Generated Code

# Size of variable arrays:
sizeAlgebraic = 6
sizeStates = 1
sizeConstants = 25
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_constants[0] = "Na_ext in component concentrations (mM)"
    legend_constants[1] = "Na_int in component concentrations (mM)"
    legend_constants[2] = "H_ext in component concentrations (mM)"
    legend_constants[3] = "H_int in component concentrations (mM)"
    legend_states[0] = "NH4_ext in component concentrations (mM)"
    legend_constants[4] = "NH4_int in component concentrations (mM)"
    legend_algebraic[2] = "J_NHE3_Na in component NHE3 (mM_per_s)"
    legend_algebraic[3] = "J_NHE3_H in component NHE3 (mM_per_s)"
    legend_algebraic[4] = "J_NHE3_NH4 in component NHE3 (mM_per_s)"
    legend_constants[23] = "J_NHE3_Na_Max in component NHE3 (mM_per_s)"
    legend_algebraic[5] = "plot in component fluxes (mM)"
    legend_constants[5] = "x_T in component NHE3 (mM)"
    legend_algebraic[1] = "sigma in component NHE3 (per_s)"
    legend_constants[20] = "P_Na in component NHE3 (per_s)"
    legend_constants[21] = "P_H in component NHE3 (per_s)"
    legend_constants[22] = "P_NH4 in component NHE3 (per_s)"
    legend_constants[6] = "P0_Na in component NHE3 (per_s)"
    legend_constants[7] = "P0_H in component NHE3 (per_s)"
    legend_constants[8] = "P0_NH4 in component NHE3 (per_s)"
    legend_constants[9] = "K_Na in component NHE3 (mM)"
    legend_constants[10] = "K_H in component NHE3 (mM)"
    legend_constants[11] = "K_NH4 in component NHE3 (mM)"
    legend_constants[12] = "K_I in component NHE3 (mM)"
    legend_constants[13] = "f_m in component NHE3 (dimensionless)"
    legend_constants[14] = "f_M in component NHE3 (dimensionless)"
    legend_constants[15] = "alpha_ext_Na in component NHE3 (dimensionless)"
    legend_constants[16] = "alpha_int_Na in component NHE3 (dimensionless)"
    legend_constants[17] = "beta_ext_H in component NHE3 (dimensionless)"
    legend_constants[18] = "beta_int_H in component NHE3 (dimensionless)"
    legend_algebraic[0] = "gamma_ext_NH4 in component NHE3 (dimensionless)"
    legend_constants[19] = "gamma_int_NH4 in component NHE3 (dimensionless)"
    legend_rates[0] = "d/dt NH4_ext in component concentrations (mM)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 0.1
    constants[1] = 0.0
    constants[2] = 3.1623e-5
    constants[3] = 1.0e-3
    states[0] = 1.0
    constants[4] = 0.0
    constants[5] = 1.0
    constants[6] = 1.6e-3
    constants[7] = 0.48e-3
    constants[8] = 1.6e-3
    constants[9] = 30.0
    constants[10] = 72e-6
    constants[11] = 27.0
    constants[12] = 1.0e-6
    constants[13] = 0.0
    constants[14] = 2.0
    constants[15] = constants[0]/constants[9]
    constants[24] = 39.0000
    constants[16] = constants[1]/constants[9]
    constants[17] = constants[2]/constants[10]
    constants[18] = constants[3]/constants[10]
    constants[19] = constants[4]/constants[11]
    constants[20] = (constants[6]*(constants[14]*constants[3]+constants[13]*constants[12]))/(constants[3]+constants[12])
    constants[21] = (constants[7]*(constants[14]*constants[3]+constants[13]*constants[12]))/(constants[3]+constants[12])
    constants[22] = (constants[8]*(constants[14]*constants[3]+constants[13]*constants[12]))/(constants[3]+constants[12])
    constants[23] = (constants[5]*constants[20]*constants[21])/(constants[20]+constants[21])
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[0] = constants[24]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = states[0]/constants[11]
    algebraic[1] = (1.00000+constants[15]+constants[17]+algebraic[0])*(constants[20]*constants[16]+constants[21]*constants[18]+constants[22]*constants[19])+(1.00000+constants[16]+constants[18]+constants[19])*(constants[20]*constants[15]+constants[21]*constants[17]+constants[22]*algebraic[0])
    algebraic[2] = (constants[5]/algebraic[1])*(constants[20]*constants[21]*(constants[16]*constants[17]-constants[15]*constants[18])+constants[20]*constants[22]*(constants[16]*algebraic[0]-constants[15]*constants[19]))
    algebraic[3] = (constants[5]/algebraic[1])*(constants[20]*constants[21]*(constants[15]*constants[18]-constants[16]*constants[17])+constants[21]*constants[22]*(constants[18]*algebraic[0]-constants[17]*constants[19]))
    algebraic[4] = (constants[5]/algebraic[1])*(constants[20]*constants[22]*(constants[15]*constants[19]-constants[16]*algebraic[0])+constants[21]*constants[22]*(constants[17]*constants[19]-algebraic[0]*constants[18]))
    algebraic[5] = -1.00000/(algebraic[2]/constants[23])
    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)