# Size of variable arrays:
sizeAlgebraic = 37
sizeStates = 19
sizeConstants = 39
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_states[0] = "q_RM2_inactive in component environment (fmol)"
    legend_states[1] = "q_L_RM2_inactive in component environment (fmol)"
    legend_algebraic[4] = "q_LM2 in component environment (fmol)"
    legend_algebraic[3] = "q_LM2_stim in component environment (fmol)"
    legend_states[2] = "q_LM2_ode in component environment (fmol)"
    legend_states[3] = "q_RM2 in component environment (fmol)"
    legend_states[4] = "q_Gi in component environment (fmol)"
    legend_states[5] = "q_RM2_Gi in component environment (fmol)"
    legend_states[6] = "q_L_RM2 in component environment (fmol)"
    legend_states[7] = "q_L_RM2_Gi in component environment (fmol)"
    legend_states[8] = "q_Gia_GTP in component environment (fmol)"
    legend_states[9] = "q_Gibetagamma in component environment (fmol)"
    legend_states[10] = "q_Gia_GDP in component environment (fmol)"
    legend_states[11] = "q_GTP in component environment (fmol)"
    legend_states[12] = "q_GDP in component environment (fmol)"
    legend_states[13] = "q_Pi in component environment (fmol)"
    legend_states[14] = "q_RM2_tag in component environment (fmol)"
    legend_states[15] = "q_L_RM2_tag in component environment (fmol)"
    legend_states[16] = "q_RM2_GRKArr in component environment (fmol)"
    legend_states[17] = "q_L_RM2_GRKArr in component environment (fmol)"
    legend_states[18] = "q_GRKArr in component environment (fmol)"
    legend_constants[0] = "stimSt in component environment (second)"
    legend_constants[1] = "stimDur in component environment (second)"
    legend_constants[2] = "tR in component environment (second)"
    legend_constants[3] = "stimMag in component environment (fmol)"
    legend_constants[4] = "stimHolding in component environment (fmol)"
    legend_constants[38] = "m in component environment (fmol_per_sec)"
    legend_algebraic[0] = "conserv_R_T in component environment (fmol)"
    legend_algebraic[5] = "conserv_L_T in component environment (fmol)"
    legend_algebraic[1] = "conserv_G_T in component environment (fmol)"
    legend_algebraic[2] = "total_R in component environment (fmol)"
    legend_algebraic[25] = "v_Rswitch_M2 in component GPCR_M2_reduced (fmol_per_sec)"
    legend_algebraic[26] = "v_LRswitch_M2 in component GPCR_M2_reduced (fmol_per_sec)"
    legend_algebraic[27] = "v_C_M2 in component GPCR_M2_reduced (fmol_per_sec)"
    legend_algebraic[28] = "v_R_M2 in component GPCR_M2_reduced (fmol_per_sec)"
    legend_algebraic[29] = "v_L_M2 in component GPCR_M2_reduced (fmol_per_sec)"
    legend_algebraic[30] = "v_Act1_Gi in component GPCR_M2_reduced (fmol_per_sec)"
    legend_algebraic[31] = "v_Act2_Gi in component GPCR_M2_reduced (fmol_per_sec)"
    legend_algebraic[33] = "v_Hyd_Gi in component GPCR_M2_reduced (fmol_per_sec)"
    legend_algebraic[35] = "v_Reassoc_Gi in component GPCR_M2_reduced (fmol_per_sec)"
    legend_algebraic[34] = "v_InternR_M2 in component GPCR_M2_reduced (fmol_per_sec)"
    legend_algebraic[36] = "v_InternLR_M2 in component GPCR_M2_reduced (fmol_per_sec)"
    legend_algebraic[32] = "v_Rsynthesis in component environment (fmol_per_sec)"
    legend_constants[5] = "kappa_Rswitch_M2 in component GPCR_M2_reduced_parameters (fmol_per_sec)"
    legend_constants[6] = "kappa_LRswitch_M2 in component GPCR_M2_reduced_parameters (fmol_per_sec)"
    legend_constants[7] = "kappa_C_M2 in component GPCR_M2_reduced_parameters (fmol_per_sec)"
    legend_constants[8] = "kappa_R_M2 in component GPCR_M2_reduced_parameters (fmol_per_sec)"
    legend_constants[9] = "kappa_L_M2 in component GPCR_M2_reduced_parameters (fmol_per_sec)"
