# Size of variable arrays:
sizeAlgebraic = 35
sizeStates = 19
sizeConstants = 40
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_RB1_inactive in component environment (fmol)"
    legend_states[1] = "q_L_RB1_inactive in component environment (fmol)"
    legend_states[2] = "q_LB1_ode in component environment (fmol)"
    legend_algebraic[0] = "q_LB1_stim in component environment (fmol)"
    legend_algebraic[3] = "q_LB1 in component environment (fmol)"
    legend_states[3] = "q_RB1 in component environment (fmol)"
    legend_states[4] = "q_Gs in component environment (fmol)"
    legend_states[5] = "q_RB1_Gs in component environment (fmol)"
    legend_states[6] = "q_L_RB1 in component environment (fmol)"
    legend_states[7] = "q_L_RB1_Gs in component environment (fmol)"
    legend_states[8] = "q_Gsa_GTP in component environment (fmol)"
    legend_states[9] = "q_Gsbetagamma in component environment (fmol)"
    legend_states[10] = "q_Gsa_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_RB1_tag in component environment (fmol)"
    legend_states[15] = "q_L_RB1_tag in component environment (fmol)"
    legend_states[16] = "q_RB1_GRKArr in component environment (fmol)"
    legend_states[17] = "q_L_RB1_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[24] = "v_Rswitch_B1 in component GPCR_B1AR_reduced (fmol_per_sec)"
    legend_algebraic[25] = "v_LRswitch_B1 in component GPCR_B1AR_reduced (fmol_per_sec)"
    legend_algebraic[26] = "v_C_B1 in component GPCR_B1AR_reduced (fmol_per_sec)"
    legend_algebraic[27] = "v_R_B1 in component GPCR_B1AR_reduced (fmol_per_sec)"
    legend_algebraic[28] = "v_L_B1 in component GPCR_B1AR_reduced (fmol_per_sec)"
    legend_algebraic[29] = "v_Act1_Gs in component GPCR_B1AR_reduced (fmol_per_sec)"
    legend_algebraic[30] = "v_Act2_Gs in component GPCR_B1AR_reduced (fmol_per_sec)"
    legend_algebraic[31] = "v_Hyd_Gs in component GPCR_B1AR_reduced (fmol_per_sec)"
    legend_algebraic[33] = "v_Reassoc_Gs in component GPCR_B1AR_reduced (fmol_per_sec)"
    legend_algebraic[32] = "v_InternR_B1 in component GPCR_B1AR_reduced (fmol_per_sec)"
    legend_algebraic[34] = "v_InternLR_B1 in component GPCR_B1AR_reduced (fmol_per_sec)"
    legend_constants[39] = "v_Rsynthesis in component environment (fmol_per_sec)"
    legend_algebraic[1] = "conserv_R_T in component environment (fmol)"
    legend_algebraic[5] = "conserv_L_T in component environment (fmol)"
    legend_algebraic[2] = "conserv_G_T in component environment (fmol)"
    legend_constants[5] = "kappa_Rswitch_B1 in component GPCR_B1AR_reduced_parameters (fmol_per_sec)"
    legend_constants[6] = "kappa_LRswitch_B1 in component GPCR_B1AR_reduced_parameters (fmol_per_sec)"
    legend_constants[7] = "kappa_C_B1 in component GPCR_B1AR_reduced_parameters (fmol_per_sec)"
    legend_constants[8] = "kappa_R_B1 in component GPCR_B1AR_reduced_parameters (fmol_per_sec)"
    legend_constants[9] = "kappa_L_B1 in component GPCR_B1AR_reduced_parameters (fmol_per_sec)"
    legend_constants[10] = "kappa_Act1_Gs in component GPCR_B1AR_reduced_parameters (fmol_per_sec)"
    legend_constants[11] = "kappa_Act2_Gs in component GPCR_B1AR_reduced_parameters (fmol_per_sec)"
    legend_constants[12] = "kappa_Hyd_Gs in component GPCR_B1AR_reduced_parameters (fmol_per_sec)"
    legend_constants[13] = "kappa_Reassoc_Gs in component GPCR_B1AR_reduced_parameters (fmol_per_sec)"
    legend_constants[14] = "kappa_InternR_B1 in component GPCR_B1AR_reduced_parameters (fmol_per_sec)"
    legend_constants[15] = "kappa_InternLR_B1 in component GPCR_B1AR_reduced_parameters (fmol_per_sec)"
    legend_constants[16] = "K_RB1_inactive in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[17] = "K_L_RB1_inactive in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[18] = "K_LB1 in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[19] = "K_RB1 in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[20] = "K_Gs in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[21] = "K_RB1_Gs in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[22] = "K_L_RB1 in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[23] = "K_L_RB1_Gs in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[24] = "K_Gsa_GTP in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[25] = "K_Gsbetagamma in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[26] = "K_Gsa_GDP in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[27] = "K_GTP in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[28] = "K_GDP in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[29] = "K_Pi in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[30] = "K_RB1_tag in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[31] = "K_L_RB1_tag in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[32] = "K_RB1_GRKArr in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[33] = "K_L_RB1_GRKArr in component GPCR_B1AR_reduced_parameters (per_fmol)"
