# Size of variable arrays:
sizeAlgebraic = 3
sizeStates = 10
sizeConstants = 2
from math import *
from numpy import *

def createLegends():
    legend_states = [""] * sizeStates
    legend_rates = [""] * sizeStates
    legend_algebraic = [""] * sizeAlgebraic
    legend_voi = ""
    legend_constants = [""] * sizeConstants
    legend_constants[0] = "p in component jung_10_lesions (per_sec)"
    legend_constants[1] = "c in component jung_10_lesions (per_sec)"
    legend_states[0] = "P0 in component jung_10_lesions (conc)"
    legend_states[1] = "P1 in component jung_10_lesions (conc)"
    legend_states[2] = "P2 in component jung_10_lesions (conc)"
    legend_states[3] = "P3 in component jung_10_lesions (conc)"
    legend_states[4] = "P4 in component jung_10_lesions (conc)"
    legend_states[5] = "P5 in component jung_10_lesions (conc)"
    legend_states[6] = "P6 in component jung_10_lesions (conc)"
    legend_states[7] = "P7 in component jung_10_lesions (conc)"
    legend_states[8] = "P8 in component jung_10_lesions (conc)"
    legend_states[9] = "P9 in component jung_10_lesions (conc)"
    legend_voi = "time in component jung_10_lesions (second)"
    legend_algebraic[0] = "A in component jung_10_lesions (conc)"
    legend_algebraic[1] = "D in component jung_10_lesions (conc)"
    legend_algebraic[2] = "S in component jung_10_lesions (conc)"
    legend_rates[0] = "d/dt P0 in component jung_10_lesions (conc)"
    legend_rates[1] = "d/dt P1 in component jung_10_lesions (conc)"
    legend_rates[2] = "d/dt P2 in component jung_10_lesions (conc)"
    legend_rates[3] = "d/dt P3 in component jung_10_lesions (conc)"
    legend_rates[4] = "d/dt P4 in component jung_10_lesions (conc)"
    legend_rates[5] = "d/dt P5 in component jung_10_lesions (conc)"
    legend_rates[6] = "d/dt P6 in component jung_10_lesions (conc)"
    legend_rates[7] = "d/dt P7 in component jung_10_lesions (conc)"
    legend_rates[8] = "d/dt P8 in component jung_10_lesions (conc)"
    legend_rates[9] = "d/dt P9 in component jung_10_lesions (conc)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 1
    constants[1] = 1
    states[0] = 1
    states[1] = 0
    states[2] = 0
    states[3] = 0
    states[4] = 0
    states[5] = 0
    states[6] = 0
    states[7] = 0
    states[8] = 0
    states[9] = 0
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[0] = -constants[0]*states[0]
    rates[1] = (constants[0]*states[0]-constants[0]*states[1])-constants[1]*states[1]
    rates[2] = (constants[0]*states[1]-constants[0]*states[2])-2.00000*constants[1]*states[2]
    rates[3] = (constants[0]*states[2]-constants[0]*states[3])-3.00000*constants[1]*states[3]
    rates[4] = (constants[0]*states[3]-constants[0]*states[4])-4.00000*constants[1]*states[4]
    rates[5] = (constants[0]*states[4]-constants[0]*states[5])-5.00000*constants[1]*states[5]
    rates[6] = (constants[0]*states[5]-constants[0]*states[6])-6.00000*constants[1]*states[6]
    rates[7] = (constants[0]*states[6]-constants[0]*states[7])-7.00000*constants[1]*states[7]
    rates[8] = (constants[0]*states[7]-constants[0]*states[8])-8.00000*constants[1]*states[8]
    rates[9] = (constants[0]*states[8]-constants[0]*states[9])-9.00000*constants[1]*states[9]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = states[0]+states[1]+states[2]+states[3]+states[4]+states[5]+states[6]+states[7]+states[8]+states[9]
    algebraic[1] = 1.00000-(states[0]+states[1]+states[2]+states[3]+states[4]+states[5]+states[6]+states[7]+states[8]+states[9])
    algebraic[2] = 1.00000*exp((constants[0]/constants[1])*((1.00000-constants[1]*voi)-exp(-(constants[1]*voi))))
    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)