# Size of variable arrays:
sizeAlgebraic = 40
sizeStates = 6
sizeConstants = 57
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] = "R in component environment (J_per_K_per_mol)"
    legend_constants[1] = "T in component environment (kelvin)"
    legend_constants[2] = "F in component environment (C_per_mol)"
    legend_constants[3] = "C_m in component environment (fF)"
    legend_constants[4] = "K_1 in component environment (per_fmol)"
    legend_constants[5] = "K_13 in component environment (per_fmol)"
    legend_constants[6] = "K_14 in component environment (per_fmol)"
    legend_constants[7] = "K_3 in component environment (per_fmol)"
    legend_constants[8] = "K_6 in component environment (per_fmol)"
    legend_constants[9] = "K_7 in component environment (per_fmol)"
    legend_constants[10] = "K_H in component environment (per_fmol)"
    legend_constants[11] = "K_Ke in component environment (per_fmol)"
    legend_constants[12] = "K_Ki in component environment (per_fmol)"
    legend_constants[13] = "K_MgADP in component environment (per_fmol)"
    legend_constants[14] = "K_MgATP in component environment (per_fmol)"
    legend_constants[15] = "K_Nae in component environment (per_fmol)"
    legend_constants[16] = "K_Nai in component environment (per_fmol)"
    legend_constants[17] = "K_P in component environment (per_fmol)"
    legend_constants[18] = "kappa_1 in component environment (fmol_per_sec)"
    legend_constants[19] = "kappa_13 in component environment (fmol_per_sec)"
    legend_constants[20] = "kappa_15 in component environment (fmol_per_sec)"
    legend_constants[21] = "kappa_3 in component environment (fmol_per_sec)"
    legend_constants[22] = "kappa_6 in component environment (fmol_per_sec)"
    legend_constants[23] = "kappa_8 in component environment (fmol_per_sec)"
    legend_constants[24] = "z_5 in component environment (dimensionless)"
    legend_constants[25] = "z_8 in component environment (dimensionless)"
    legend_constants[40] = "zF_5 in component environment (C_per_mol)"
    legend_constants[41] = "zF_8 in component environment (C_per_mol)"
    legend_constants[39] = "x_H in component environment (fmol)"
    legend_constants[37] = "x_Ke in component environment (fmol)"
    legend_constants[49] = "x_Ki in component environment (fmol)"
    legend_constants[52] = "x_MgADP in component environment (fmol)"
    legend_constants[38] = "x_MgATP in component environment (fmol)"
    legend_constants[35] = "x_Nae in component environment (fmol)"
    legend_constants[36] = "x_Nai in component environment (fmol)"
    legend_states[0] = "x_P7 in component environment (fmol)"
    legend_constants[55] = "x_P_i in component environment (fmol)"
    legend_constants[26] = "q_mem in component environment (fC)"
    legend_states[1] = "x_P14 in component environment (fmol)"
    legend_states[2] = "x_P1 in component environment (fmol)"
    legend_states[3] = "x_P3 in component environment (fmol)"
    legend_states[4] = "x_P6 in component environment (fmol)"
    legend_states[5] = "x_P13 in component environment (fmol)"
    legend_algebraic[0] = "x_tot in component environment (fmol)"
    legend_constants[27] = "small_C in component environment (mM)"
    legend_constants[28] = "W_i in component environment (pL)"
    legend_constants[29] = "W_e in component environment (pL)"
    legend_constants[30] = "c_Ke in component environment (mM)"
    legend_constants[48] = "c_Ki in component environment (mM)"
    legend_constants[51] = "c_MgADP in component environment (mM)"
    legend_constants[31] = "c_MgATP in component environment (mM)"
    legend_constants[32] = "c_Nae in component environment (mM)"
    legend_constants[33] = "c_Nai in component environment (mM)"
    legend_constants[54] = "c_P_i in component environment (mM)"
