# Size of variable arrays:
sizeAlgebraic = 29
sizeStates = 7
sizeConstants = 20
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 (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_r0s0_TO in component environment (fmol)"
    legend_states[3] = "q_r1s0_TO in component environment (fmol)"
    legend_states[4] = "q_r0s1_TO in component environment (fmol)"
    legend_states[5] = "q_r1s1_TO in component environment (fmol)"
    legend_states[6] = "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[20] = "v_TO in component TO (fmol_per_sec)"
    legend_algebraic[26] = "I_mem_TO in component TO (fA)"
    legend_constants[4] = "kappa_TO in component TO_parameters (fmol_per_sec)"
    legend_constants[5] = "kappa_gTO_1 in component TO_parameters (fmol_per_sec)"
    legend_constants[6] = "kappa_gTO_2 in component TO_parameters (fmol_per_sec)"
    legend_constants[7] = "kappa_gTO_3 in component TO_parameters (fmol_per_sec)"
    legend_constants[8] = "kappa_gTO_4 in component TO_parameters (fmol_per_sec)"
    legend_constants[9] = "K_K_i in component TO_parameters (per_fmol)"
    legend_constants[10] = "K_K_o in component TO_parameters (per_fmol)"
    legend_constants[11] = "K_r0s0_TO in component TO_parameters (per_fmol)"
    legend_constants[12] = "K_r1s0_TO in component TO_parameters (per_fmol)"
    legend_constants[13] = "K_r0s1_TO in component TO_parameters (per_fmol)"
    legend_constants[14] = "K_r1s1_TO in component TO_parameters (per_fmol)"
    legend_constants[15] = "zK in component TO_parameters (dimensionless)"
    legend_constants[16] = "z_rTO_f in component TO_parameters (dimensionless)"
    legend_constants[17] = "z_sTO_f in component TO_parameters (dimensionless)"
    legend_constants[18] = "z_rTO_r in component TO_parameters (dimensionless)"
    legend_constants[19] = "z_sTO_r in component TO_parameters (dimensionless)"
    legend_algebraic[1] = "u_K_i in component TO (J_per_mol)"
    legend_algebraic[2] = "u_K_o in component TO (J_per_mol)"
    legend_algebraic[3] = "V_mem in component TO (J_per_C)"
    legend_algebraic[4] = "Am_TO in component TO (J_per_mol)"
    legend_algebraic[18] = "Af_TO in component TO (J_per_mol)"
    legend_algebraic[19] = "Ar_TO in component TO (J_per_mol)"
    legend_algebraic[16] = "v_r0s0_TO in component TO (fmol_per_sec)"
    legend_algebraic[27] = "v_r1s0_TO in component TO (fmol_per_sec)"
    legend_algebraic[25] = "v_r0s1_TO in component TO (fmol_per_sec)"
    legend_algebraic[28] = "v_r1s1_TO in component TO (fmol_per_sec)"
    legend_algebraic[11] = "v_gTO_1 in component TO (fmol_per_sec)"
    legend_algebraic[15] = "v_gTO_3 in component TO (fmol_per_sec)"
    legend_algebraic[23] = "v_gTO_2 in component TO (fmol_per_sec)"
    legend_algebraic[24] = "v_gTO_4 in component TO (fmol_per_sec)"
    legend_algebraic[5] = "mu_r0s0_TO in component TO (J_per_mol)"
    legend_algebraic[8] = "mu_r1s0_TO in component TO (J_per_mol)"
    legend_algebraic[12] = "mu_r0s1_TO in component TO (J_per_mol)"
    legend_algebraic[17] = "mu_r1s1_TO in component TO (J_per_mol)"
    legend_algebraic[6] = "Af_gTO_1 in component TO (J_per_mol)"
    legend_algebraic[9] = "Ar_gTO_1 in component TO (J_per_mol)"
    legend_algebraic[7] = "Af_gTO_3 in component TO (J_per_mol)"
    legend_algebraic[13] = "Ar_gTO_3 in component TO (J_per_mol)"
