# Size of variable arrays:
sizeAlgebraic = 40
sizeStates = 11
sizeConstants = 24
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_states[0] = "q_Ca_o in component environment (fmol)"
    legend_states[1] = "q_Ca_i in component environment (fmol)"
    legend_states[2] = "q_Na_o in component environment (fmol)"
    legend_states[3] = "q_Na_i in component environment (fmol)"
    legend_states[4] = "q_P1_NCX in component environment (fmol)"
    legend_states[5] = "q_P2_NCX in component environment (fmol)"
    legend_states[6] = "q_P3_NCX in component environment (fmol)"
    legend_states[7] = "q_P4_NCX in component environment (fmol)"
    legend_states[8] = "q_P5_NCX in component environment (fmol)"
    legend_states[9] = "q_P6_NCX in component environment (fmol)"
    legend_algebraic[29] = "v_Ca_o_NCX in component NCX (fmol_per_sec)"
    legend_algebraic[22] = "v_Ca_i_NCX in component NCX (fmol_per_sec)"
    legend_algebraic[33] = "v_Na_o_NCX in component NCX (fmol_per_sec)"
    legend_algebraic[19] = "v_Na_i_NCX in component NCX (fmol_per_sec)"
    legend_states[10] = "q_mem in component environment (fC)"
    legend_algebraic[37] = "I_mem_NCX in component NCX (fA)"
    legend_constants[4] = "kappa_1_NCX in component NCX_parameters (fmol_per_sec)"
    legend_constants[5] = "kappa_2_NCX in component NCX_parameters (fmol_per_sec)"
    legend_constants[6] = "kappa_3_NCX in component NCX_parameters (fmol_per_sec)"
    legend_constants[7] = "kappa_4_NCX in component NCX_parameters (fmol_per_sec)"
    legend_constants[8] = "kappa_5_NCX in component NCX_parameters (fmol_per_sec)"
    legend_constants[9] = "kappa_6_NCX in component NCX_parameters (fmol_per_sec)"
    legend_constants[10] = "K_1_NCX in component NCX_parameters (per_fmol)"
    legend_constants[11] = "K_2_NCX in component NCX_parameters (per_fmol)"
    legend_constants[12] = "K_3_NCX in component NCX_parameters (per_fmol)"
    legend_constants[13] = "K_4_NCX in component NCX_parameters (per_fmol)"
    legend_constants[14] = "K_5_NCX in component NCX_parameters (per_fmol)"
    legend_constants[15] = "K_6_NCX in component NCX_parameters (per_fmol)"
    legend_constants[16] = "K_Na_i in component NCX_parameters (per_fmol)"
    legend_constants[17] = "K_Ca_i in component NCX_parameters (per_fmol)"
    legend_constants[18] = "K_Na_o in component NCX_parameters (per_fmol)"
    legend_constants[19] = "K_Ca_o in component NCX_parameters (per_fmol)"
    legend_constants[20] = "nNa_o_NCX in component NCX_parameters (dimensionless)"
    legend_constants[21] = "nNa_i_NCX in component NCX_parameters (dimensionless)"
    legend_constants[22] = "zf_NCX in component NCX_parameters (dimensionless)"
    legend_constants[23] = "zr_NCX in component NCX_parameters (dimensionless)"
    legend_algebraic[1] = "mu_Ca_o in component NCX (J_per_mol)"
    legend_algebraic[2] = "mu_Ca_i in component NCX (J_per_mol)"
    legend_algebraic[3] = "mu_Na_o in component NCX (J_per_mol)"
    legend_algebraic[4] = "mu_Na_i in component NCX (J_per_mol)"
    legend_algebraic[5] = "mu_P1_NCX in component NCX (J_per_mol)"
    legend_algebraic[6] = "mu_P2_NCX in component NCX (J_per_mol)"
    legend_algebraic[7] = "mu_P3_NCX in component NCX (J_per_mol)"
    legend_algebraic[8] = "mu_P4_NCX in component NCX (J_per_mol)"
