# Size of variable arrays:
sizeAlgebraic = 1
sizeStates = 1
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 = "time in component environment (millisecond)"
    legend_constants[0] = "C in component membrane (microF_per_mm2)"
    legend_constants[1] = "T in component membrane (per_millisecond)"
    legend_states[0] = "Y in component membrane (dimensionless)"
    legend_constants[7] = "Y_infinity_Vm in component membrane (dimensionless)"
    legend_constants[2] = "Vm in component membrane (millivolt)"
    legend_algebraic[0] = "I_ion in component membrane (microA_per_mm2)"
    legend_constants[8] = "i1_Vm in component membrane (microA_per_mm2)"
    legend_constants[10] = "i0_Vm in component membrane (microA_per_mm2)"
    legend_constants[9] = "f_Vm in component membrane (microA_per_mm2)"
    legend_constants[3] = "af in component membrane (dimensionless)"
    legend_constants[4] = "bf in component membrane (dimensionless)"
    legend_constants[5] = "cf in component membrane (dimensionless)"
    legend_constants[6] = "df in component membrane (dimensionless)"
    legend_rates[0] = "d/dt Y in component membrane (dimensionless)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 0.01
    constants[1] = 50.0
    states[0] = 0.07
    constants[2] = -78.6
    constants[3] = 0.00003837854
    constants[4] = 0.00584649
    constants[5] = 0.2531834
    constants[6] = 2.356256
    constants[7] = custom_piecewise([less(constants[2] , -80.0000), 0.00000 , greater(constants[2] , -60.0000), 1.00000 , True, (constants[2]+80.0000)/20.0000])
    constants[8] = custom_piecewise([less(constants[2] , -70.0000), 0.0500000+0.00500000*(constants[2]+70.0000) , greater(constants[2] , 0.00000), 0.0600000+0.00425000*constants[2] , True, 0.0500000+(0.0100000*(constants[2]+70.0000))/70.0000])
    constants[9] = custom_piecewise([less(constants[2] , -74.3000), 0.0784000+0.0200000*(constants[2]+74.3000) , greater(constants[2] , -27.8000), -0.988400+0.0171000*(constants[2]+27.8000) , True, constants[3]*(power(constants[2], 3.00000))+constants[4]*(power(constants[2], 2.00000))+constants[5]*constants[2]+constants[6]])
    constants[10] = constants[8]+constants[9]
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[0] = (1.00000/constants[1])*(constants[7]-states[0])
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = -states[0]*constants[8]-(1.00000-states[0])*constants[10]
    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)