    legend_constants[34] = "K_GRKArr in component GPCR_B1AR_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[4] = "mu_RB1_inactive in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[6] = "mu_L_RB1_inactive in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[7] = "mu_LB1 in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[8] = "mu_RB1 in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[9] = "mu_Gs in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[10] = "mu_RB1_Gs in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[11] = "mu_L_RB1 in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[12] = "mu_L_RB1_Gs in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[13] = "mu_Gsa_GTP in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[14] = "mu_Gsbetagamma in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[15] = "mu_Gsa_GDP in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[16] = "mu_GTP in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[17] = "mu_GDP in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[18] = "mu_Pi in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[19] = "mu_RB1_tag in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[20] = "mu_L_RB1_tag in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[21] = "mu_RB1_GRKArr in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[22] = "mu_L_RB1_GRKArr in component GPCR_B1AR_reduced (J_per_mol)"
    legend_algebraic[23] = "mu_GRKArr in component GPCR_B1AR_reduced (J_per_mol)"
    legend_constants[37] = "F in component constants (C_per_mol)"
    legend_rates[0] = "d/dt q_RB1_inactive in component environment (fmol)"
    legend_rates[1] = "d/dt q_L_RB1_inactive in component environment (fmol)"
    legend_rates[2] = "d/dt q_LB1_ode in component environment (fmol)"
    legend_rates[3] = "d/dt q_RB1 in component environment (fmol)"
    legend_rates[4] = "d/dt q_Gs in component environment (fmol)"
    legend_rates[5] = "d/dt q_RB1_Gs in component environment (fmol)"
    legend_rates[6] = "d/dt q_L_RB1 in component environment (fmol)"
    legend_rates[7] = "d/dt q_L_RB1_Gs in component environment (fmol)"
    legend_rates[8] = "d/dt q_Gsa_GTP in component environment (fmol)"
    legend_rates[9] = "d/dt q_Gsbetagamma in component environment (fmol)"
    legend_rates[10] = "d/dt q_Gsa_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_RB1_tag in component environment (fmol)"
    legend_rates[15] = "d/dt q_L_RB1_tag in component environment (fmol)"
    legend_rates[16] = "d/dt q_RB1_GRKArr in component environment (fmol)"
    legend_rates[17] = "d/dt q_L_RB1_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] = 0.0004579000e0
    states[1] = 1e-18
    states[2] = 0
    states[3] = 1e-18
    states[4] = 0.1455400000
    states[5] = 1e-18
    states[6] = 1e-18
    states[7] = 1e-18
    states[8] = 0.01
    states[9] = 0.02
    states[10] = 0.01
    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-3
    constants[0] = 0.5e1
    constants[1] = 5e-1
    constants[2] = 5e-1
    constants[3] = 1e1
    constants[4] = 1e-8
    constants[5] = 1036.38
    constants[6] = 1.83921e-07
    constants[7] = 891573
    constants[8] = 1.58222e+06
    constants[9] = 52417.5
    constants[10] = 0.000610519
    constants[11] = 0.576677
    constants[12] = 0.0661821
    constants[13] = 8.60273e-06
    constants[14] = 0.00230556
    constants[15] = 2.17775
    constants[16] = 28.0492
    constants[17] = 1.58056e+11
    constants[18] = 0.0574759
    constants[19] = 0.280492
    constants[20] = 0.00337913
    constants[21] = 1.07597
    constants[22] = 0.158056
    constants[23] = 0.00113911
    constants[24] = 0.00878478
    constants[25] = 736.699
    constants[26] = 161.34
    constants[27] = 823.314
    constants[28] = 3.61368e-10
    constants[29] = 7.91408e-11
    constants[30] = 0.500146
    constants[31] = 0.000529497
    constants[32] = 1.26086e-05
    constants[33] = 1.33485e-08
    constants[34] = 732843
