# Size of variable arrays:
sizeAlgebraic = 17
sizeStates = 7
sizeConstants = 1
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 (millisecond)"
    legend_states[0] = "V in component membrane (millivolt)"
    legend_constants[0] = "Cm in component membrane (microF_per_cm2)"
    legend_algebraic[0] = "i_Na in component sodium_channel (microA_per_cm2)"
    legend_algebraic[7] = "i_K in component potassium_channel (microA_per_cm2)"
    legend_algebraic[14] = "i_Leak in component leakage_current (microA_per_cm2)"
    legend_algebraic[15] = "i_s in component calcium_channel (microA_per_cm2)"
    legend_algebraic[16] = "i_h in component hyperpolarization_activated_channel (microA_per_cm2)"
    legend_states[1] = "m in component sodium_channel_m_gate (dimensionless)"
    legend_states[2] = "h in component sodium_channel_h_gate (dimensionless)"
    legend_algebraic[1] = "alpha_m in component sodium_channel_m_gate (per_millisecond)"
    legend_algebraic[8] = "beta_m in component sodium_channel_m_gate (per_millisecond)"
    legend_algebraic[2] = "alpha_h in component sodium_channel_h_gate (per_millisecond)"
    legend_algebraic[9] = "beta_h in component sodium_channel_h_gate (per_millisecond)"
    legend_states[3] = "n in component potassium_channel_n_gate (dimensionless)"
    legend_algebraic[3] = "alpha_n in component potassium_channel_n_gate (per_millisecond)"
    legend_algebraic[10] = "beta_n in component potassium_channel_n_gate (per_millisecond)"
    legend_states[4] = "d in component calcium_channel_d_gate (dimensionless)"
    legend_states[5] = "f in component calcium_channel_f_gate (dimensionless)"
    legend_algebraic[4] = "alpha_d in component calcium_channel_d_gate (per_millisecond)"
    legend_algebraic[11] = "beta_d in component calcium_channel_d_gate (per_millisecond)"
    legend_algebraic[5] = "alpha_f in component calcium_channel_f_gate (per_millisecond)"
    legend_algebraic[12] = "beta_f in component calcium_channel_f_gate (per_millisecond)"
    legend_states[6] = "q in component hyperpolarization_activated_channel_q_gate (dimensionless)"
    legend_algebraic[6] = "alpha_q in component hyperpolarization_activated_channel_q_gate (per_millisecond)"
    legend_algebraic[13] = "beta_q in component hyperpolarization_activated_channel_q_gate (per_millisecond)"
    legend_rates[0] = "d/dt V in component membrane (millivolt)"
    legend_rates[1] = "d/dt m in component sodium_channel_m_gate (dimensionless)"
    legend_rates[2] = "d/dt h in component sodium_channel_h_gate (dimensionless)"
    legend_rates[3] = "d/dt n in component potassium_channel_n_gate (dimensionless)"
    legend_rates[4] = "d/dt d in component calcium_channel_d_gate (dimensionless)"
    legend_rates[5] = "d/dt f in component calcium_channel_f_gate (dimensionless)"
    legend_rates[6] = "d/dt q in component hyperpolarization_activated_channel_q_gate (dimensionless)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = -62.83
    constants[0] = 1
    states[1] = 0.047938
    states[2] = 0.95994
    states[3] = 0.509494
    states[4] = 0.000032
    states[5] = 1
    states[6] = 0.010759
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[1] = (1.00000*(states[0]+37.0000))/(-exp((states[0]+37.0000)/-10.0000)+1.00000)
    algebraic[8] = 40.0000*exp((states[0]+62.0000)/-17.8000)
    rates[1] = algebraic[1]*(1.00000-states[1])-algebraic[8]*states[1]
    algebraic[2] = 0.00120900*exp((states[0]+20.0000)/-6.53400)
    algebraic[9] = 1.00000/(1.00000+exp((states[0]+30.0000)/-10.0000))
