# Size of variable arrays:
sizeAlgebraic = 21
sizeStates = 3
sizeConstants = 19
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] = "q_K_o in component environment (fmol)"
    legend_constants[2] = "q_K_i in component environment (fmol)"
    legend_states[0] = "q_S_Ks0 in component environment (fmol)"
    legend_states[1] = "q_S_Ks1 in component environment (fmol)"
    legend_states[2] = "q_S_Ks2 in component environment (fmol)"
    legend_algebraic[1] = "q_mem in component environment (fC)"
    legend_algebraic[0] = "Vmem in component environment (volt)"
    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[14] = "v_Ks in component Ks (fmol_per_sec)"
    legend_algebraic[18] = "I_mem_Ks in component Ks (fA)"
    legend_algebraic[15] = "i_Ks in component environment (uA_per_uF)"
    legend_constants[6] = "kappa_Ks in component Ks_parameters (fmol_per_sec)"
    legend_constants[7] = "kappa_xs1 in component Ks_parameters (fmol_per_sec)"
    legend_constants[8] = "kappa_xs2 in component Ks_parameters (fmol_per_sec)"
    legend_constants[9] = "K_K_i in component Ks_parameters (per_fmol)"
    legend_constants[10] = "K_K_o in component Ks_parameters (per_fmol)"
    legend_constants[11] = "K_S_Ks0 in component Ks_parameters (per_fmol)"
    legend_constants[12] = "K_S_Ks1 in component Ks_parameters (per_fmol)"
    legend_constants[13] = "K_S_Ks2 in component Ks_parameters (per_fmol)"
    legend_constants[14] = "zK in component Ks_parameters (dimensionless)"
    legend_constants[15] = "z_xs_f in component Ks_parameters (dimensionless)"
    legend_constants[16] = "z_xs_r in component Ks_parameters (dimensionless)"
    legend_constants[17] = "u_K_i in component Ks (J_per_mol)"
    legend_constants[18] = "u_K_o in component Ks (J_per_mol)"
    legend_algebraic[2] = "V_mem in component Ks (J_per_C)"
    legend_algebraic[3] = "Am_Ks in component Ks (J_per_mol)"
    legend_algebraic[12] = "Af_Ks in component Ks (J_per_mol)"
    legend_algebraic[13] = "Ar_Ks in component Ks (J_per_mol)"
    legend_algebraic[10] = "v_S_Ks0 in component Ks (fmol_per_sec)"
    legend_algebraic[19] = "v_S_Ks1 in component Ks (fmol_per_sec)"
    legend_algebraic[20] = "v_S_Ks2 in component Ks (fmol_per_sec)"
    legend_algebraic[9] = "v_xs1 in component Ks (fmol_per_sec)"
    legend_algebraic[17] = "v_xs2 in component Ks (fmol_per_sec)"
    legend_algebraic[4] = "mu_S_Ks0 in component Ks (J_per_mol)"
    legend_algebraic[6] = "mu_S_Ks1 in component Ks (J_per_mol)"
    legend_algebraic[11] = "mu_S_Ks2 in component Ks (J_per_mol)"
    legend_algebraic[5] = "Af_xs1 in component Ks (J_per_mol)"
    legend_algebraic[7] = "Ar_xs1 in component Ks (J_per_mol)"
    legend_algebraic[8] = "Af_xs2 in component Ks (J_per_mol)"
    legend_algebraic[16] = "Ar_xs2 in component Ks (J_per_mol)"
    legend_rates[0] = "d/dt q_S_Ks0 in component environment (fmol)"
    legend_rates[1] = "d/dt q_S_Ks1 in component environment (fmol)"
    legend_rates[2] = "d/dt q_S_Ks2 in component environment (fmol)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 60000
    constants[1] = 20.0448
    constants[2] = 388.832
    states[0] = 9.742056902468725e-06
    states[1] = 9.742056902468725e-06
    states[2] = 9.742056902468725e-06
    constants[3] = 8.31
    constants[4] = 310
    constants[5] = 96500
    constants[6] = 27.8683
    constants[7] = 0.00829152
    constants[8] = 0.0295644
    constants[9] = 1.42292
    constants[10] = 10.4348
    constants[11] = 0.281155
    constants[12] = 0.0394258
    constants[13] = 0.0221145
    constants[14] = 1
    constants[15] = 0.000400323747581994
    constants[16] = -1.41544821457997