    legend_algebraic[9] = "mu_P5_NCX in component NCX (J_per_mol)"
    legend_algebraic[10] = "mu_P6_NCX in component NCX (J_per_mol)"
    legend_algebraic[38] = "v_P1_NCX in component NCX (fmol_per_sec)"
    legend_algebraic[23] = "v_P2_NCX in component NCX (fmol_per_sec)"
    legend_algebraic[26] = "v_P3_NCX in component NCX (fmol_per_sec)"
    legend_algebraic[30] = "v_P4_NCX in component NCX (fmol_per_sec)"
    legend_algebraic[35] = "v_P5_NCX in component NCX (fmol_per_sec)"
    legend_algebraic[39] = "v_P6_NCX in component NCX (fmol_per_sec)"
    legend_algebraic[11] = "Af_r1 in component NCX (J_per_mol)"
    legend_algebraic[17] = "Ar_r1 in component NCX (J_per_mol)"
    legend_algebraic[18] = "v_r1 in component NCX (fmol_per_sec)"
    legend_algebraic[12] = "Af_r2 in component NCX (J_per_mol)"
    legend_algebraic[20] = "Ar_r2 in component NCX (J_per_mol)"
    legend_algebraic[21] = "v_r2 in component NCX (fmol_per_sec)"
    legend_algebraic[13] = "Af_r3 in component NCX (J_per_mol)"
    legend_algebraic[24] = "Ar_r3 in component NCX (J_per_mol)"
    legend_algebraic[25] = "v_r3 in component NCX (fmol_per_sec)"
    legend_algebraic[14] = "Af_r4 in component NCX (J_per_mol)"
    legend_algebraic[27] = "Ar_r4 in component NCX (J_per_mol)"
    legend_algebraic[28] = "v_r4 in component NCX (fmol_per_sec)"
    legend_algebraic[15] = "Af_r5 in component NCX (J_per_mol)"
    legend_algebraic[31] = "Ar_r5 in component NCX (J_per_mol)"
    legend_algebraic[32] = "v_r5 in component NCX (fmol_per_sec)"
    legend_algebraic[16] = "Af_r6 in component NCX (J_per_mol)"
    legend_algebraic[34] = "Ar_r6 in component NCX (J_per_mol)"
    legend_algebraic[36] = "v_r6 in component NCX (fmol_per_sec)"
    legend_algebraic[0] = "V_mem in component NCX (volt)"
    legend_rates[0] = "d/dt q_Ca_o in component environment (fmol)"
    legend_rates[1] = "d/dt q_Ca_i in component environment (fmol)"
    legend_rates[2] = "d/dt q_Na_o in component environment (fmol)"
    legend_rates[3] = "d/dt q_Na_i in component environment (fmol)"
    legend_rates[10] = "d/dt q_mem in component environment (fC)"
    legend_rates[4] = "d/dt q_P1_NCX in component environment (fmol)"
    legend_rates[5] = "d/dt q_P2_NCX in component environment (fmol)"
    legend_rates[6] = "d/dt q_P3_NCX in component environment (fmol)"
    legend_rates[7] = "d/dt q_P4_NCX in component environment (fmol)"
    legend_rates[8] = "d/dt q_P5_NCX in component environment (fmol)"
    legend_rates[9] = "d/dt q_P6_NCX 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
    states[0] = 9.3276
    states[1] = 0.00456
    states[2] = 725.48
    states[3] = 380
    states[4] = 0.000103509
    states[5] = 0.000103509
    states[6] = 0.000103509
    states[7] = 0.000103509
    states[8] = 0.000103509
    states[9] = 0.000103509
    states[10] = -13039
    constants[4] = 417309
    constants[5] = 1.39522e+07
    constants[6] = 472.755
    constants[7] = 1.39522e+07
    constants[8] = 417309
    constants[9] = 0.370405
    constants[10] = 2.93394e+08
    constants[11] = 14.1045
    constants[12] = 263471
    constants[13] = 2.39875e+06
    constants[14] = 2373.73
    constants[15] = 956.214
    constants[16] = 0.0137751
    constants[17] = 10.2446
    constants[18] = 0.470129
    constants[19] = 7572.91
