# Size of variable arrays:
sizeAlgebraic = 26
sizeStates = 17
sizeConstants = 49
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] = "A in component differentials (molar)"
    legend_states[1] = "G in component differentials (molar)"
    legend_states[2] = "GA in component differentials (molar)"
    legend_states[3] = "T in component differentials (molar)"
    legend_states[4] = "R in component differentials (molar)"
    legend_states[5] = "GT in component differentials (molar)"
    legend_states[6] = "GD in component differentials (molar)"
    legend_states[7] = "Pi_ in component differentials (molar)"
    legend_states[8] = "D in component differentials (molar)"
    legend_states[9] = "RG in component differentials (molar)"
    legend_states[10] = "RGT in component differentials (molar)"
    legend_states[11] = "GAT in component differentials (molar)"
    legend_states[12] = "GAD in component differentials (molar)"
    legend_states[13] = "RGD in component differentials (molar)"
    legend_states[14] = "RGA in component differentials (molar)"
    legend_states[15] = "RGAT in component differentials (molar)"
    legend_states[16] = "RGAD in component differentials (molar)"
    legend_algebraic[0] = "A1 in component A1 (molar_per_second)"
    legend_algebraic[9] = "A2 in component A2 (molar_per_second)"
    legend_algebraic[10] = "A3 in component A3 (molar_per_second)"
    legend_algebraic[17] = "A4 in component A4 (molar_per_second)"
    legend_algebraic[21] = "A5 in component A5 (molar_per_second)"
    legend_algebraic[23] = "A6 in component A6 (molar_per_second)"
    legend_algebraic[4] = "R1 in component R1 (molar_per_second)"
    legend_algebraic[8] = "R2 in component R2 (molar_per_second)"
    legend_algebraic[11] = "R3 in component R3 (molar_per_second)"
    legend_algebraic[18] = "R4 in component R4 (molar_per_second)"
    legend_algebraic[20] = "R5 in component R5 (molar_per_second)"
    legend_algebraic[24] = "R6 in component R6 (molar_per_second)"
    legend_algebraic[3] = "T1 in component T1 (molar_per_second)"
    legend_algebraic[14] = "T2 in component T2 (molar_per_second)"
    legend_algebraic[7] = "T3 in component T3 (molar_per_second)"
    legend_algebraic[19] = "T4 in component T4 (molar_per_second)"
    legend_algebraic[5] = "P1 in component P1 (molar_per_second)"
    legend_algebraic[15] = "P2 in component P2 (molar_per_second)"
    legend_algebraic[12] = "P3 in component P3 (molar_per_second)"
    legend_algebraic[22] = "P4 in component P4 (molar_per_second)"
    legend_algebraic[6] = "D1 in component D1 (molar_per_second)"
    legend_algebraic[16] = "D2 in component D2 (molar_per_second)"
    legend_algebraic[13] = "D3 in component D3 (molar_per_second)"
    legend_algebraic[25] = "D4 in component D4 (molar_per_second)"
    legend_algebraic[1] = "Z in component output (dimensionless)"
    legend_algebraic[2] = "v in component output (per_second)"
    legend_constants[0] = "G_tot in component output (molar)"
    legend_constants[1] = "k1 in component P1 (per_second)"
    legend_constants[2] = "k1 in component P2 (per_second)"
    legend_constants[3] = "k1 in component P3 (per_second)"
    legend_constants[4] = "k1 in component P4 (per_second)"
    legend_constants[5] = "k1 in component A1 (per_molar_per_second)"
    legend_constants[6] = "k2 in component A1 (per_second)"
    legend_constants[7] = "k1 in component T1 (per_molar_per_second)"
    legend_constants[8] = "k2 in component T1 (per_second)"
    legend_constants[9] = "k1 in component R1 (per_molar_per_second)"
    legend_constants[10] = "k2 in component R1 (per_second)"