    rates[2] = algebraic[2]*(1.00000-states[2])-algebraic[9]*states[2]
    algebraic[3] = (0.00900000*1.00000)/(1.00000+exp(-(states[0]+3.80000)/9.71000))+0.000600000
    algebraic[10] = (-0.000225000*(states[0]+40.0000))/(1.00000-exp((states[0]+40.0000)/13.3000))
    rates[3] = algebraic[3]*(1.00000-states[3])-algebraic[10]*states[3]
    algebraic[4] = (0.0145000*(states[0]+35.0000))/(1.00000-exp(-(states[0]+35.0000)/2.50000))+(0.0312500*states[0])/(1.00000-exp(-states[0]/4.80000))
    algebraic[11] = (-0.00421000*(states[0]-5.00000))/(-exp((states[0]-5.00000)/2.50000)+1.00000)
    rates[4] = algebraic[4]*(1.00000-states[4])-algebraic[11]*states[4]
    algebraic[5] = (-0.000355000*(states[0]+20.0000))/(-exp((states[0]+20.0000)/5.63300)+1.00000)
    algebraic[12] = (0.000944000*(states[0]+60.0000))/(1.00000+exp(-(states[0]+29.5000)/4.16000))
    rates[5] = algebraic[5]*(1.00000-states[5])-algebraic[12]*states[5]
    algebraic[6] = (0.000340000*(states[0]+100.000))/(exp((states[0]+100.000)/4.40000)-1.00000)+4.95000e-05
    algebraic[13] = (0.000500000*(states[0]+40.0000))/(1.00000-exp(-(states[0]+40.0000)/6.00000))+8.45000e-05
    rates[6] = algebraic[6]*(1.00000-states[6])-algebraic[13]*states[6]
    algebraic[0] = 0.500000*(power(states[1], 3.00000))*states[2]*(states[0]-30.0000)
    algebraic[7] = (0.700000*states[3]*(exp(0.0277000*(states[0]+90.0000))-1.00000))/exp(0.0277000*(states[0]+40.0000))
    algebraic[14] = 0.800000*(1.00000-exp(-(states[0]+60.0000)/20.0000))
    algebraic[15] = 12.5000*(0.950000*states[4]+0.0500000)*(0.950000*states[5]+0.0500000)*(exp((states[0]-10.0000)/15.0000)-1.00000)
    algebraic[16] = 0.400000*states[6]*(states[0]+45.0000)
    rates[0] = -(algebraic[0]+algebraic[7]+algebraic[14]+algebraic[15]+algebraic[16])/constants[0]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[1] = (1.00000*(states[0]+37.0000))/(-exp((states[0]+37.0000)/-10.0000)+1.00000)
    algebraic[8] = 40.0000*exp((states[0]+62.0000)/-17.8000)
    algebraic[2] = 0.00120900*exp((states[0]+20.0000)/-6.53400)
    algebraic[9] = 1.00000/(1.00000+exp((states[0]+30.0000)/-10.0000))
    algebraic[3] = (0.00900000*1.00000)/(1.00000+exp(-(states[0]+3.80000)/9.71000))+0.000600000
    algebraic[10] = (-0.000225000*(states[0]+40.0000))/(1.00000-exp((states[0]+40.0000)/13.3000))
    algebraic[4] = (0.0145000*(states[0]+35.0000))/(1.00000-exp(-(states[0]+35.0000)/2.50000))+(0.0312500*states[0])/(1.00000-exp(-states[0]/4.80000))
    algebraic[11] = (-0.00421000*(states[0]-5.00000))/(-exp((states[0]-5.00000)/2.50000)+1.00000)
    algebraic[5] = (-0.000355000*(states[0]+20.0000))/(-exp((states[0]+20.0000)/5.63300)+1.00000)
    algebraic[12] = (0.000944000*(states[0]+60.0000))/(1.00000+exp(-(states[0]+29.5000)/4.16000))
    algebraic[6] = (0.000340000*(states[0]+100.000))/(exp((states[0]+100.000)/4.40000)-1.00000)+4.95000e-05
    algebraic[13] = (0.000500000*(states[0]+40.0000))/(1.00000-exp(-(states[0]+40.0000)/6.00000))+8.45000e-05
    algebraic[0] = 0.500000*(power(states[1], 3.00000))*states[2]*(states[0]-30.0000)
    algebraic[7] = (0.700000*states[3]*(exp(0.0277000*(states[0]+90.0000))-1.00000))/exp(0.0277000*(states[0]+40.0000))
    algebraic[14] = 0.800000*(1.00000-exp(-(states[0]+60.0000)/20.0000))
    algebraic[15] = 12.5000*(0.950000*states[4]+0.0500000)*(0.950000*states[5]+0.0500000)*(exp((states[0]-10.0000)/15.0000)-1.00000)
    algebraic[16] = 0.400000*states[6]*(states[0]+45.0000)
    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)