# Size of variable arrays:
sizeAlgebraic = 16
sizeStates = 6
sizeConstants = 11
from math import *
from numpy import *

def createLegends():
    legend_states = [""] * sizeStates
    legend_rates = [""] * sizeStates
    legend_algebraic = [""] * sizeAlgebraic
    legend_voi = ""
    legend_constants = [""] * sizeConstants
    legend_voi = "t in component environment (ms)"
    legend_states[0] = "V_m in component membrane (mV)"
    legend_algebraic[0] = "i_Stim in component membrane (mA_per_cm2)"
    legend_constants[0] = "stim_amplitude in component membrane (mA_per_cm2)"
    legend_constants[1] = "stim_duration in component membrane (ms)"
    legend_algebraic[6] = "i_Naf in component fast_sodium_channel (mA_per_cm2)"
    legend_algebraic[12] = "i_Nap in component persistent_sodium_channel (mA_per_cm2)"
    legend_algebraic[13] = "i_Ks in component slow_potassium_channel (mA_per_cm2)"
    legend_algebraic[14] = "i_Kf in component juxtaparanodal_fast_potassium_channel (mA_per_cm2)"
    legend_algebraic[15] = "i_Lk in component leakage_channel (mA_per_cm2)"
    legend_constants[2] = "C_n in component membrane (mF_per_cm2)"
    legend_constants[3] = "E_Na in component membrane (mV)"
    legend_constants[4] = "E_K in component membrane (mV)"
    legend_constants[5] = "E_Lk in component membrane (mV)"
    legend_constants[6] = "g_Naf in component fast_sodium_channel (S_per_cm2)"
    legend_states[1] = "m in component fast_sodium_channel_m_gate (dimensionless)"
    legend_states[2] = "h in component fast_sodium_channel_h_gate (dimensionless)"
    legend_algebraic[1] = "alpha_m in component fast_sodium_channel_m_gate (per_ms)"
    legend_algebraic[7] = "beta_m in component fast_sodium_channel_m_gate (per_ms)"
    legend_algebraic[2] = "alpha_h in component fast_sodium_channel_h_gate (per_ms)"
    legend_algebraic[8] = "beta_h in component fast_sodium_channel_h_gate (per_ms)"
    legend_constants[7] = "g_Nap in component persistent_sodium_channel (S_per_cm2)"
    legend_states[3] = "p in component persistent_sodium_channel_p_gate (dimensionless)"
    legend_algebraic[3] = "alpha_p in component persistent_sodium_channel_p_gate (per_ms)"
    legend_algebraic[9] = "beta_p in component persistent_sodium_channel_p_gate (per_ms)"
    legend_constants[8] = "g_Ks in component slow_potassium_channel (S_per_cm2)"
    legend_states[4] = "s in component slow_potassium_channel_s_gate (dimensionless)"
    legend_algebraic[4] = "alpha_s in component slow_potassium_channel_s_gate (per_ms)"
    legend_algebraic[10] = "beta_s in component slow_potassium_channel_s_gate (per_ms)"
    legend_constants[9] = "g_Kf in component juxtaparanodal_fast_potassium_channel (S_per_cm2)"
    legend_states[5] = "n in component juxtaparanodal_fast_potassium_channel_n_gate (dimensionless)"
    legend_algebraic[5] = "alpha_n in component juxtaparanodal_fast_potassium_channel_n_gate (per_ms)"
    legend_algebraic[11] = "beta_n in component juxtaparanodal_fast_potassium_channel_n_gate (per_ms)"
    legend_constants[10] = "g_Lk in component leakage_channel (S_per_cm2)"
    legend_rates[0] = "d/dt V_m in component membrane (mV)"
    legend_rates[1] = "d/dt m in component fast_sodium_channel_m_gate (dimensionless)"
    legend_rates[2] = "d/dt h in component fast_sodium_channel_h_gate (dimensionless)"
    legend_rates[3] = "d/dt p in component persistent_sodium_channel_p_gate (dimensionless)"
    legend_rates[4] = "d/dt s in component slow_potassium_channel_s_gate (dimensionless)"
    legend_rates[5] = "d/dt n in component juxtaparanodal_fast_potassium_channel_n_gate (dimensionless)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = -88.5901439103062
    constants[0] = 0.05
    constants[1] = 0.5
    constants[2] = 0.002
    constants[3] = 50
