# Size of variable arrays:
sizeAlgebraic = 8
sizeStates = 3
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 = "t in component environment (second)"
    legend_constants[0] = "C_m in component environment (fF)"
    legend_constants[1] = "w_i in component environment (pL)"
    legend_constants[2] = "w_o in component environment (pL)"
    legend_states[0] = "q_mem in component environment (fC)"
    legend_constants[3] = "R in component environment (J_per_K_per_mol)"
    legend_constants[4] = "T in component environment (kelvin)"
    legend_constants[5] = "F in component environment (C_per_mol)"
    legend_algebraic[6] = "v_NaB in component NaB (fmol_per_sec)"
    legend_states[1] = "q_Na_o in component environment (fmol)"
    legend_states[2] = "q_Na_i in component environment (fmol)"
    legend_algebraic[0] = "V_mem in component environment (J_per_C)"
    legend_algebraic[7] = "I_mem_NaB in component NaB (fA)"
    legend_constants[6] = "kappa_NaB in component NaB_parameters (fmol_per_sec)"
    legend_constants[7] = "K_Na_i in component NaB_parameters (per_fmol)"
    legend_constants[8] = "K_Na_o in component NaB_parameters (per_fmol)"
    legend_constants[9] = "zNa in component NaB_parameters (dimensionless)"
    legend_algebraic[1] = "mu_Na_i in component NaB (J_per_mol)"
    legend_algebraic[2] = "mu_Na_o in component NaB (J_per_mol)"
    legend_algebraic[3] = "Af_NaB in component NaB (J_per_mol)"
    legend_algebraic[4] = "Ar_NaB in component NaB (J_per_mol)"
    legend_algebraic[5] = "Am_NaB in component NaB (J_per_mol)"
    legend_rates[2] = "d/dt q_Na_i in component environment (fmol)"
    legend_rates[1] = "d/dt q_Na_o in component environment (fmol)"
    legend_rates[0] = "d/dt q_mem in component environment (fC)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 1e6
    constants[1] = 25.8
    constants[2] = 3.52
    states[0] = -8.5e4
    constants[3] = 8.31
    constants[4] = 310
    constants[5] = 96500
    states[1] = 9.3276
    states[2] = 0.00456
    constants[6] = 0.217237
    constants[7] = 0.013549
    constants[8] = 0.0899434
    constants[9] = 1
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = states[0]/constants[0]
    algebraic[1] = constants[3]*constants[4]*log(constants[7]*states[2])
    algebraic[3] = algebraic[1]+(constants[9])*constants[5]*algebraic[0]
    algebraic[2] = constants[3]*constants[4]*log(constants[8]*states[1])
    algebraic[4] = algebraic[2]
    algebraic[5] = constants[9]*constants[5]*algebraic[0]
    algebraic[6] = custom_piecewise([equal(algebraic[5] , 0.00000), constants[6]*(exp(algebraic[3]/(constants[3]*constants[4]))-exp(algebraic[4]/(constants[3]*constants[4]))) , True, (((constants[6]*algebraic[5])/(constants[3]*constants[4]))/(exp(algebraic[5]/(constants[3]*constants[4]))-1.00000))*(exp(algebraic[3]/(constants[3]*constants[4]))-exp(algebraic[4]/(constants[3]*constants[4])))])
    rates[2] = -algebraic[6]
    rates[1] = algebraic[6]
    algebraic[7] = -constants[9]*constants[5]*algebraic[6]
    rates[0] = algebraic[7]
    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[0]
    algebraic[1] = constants[3]*constants[4]*log(constants[7]*states[2])
    algebraic[3] = algebraic[1]+(constants[9])*constants[5]*algebraic[0]
    algebraic[2] = constants[3]*constants[4]*log(constants[8]*states[1])
    algebraic[4] = algebraic[2]
    algebraic[5] = constants[9]*constants[5]*algebraic[0]
    algebraic[6] = custom_piecewise([equal(algebraic[5] , 0.00000), constants[6]*(exp(algebraic[3]/(constants[3]*constants[4]))-exp(algebraic[4]/(constants[3]*constants[4]))) , True, (((constants[6]*algebraic[5])/(constants[3]*constants[4]))/(exp(algebraic[5]/(constants[3]*constants[4]))-1.00000))*(exp(algebraic[3]/(constants[3]*constants[4]))-exp(algebraic[4]/(constants[3]*constants[4])))])
    algebraic[7] = -constants[9]*constants[5]*algebraic[6]
    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)