    legend_algebraic[14] = "Af_gTO_2 in component TO (J_per_mol)"
    legend_algebraic[21] = "Ar_gTO_2 in component TO (J_per_mol)"
    legend_algebraic[10] = "Af_gTO_4 in component TO (J_per_mol)"
    legend_algebraic[22] = "Ar_gTO_4 in component TO (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[6] = "d/dt q_mem in component environment (fC)"
    legend_rates[2] = "d/dt q_r0s0_TO in component environment (fmol)"
    legend_rates[3] = "d/dt q_r1s0_TO in component environment (fmol)"
    legend_rates[4] = "d/dt q_r0s1_TO in component environment (fmol)"
    legend_rates[5] = "d/dt q_r1s1_TO 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] = 1.0e6
    states[0] = 0.116325
    states[1] = 3.65002
    states[2] = 3.1966124E-07
    states[3] = 3.1966124E-07
    states[4] = 3.1966124E-07
    states[5] = 3.1966124E-07
    states[6] = -8.5e4
    constants[1] = 8.31
    constants[2] = 310
    constants[3] = 96500
    constants[4] = 1.91513
    constants[5] = 10.0063
    constants[6] = 0.053573
    constants[7] = 0.0622138
    constants[8] = 0.0155957
    constants[9] = 0.0402291
    constants[10] = 0.267055
    constants[11] = 0.00553253
    constants[12] = 0.0220702
    constants[13] = 1.03336
    constants[14] = 4.12222
    constants[15] = 1
    constants[16] = 2.28623234372134
    constants[17] = -1.51477720975217
    constants[18] = -0.131848324558065
    constants[19] = 1.75042355789096
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[3] = states[6]/constants[0]
    algebraic[5] = constants[1]*constants[2]*log(constants[11]*states[2])
    algebraic[6] = algebraic[5]+constants[16]*constants[3]*algebraic[3]
    algebraic[8] = constants[1]*constants[2]*log(constants[12]*states[3])
    algebraic[9] = algebraic[8]+constants[18]*constants[3]*algebraic[3]
    algebraic[11] = constants[5]*(exp(algebraic[6]/(constants[1]*constants[2]))-exp(algebraic[9]/(constants[1]*constants[2])))
    algebraic[7] = algebraic[5]+constants[17]*constants[3]*algebraic[3]
    algebraic[12] = constants[1]*constants[2]*log(constants[13]*states[4])
    algebraic[13] = algebraic[12]+constants[19]*constants[3]*algebraic[3]
    algebraic[15] = constants[7]*(exp(algebraic[7]/(constants[1]*constants[2]))-exp(algebraic[13]/(constants[1]*constants[2])))
    algebraic[16] = -algebraic[11]+algebraic[15]
    rates[2] = algebraic[16]
    algebraic[4] = constants[3]*algebraic[3]
    algebraic[1] = constants[1]*constants[2]*log(constants[9]*states[1])
    algebraic[17] = constants[1]*constants[2]*log(constants[14]*states[5])
    algebraic[18] = algebraic[17]+algebraic[1]+algebraic[4]
    algebraic[2] = constants[1]*constants[2]*log(constants[10]*states[0])
    algebraic[19] = algebraic[17]+algebraic[2]
    algebraic[20] = custom_piecewise([equal(algebraic[4] , 0.00000), 1.00000*constants[4]*(exp(algebraic[18]/(constants[1]*constants[2]))-exp(algebraic[19]/(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[18]/(constants[1]*constants[2]))-exp(algebraic[19]/(constants[1]*constants[2])))])
    rates[1] = -algebraic[20]
    rates[0] = algebraic[20]
    algebraic[14] = algebraic[12]+constants[16]*constants[3]*algebraic[3]
    algebraic[21] = algebraic[17]+constants[18]*constants[3]*algebraic[3]
    algebraic[23] = constants[6]*(exp(algebraic[14]/(constants[1]*constants[2]))-exp(algebraic[21]/(constants[1]*constants[2])))
