# Size of variable arrays:
sizeAlgebraic = 5
sizeStates = 2
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 (minute)"
    legend_states[0] = "G in component G (mg_l)"
    legend_constants[0] = "Vg in component G (litre)"
    legend_constants[1] = "Gin in component G (mg_l_min)"
    legend_algebraic[0] = "f2_G in component G (mg_min)"
    legend_algebraic[2] = "f3_G in component G (per_l)"
    legend_algebraic[3] = "f4_I in component G (mg_min)"
    legend_algebraic[4] = "f5_I in component G (mg_min)"
    legend_constants[2] = "C2 in component G (mg_l)"
    legend_constants[3] = "C3 in component G (mg_l)"
    legend_constants[4] = "C4 in component G (mU_l)"
    legend_constants[5] = "C5 in component G (mU_l)"
    legend_constants[6] = "U0 in component G (mg_min)"
    legend_constants[7] = "Um in component G (mg_min)"
    legend_constants[8] = "Ub in component G (mg_min)"
    legend_constants[9] = "beta in component G (dimensionless)"
    legend_constants[10] = "Rg in component G (mg_min)"
    legend_constants[11] = "alpha in component G (l_mU)"
    legend_constants[12] = "ti in component G (minute)"
    legend_constants[13] = "E in component G (l_min)"
    legend_constants[14] = "Vp in component G (litre)"
    legend_constants[15] = "Vi in component G (litre)"
    legend_states[1] = "I in component I (mU_l)"
    legend_algebraic[1] = "f1_G in component I (mU_min)"
    legend_constants[16] = "Rm in component I (mU_min)"
    legend_constants[17] = "C1 in component I (mg_l)"
    legend_constants[18] = "a1 in component I (mg_l)"
    legend_constants[19] = "di in component I (first_order_rate_constant)"
    legend_rates[0] = "d/dt G in component G (mg_l)"
    legend_rates[1] = "d/dt I in component I (mU_l)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 1000.0
    constants[0] = 10.0
    constants[1] = 0.54
    constants[2] = 144.0
    constants[3] = 1000.0
    constants[4] = 80.0
    constants[5] = 26.0
    constants[6] = 40.0
    constants[7] = 940.0
    constants[8] = 72.0
    constants[9] = 1.77
    constants[10] = 180.0
    constants[11] = 0.29
    constants[12] = 100
    constants[13] = 0.2
    constants[14] = 3.0
    constants[15] = 11.0
    states[1] = 9000.0
    constants[16] = 210.0
    constants[17] = 2000.0
    constants[18] = 300.0
    constants[19] = 0.06
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[1] = constants[16]/(1.00000+exp(((constants[17]-states[0])/(1.00000*constants[0]))/constants[18]))
    rates[1] = 1.00000*algebraic[1]-constants[19]*states[1]
    algebraic[0] = constants[8]*(1.00000-exp(1.00000*(-states[0]/(constants[2]*constants[0]))))
    algebraic[2] = states[0]/(constants[3]*constants[0])
    algebraic[3] = constants[6]+(constants[7]-constants[6])/(1.00000+exp(-constants[9]*log(1.00000*(states[1]/(constants[4]*(1.00000/constants[15]+1.00000/(constants[13]*constants[12])))))))
    algebraic[4] = constants[10]/(1.00000+exp(constants[11]*(states[1]/(1.00000*constants[14]-1.00000*constants[5]))))
    rates[0] = constants[1]+1.00000*algebraic[4]+-(1.00000*algebraic[0]+algebraic[2]*algebraic[3])
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[1] = constants[16]/(1.00000+exp(((constants[17]-states[0])/(1.00000*constants[0]))/constants[18]))
    algebraic[0] = constants[8]*(1.00000-exp(1.00000*(-states[0]/(constants[2]*constants[0]))))
    algebraic[2] = states[0]/(constants[3]*constants[0])
    algebraic[3] = constants[6]+(constants[7]-constants[6])/(1.00000+exp(-constants[9]*log(1.00000*(states[1]/(constants[4]*(1.00000/constants[15]+1.00000/(constants[13]*constants[12])))))))
    algebraic[4] = constants[10]/(1.00000+exp(constants[11]*(states[1]/(1.00000*constants[14]-1.00000*constants[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)