# Size of variable arrays:
sizeAlgebraic = 17
sizeStates = 11
sizeConstants = 20
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_L in component environment (fmol)"
    legend_states[1] = "q_K1 in component environment (fmol)"
    legend_states[2] = "q_K2 in component environment (fmol)"
    legend_states[3] = "q_LK1 in component environment (fmol)"
    legend_states[4] = "q_P in component environment (fmol)"
    legend_states[5] = "q_LK1K2 in component environment (fmol)"
    legend_states[6] = "q_LK1K2P in component environment (fmol)"
    legend_states[7] = "q_Ubiq in component environment (fmol)"
    legend_states[8] = "q_LKKPU in component environment (fmol)"
    legend_states[9] = "q_LKKPUtag in component environment (fmol)"
    legend_states[10] = "q_LPUtag in component environment (fmol)"
    legend_algebraic[11] = "v_Re1 in component RTK (fmol_per_sec)"
    legend_algebraic[12] = "v_Re2 in component RTK (fmol_per_sec)"
    legend_algebraic[13] = "v_Re3 in component RTK (fmol_per_sec)"
    legend_algebraic[14] = "v_Re4 in component RTK (fmol_per_sec)"
    legend_algebraic[15] = "v_Re5 in component RTK (fmol_per_sec)"
    legend_algebraic[16] = "v_Re6 in component RTK (fmol_per_sec)"
    legend_constants[0] = "kappa_Re1 in component RTK_parameters (fmol_per_sec)"
    legend_constants[1] = "kappa_Re2 in component RTK_parameters (fmol_per_sec)"
    legend_constants[2] = "kappa_Re3 in component RTK_parameters (fmol_per_sec)"
    legend_constants[3] = "kappa_Re4 in component RTK_parameters (fmol_per_sec)"
    legend_constants[4] = "kappa_Re5 in component RTK_parameters (fmol_per_sec)"
    legend_constants[5] = "kappa_Re6 in component RTK_parameters (fmol_per_sec)"
    legend_constants[6] = "K_L in component RTK_parameters (per_fmol)"
    legend_constants[7] = "K_K1 in component RTK_parameters (per_fmol)"
    legend_constants[8] = "K_K2 in component RTK_parameters (per_fmol)"
    legend_constants[9] = "K_LK1 in component RTK_parameters (per_fmol)"
    legend_constants[10] = "K_P in component RTK_parameters (per_fmol)"
    legend_constants[11] = "K_LK1K2 in component RTK_parameters (per_fmol)"
    legend_constants[12] = "K_LK1K2P in component RTK_parameters (per_fmol)"
    legend_constants[13] = "K_Ubiq in component RTK_parameters (per_fmol)"
    legend_constants[14] = "K_LKKPU in component RTK_parameters (per_fmol)"
    legend_constants[15] = "K_LKKPUtag in component RTK_parameters (per_fmol)"
    legend_constants[16] = "K_LPUtag in component RTK_parameters (per_fmol)"
    legend_constants[17] = "R in component constants (J_per_K_per_mol)"
    legend_constants[18] = "T in component constants (kelvin)"
    legend_algebraic[0] = "mu_L in component RTK (J_per_mol)"
    legend_algebraic[1] = "mu_K1 in component RTK (J_per_mol)"
    legend_algebraic[2] = "mu_K2 in component RTK (J_per_mol)"
    legend_algebraic[3] = "mu_LK1 in component RTK (J_per_mol)"
    legend_algebraic[4] = "mu_P in component RTK (J_per_mol)"
    legend_algebraic[5] = "mu_LK1K2 in component RTK (J_per_mol)"
    legend_algebraic[6] = "mu_LK1K2P in component RTK (J_per_mol)"
    legend_algebraic[7] = "mu_Ubiq in component RTK (J_per_mol)"
    legend_algebraic[8] = "mu_LKKPU in component RTK (J_per_mol)"
    legend_algebraic[9] = "mu_LKKPUtag in component RTK (J_per_mol)"
    legend_algebraic[10] = "mu_LPUtag in component RTK (J_per_mol)"
    legend_constants[19] = "F in component constants (C_per_mol)"
    legend_rates[0] = "d/dt q_L in component environment (fmol)"
    legend_rates[1] = "d/dt q_K1 in component environment (fmol)"
    legend_rates[2] = "d/dt q_K2 in component environment (fmol)"
    legend_rates[3] = "d/dt q_LK1 in component environment (fmol)"
    legend_rates[4] = "d/dt q_P in component environment (fmol)"
    legend_rates[5] = "d/dt q_LK1K2 in component environment (fmol)"
    legend_rates[6] = "d/dt q_LK1K2P in component environment (fmol)"
    legend_rates[7] = "d/dt q_Ubiq in component environment (fmol)"
    legend_rates[8] = "d/dt q_LKKPU in component environment (fmol)"
    legend_rates[9] = "d/dt q_LKKPUtag in component environment (fmol)"
    legend_rates[10] = "d/dt q_LPUtag 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] = 1
    states[1] = 1e-3
    states[2] = 1e-3
    states[3] = 1e-6
    states[4] = 1
    states[5] = 1e-9
    states[6] = 1e-9
    states[7] = 1
    states[8] = 1e-88
    states[9] = 1e-88
    states[10] = 1e-88
    constants[0] = 1.31758e-07
    constants[1] = 0.0862846
