# Size of variable arrays:
sizeAlgebraic = 22
sizeStates = 6
sizeConstants = 15
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_states[0] = "q_K_o in component environment (fmol)"
    legend_states[1] = "q_K_i in component environment (fmol)"
    legend_states[2] = "q_S_Ks0 in component environment (fmol)"
    legend_states[3] = "q_S_Ks1 in component environment (fmol)"
    legend_states[4] = "q_S_Ks2 in component environment (fmol)"
    legend_states[5] = "q_mem in component environment (fC)"
    legend_algebraic[0] = "Vmem in component environment (volt)"
    legend_constants[1] = "R in component environment (J_per_K_per_mol)"
    legend_constants[2] = "T in component environment (kelvin)"
    legend_constants[3] = "F in component environment (C_per_mol)"
    legend_algebraic[15] = "v_Ks in component Ks (fmol_per_sec)"
    legend_algebraic[19] = "I_mem_Ks in component Ks (fA)"
    legend_algebraic[17] = "i_Ks in component environment (uA_per_uF)"
    legend_constants[4] = "kappa_Ks in component Ks_parameters (fmol_per_sec)"
    legend_constants[5] = "kappa_xs1 in component Ks_parameters (fmol_per_sec)"
    legend_constants[6] = "kappa_xs2 in component Ks_parameters (fmol_per_sec)"
    legend_constants[7] = "K_K_i in component Ks_parameters (per_fmol)"
    legend_constants[8] = "K_K_o in component Ks_parameters (per_fmol)"
    legend_constants[9] = "K_S_Ks0 in component Ks_parameters (per_fmol)"
    legend_constants[10] = "K_S_Ks1 in component Ks_parameters (per_fmol)"
    legend_constants[11] = "K_S_Ks2 in component Ks_parameters (per_fmol)"
    legend_constants[12] = "zK in component Ks_parameters (dimensionless)"
    legend_constants[13] = "z_xs_f in component Ks_parameters (dimensionless)"
    legend_constants[14] = "z_xs_r in component Ks_parameters (dimensionless)"
    legend_algebraic[1] = "u_K_i in component Ks (J_per_mol)"
    legend_algebraic[2] = "u_K_o in component Ks (J_per_mol)"
    legend_algebraic[3] = "V_mem in component Ks (J_per_C)"
    legend_algebraic[4] = "Am_Ks in component Ks (J_per_mol)"
    legend_algebraic[13] = "Af_Ks in component Ks (J_per_mol)"
    legend_algebraic[14] = "Ar_Ks in component Ks (J_per_mol)"
    legend_algebraic[11] = "v_S_Ks0 in component Ks (fmol_per_sec)"
    legend_algebraic[20] = "v_S_Ks1 in component Ks (fmol_per_sec)"
    legend_algebraic[21] = "v_S_Ks2 in component Ks (fmol_per_sec)"
    legend_algebraic[10] = "v_xs1 in component Ks (fmol_per_sec)"
    legend_algebraic[18] = "v_xs2 in component Ks (fmol_per_sec)"
    legend_algebraic[5] = "mu_S_Ks0 in component Ks (J_per_mol)"
    legend_algebraic[7] = "mu_S_Ks1 in component Ks (J_per_mol)"
    legend_algebraic[12] = "mu_S_Ks2 in component Ks (J_per_mol)"
    legend_algebraic[6] = "Af_xs1 in component Ks (J_per_mol)"
    legend_algebraic[8] = "Ar_xs1 in component Ks (J_per_mol)"
    legend_algebraic[9] = "Af_xs2 in component Ks (J_per_mol)"
    legend_algebraic[16] = "Ar_xs2 in component Ks (J_per_mol)"
    legend_rates[1] = "d/dt q_K_i in component environment (fmol)"
    legend_rates[0] = "d/dt q_K_o in component environment (fmol)"
    legend_rates[5] = "d/dt q_mem in component environment (fC)"
    legend_rates[2] = "d/dt q_S_Ks0 in component environment (fmol)"
    legend_rates[3] = "d/dt q_S_Ks1 in component environment (fmol)"
    legend_rates[4] = "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] = 153400
    states[0] = 27.9828
    states[1] = 5510
    states[2] = 9.742056902468725e-06
    states[3] = 9.742056902468725e-06
    states[4] = 9.742056902468725e-06
    states[5] = -13039
    constants[1] = 8.31
    constants[2] = 310
    constants[3] = 96500
    constants[4] = 27.8683
    constants[5] = 0.523159
    constants[6] = 1.86539
    constants[7] = 0.153461
    constants[8] = 1.01873
    constants[9] = 4.456
    constants[10] = 0.624857
    constants[11] = 0.350491
    constants[12] = 1
    constants[13] = 0.000400323747581994
    constants[14] = -1.41544821457997
