE1_rate_constants (mM)"
    legend_constants[9] = "Pc_p in component AE1_rate_constants (per_s)"
    legend_constants[10] = "Pc_pp in component AE1_rate_constants (per_s)"
    legend_constants[11] = "Pb_p in component AE1_rate_constants (per_s)"
    legend_constants[12] = "Pb_pp in component AE1_rate_constants (per_s)"
    legend_constants[13] = "beta_p in component AE1 (dimensionless)"
    legend_algebraic[1] = "beta_pp in component AE1 (dimensionless)"
    legend_constants[14] = "gamma_p in component AE1 (dimensionless)"
    legend_constants[15] = "gamma_pp in component AE1 (dimensionless)"
    legend_algebraic[8] = "sigma in component AE1 (per_s)"
    legend_algebraic[9] = "x_p in component AE1 (nmol_per_cm2)"
    legend_algebraic[10] = "x_pp in component AE1 (nmol_per_cm2)"
    legend_algebraic[11] = "J_HCO3 in component AE1 (nmol_per_s_per_cm2)"
    legend_algebraic[14] = "J_Cl in component AE1 (nmol_per_s_per_cm2)"
    legend_algebraic[12] = "Jb_influx in component AE1 (nmol_per_s_per_cm2)"
    legend_algebraic[13] = "Jc_influx in component AE1 (nmol_per_s_per_cm2)"
    legend_algebraic[2] = "Jo_bm in component AE1 (nmol_per_s_per_cm2)"
    legend_algebraic[3] = "Ji_bm in component AE1 (nmol_per_s_per_cm2)"
    legend_algebraic[4] = "Js_bm in component AE1 (nmol_per_s_per_cm2)"
    legend_algebraic[5] = "Jo_cm in component AE1 (nmol_per_s_per_cm2)"
    legend_algebraic[6] = "Ji_cm in component AE1 (nmol_per_s_per_cm2)"
    legend_algebraic[7] = "Js_cm in component AE1 (nmol_per_s_per_cm2)"
    legend_rates[0] = "d/dt HCO3_i 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] = 0
    constants[0] = 26
    constants[1] = 29
    constants[2] = 114
    constants[3] = 1
    constants[4] = 172
    constants[5] = 50
    constants[6] = 50
    constants[7] = 198
    constants[8] = 198
    constants[9] = 562
    constants[10] = 61
    constants[11] = 1247
    constants[12] = 135
    constants[13] = constants[0]/constants[7]
    constants[16] = 60.0000
    constants[14] = constants[2]/constants[5]
    constants[15] = constants[1]/constants[6]
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[0] = constants[16]
    return(rates)

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