    legend_constants[34] = "pH in component environment (dimensionless)"
    legend_constants[42] = "mu_H in component environment (J_per_mol)"
    legend_algebraic[29] = "v_H in component environment (fmol_per_sec)"
    legend_constants[43] = "mu_Ke in component environment (J_per_mol)"
    legend_algebraic[35] = "v_Ke in component environment (fmol_per_sec)"
    legend_constants[50] = "mu_Ki in component environment (J_per_mol)"
    legend_algebraic[18] = "v_Ki in component environment (fmol_per_sec)"
    legend_constants[53] = "mu_MgADP in component environment (J_per_mol)"
    legend_algebraic[14] = "v_MgADP in component environment (fmol_per_sec)"
    legend_constants[44] = "mu_MgATP in component environment (J_per_mol)"
    legend_algebraic[9] = "v_MgATP in component environment (fmol_per_sec)"
    legend_constants[45] = "mu_Nae in component environment (J_per_mol)"
    legend_algebraic[36] = "v_Nae in component environment (fmol_per_sec)"
    legend_constants[46] = "mu_Nai in component environment (J_per_mol)"
    legend_algebraic[23] = "v_Nai in component environment (fmol_per_sec)"
    legend_algebraic[1] = "mu_P7 in component environment (J_per_mol)"
    legend_algebraic[37] = "v_P7 in component environment (fmol_per_sec)"
    legend_constants[56] = "mu_P_i in component environment (J_per_mol)"
    legend_algebraic[30] = "v_P_i in component environment (fmol_per_sec)"
    legend_constants[47] = "V_mem in component environment (volt)"
    legend_algebraic[38] = "I_mem in component environment (fA)"
    legend_algebraic[27] = "Af_R13 in component environment (J_per_mol)"
    legend_algebraic[4] = "Ar_R13 in component environment (J_per_mol)"
    legend_algebraic[28] = "v_R13 in component environment (fmol_per_sec)"
    legend_algebraic[5] = "Af_R15 in component environment (J_per_mol)"
    legend_algebraic[7] = "Ar_R15 in component environment (J_per_mol)"
    legend_algebraic[8] = "v_R15 in component environment (fmol_per_sec)"
    legend_algebraic[12] = "Af_R6 in component environment (J_per_mol)"
    legend_algebraic[2] = "Ar_R6 in component environment (J_per_mol)"
    legend_algebraic[13] = "v_R6 in component environment (fmol_per_sec)"
    legend_algebraic[3] = "mu_P14 in component environment (J_per_mol)"
    legend_algebraic[31] = "v_P14 in component environment (fmol_per_sec)"
    legend_algebraic[6] = "mu_P1 in component environment (J_per_mol)"
    legend_algebraic[19] = "v_P1 in component environment (fmol_per_sec)"
    legend_algebraic[10] = "mu_P3 in component environment (J_per_mol)"
    legend_algebraic[24] = "v_P3 in component environment (fmol_per_sec)"
    legend_algebraic[11] = "mu_P6 in component environment (J_per_mol)"
    legend_algebraic[25] = "v_P6 in component environment (fmol_per_sec)"
    legend_algebraic[15] = "Af_R1 in component environment (J_per_mol)"
    legend_algebraic[16] = "Ar_R1 in component environment (J_per_mol)"
    legend_algebraic[17] = "v_R1 in component environment (fmol_per_sec)"
    legend_algebraic[20] = "Af_R3 in component environment (J_per_mol)"
    legend_algebraic[21] = "Ar_R3 in component environment (J_per_mol)"
    legend_algebraic[22] = "v_R3 in component environment (fmol_per_sec)"
    legend_algebraic[26] = "mu_P13 in component environment (J_per_mol)"
    legend_algebraic[39] = "v_P13 in component environment (fmol_per_sec)"
    legend_algebraic[32] = "Af_R8 in component environment (J_per_mol)"
    legend_algebraic[33] = "Ar_R8 in component environment (J_per_mol)"
    legend_algebraic[34] = "v_R8 in component environment (fmol_per_sec)"
    legend_rates[0] = "d/dt x_P7 in component environment (fmol)"
    legend_rates[1] = "d/dt x_P14 in component environment (fmol)"
    legend_rates[2] = "d/dt x_P1 in component environment (fmol)"
    legend_rates[3] = "d/dt x_P3 in component environment (fmol)"