    constants[35] = 8.31
    constants[36] = 310
    constants[37] = 96485
    constants[38] = constants[3]/constants[2]
    constants[39] = 0.000100000
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[4] = constants[35]*constants[36]*log(constants[16]*states[0])
    algebraic[8] = constants[35]*constants[36]*log(constants[19]*states[3])
    algebraic[24] = constants[5]*(exp(algebraic[4]/(constants[35]*constants[36]))-exp(algebraic[8]/(constants[35]*constants[36])))
    rates[0] = -algebraic[24]+0.00000*constants[39]
    algebraic[6] = constants[35]*constants[36]*log(constants[17]*states[1])
    algebraic[11] = constants[35]*constants[36]*log(constants[22]*states[6])
    algebraic[25] = constants[6]*(exp(algebraic[6]/(constants[35]*constants[36]))-exp(algebraic[11]/(constants[35]*constants[36])))
    rates[1] = -algebraic[25]
    algebraic[0] = 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_equal(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[3] = algebraic[0]+states[2]
    algebraic[7] = constants[35]*constants[36]*log(constants[18]*algebraic[3])
    algebraic[28] = constants[9]*(exp((algebraic[8]+algebraic[7])/(constants[35]*constants[36]))-exp(algebraic[11]/(constants[35]*constants[36])))
    rates[2] = -algebraic[28]
    algebraic[9] = constants[35]*constants[36]*log(constants[20]*states[4])
    algebraic[10] = constants[35]*constants[36]*log(constants[21]*states[5])
    algebraic[26] = constants[7]*(exp((algebraic[8]+algebraic[9])/(constants[35]*constants[36]))-exp(algebraic[10]/(constants[35]*constants[36])))
    rates[3] = (algebraic[24]-algebraic[26])-algebraic[28]
    algebraic[13] = constants[35]*constants[36]*log(constants[24]*states[8])
    algebraic[14] = constants[35]*constants[36]*log(constants[25]*states[9])
    algebraic[16] = constants[35]*constants[36]*log(constants[27]*states[11])
    algebraic[17] = constants[35]*constants[36]*log(constants[28]*states[12])
    algebraic[19] = constants[35]*constants[36]*log(constants[30]*states[14])
    algebraic[29] = constants[10]*(exp((algebraic[10]+algebraic[16])/(constants[35]*constants[36]))-exp((algebraic[13]+algebraic[14]+algebraic[19]+algebraic[17])/(constants[35]*constants[36])))
    rates[5] = algebraic[26]-algebraic[29]
    algebraic[12] = constants[35]*constants[36]*log(constants[23]*states[7])
    algebraic[27] = constants[8]*(exp((algebraic[11]+algebraic[9])/(constants[35]*constants[36]))-exp(algebraic[12]/(constants[35]*constants[36])))
    rates[6] = (algebraic[25]-algebraic[27])+algebraic[28]
    algebraic[20] = constants[35]*constants[36]*log(constants[31]*states[15])
    algebraic[30] = constants[11]*(exp((algebraic[12]+algebraic[16])/(constants[35]*constants[36]))-exp((algebraic[13]+algebraic[14]+algebraic[20]+algebraic[17])/(constants[35]*constants[36])))
    rates[7] = algebraic[27]-algebraic[30]
    rates[11] = -algebraic[29]-algebraic[30]
    rates[12] = algebraic[29]+algebraic[30]
    algebraic[15] = constants[35]*constants[36]*log(constants[26]*states[10])
    algebraic[18] = constants[35]*constants[36]*log(constants[29]*states[13])
    algebraic[31] = constants[12]*(exp(algebraic[13]/(constants[35]*constants[36]))-exp((algebraic[15]+algebraic[18])/(constants[35]*constants[36])))
    rates[8] = (algebraic[29]+algebraic[30])-algebraic[31]
    rates[13] = algebraic[31]
    algebraic[21] = constants[35]*constants[36]*log(constants[32]*states[16])
    algebraic[23] = constants[35]*constants[36]*log(constants[34]*states[18])
    algebraic[32] = constants[14]*(exp((algebraic[19]+algebraic[23])/(constants[35]*constants[36]))-exp(algebraic[21]/(constants[35]*constants[36])))
    rates[14] = algebraic[29]-algebraic[32]
    rates[16] = algebraic[32]
    algebraic[33] = constants[13]*(exp((algebraic[15]+algebraic[14])/(constants[35]*constants[36]))-exp(algebraic[9]/(constants[35]*constants[36])))
    rates[4] = (-algebraic[26]-algebraic[27])+algebraic[33]
    rates[9] = (algebraic[29]+algebraic[30])-algebraic[33]
    rates[10] = algebraic[31]-algebraic[33]
    algebraic[22] = constants[35]*constants[36]*log(constants[33]*states[17])
    algebraic[34] = constants[15]*(exp((algebraic[20]+algebraic[23])/(constants[35]*constants[36]))-exp(algebraic[22]/(constants[35]*constants[36])))
    rates[15] = algebraic[30]-algebraic[34]
    rates[17] = algebraic[34]
    rates[18] = -algebraic[32]-algebraic[34]
    return(rates)

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