    constants[20] = 3
    constants[21] = 3
    constants[22] = -0.55679
    constants[23] = 0.44321
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[5] = constants[0]*constants[1]*log(constants[10]*states[4])
    algebraic[11] = algebraic[5]
    algebraic[4] = constants[0]*constants[1]*log(constants[16]*states[3])
    algebraic[6] = constants[0]*constants[1]*log(constants[11]*states[5])
    algebraic[17] = constants[21]*algebraic[4]+algebraic[6]
    algebraic[18] = constants[4]*(exp(algebraic[11]/(constants[0]*constants[1]))-exp(algebraic[17]/(constants[0]*constants[1])))
    algebraic[19] = constants[21]*algebraic[18]
    rates[3] = algebraic[19]
    algebraic[2] = constants[0]*constants[1]*log(constants[17]*states[1])
    algebraic[12] = algebraic[6]+algebraic[2]
    algebraic[7] = constants[0]*constants[1]*log(constants[12]*states[6])
    algebraic[20] = algebraic[7]
    algebraic[21] = constants[5]*(exp(algebraic[12]/(constants[0]*constants[1]))-exp(algebraic[20]/(constants[0]*constants[1])))
    algebraic[22] = -algebraic[21]
    rates[1] = algebraic[22]
    algebraic[23] = algebraic[18]-algebraic[21]
    rates[5] = algebraic[23]
    algebraic[13] = algebraic[7]
    algebraic[8] = constants[0]*constants[1]*log(constants[13]*states[7])
    algebraic[24] = algebraic[8]
    algebraic[25] = constants[6]*(exp(algebraic[13]/(constants[0]*constants[1]))-exp(algebraic[24]/(constants[0]*constants[1])))
    algebraic[26] = algebraic[21]-algebraic[25]
    rates[6] = algebraic[26]
    algebraic[14] = algebraic[8]
    algebraic[1] = constants[0]*constants[1]*log(constants[19]*states[0])
    algebraic[9] = constants[0]*constants[1]*log(constants[14]*states[8])
    algebraic[27] = algebraic[9]+algebraic[1]
    algebraic[28] = constants[7]*(exp(algebraic[14]/(constants[0]*constants[1]))-exp(algebraic[27]/(constants[0]*constants[1])))
    algebraic[29] = algebraic[28]
    rates[0] = algebraic[29]
    algebraic[30] = -algebraic[28]+algebraic[25]
    rates[7] = algebraic[30]
    algebraic[3] = constants[0]*constants[1]*log(constants[18]*states[2])
    algebraic[15] = algebraic[9]+constants[20]*algebraic[3]
    algebraic[10] = constants[0]*constants[1]*log(constants[15]*states[9])
    algebraic[31] = algebraic[10]
    algebraic[32] = constants[8]*(exp(algebraic[15]/(constants[0]*constants[1]))-exp(algebraic[31]/(constants[0]*constants[1])))
    algebraic[33] = -constants[20]*algebraic[32]
    rates[2] = algebraic[33]
    algebraic[35] = -algebraic[32]+algebraic[28]
    rates[8] = algebraic[35]
    algebraic[0] = states[10]/constants[3]
    algebraic[16] = constants[0]*constants[1]*log(constants[15]*states[9])+constants[22]*constants[2]*algebraic[0]
    algebraic[34] = constants[0]*constants[1]*log(constants[10]*states[4])+constants[23]*constants[2]*algebraic[0]
    algebraic[36] = constants[9]*(exp(algebraic[16]/(constants[0]*constants[1]))-exp(algebraic[34]/(constants[0]*constants[1])))
    algebraic[37] = constants[2]*(-constants[22]*algebraic[36]+constants[23]*algebraic[36])
    rates[10] = algebraic[37]
    algebraic[38] = algebraic[36]-algebraic[18]
    rates[4] = algebraic[38]
    algebraic[39] = -algebraic[36]+algebraic[32]
    rates[9] = algebraic[39]
    return(rates)

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