    constants[4] = -90
    constants[5] = -90
    constants[6] = 3
    states[1] = 0.0302964457761589
    states[2] = 0.841520865130776
    constants[7] = 0.01
    states[3] = 0.0969864645712442
    constants[8] = 0.08
    states[4] = 0.00997371545602793
    constants[9] = 0
    states[5] = 0.000886041197111556
    constants[10] = 0.007
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[1] = (6.57000*(states[0]+20.4000))/(1.00000-exp(-(states[0]+20.4000)/10.3000))
    algebraic[7] = (-0.304000*(states[0]+25.7000))/(1.00000-exp((states[0]+25.7000)/9.16000))
    rates[1] = algebraic[1]*(1.00000-states[1])-algebraic[7]*states[1]
    algebraic[2] = (-0.340000*(states[0]+114.000))/(1.00000-exp((states[0]+114.000)/11.0000))
    algebraic[8] = 12.6000/(1.00000+exp(-(states[0]+31.8000)/13.4000))
    rates[2] = algebraic[2]*(1.00000-states[2])-algebraic[8]*states[2]
    algebraic[3] = (0.0353000*(states[0]+27.0000))/(1.00000-exp(-(states[0]+27.0000)/10.2000))
    algebraic[9] = (-0.000883000*(states[0]+34.0000))/(1.00000-exp((states[0]+34.0000)/10.0000))
    rates[3] = algebraic[3]*(1.00000-states[3])-algebraic[9]*states[3]
    algebraic[4] = 0.300000/(1.00000+exp(-(states[0]+53.0000)/5.00000))
    algebraic[10] = 0.0300000/(1.00000+exp(-(states[0]+90.0000)/1.00000))
    rates[4] = algebraic[4]*(1.00000-states[4])-algebraic[10]*states[4]
    algebraic[5] = (0.0462000*(states[0]+83.2000))/(1.00000-exp(-(states[0]+83.2000)/1.10000))
    algebraic[11] = (-0.0824000*(states[0]+66.0000))/(1.00000-exp((states[0]+66.0000)/10.5000))
    rates[5] = algebraic[5]*(1.00000-states[5])-algebraic[11]*states[5]
    algebraic[0] = custom_piecewise([greater_equal(voi , 10.0000) & less_equal(voi , 10.0000+constants[1]), constants[0] , True, 0.00000])
    algebraic[6] = constants[6]*(power(states[1], 3.00000))*states[2]*(states[0]-constants[3])
    algebraic[12] = constants[7]*(power(states[3], 3.00000))*(states[0]-constants[3])
    algebraic[13] = constants[8]*states[4]*(states[0]-constants[4])
    algebraic[14] = constants[9]*(power(states[5], 4.00000))*(states[0]-constants[4])
    algebraic[15] = constants[10]*(states[0]-constants[5])
    rates[0] = -(-algebraic[0]+algebraic[6]+algebraic[12]+algebraic[13]+algebraic[14]+algebraic[15])/constants[2]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[1] = (6.57000*(states[0]+20.4000))/(1.00000-exp(-(states[0]+20.4000)/10.3000))
    algebraic[7] = (-0.304000*(states[0]+25.7000))/(1.00000-exp((states[0]+25.7000)/9.16000))
    algebraic[2] = (-0.340000*(states[0]+114.000))/(1.00000-exp((states[0]+114.000)/11.0000))
    algebraic[8] = 12.6000/(1.00000+exp(-(states[0]+31.8000)/13.4000))
    algebraic[3] = (0.0353000*(states[0]+27.0000))/(1.00000-exp(-(states[0]+27.0000)/10.2000))
    algebraic[9] = (-0.000883000*(states[0]+34.0000))/(1.00000-exp((states[0]+34.0000)/10.0000))
    algebraic[4] = 0.300000/(1.00000+exp(-(states[0]+53.0000)/5.00000))
    algebraic[10] = 0.0300000/(1.00000+exp(-(states[0]+90.0000)/1.00000))
    algebraic[5] = (0.0462000*(states[0]+83.2000))/(1.00000-exp(-(states[0]+83.2000)/1.10000))
    algebraic[11] = (-0.0824000*(states[0]+66.0000))/(1.00000-exp((states[0]+66.0000)/10.5000))
    algebraic[0] = custom_piecewise([greater_equal(voi , 10.0000) & less_equal(voi , 10.0000+constants[1]), constants[0] , True, 0.00000])
    algebraic[6] = constants[6]*(power(states[1], 3.00000))*states[2]*(states[0]-constants[3])
    algebraic[12] = constants[7]*(power(states[3], 3.00000))*(states[0]-constants[3])
    algebraic[13] = constants[8]*states[4]*(states[0]-constants[4])
    algebraic[14] = constants[9]*(power(states[5], 4.00000))*(states[0]-constants[4])
    algebraic[15] = constants[10]*(states[0]-constants[5])
    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)