    legend_rates[4] = "d/dt x_P6 in component environment (fmol)"
    legend_rates[5] = "d/dt x_P13 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] = 8.314
    constants[1] = 310
    constants[2] = 96485
    constants[3] = 153400
    constants[4] = 13085378.038167767
    constants[5] = 0.6020622798357556
    constants[6] = 69.38568269665376
    constants[7] = 46.24091666474313
    constants[8] = 79.09015560598799
    constants[9] = 4239.416835123694
    constants[10] = 0.04565
    constants[11] = 0.009236
    constants[12] = 0.0012595
    constants[13] = 7.976e-05
    constants[14] = 2.3715
    constants[15] = 0.0061242
    constants[16] = 0.00083514
    constants[17] = 0.04565
    constants[18] = 6.973455976480863
    constants[19] = 475.81557480252013
    constants[20] = 0.035418056157766185
    constants[21] = 861399.5138047301
    constants[22] = 1.4100547742408052
    constants[23] = 2.2855
    constants[24] = -0.054951
    constants[25] = -0.94505
    states[0] = 0.8590
    constants[26] = -18408
    states[1] = 0.0100192141898171
    states[2] = 6.50836196830909e-10
    states[3] = 0.00292644413780957
    states[4] = 0.0154965229998754
    states[5] = 0.112426414453276
    constants[27] = 1e-3
    constants[28] = 38
    constants[29] = 5.182
    constants[30] = 5.4
    constants[31] = 10
    constants[32] = 150
    constants[33] = 50
    constants[34] = 7.4
    constants[35] = constants[32]*constants[29]
    constants[36] = constants[33]*constants[28]
    constants[37] = constants[30]*constants[29]
    constants[38] = constants[31]*constants[28]
    constants[39] = (power(10.0000, -constants[34]))*1000.00*constants[28]
    constants[40] = constants[24]*constants[2]
    constants[41] = constants[25]*constants[2]
    constants[42] = constants[0]*constants[1]*log(constants[10]*constants[39])
    constants[43] = constants[0]*constants[1]*log(constants[11]*constants[37])
    constants[44] = constants[0]*constants[1]*log(constants[14]*constants[38])
    constants[45] = constants[0]*constants[1]*log(constants[15]*constants[35])
    constants[46] = constants[0]*constants[1]*log(constants[16]*constants[36])
    constants[47] = constants[26]/constants[3]
    constants[48] = constants[27]
    constants[49] = constants[48]*constants[28]
    constants[50] = constants[0]*constants[1]*log(constants[12]*constants[49])
    constants[51] = constants[27]
    constants[52] = constants[51]*constants[28]
    constants[53] = constants[0]*constants[1]*log(constants[13]*constants[52])
    constants[54] = constants[27]
    constants[55] = constants[54]*constants[28]
    constants[56] = constants[0]*constants[1]*log(constants[17]*constants[55])
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[3] = constants[0]*constants[1]*log(constants[6]*states[1])
    algebraic[5] = algebraic[3]+constants[44]
    algebraic[6] = constants[0]*constants[1]*log(constants[4]*states[2])
    algebraic[7] = algebraic[6]
    algebraic[8] = constants[20]*(exp(algebraic[5]/(constants[0]*constants[1]))-exp(algebraic[7]/(constants[0]*constants[1])))
    algebraic[15] = algebraic[6]
    algebraic[10] = constants[0]*constants[1]*log(constants[7]*states[3])
    algebraic[16] = algebraic[10]+2.00000*constants[50]
    algebraic[17] = constants[18]*(exp(algebraic[15]/(constants[0]*constants[1]))-exp(algebraic[16]/(constants[0]*constants[1])))
    algebraic[19] = algebraic[8]-algebraic[17]
    rates[2] = algebraic[19]
    algebraic[20] = algebraic[10]+3.00000*constants[46]
    algebraic[11] = constants[0]*constants[1]*log(constants[8]*states[4])
    algebraic[21] = constants[40]*constants[47]+algebraic[11]
    algebraic[22] = constants[21]*(exp(algebraic[20]/(constants[0]*constants[1]))-exp(algebraic[21]/(constants[0]*constants[1])))
    algebraic[24] = algebraic[17]-algebraic[22]
    rates[3] = algebraic[24]