    legend_constants[11] = "k2 in component P1 (per_molar_per_second)"
    legend_constants[12] = "k1 in component D1 (per_second)"
    legend_constants[13] = "k2 in component D1 (per_molar_per_second)"
    legend_constants[14] = "k1 in component T3 (per_molar_per_second)"
    legend_constants[15] = "k2 in component T3 (per_second)"
    legend_constants[16] = "k1 in component R2 (per_molar_per_second)"
    legend_constants[17] = "k2 in component R2 (per_second)"
    legend_constants[18] = "k1 in component A2 (per_molar_per_second)"
    legend_constants[19] = "k2 in component A2 (per_second)"
    legend_constants[20] = "k1 in component A3 (per_molar_per_second)"
    legend_constants[21] = "k2 in component A3 (per_second)"
    legend_constants[22] = "k1 in component R3 (per_molar_per_second)"
    legend_constants[23] = "k2 in component R3 (per_second)"
    legend_constants[24] = "k2 in component P3 (per_molar_per_second)"
    legend_constants[25] = "k1 in component D3 (per_second)"
    legend_constants[26] = "k2 in component D3 (per_molar_per_second)"
    legend_constants[27] = "k1 in component T2 (per_molar_per_second)"
    legend_constants[28] = "k2 in component T2 (per_second)"
    legend_constants[29] = "k2 in component P2 (per_molar_per_second)"
    legend_constants[30] = "k1 in component D2 (per_second)"
    legend_constants[31] = "k2 in component D2 (per_molar_per_second)"
    legend_constants[32] = "k1 in component A4 (per_molar_per_second)"
    legend_constants[33] = "k2 in component A4 (per_second)"
    legend_constants[34] = "k1 in component R4 (per_molar_per_second)"
    legend_constants[35] = "k2 in component R4 (per_second)"
    legend_constants[36] = "k1 in component T4 (per_molar_per_second)"
    legend_constants[37] = "k2 in component T4 (per_second)"
    legend_constants[38] = "k1 in component R5 (per_molar_per_second)"
    legend_constants[39] = "k2 in component R5 (per_second)"
    legend_constants[40] = "k1 in component A5 (per_molar_per_second)"
    legend_constants[41] = "k2 in component A5 (per_second)"
    legend_constants[42] = "k2 in component P4 (per_molar_per_second)"
    legend_constants[43] = "k1 in component A6 (per_molar_per_second)"
    legend_constants[44] = "k2 in component A6 (per_second)"
    legend_constants[45] = "k1 in component R6 (per_molar_per_second)"
    legend_constants[46] = "k2 in component R6 (per_second)"
    legend_constants[47] = "k1 in component D4 (per_second)"
    legend_constants[48] = "k2 in component D4 (per_molar_per_second)"
    legend_rates[0] = "d/dt A in component differentials (molar)"
    legend_rates[1] = "d/dt G in component differentials (molar)"
    legend_rates[2] = "d/dt GA in component differentials (molar)"
    legend_rates[3] = "d/dt T in component differentials (molar)"
    legend_rates[4] = "d/dt R in component differentials (molar)"
    legend_rates[5] = "d/dt GT in component differentials (molar)"
    legend_rates[6] = "d/dt GD in component differentials (molar)"
    legend_rates[7] = "d/dt Pi_ in component differentials (molar)"
    legend_rates[8] = "d/dt D in component differentials (molar)"
    legend_rates[9] = "d/dt RG in component differentials (molar)"
    legend_rates[10] = "d/dt RGT in component differentials (molar)"
    legend_rates[11] = "d/dt GAT in component differentials (molar)"
    legend_rates[12] = "d/dt GAD in component differentials (molar)"
    legend_rates[13] = "d/dt RGD in component differentials (molar)"
    legend_rates[14] = "d/dt RGA in component differentials (molar)"