    constants[17] = constants[3]*constants[4]*log(constants[9]*constants[2])
    constants[18] = constants[3]*constants[4]*log(constants[10]*constants[1])
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = custom_piecewise([greater_equal(voi , 0.00000) & less(voi , 4.00000), -0.0900000 , greater(voi , 10.1000) & less(voi , 13.1000), -0.0600000 , greater(voi , 14.1000) & less(voi , 15.1000), -0.0400000 , greater(voi , 17.0000), 0.0900000 , True, -0.0800000])
    algebraic[1] = algebraic[0]*constants[0]
    algebraic[2] = algebraic[1]/constants[0]
    algebraic[4] = constants[3]*constants[4]*log(constants[11]*states[0])
    algebraic[5] = algebraic[4]+constants[15]*constants[5]*algebraic[2]
    algebraic[6] = constants[3]*constants[4]*log(constants[12]*states[1])
    algebraic[7] = algebraic[6]+constants[16]*constants[5]*algebraic[2]
    algebraic[9] = constants[7]*(exp(algebraic[5]/(constants[3]*constants[4]))-exp(algebraic[7]/(constants[3]*constants[4])))
    algebraic[10] = -algebraic[9]
    rates[0] = algebraic[10]
    algebraic[8] = algebraic[6]+constants[15]*constants[5]*algebraic[2]
    algebraic[11] = constants[3]*constants[4]*log(constants[13]*states[2])
    algebraic[16] = algebraic[11]+constants[16]*constants[5]*algebraic[2]
    algebraic[17] = constants[8]*(exp(algebraic[8]/(constants[3]*constants[4]))-exp(algebraic[16]/(constants[3]*constants[4])))
    algebraic[19] = algebraic[9]-algebraic[17]
    rates[1] = algebraic[19]
    algebraic[20] = algebraic[17]
    rates[2] = algebraic[20]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = custom_piecewise([greater_equal(voi , 0.00000) & less(voi , 4.00000), -0.0900000 , greater(voi , 10.1000) & less(voi , 13.1000), -0.0600000 , greater(voi , 14.1000) & less(voi , 15.1000), -0.0400000 , greater(voi , 17.0000), 0.0900000 , True, -0.0800000])
    algebraic[1] = algebraic[0]*constants[0]
    algebraic[2] = algebraic[1]/constants[0]
    algebraic[4] = constants[3]*constants[4]*log(constants[11]*states[0])
    algebraic[5] = algebraic[4]+constants[15]*constants[5]*algebraic[2]
    algebraic[6] = constants[3]*constants[4]*log(constants[12]*states[1])
    algebraic[7] = algebraic[6]+constants[16]*constants[5]*algebraic[2]
    algebraic[9] = constants[7]*(exp(algebraic[5]/(constants[3]*constants[4]))-exp(algebraic[7]/(constants[3]*constants[4])))
    algebraic[10] = -algebraic[9]
    algebraic[8] = algebraic[6]+constants[15]*constants[5]*algebraic[2]
    algebraic[11] = constants[3]*constants[4]*log(constants[13]*states[2])
    algebraic[16] = algebraic[11]+constants[16]*constants[5]*algebraic[2]
    algebraic[17] = constants[8]*(exp(algebraic[8]/(constants[3]*constants[4]))-exp(algebraic[16]/(constants[3]*constants[4])))
    algebraic[19] = algebraic[9]-algebraic[17]
    algebraic[20] = algebraic[17]
    algebraic[3] = constants[14]*constants[5]*algebraic[2]
    algebraic[12] = algebraic[11]+constants[17]+algebraic[3]
    algebraic[13] = algebraic[11]+constants[18]
    algebraic[14] = custom_piecewise([equal(algebraic[3] , 0.00000), 1.00000*constants[6]*(exp(algebraic[12]/(constants[3]*constants[4]))-exp(algebraic[13]/(constants[3]*constants[4]))) , True, (((1.00000*constants[6]*algebraic[3])/(constants[3]*constants[4]))/(exp(algebraic[3]/(constants[3]*constants[4]))-1.00000))*(exp(algebraic[12]/(constants[3]*constants[4]))-exp(algebraic[13]/(constants[3]*constants[4])))])
    algebraic[15] = ((1.00000e-09*constants[5])/constants[0])*algebraic[14]
    algebraic[18] = constants[5]*(-constants[14]*algebraic[14]+(algebraic[9]+algebraic[17])*(constants[16]-constants[15]))
    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)