    legend_constants[10] = "kappa_Act1_Gi in component GPCR_M2_reduced_parameters (fmol_per_sec)"
    legend_constants[11] = "kappa_Act2_Gi in component GPCR_M2_reduced_parameters (fmol_per_sec)"
    legend_constants[12] = "kappa_Hyd_Gi in component GPCR_M2_reduced_parameters (fmol_per_sec)"
    legend_constants[13] = "kappa_Reassoc_Gi in component GPCR_M2_reduced_parameters (fmol_per_sec)"
    legend_constants[14] = "kappa_InternR_M2 in component GPCR_M2_reduced_parameters (fmol_per_sec)"
    legend_constants[15] = "kappa_InternLR_M2 in component GPCR_M2_reduced_parameters (fmol_per_sec)"
    legend_constants[16] = "K_RM2_inactive in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[17] = "K_L_RM2_inactive in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[18] = "K_LM2 in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[19] = "K_RM2 in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[20] = "K_Gi in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[21] = "K_RM2_Gi in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[22] = "K_L_RM2 in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[23] = "K_L_RM2_Gi in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[24] = "K_Gia_GTP in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[25] = "K_Gibetagamma in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[26] = "K_Gia_GDP in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[27] = "K_GTP in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[28] = "K_GDP in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[29] = "K_Pi in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[30] = "K_RM2_tag in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[31] = "K_L_RM2_tag in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[32] = "K_RM2_GRKArr in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[33] = "K_L_RM2_GRKArr in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[34] = "K_GRKArr in component GPCR_M2_reduced_parameters (per_fmol)"
    legend_constants[35] = "R in component constants (J_per_K_per_mol)"
    legend_constants[36] = "T in component constants (kelvin)"
    legend_algebraic[6] = "mu_RM2_inactive in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[7] = "mu_L_RM2_inactive in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[8] = "mu_LM2 in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[9] = "mu_RM2 in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[10] = "mu_Gi in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[11] = "mu_RM2_Gi in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[12] = "mu_L_RM2 in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[13] = "mu_L_RM2_Gi in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[14] = "mu_Gia_GTP in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[15] = "mu_Gibetagamma in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[16] = "mu_Gia_GDP in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[17] = "mu_GTP in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[18] = "mu_GDP in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[19] = "mu_Pi in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[20] = "mu_RM2_tag in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[21] = "mu_L_RM2_tag in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[22] = "mu_RM2_GRKArr in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[23] = "mu_L_RM2_GRKArr in component GPCR_M2_reduced (J_per_mol)"
    legend_algebraic[24] = "mu_GRKArr in component GPCR_M2_reduced (J_per_mol)"
    legend_constants[37] = "F in component constants (C_per_mol)"
    legend_rates[0] = "d/dt q_RM2_inactive in component environment (fmol)"
    legend_rates[1] = "d/dt q_L_RM2_inactive in component environment (fmol)"
