# Size of variable arrays:
sizeAlgebraic = 18
sizeStates = 8
sizeConstants = 10
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 (ms)"
    legend_states[0] = "V in component membrane (mV)"
    legend_constants[0] = "C in component membrane (uF_per_mm2)"
    legend_algebraic[0] = "i_Na in component sodium_current (uA_per_mm2)"
    legend_algebraic[14] = "i_s in component slow_inward_current (uA_per_mm2)"
    legend_algebraic[15] = "i_x1 in component time_dependent_outward_current (uA_per_mm2)"
    legend_algebraic[16] = "i_K1 in component time_independent_outward_current (uA_per_mm2)"
    legend_algebraic[17] = "Istim in component stimulus_protocol (uA_per_mm2)"
    legend_constants[1] = "g_Na in component sodium_current (mS_per_mm2)"
    legend_constants[2] = "E_Na in component sodium_current (mV)"
    legend_constants[3] = "g_Nac in component sodium_current (mS_per_mm2)"
    legend_states[1] = "m in component sodium_current_m_gate (dimensionless)"
    legend_states[2] = "h in component sodium_current_h_gate (dimensionless)"
    legend_states[3] = "j in component sodium_current_j_gate (dimensionless)"
    legend_algebraic[1] = "alpha_m in component sodium_current_m_gate (per_ms)"
    legend_algebraic[8] = "beta_m in component sodium_current_m_gate (per_ms)"
    legend_algebraic[2] = "alpha_h in component sodium_current_h_gate (per_ms)"
    legend_algebraic[9] = "beta_h in component sodium_current_h_gate (per_ms)"
    legend_algebraic[3] = "alpha_j in component sodium_current_j_gate (per_ms)"
    legend_algebraic[10] = "beta_j in component sodium_current_j_gate (per_ms)"
    legend_constants[4] = "g_s in component slow_inward_current (mS_per_mm2)"
    legend_algebraic[7] = "E_s in component slow_inward_current (mV)"
    legend_states[4] = "Cai in component slow_inward_current (concentration_units)"
    legend_states[5] = "d in component slow_inward_current_d_gate (dimensionless)"
    legend_states[6] = "f in component slow_inward_current_f_gate (dimensionless)"
    legend_algebraic[4] = "alpha_d in component slow_inward_current_d_gate (per_ms)"
    legend_algebraic[11] = "beta_d in component slow_inward_current_d_gate (per_ms)"
    legend_algebraic[5] = "alpha_f in component slow_inward_current_f_gate (per_ms)"
    legend_algebraic[12] = "beta_f in component slow_inward_current_f_gate (per_ms)"
    legend_states[7] = "x1 in component time_dependent_outward_current_x1_gate (dimensionless)"
    legend_algebraic[6] = "alpha_x1 in component time_dependent_outward_current_x1_gate (per_ms)"
    legend_algebraic[13] = "beta_x1 in component time_dependent_outward_current_x1_gate (per_ms)"
    legend_constants[5] = "IstimStart in component stimulus_protocol (ms)"
    legend_constants[6] = "IstimEnd in component stimulus_protocol (ms)"
    legend_constants[7] = "IstimAmplitude in component stimulus_protocol (uA_per_mm2)"
    legend_constants[8] = "IstimPeriod in component stimulus_protocol (ms)"
    legend_constants[9] = "IstimPulseDuration in component stimulus_protocol (ms)"
    legend_rates[0] = "d/dt V in component membrane (mV)"
    legend_rates[1] = "d/dt m in component sodium_current_m_gate (dimensionless)"
    legend_rates[2] = "d/dt h in component sodium_current_h_gate (dimensionless)"
    legend_rates[3] = "d/dt j in component sodium_current_j_gate (dimensionless)"
    legend_rates[4] = "d/dt Cai in component slow_inward_current (concentration_units)"
    legend_rates[5] = "d/dt d in component slow_inward_current_d_gate (dimensionless)"
    legend_rates[6] = "d/dt f in component slow_inward_current_f_gate (dimensionless)"
    legend_rates[7] = "d/dt x1 in component time_dependent_outward_current_x1_gate (dimensionless)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = -84.624
    constants[0] = 0.01
    constants[1] = 4e-2
    constants[2] = 50
    constants[3] = 3e-5
    states[1] = 0.011
    states[2] = 0.988
    states[3] = 0.975
    constants[4] = 9e-4
    states[4] = 1e-4
    states[5] = 0.003
    states[6] = 0.994
    states[7] = 0.0001
    constants[5] = 10
    constants[6] = 50000
    constants[7] = 0.5
    constants[8] = 1000
    constants[9] = 1
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[1] = (-1.00000*(states[0]+47.0000))/(exp(-0.100000*(states[0]+47.0000))-1.00000)
    algebraic[8] = 40.0000*exp(-0.0560000*(states[0]+72.0000))
    rates[1] = algebraic[1]*(1.00000-states[1])-algebraic[8]*states[1]