    constants[2] = 0.00038952
    constants[3] = 2.66799e-09
    constants[4] = 26.6799
    constants[5] = 2667.99
    constants[6] = 8.32274e+08
    constants[7] = 0.000770619
    constants[8] = 44390
    constants[9] = 0.22063
    constants[10] = 6.4394e+12
    constants[11] = 3.36906e-07
    constants[12] = 7.46298e-05
    constants[13] = 4.24411e+13
    constants[14] = 10.8958
    constants[15] = 1.08958e-11
    constants[16] = 2.69163e-14
    constants[17] = 8.31
    constants[18] = 310
    constants[19] = 96485
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = constants[17]*constants[18]*log(constants[6]*states[0])
    algebraic[1] = constants[17]*constants[18]*log(constants[7]*states[1])
    algebraic[3] = constants[17]*constants[18]*log(constants[9]*states[3])
    algebraic[11] = constants[0]*(exp((algebraic[0]+algebraic[1])/(constants[17]*constants[18]))-exp(algebraic[3]/(constants[17]*constants[18])))
    rates[0] = -algebraic[11]
    algebraic[2] = constants[17]*constants[18]*log(constants[8]*states[2])
    algebraic[5] = constants[17]*constants[18]*log(constants[11]*states[5])
    algebraic[12] = constants[1]*(exp((algebraic[3]+algebraic[2])/(constants[17]*constants[18]))-exp(algebraic[5]/(constants[17]*constants[18])))
    rates[3] = algebraic[11]-algebraic[12]
    algebraic[4] = constants[17]*constants[18]*log(constants[10]*states[4])
    algebraic[6] = constants[17]*constants[18]*log(constants[12]*states[6])
    algebraic[13] = constants[2]*(exp((algebraic[4]+algebraic[5])/(constants[17]*constants[18]))-exp(algebraic[6]/(constants[17]*constants[18])))
    rates[4] = -algebraic[13]
    rates[5] = algebraic[12]-algebraic[13]
    algebraic[7] = constants[17]*constants[18]*log(constants[13]*states[7])
    algebraic[8] = constants[17]*constants[18]*log(constants[14]*states[8])
    algebraic[14] = constants[3]*(exp((algebraic[7]+algebraic[6])/(constants[17]*constants[18]))-exp(algebraic[8]/(constants[17]*constants[18])))
    rates[6] = algebraic[13]-algebraic[14]
    rates[7] = -algebraic[14]
    algebraic[10] = constants[17]*constants[18]*log(constants[16]*states[10])
    algebraic[15] = constants[4]*(exp(algebraic[8]/(constants[17]*constants[18]))-exp((algebraic[1]+algebraic[2]+algebraic[10])/(constants[17]*constants[18])))
    rates[1] = -algebraic[11]+algebraic[15]
    rates[2] = -algebraic[12]+algebraic[15]
    rates[10] = algebraic[15]
    algebraic[9] = constants[17]*constants[18]*log(constants[15]*states[9])
    algebraic[16] = constants[5]*(exp(algebraic[8]/(constants[17]*constants[18]))-exp(algebraic[9]/(constants[17]*constants[18])))
    rates[8] = (algebraic[14]-algebraic[15])-algebraic[16]
    rates[9] = algebraic[16]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = constants[17]*constants[18]*log(constants[6]*states[0])
    algebraic[1] = constants[17]*constants[18]*log(constants[7]*states[1])
    algebraic[3] = constants[17]*constants[18]*log(constants[9]*states[3])
    algebraic[11] = constants[0]*(exp((algebraic[0]+algebraic[1])/(constants[17]*constants[18]))-exp(algebraic[3]/(constants[17]*constants[18])))
    algebraic[2] = constants[17]*constants[18]*log(constants[8]*states[2])
    algebraic[5] = constants[17]*constants[18]*log(constants[11]*states[5])
    algebraic[12] = constants[1]*(exp((algebraic[3]+algebraic[2])/(constants[17]*constants[18]))-exp(algebraic[5]/(constants[17]*constants[18])))
    algebraic[4] = constants[17]*constants[18]*log(constants[10]*states[4])
    algebraic[6] = constants[17]*constants[18]*log(constants[12]*states[6])
    algebraic[13] = constants[2]*(exp((algebraic[4]+algebraic[5])/(constants[17]*constants[18]))-exp(algebraic[6]/(constants[17]*constants[18])))
    algebraic[7] = constants[17]*constants[18]*log(constants[13]*states[7])
    algebraic[8] = constants[17]*constants[18]*log(constants[14]*states[8])
    algebraic[14] = constants[3]*(exp((algebraic[7]+algebraic[6])/(constants[17]*constants[18]))-exp(algebraic[8]/(constants[17]*constants[18])))
    algebraic[10] = constants[17]*constants[18]*log(constants[16]*states[10])
    algebraic[15] = constants[4]*(exp(algebraic[8]/(constants[17]*constants[18]))-exp((algebraic[1]+algebraic[2]+algebraic[10])/(constants[17]*constants[18])))
    algebraic[9] = constants[17]*constants[18]*log(constants[15]*states[9])
    algebraic[16] = constants[5]*(exp(algebraic[8]/(constants[17]*constants[18]))-exp(algebraic[9]/(constants[17]*constants[18])))
    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)