    legend_rates[2] = "d/dt q_LM2_ode in component environment (fmol)"
    legend_rates[3] = "d/dt q_RM2 in component environment (fmol)"
    legend_rates[4] = "d/dt q_Gi in component environment (fmol)"
    legend_rates[5] = "d/dt q_RM2_Gi in component environment (fmol)"
    legend_rates[6] = "d/dt q_L_RM2 in component environment (fmol)"
    legend_rates[7] = "d/dt q_L_RM2_Gi in component environment (fmol)"
    legend_rates[8] = "d/dt q_Gia_GTP in component environment (fmol)"
    legend_rates[9] = "d/dt q_Gibetagamma in component environment (fmol)"
    legend_rates[10] = "d/dt q_Gia_GDP in component environment (fmol)"
    legend_rates[11] = "d/dt q_GTP in component environment (fmol)"
    legend_rates[12] = "d/dt q_GDP in component environment (fmol)"
    legend_rates[13] = "d/dt q_Pi in component environment (fmol)"
    legend_rates[14] = "d/dt q_RM2_tag in component environment (fmol)"
    legend_rates[15] = "d/dt q_L_RM2_tag in component environment (fmol)"
    legend_rates[16] = "d/dt q_RM2_GRKArr in component environment (fmol)"
    legend_rates[17] = "d/dt q_L_RM2_GRKArr in component environment (fmol)"
    legend_rates[18] = "d/dt q_GRKArr in component environment (fmol)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 0.00072162
    states[1] = 1e-18
    states[2] = 0
    states[3] = 1e-2
    states[4] = 0.00836
    states[5] = 1e-18
    states[6] = 1e-18
    states[7] = 1e-18
    states[8] = 1e-18
    states[9] = 1e-18
    states[10] = 1e-18
    states[11] = 2.2
    states[12] = 1.1
    states[13] = 570
    states[14] = 1e-18
    states[15] = 1e-18
    states[16] = 1e-18
    states[17] = 1e-18
    states[18] = 1e-18
    constants[0] = 2e1
    constants[1] = 2e1
    constants[2] = 1e1
    constants[3] = 1e2
    constants[4] = 1e-8
    constants[5] = 3.25763
    constants[6] = 0.00165864
    constants[7] = 14461.5
    constants[8] = 736.312
    constants[9] = 5769.58
    constants[10] = 0.0114404
    constants[11] = 0.381268
    constants[12] = 0.585749
    constants[13] = 0.0140382
    constants[14] = 0.0665538
    constants[15] = 2.218
    constants[16] = 0.892359
    constants[17] = 1752.63
    constants[18] = 0.0519039
    constants[19] = 0.00892359
    constants[20] = 0.0207076
    constants[21] = 0.1907
    constants[22] = 0.175263
    constants[23] = 0.286109
    constants[24] = 0.0397027
    constants[25] = 0.412109
    constants[26] = 0.176744
    constants[27] = 0.019367
    constants[28] = 0.000190324
    constants[29] = 8.16257e-05
    constants[30] = 0.200446
    constants[31] = 0.00601463
    constants[32] = 0.00436786
    constants[33] = 0.000131063
    constants[34] = 6.3345
    constants[35] = 8.31
    constants[36] = 310
    constants[37] = 96485
    constants[38] = constants[3]/constants[2]
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[7] = constants[35]*constants[36]*log(constants[17]*states[1])
    algebraic[12] = constants[35]*constants[36]*log(constants[22]*states[6])
    algebraic[26] = constants[6]*(exp(algebraic[7]/(constants[35]*constants[36]))-exp(algebraic[12]/(constants[35]*constants[36])))
    rates[1] = -algebraic[26]
    algebraic[6] = constants[35]*constants[36]*log(constants[16]*states[0])
    algebraic[9] = constants[35]*constants[36]*log(constants[19]*states[3])
    algebraic[25] = constants[5]*(exp(algebraic[6]/(constants[35]*constants[36]))-exp(algebraic[9]/(constants[35]*constants[36])))
    algebraic[3] = custom_piecewise([less(voi , constants[0]) & greater(voi , constants[0]-constants[2]), constants[4]+constants[38]*((voi-constants[0])+constants[2]) , greater_equal(voi , constants[0]) & less(voi , constants[0]+constants[1]), constants[3]+constants[4] , less(voi , constants[0]+constants[2]+constants[1]) & greater_equal(voi , constants[0]+constants[1]), constants[4]+-constants[38]*(((voi-constants[0])-constants[2])-constants[1]) , True, constants[4]])
