# Size of variable arrays:
sizeAlgebraic = 8
sizeStates = 8
sizeConstants = 18
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 (day)"
    legend_constants[0] = "mu_T in component uninfected_CD4 (per_day)"
    legend_constants[1] = "r in component uninfected_CD4 (per_day)"
    legend_constants[2] = "T_max in component uninfected_CD4 (per_micro_L)"
    legend_constants[3] = "s_0 in component uninfected_CD4 (per_micro_L_day)"
    legend_constants[4] = "theta in component uninfected_CD4 (per_micro_L)"
    legend_constants[5] = "k_1 in component HIV1 (micro_L_per_day)"
    legend_constants[6] = "k_1_ in component hybrid_HIV1 (micro_L_per_day)"
    legend_states[0] = "T_1 in component latently_infected_CD4 (per_micro_L)"
    legend_states[1] = "V in component HIV1 (per_micro_L)"
    legend_states[2] = "V_ in component hybrid_HIV1 (per_micro_L)"
    legend_algebraic[0] = "s_V in component uninfected_CD4 (per_micro_L_day)"
    legend_states[3] = "T in component uninfected_CD4 (per_micro_L)"
    legend_constants[7] = "k_2 in component latently_infected_CD4 (per_day)"
    legend_constants[8] = "k_1D in component actively_infected_CD4 (micro_L_per_day)"
    legend_constants[9] = "mu_b in component actively_infected_CD4 (per_day)"
    legend_states[4] = "D in component DIV (per_micro_L)"
    legend_states[5] = "T_2 in component actively_infected_CD4 (per_micro_L)"
    legend_constants[10] = "k_s in component actively_coinfected_CD4 (per_day)"
    legend_constants[11] = "mu_bD in component actively_coinfected_CD4 (per_day)"
    legend_states[6] = "T_D2 in component actively_coinfected_CD4 (per_micro_L)"
    legend_constants[12] = "mu_TD in component stably_coinfected_CD4 (per_day)"
    legend_states[7] = "T_D1 in component stably_coinfected_CD4 (per_micro_L)"
    legend_constants[13] = "mu_D in component DIV (per_day)"
    legend_algebraic[1] = "N_t in component production_function (dimensionless)"
    legend_algebraic[3] = "N_D_t in component DIV (dimensionless)"
    legend_algebraic[6] = "pi_D_t in component DIV (per_day)"
    legend_constants[14] = "mu_V in component HIV1 (per_day)"
    legend_algebraic[4] = "N_2_t in component HIV1 (dimensionless)"
    legend_algebraic[5] = "N_t_ in component hybrid_HIV1 (dimensionless)"
    legend_algebraic[7] = "pi_t_ in component hybrid_HIV1 (per_day)"
    legend_constants[15] = "N_0 in component production_function (dimensionless)"
    legend_constants[16] = "gamma in component production_function (dimensionless)"
    legend_constants[17] = "t_c in component production_function (day)"
    legend_algebraic[2] = "T_tot in component cell_population (per_micro_L)"
    legend_rates[3] = "d/dt T in component uninfected_CD4 (per_micro_L)"
    legend_rates[0] = "d/dt T_1 in component latently_infected_CD4 (per_micro_L)"
    legend_rates[5] = "d/dt T_2 in component actively_infected_CD4 (per_micro_L)"
    legend_rates[6] = "d/dt T_D2 in component actively_coinfected_CD4 (per_micro_L)"
    legend_rates[7] = "d/dt T_D1 in component stably_coinfected_CD4 (per_micro_L)"
    legend_rates[4] = "d/dt D in component DIV (per_micro_L)"
    legend_rates[1] = "d/dt V in component HIV1 (per_micro_L)"
    legend_rates[2] = "d/dt V_ in component hybrid_HIV1 (per_micro_L)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 0.02
    constants[1] = 0.03
    constants[2] = 1500
    constants[3] = 10
    constants[4] = 1
    constants[5] = 2.4E-5
    constants[6] = 2.4E-6
    states[0] = 0
    states[1] = 1E-3
    states[2] = 0
    states[3] = 1000
    constants[7] = 0.017
    constants[8] = 2.4E-6
    constants[9] = 0.24
    states[4] = 0
    states[5] = 0
    constants[10] = 0.24
    constants[11] = 0.17
    states[6] = 0
    constants[12] = 0.02
    states[7] = 0
    constants[13] = 2.4
    constants[14] = 2.4
    constants[15] = 300
    constants[16] = 25
    constants[17] = 7305
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[0] = ((constants[5]*states[1]*states[3]+constants[6]*states[2]*states[3])-constants[0]*states[0])-constants[7]*states[0]
    rates[5] = (constants[7]*states[0]-constants[8]*states[4]*states[5])-constants[9]*states[5]
    rates[6] = (constants[8]*states[4]*states[5]-constants[10]*states[6])-constants[11]*states[6]
    rates[7] = constants[10]*states[6]-constants[12]*states[7]
    algebraic[0] = (constants[3]*constants[4])/(constants[4]+states[1])
    rates[3] = (((algebraic[0]-constants[0]*states[3])+constants[1]*states[3]*(1.00000-(states[3]+states[0])/constants[2]))-constants[5]*states[1]*states[3])-constants[6]*states[2]*states[3]
    algebraic[1] = constants[15]*(1.00000+constants[16]*((power(voi, 2.00000))/(power(voi, 2.00000)+power(constants[17], 2.00000))))
    algebraic[4] = 0.600000*algebraic[1]
    rates[1] = ((algebraic[1]*constants[9]*states[5]+algebraic[4]*constants[11]*states[6])-constants[5]*states[1]*states[3])-constants[14]*states[1]
    algebraic[3] = 0.200000*algebraic[1]
    algebraic[6] = 0.300000*constants[9]*algebraic[1]
    rates[4] = (algebraic[3]*constants[11]*states[6]+algebraic[6]*states[7])-constants[13]*states[4]
    algebraic[5] = 0.200000*algebraic[1]
    algebraic[7] = 0.100000*constants[9]*algebraic[1]
    rates[2] = ((algebraic[5]*constants[11]*states[6]+algebraic[7]*states[7])-constants[14]*states[2])-constants[6]*states[3]*states[2]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = (constants[3]*constants[4])/(constants[4]+states[1])
    algebraic[1] = constants[15]*(1.00000+constants[16]*((power(voi, 2.00000))/(power(voi, 2.00000)+power(constants[17], 2.00000))))
    algebraic[4] = 0.600000*algebraic[1]
    algebraic[3] = 0.200000*algebraic[1]
    algebraic[6] = 0.300000*constants[9]*algebraic[1]
    algebraic[5] = 0.200000*algebraic[1]
    algebraic[7] = 0.100000*constants[9]*algebraic[1]
    algebraic[2] = states[3]+states[0]+states[5]
    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)