# Size of variable arrays:
sizeAlgebraic = 3
sizeStates = 1
sizeConstants = 9
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] = "Na_int in component concentrations (mM)"
    legend_constants[0] = "Na_ext in component concentrations (mM)"
    legend_constants[1] = "K_int in component concentrations (mM)"
    legend_constants[2] = "K_ext in component concentrations (mM)"
    legend_constants[3] = "NH4_ext in component concentrations (mM)"
    legend_algebraic[0] = "J_NaK_Na in component NaK (mM_per_s)"
    legend_algebraic[1] = "J_NaK_K in component NaK (mM_per_s)"
    legend_algebraic[2] = "J_NaK_NH4 in component NaK (mM_per_s)"
    legend_constants[5] = "K_Na in component NaK (mM)"
    legend_constants[6] = "K_K in component NaK (mM)"
    legend_constants[7] = "K_NH4 in component NaK (mM)"
    legend_constants[4] = "J_NaK_Na_Max in component NaK (mM_per_s)"
    legend_rates[0] = "d/dt Na_int 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] = 0.0
    constants[0] = 0.0
    constants[1] = 39.0
    constants[2] = 10.0
    constants[3] = 0.0
    constants[4] = 10.8
    constants[5] = 0.200000*(1.00000+constants[1]/8.33000)
    constants[6] = 0.100000*(1.00000+constants[0]/18.5000)
    constants[8] = 1.00000
    constants[7] = 0.200000*constants[6]
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[0] = constants[8]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = constants[4]*(power(states[0]/(states[0]+constants[5]), 3.00000))*(power(constants[2]/(constants[2]+constants[6]), 2.00000))
    algebraic[1] = ((-2.00000/3.00000)*algebraic[0])/(1.00000+(constants[3]*constants[6])/(constants[2]*constants[7]))
    algebraic[2] = algebraic[1]*(power(constants[3]/constants[7], 1.00000))*(power(constants[6]/constants[2], 1.00000))
    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)