    algebraic[2] = 0.126000*exp(-0.250000*(states[0]+77.0000))
    algebraic[9] = 1.70000/(exp(-0.0820000*(states[0]+22.5000))+1.00000)
    rates[2] = algebraic[2]*(1.00000-states[2])-algebraic[9]*states[2]
    algebraic[3] = (0.0550000*exp(-0.250000*(states[0]+78.0000)))/(exp(-0.200000*(states[0]+78.0000))+1.00000)
    algebraic[10] = 0.300000/(exp(-0.100000*(states[0]+32.0000))+1.00000)
    rates[3] = algebraic[3]*(1.00000-states[3])-algebraic[10]*states[3]
    algebraic[4] = (0.0950000*exp(-(states[0]-5.00000)/100.000))/(1.00000+exp(-(states[0]-5.00000)/13.8900))
    algebraic[11] = (0.0700000*exp(-(states[0]+44.0000)/59.0000))/(1.00000+exp((states[0]+44.0000)/20.0000))
    rates[5] = algebraic[4]*(1.00000-states[5])-algebraic[11]*states[5]
    algebraic[5] = (0.0120000*exp(-(states[0]+28.0000)/125.000))/(1.00000+exp((states[0]+28.0000)/6.67000))
    algebraic[12] = (0.00650000*exp(-(states[0]+30.0000)/50.0000))/(1.00000+exp(-(states[0]+30.0000)/5.00000))
    rates[6] = algebraic[5]*(1.00000-states[6])-algebraic[12]*states[6]
    algebraic[6] = (0.000500000*exp((states[0]+50.0000)/12.1000))/(1.00000+exp((states[0]+50.0000)/17.5000))
    algebraic[13] = (0.00130000*exp(-(states[0]+20.0000)/16.6700))/(1.00000+exp(-(states[0]+20.0000)/25.0000))
    rates[7] = algebraic[6]*(1.00000-states[7])-algebraic[13]*states[7]
    algebraic[7] = -82.3000-13.0287*log(states[4]*0.00100000)
    algebraic[14] = constants[4]*states[5]*states[6]*(states[0]-algebraic[7])
    rates[4] = (-0.0100000*algebraic[14])/1.00000+0.0700000*(0.000100000-states[4])
    algebraic[0] = (constants[1]*(power(states[1], 3.00000))*states[2]*states[3]+constants[3])*(states[0]-constants[2])
    algebraic[15] = (states[7]*0.00800000*(exp(0.0400000*(states[0]+77.0000))-1.00000))/exp(0.0400000*(states[0]+35.0000))
    algebraic[16] = 0.00350000*((4.00000*(exp(0.0400000*(states[0]+85.0000))-1.00000))/(exp(0.0800000*(states[0]+53.0000))+exp(0.0400000*(states[0]+53.0000)))+(0.200000*(states[0]+23.0000))/(1.00000-exp(-0.0400000*(states[0]+23.0000))))
    algebraic[17] = custom_piecewise([greater_equal(voi , constants[5]) & less_equal(voi , constants[6]) & less_equal((voi-constants[5])-floor((voi-constants[5])/constants[8])*constants[8] , constants[9]), constants[7] , True, 0.00000])
    rates[0] = (algebraic[17]-(algebraic[0]+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]+47.0000))/(exp(-0.100000*(states[0]+47.0000))-1.00000)
    algebraic[8] = 40.0000*exp(-0.0560000*(states[0]+72.0000))
    algebraic[2] = 0.126000*exp(-0.250000*(states[0]+77.0000))
    algebraic[9] = 1.70000/(exp(-0.0820000*(states[0]+22.5000))+1.00000)
    algebraic[3] = (0.0550000*exp(-0.250000*(states[0]+78.0000)))/(exp(-0.200000*(states[0]+78.0000))+1.00000)
    algebraic[10] = 0.300000/(exp(-0.100000*(states[0]+32.0000))+1.00000)
    algebraic[4] = (0.0950000*exp(-(states[0]-5.00000)/100.000))/(1.00000+exp(-(states[0]-5.00000)/13.8900))
    algebraic[11] = (0.0700000*exp(-(states[0]+44.0000)/59.0000))/(1.00000+exp((states[0]+44.0000)/20.0000))
    algebraic[5] = (0.0120000*exp(-(states[0]+28.0000)/125.000))/(1.00000+exp((states[0]+28.0000)/6.67000))
    algebraic[12] = (0.00650000*exp(-(states[0]+30.0000)/50.0000))/(1.00000+exp(-(states[0]+30.0000)/5.00000))
    algebraic[6] = (0.000500000*exp((states[0]+50.0000)/12.1000))/(1.00000+exp((states[0]+50.0000)/17.5000))
    algebraic[13] = (0.00130000*exp(-(states[0]+20.0000)/16.6700))/(1.00000+exp(-(states[0]+20.0000)/25.0000))
    algebraic[7] = -82.3000-13.0287*log(states[4]*0.00100000)
    algebraic[14] = constants[4]*states[5]*states[6]*(states[0]-algebraic[7])
    algebraic[0] = (constants[1]*(power(states[1], 3.00000))*states[2]*states[3]+constants[3])*(states[0]-constants[2])
    algebraic[15] = (states[7]*0.00800000*(exp(0.0400000*(states[0]+77.0000))-1.00000))/exp(0.0400000*(states[0]+35.0000))
    algebraic[16] = 0.00350000*((4.00000*(exp(0.0400000*(states[0]+85.0000))-1.00000))/(exp(0.0800000*(states[0]+53.0000))+exp(0.0400000*(states[0]+53.0000)))+(0.200000*(states[0]+23.0000))/(1.00000-exp(-0.0400000*(states[0]+23.0000))))
    algebraic[17] = custom_piecewise([greater_equal(voi , constants[5]) & less_equal(voi , constants[6]) & less_equal((voi-constants[5])-floor((voi-constants[5])/constants[8])*constants[8] , constants[9]), constants[7] , True, 0.00000])
    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)