    algebraic[25] = -algebraic[23]+algebraic[15]
    rates[4] = algebraic[25]
    algebraic[10] = algebraic[8]+constants[17]*constants[3]*algebraic[3]
    algebraic[22] = algebraic[17]+constants[19]*constants[3]*algebraic[3]
    algebraic[24] = constants[8]*(exp(algebraic[10]/(constants[1]*constants[2]))-exp(algebraic[22]/(constants[1]*constants[2])))
    algebraic[26] = constants[3]*(-constants[15]*algebraic[20]+(algebraic[11]+algebraic[23])*(constants[18]-constants[16])+(algebraic[15]+algebraic[24])*(constants[19]-constants[17]))
    rates[6] = algebraic[26]
    algebraic[27] = algebraic[11]-algebraic[24]
    rates[3] = algebraic[27]
    algebraic[28] = algebraic[23]+algebraic[24]
    rates[5] = algebraic[28]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[3] = states[6]/constants[0]
    algebraic[5] = constants[1]*constants[2]*log(constants[11]*states[2])
    algebraic[6] = algebraic[5]+constants[16]*constants[3]*algebraic[3]
    algebraic[8] = constants[1]*constants[2]*log(constants[12]*states[3])
    algebraic[9] = algebraic[8]+constants[18]*constants[3]*algebraic[3]
    algebraic[11] = constants[5]*(exp(algebraic[6]/(constants[1]*constants[2]))-exp(algebraic[9]/(constants[1]*constants[2])))
    algebraic[7] = algebraic[5]+constants[17]*constants[3]*algebraic[3]
    algebraic[12] = constants[1]*constants[2]*log(constants[13]*states[4])
    algebraic[13] = algebraic[12]+constants[19]*constants[3]*algebraic[3]
    algebraic[15] = constants[7]*(exp(algebraic[7]/(constants[1]*constants[2]))-exp(algebraic[13]/(constants[1]*constants[2])))
    algebraic[16] = -algebraic[11]+algebraic[15]
    algebraic[4] = constants[3]*algebraic[3]
    algebraic[1] = constants[1]*constants[2]*log(constants[9]*states[1])
    algebraic[17] = constants[1]*constants[2]*log(constants[14]*states[5])
    algebraic[18] = algebraic[17]+algebraic[1]+algebraic[4]
    algebraic[2] = constants[1]*constants[2]*log(constants[10]*states[0])
    algebraic[19] = algebraic[17]+algebraic[2]
    algebraic[20] = custom_piecewise([equal(algebraic[4] , 0.00000), 1.00000*constants[4]*(exp(algebraic[18]/(constants[1]*constants[2]))-exp(algebraic[19]/(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[18]/(constants[1]*constants[2]))-exp(algebraic[19]/(constants[1]*constants[2])))])
    algebraic[14] = algebraic[12]+constants[16]*constants[3]*algebraic[3]
    algebraic[21] = algebraic[17]+constants[18]*constants[3]*algebraic[3]
    algebraic[23] = constants[6]*(exp(algebraic[14]/(constants[1]*constants[2]))-exp(algebraic[21]/(constants[1]*constants[2])))
    algebraic[25] = -algebraic[23]+algebraic[15]
    algebraic[10] = algebraic[8]+constants[17]*constants[3]*algebraic[3]
    algebraic[22] = algebraic[17]+constants[19]*constants[3]*algebraic[3]
    algebraic[24] = constants[8]*(exp(algebraic[10]/(constants[1]*constants[2]))-exp(algebraic[22]/(constants[1]*constants[2])))
    algebraic[26] = constants[3]*(-constants[15]*algebraic[20]+(algebraic[11]+algebraic[23])*(constants[18]-constants[16])+(algebraic[15]+algebraic[24])*(constants[19]-constants[17]))
    algebraic[27] = algebraic[11]-algebraic[24]
    algebraic[28] = algebraic[23]+algebraic[24]
    algebraic[0] = states[6]/constants[0]
    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)