    legend_rates[15] = "d/dt RGAT in component differentials (molar)"
    legend_rates[16] = "d/dt RGAD in component differentials (molar)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 0
    states[1] = 0
    states[2] = 0
    states[3] = 0.000468
    states[4] = 1e-6
    states[5] = 0
    states[6] = 1e-8
    states[7] = 0.0044
    states[8] = 0.000149
    states[9] = 0
    states[10] = 0
    states[11] = 0
    states[12] = 0
    states[13] = 0
    states[14] = 0
    states[15] = 0
    states[16] = 0
    constants[0] = 1e-8
    constants[1] = 0.013
    constants[2] = 25
    constants[3] = 0.013
    constants[4] = 25
    constants[5] = 8780000
    constants[6] = 8
    constants[7] = 529000
    constants[8] = 8.38e-6
    constants[9] = 636000000
    constants[10] = 0.0179
    constants[11] = 9.03e-7
    constants[12] = 0.0001
    constants[13] = 62.3
    constants[14] = 853000
    constants[15] = 0.00468
    constants[16] = 132000000
    constants[17] = 1.28
    constants[18] = 386000
    constants[19] = 0.0408
    constants[20] = 64100
    constants[21] = 0.95
    constants[22] = 94700000
    constants[23] = 0.00227
    constants[24] = 2.22e-9
    constants[25] = 2
    constants[26] = 1470000
    constants[27] = 44700
    constants[28] = 8.32e-8
    constants[29] = 0.244
    constants[30] = 0.0001
    constants[31] = 3.83
    constants[32] = 74300
    constants[33] = 0.00572
    constants[34] = 22800000
    constants[35] = 5.43e-5
    constants[36] = 1620000
    constants[37] = 0.00875
    constants[38] = 6200000
    constants[39] = 0.0433
    constants[40] = 6300000
    constants[41] = 0.478
    constants[42] = 0.00297
    constants[43] = 13000
    constants[44] = 0.685
    constants[45] = 49400000
    constants[46] = 0.00421
    constants[47] = 2.75
    constants[48] = 2940
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = constants[5]*states[1]*states[0]-constants[6]*states[2]
    algebraic[4] = constants[9]*states[1]*states[4]-constants[10]*states[9]
    algebraic[3] = constants[7]*states[1]*states[3]-constants[8]*states[5]
    algebraic[6] = constants[12]*states[6]-constants[13]*states[1]*states[8]
    rates[1] = algebraic[6]-(algebraic[0]+algebraic[3]+algebraic[4])
    algebraic[9] = constants[18]*states[5]*states[0]-constants[19]*states[11]
    algebraic[8] = constants[16]*states[5]*states[4]-constants[17]*states[10]
    algebraic[5] = constants[1]*states[5]-constants[11]*states[6]*states[7]
    rates[5] = ((algebraic[3]-algebraic[5])-algebraic[8])-algebraic[9]
    algebraic[10] = constants[20]*states[6]*states[0]-constants[21]*states[12]
    algebraic[11] = constants[22]*states[6]*states[4]-constants[23]*states[13]
    rates[6] = ((algebraic[5]-algebraic[6])-algebraic[10])-algebraic[11]
    algebraic[17] = constants[32]*states[9]*states[0]-constants[33]*states[14]
    algebraic[7] = constants[14]*states[9]*states[3]-constants[15]*states[10]
    algebraic[13] = constants[25]*states[13]-constants[26]*states[9]*states[8]
    rates[9] = ((algebraic[4]-algebraic[7])+algebraic[13])-algebraic[17]
    algebraic[18] = constants[34]*states[2]*states[4]-constants[35]*states[14]
    algebraic[14] = constants[27]*states[2]*states[3]-constants[28]*states[11]
    algebraic[16] = constants[30]*states[12]-constants[31]*states[2]*states[8]
    rates[2] = ((algebraic[0]-algebraic[14])+algebraic[16])-algebraic[18]
    algebraic[19] = constants[36]*states[14]*states[3]-constants[37]*states[15]
    rates[3] = -(algebraic[3]+algebraic[7]+algebraic[14]+algebraic[19])
    algebraic[20] = constants[38]*states[11]*states[4]-constants[39]*states[15]