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[3] = states[5]/constants[0]
    algebraic[5] = constants[1]*constants[2]*log(constants[9]*states[2])
    algebraic[6] = algebraic[5]+constants[13]*constants[3]*algebraic[3]
    algebraic[7] = constants[1]*constants[2]*log(constants[10]*states[3])
    algebraic[8] = algebraic[7]+constants[14]*constants[3]*algebraic[3]
    algebraic[10] = constants[5]*(exp(algebraic[6]/(constants[1]*constants[2]))-exp(algebraic[8]/(constants[1]*constants[2])))
    algebraic[11] = -algebraic[10]
    rates[2] = algebraic[11]
    algebraic[4] = constants[12]*constants[3]*algebraic[3]
    algebraic[1] = constants[1]*constants[2]*log(constants[7]*states[1])
    algebraic[12] = constants[1]*constants[2]*log(constants[11]*states[4])
    algebraic[13] = algebraic[12]+algebraic[1]+algebraic[4]
    algebraic[2] = constants[1]*constants[2]*log(constants[8]*states[0])
    algebraic[14] = algebraic[12]+algebraic[2]
    algebraic[15] = custom_piecewise([equal(algebraic[4] , 0.00000), 1.00000*constants[4]*(exp(algebraic[13]/(constants[1]*constants[2]))-exp(algebraic[14]/(constants[1]*constants[2]))) , True, (((1.00000*constants[4]*algebraic[4])/(constants[1]*constants[2]))/(exp(algebraic[4]/(constants[1]*constants[2]))-1.00000))*(exp(algebraic[13]/(constants[1]*constants[2]))-exp(algebraic[14]/(constants[1]*constants[2])))])
    rates[1] = -algebraic[15]
    rates[0] = algebraic[15]
    algebraic[9] = algebraic[7]+constants[13]*constants[3]*algebraic[3]
    algebraic[16] = algebraic[12]+constants[14]*constants[3]*algebraic[3]
    algebraic[18] = constants[6]*(exp(algebraic[9]/(constants[1]*constants[2]))-exp(algebraic[16]/(constants[1]*constants[2])))
    algebraic[19] = constants[3]*(-constants[12]*algebraic[15]+(algebraic[10]+algebraic[18])*(constants[14]-constants[13]))
    rates[5] = algebraic[19]
    algebraic[20] = algebraic[10]-algebraic[18]
    rates[3] = algebraic[20]
    algebraic[21] = algebraic[18]
    rates[4] = algebraic[21]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[3] = states[5]/constants[0]
    algebraic[5] = constants[1]*constants[2]*log(constants[9]*states[2])
    algebraic[6] = algebraic[5]+constants[13]*constants[3]*algebraic[3]
    algebraic[7] = constants[1]*constants[2]*log(constants[10]*states[3])
    algebraic[8] = algebraic[7]+constants[14]*constants[3]*algebraic[3]
    algebraic[10] = constants[5]*(exp(algebraic[6]/(constants[1]*constants[2]))-exp(algebraic[8]/(constants[1]*constants[2])))
    algebraic[11] = -algebraic[10]
    algebraic[4] = constants[12]*constants[3]*algebraic[3]
    algebraic[1] = constants[1]*constants[2]*log(constants[7]*states[1])
    algebraic[12] = constants[1]*constants[2]*log(constants[11]*states[4])
    algebraic[13] = algebraic[12]+algebraic[1]+algebraic[4]
    algebraic[2] = constants[1]*constants[2]*log(constants[8]*states[0])
    algebraic[14] = algebraic[12]+algebraic[2]
    algebraic[15] = custom_piecewise([equal(algebraic[4] , 0.00000), 1.00000*constants[4]*(exp(algebraic[13]/(constants[1]*constants[2]))-exp(algebraic[14]/(constants[1]*constants[2]))) , True, (((1.00000*constants[4]*algebraic[4])/(constants[1]*constants[2]))/(exp(algebraic[4]/(constants[1]*constants[2]))-1.00000))*(exp(algebraic[13]/(constants[1]*constants[2]))-exp(algebraic[14]/(constants[1]*constants[2])))])
    algebraic[9] = algebraic[7]+constants[13]*constants[3]*algebraic[3]
    algebraic[16] = algebraic[12]+constants[14]*constants[3]*algebraic[3]
    algebraic[18] = constants[6]*(exp(algebraic[9]/(constants[1]*constants[2]))-exp(algebraic[16]/(constants[1]*constants[2])))
    algebraic[19] = constants[3]*(-constants[12]*algebraic[15]+(algebraic[10]+algebraic[18])*(constants[14]-constants[13]))
    algebraic[20] = algebraic[10]-algebraic[18]
    algebraic[21] = algebraic[18]
    algebraic[0] = states[5]/constants[0]
    algebraic[17] = ((1.00000e-09*constants[3])/constants[0])*algebraic[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)