    algebraic[12] = algebraic[11]
    algebraic[1] = constants[0]*constants[1]*log(constants[9]*states[0])
    algebraic[2] = algebraic[1]+constants[53]
    algebraic[13] = constants[22]*(exp(algebraic[12]/(constants[0]*constants[1]))-exp(algebraic[2]/(constants[0]*constants[1])))
    algebraic[25] = algebraic[22]-algebraic[13]
    rates[4] = algebraic[25]
    algebraic[26] = constants[0]*constants[1]*log(constants[5]*states[5])
    algebraic[27] = algebraic[26]
    algebraic[4] = algebraic[3]+constants[56]+constants[42]
    algebraic[28] = constants[19]*(exp(algebraic[27]/(constants[0]*constants[1]))-exp(algebraic[4]/(constants[0]*constants[1])))
    algebraic[31] = algebraic[28]-algebraic[8]
    rates[1] = algebraic[31]
    algebraic[32] = algebraic[1]+2.00000*constants[43]
    algebraic[33] = algebraic[26]+3.00000*constants[45]+constants[41]*constants[47]
    algebraic[34] = constants[23]*(exp(algebraic[32]/(constants[0]*constants[1]))-exp(algebraic[33]/(constants[0]*constants[1])))
    algebraic[37] = algebraic[13]-algebraic[34]
    rates[0] = algebraic[37]
    algebraic[39] = algebraic[34]-algebraic[28]
    rates[5] = algebraic[39]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[3] = constants[0]*constants[1]*log(constants[6]*states[1])
    algebraic[5] = algebraic[3]+constants[44]
    algebraic[6] = constants[0]*constants[1]*log(constants[4]*states[2])
    algebraic[7] = algebraic[6]
    algebraic[8] = constants[20]*(exp(algebraic[5]/(constants[0]*constants[1]))-exp(algebraic[7]/(constants[0]*constants[1])))
    algebraic[15] = algebraic[6]
    algebraic[10] = constants[0]*constants[1]*log(constants[7]*states[3])
    algebraic[16] = algebraic[10]+2.00000*constants[50]
    algebraic[17] = constants[18]*(exp(algebraic[15]/(constants[0]*constants[1]))-exp(algebraic[16]/(constants[0]*constants[1])))
    algebraic[19] = algebraic[8]-algebraic[17]
    algebraic[20] = algebraic[10]+3.00000*constants[46]
    algebraic[11] = constants[0]*constants[1]*log(constants[8]*states[4])
    algebraic[21] = constants[40]*constants[47]+algebraic[11]
    algebraic[22] = constants[21]*(exp(algebraic[20]/(constants[0]*constants[1]))-exp(algebraic[21]/(constants[0]*constants[1])))
    algebraic[24] = algebraic[17]-algebraic[22]
    algebraic[12] = algebraic[11]
    algebraic[1] = constants[0]*constants[1]*log(constants[9]*states[0])
    algebraic[2] = algebraic[1]+constants[53]
    algebraic[13] = constants[22]*(exp(algebraic[12]/(constants[0]*constants[1]))-exp(algebraic[2]/(constants[0]*constants[1])))
    algebraic[25] = algebraic[22]-algebraic[13]
    algebraic[26] = constants[0]*constants[1]*log(constants[5]*states[5])
    algebraic[27] = algebraic[26]
    algebraic[4] = algebraic[3]+constants[56]+constants[42]
    algebraic[28] = constants[19]*(exp(algebraic[27]/(constants[0]*constants[1]))-exp(algebraic[4]/(constants[0]*constants[1])))
    algebraic[31] = algebraic[28]-algebraic[8]
    algebraic[32] = algebraic[1]+2.00000*constants[43]
    algebraic[33] = algebraic[26]+3.00000*constants[45]+constants[41]*constants[47]
    algebraic[34] = constants[23]*(exp(algebraic[32]/(constants[0]*constants[1]))-exp(algebraic[33]/(constants[0]*constants[1])))
    algebraic[37] = algebraic[13]-algebraic[34]
    algebraic[39] = algebraic[34]-algebraic[28]
    algebraic[0] = states[2]+states[3]+states[4]+states[5]+states[0]+states[1]
    algebraic[9] = -algebraic[8]
    algebraic[14] = algebraic[13]
    algebraic[18] = 2.00000*algebraic[17]
    algebraic[23] = -3.00000*algebraic[22]
    algebraic[29] = algebraic[28]
    algebraic[30] = algebraic[28]
    algebraic[35] = -2.00000*algebraic[34]
    algebraic[36] = 3.00000*algebraic[34]
    algebraic[38] = constants[40]*algebraic[22]+constants[41]*algebraic[34]
    return algebraic

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)