# Size of variable arrays:
sizeAlgebraic = 7
sizeStates = 2
sizeConstants = 2
from math import *
from numpy import *

def createLegends():
    legend_states = [""] * sizeStates
    legend_rates = [""] * sizeStates
    legend_algebraic = [""] * sizeAlgebraic
    legend_voi = ""
    legend_constants = [""] * sizeConstants
    legend_algebraic[0] = "V in component environment (millivolt)"
    legend_voi = "t in component environment (millisec)"
    legend_states[0] = "m in component sodium_channel_m_gate (dimensionless)"
    legend_states[1] = "h in component sodium_channel_h_gate (dimensionless)"
    legend_constants[0] = "g_Na in component sodium_channel (milliS_per_cm2)"
    legend_constants[1] = "E_Na in component sodium_channel (millivolt)"
    legend_algebraic[1] = "Na_conductance in component sodium_channel (milliS_per_cm2)"
    legend_algebraic[4] = "i_Na in component sodium_channel (microA_per_cm2)"
    legend_algebraic[2] = "alpha_m in component sodium_channel_m_gate (per_millisec)"
    legend_algebraic[5] = "beta_m in component sodium_channel_m_gate (per_millisec)"
    legend_algebraic[3] = "alpha_h in component sodium_channel_h_gate (per_millisec)"
    legend_algebraic[6] = "beta_h in component sodium_channel_h_gate (per_millisec)"
    legend_rates[0] = "d/dt m in component sodium_channel_m_gate (dimensionless)"
    legend_rates[1] = "d/dt h in component sodium_channel_h_gate (dimensionless)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 0.05
    states[1] = 0.6
    constants[0] = 120
    constants[1] = 35
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = custom_piecewise([greater(voi , 5.00000) & less(voi , 15.0000), 0.00000 , True, -85.0000])
    algebraic[2] = (-0.100000*(algebraic[0]+50.0000))/(exp(-(algebraic[0]+50.0000)/10.0000)-1.00000)
    algebraic[5] = 4.00000*exp(-(algebraic[0]+75.0000)/18.0000)
    rates[0] = algebraic[2]*(1.00000-states[0])-algebraic[5]*states[0]
    algebraic[3] = 0.0700000*exp(-(algebraic[0]+75.0000)/20.0000)
    algebraic[6] = 1.00000/(exp(-(algebraic[0]+45.0000)/10.0000)+1.00000)
    rates[1] = algebraic[3]*(1.00000-states[1])-algebraic[6]*states[1]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = custom_piecewise([greater(voi , 5.00000) & less(voi , 15.0000), 0.00000 , True, -85.0000])
    algebraic[2] = (-0.100000*(algebraic[0]+50.0000))/(exp(-(algebraic[0]+50.0000)/10.0000)-1.00000)
    algebraic[5] = 4.00000*exp(-(algebraic[0]+75.0000)/18.0000)
    algebraic[3] = 0.0700000*exp(-(algebraic[0]+75.0000)/20.0000)
    algebraic[6] = 1.00000/(exp(-(algebraic[0]+45.0000)/10.0000)+1.00000)
    algebraic[1] = constants[0]*(power(states[0], 3.00000))*states[1]
    algebraic[4] = algebraic[1]*(algebraic[0]-constants[1])
    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)