    algebraic[15] = constants[2]*states[11]-constants[29]*states[12]*states[7]
    rates[11] = ((algebraic[9]+algebraic[14])-algebraic[15])-algebraic[20]
    algebraic[21] = constants[40]*states[10]*states[0]-constants[41]*states[15]
    algebraic[12] = constants[3]*states[10]-constants[24]*states[13]*states[7]
    rates[10] = ((algebraic[7]+algebraic[8])-algebraic[12])-algebraic[21]
    algebraic[22] = constants[4]*states[15]-constants[42]*states[16]*states[7]
    rates[7] = algebraic[5]+algebraic[12]+algebraic[15]+algebraic[22]
    rates[15] = (algebraic[19]+algebraic[20]+algebraic[21])-algebraic[22]
    algebraic[23] = constants[43]*states[13]*states[0]-constants[44]*states[16]
    rates[0] = -(algebraic[0]+algebraic[9]+algebraic[10]+algebraic[17]+algebraic[21]+algebraic[23])
    rates[13] = ((algebraic[11]+algebraic[12])-algebraic[13])-algebraic[23]
    algebraic[24] = constants[45]*states[12]*states[4]-constants[46]*states[16]
    rates[4] = -(algebraic[4]+algebraic[8]+algebraic[11]+algebraic[18]+algebraic[20]+algebraic[24])
    rates[12] = ((algebraic[10]+algebraic[15])-algebraic[16])-algebraic[24]
    algebraic[25] = constants[47]*states[16]-constants[48]*states[14]*states[8]
    rates[8] = algebraic[6]+algebraic[13]+algebraic[16]+algebraic[25]
    rates[14] = ((algebraic[17]+algebraic[18])-algebraic[19])+algebraic[25]
    rates[16] = (algebraic[22]+algebraic[23]+algebraic[24])-algebraic[25]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = constants[5]*states[1]*states[0]-constants[6]*states[2]
    algebraic[4] = constants[9]*states[1]*states[4]-constants[10]*states[9]
    algebraic[3] = constants[7]*states[1]*states[3]-constants[8]*states[5]
    algebraic[6] = constants[12]*states[6]-constants[13]*states[1]*states[8]
    algebraic[9] = constants[18]*states[5]*states[0]-constants[19]*states[11]
    algebraic[8] = constants[16]*states[5]*states[4]-constants[17]*states[10]
    algebraic[5] = constants[1]*states[5]-constants[11]*states[6]*states[7]
    algebraic[10] = constants[20]*states[6]*states[0]-constants[21]*states[12]
    algebraic[11] = constants[22]*states[6]*states[4]-constants[23]*states[13]
    algebraic[17] = constants[32]*states[9]*states[0]-constants[33]*states[14]
    algebraic[7] = constants[14]*states[9]*states[3]-constants[15]*states[10]
    algebraic[13] = constants[25]*states[13]-constants[26]*states[9]*states[8]
    algebraic[18] = constants[34]*states[2]*states[4]-constants[35]*states[14]
    algebraic[14] = constants[27]*states[2]*states[3]-constants[28]*states[11]
    algebraic[16] = constants[30]*states[12]-constants[31]*states[2]*states[8]
    algebraic[19] = constants[36]*states[14]*states[3]-constants[37]*states[15]
    algebraic[20] = constants[38]*states[11]*states[4]-constants[39]*states[15]
    algebraic[15] = constants[2]*states[11]-constants[29]*states[12]*states[7]
    algebraic[21] = constants[40]*states[10]*states[0]-constants[41]*states[15]
    algebraic[12] = constants[3]*states[10]-constants[24]*states[13]*states[7]
    algebraic[22] = constants[4]*states[15]-constants[42]*states[16]*states[7]
    algebraic[23] = constants[43]*states[13]*states[0]-constants[44]*states[16]
    algebraic[24] = constants[45]*states[12]*states[4]-constants[46]*states[16]
    algebraic[25] = constants[47]*states[16]-constants[48]*states[14]*states[8]
    algebraic[1] = (states[5]+states[10]+states[15]+states[11])/constants[0]
    algebraic[2] = (constants[4]*states[15]+constants[2]*states[11]+constants[3]*states[10]+constants[1]*states[5])/constants[0]
    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)