    algebraic[4] = algebraic[3]+states[2]
    algebraic[8] = constants[35]*constants[36]*log(constants[18]*algebraic[4])
    algebraic[29] = constants[9]*(exp((algebraic[9]+algebraic[8])/(constants[35]*constants[36]))-exp(algebraic[12]/(constants[35]*constants[36])))
    rates[0] = -algebraic[25]-algebraic[29]
    rates[2] = -algebraic[29]
    algebraic[10] = constants[35]*constants[36]*log(constants[20]*states[4])
    algebraic[11] = constants[35]*constants[36]*log(constants[21]*states[5])
    algebraic[27] = constants[7]*(exp((algebraic[9]+algebraic[10])/(constants[35]*constants[36]))-exp(algebraic[11]/(constants[35]*constants[36])))
    algebraic[14] = constants[35]*constants[36]*log(constants[24]*states[8])
    algebraic[15] = constants[35]*constants[36]*log(constants[25]*states[9])
    algebraic[17] = constants[35]*constants[36]*log(constants[27]*states[11])
    algebraic[18] = constants[35]*constants[36]*log(constants[28]*states[12])
    algebraic[20] = constants[35]*constants[36]*log(constants[30]*states[14])
    algebraic[30] = constants[10]*(exp((algebraic[11]+algebraic[17])/(constants[35]*constants[36]))-exp((algebraic[14]+algebraic[15]+algebraic[20]+algebraic[18])/(constants[35]*constants[36])))
    rates[5] = algebraic[27]-algebraic[30]
    algebraic[13] = constants[35]*constants[36]*log(constants[23]*states[7])
    algebraic[28] = constants[8]*(exp((algebraic[12]+algebraic[10])/(constants[35]*constants[36]))-exp(algebraic[13]/(constants[35]*constants[36])))
    rates[6] = -algebraic[28]+algebraic[29]+algebraic[26]
    algebraic[32] = (algebraic[27])+algebraic[29]
    rates[3] = (-algebraic[27]-algebraic[29])+1.00000*algebraic[32]+algebraic[25]
    algebraic[21] = constants[35]*constants[36]*log(constants[31]*states[15])
    algebraic[31] = constants[11]*(exp((algebraic[13]+algebraic[17])/(constants[35]*constants[36]))-exp((algebraic[14]+algebraic[15]+algebraic[21]+algebraic[18])/(constants[35]*constants[36])))
    rates[7] = algebraic[28]-algebraic[31]
    rates[11] = -algebraic[30]-algebraic[31]
    rates[12] = algebraic[30]+algebraic[31]
    algebraic[16] = constants[35]*constants[36]*log(constants[26]*states[10])
    algebraic[19] = constants[35]*constants[36]*log(constants[29]*states[13])
    algebraic[33] = constants[12]*(exp(algebraic[14]/(constants[35]*constants[36]))-exp((algebraic[16]+algebraic[19])/(constants[35]*constants[36])))
    rates[8] = (algebraic[30]+algebraic[31])-algebraic[33]
    rates[13] = algebraic[33]
    algebraic[22] = constants[35]*constants[36]*log(constants[32]*states[16])
    algebraic[24] = constants[35]*constants[36]*log(constants[34]*states[18])
    algebraic[34] = constants[14]*(exp((algebraic[20]+algebraic[24])/(constants[35]*constants[36]))-exp(algebraic[22]/(constants[35]*constants[36])))
    rates[14] = algebraic[30]-algebraic[34]
    rates[16] = algebraic[34]
    algebraic[35] = constants[13]*(exp((algebraic[16]+algebraic[15])/(constants[35]*constants[36]))-exp(algebraic[10]/(constants[35]*constants[36])))
    rates[4] = (-algebraic[27]-algebraic[28])+algebraic[35]
    rates[9] = (algebraic[30]+algebraic[31])-algebraic[35]
    rates[10] = algebraic[33]-algebraic[35]
    algebraic[23] = constants[35]*constants[36]*log(constants[33]*states[17])
    algebraic[36] = constants[15]*(exp((algebraic[21]+algebraic[24])/(constants[35]*constants[36]))-exp(algebraic[23]/(constants[35]*constants[36])))
    rates[15] = algebraic[31]-algebraic[36]
    rates[17] = algebraic[36]
    rates[18] = -algebraic[34]-algebraic[36]
    return(rates)

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