# Size of variable arrays:
sizeAlgebraic = 2
sizeStates = 3
sizeConstants = 13
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] = "C in component C (micromolar)"
    legend_constants[0] = "v_i in component C (micromolar_per_minute)"
    legend_constants[1] = "v_d in component C (micromolar_per_minute)"
    legend_states[1] = "X in component X (micromolar)"
    legend_constants[2] = "K_d in component C (micromolar)"
    legend_constants[3] = "k_d in component C (per_minute)"
    legend_states[2] = "M in component M (micromolar)"
    legend_algebraic[0] = "V_1 in component V_1 (micromolar_per_minute)"
    legend_constants[4] = "K_1 in component M (per_minute)"
    legend_constants[5] = "V_2 in component M (per_minute)"
    legend_constants[6] = "K_2 in component M (per_minute)"
    legend_algebraic[1] = "V_3 in component V_3 (micromolar_per_minute)"
    legend_constants[7] = "K_3 in component X (per_minute)"
    legend_constants[8] = "V_4 in component X (per_minute)"
    legend_constants[9] = "K_4 in component X (per_minute)"
    legend_constants[10] = "K_c in component V_1 (micromolar)"
    legend_constants[11] = "V_M1 in component V_1 (per_minute)"
    legend_constants[12] = "V_M3 in component V_3 (per_minute)"
    legend_rates[0] = "d/dt C in component C (micromolar)"
    legend_rates[2] = "d/dt M in component M (micromolar)"
    legend_rates[1] = "d/dt X in component X (micromolar)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 0.1
    constants[0] = 0.05
    constants[1] = 0.25
    states[1] = 0.1
    constants[2] = 0.02
    constants[3] = 0.01
    states[2] = 0.1
    constants[4] = 0.01
    constants[5] = 1.5
    constants[6] = 0.01
    constants[7] = 0.01
    constants[8] = 0.5
    constants[9] = 0.01
    constants[10] = 0.5
    constants[11] = 3
    constants[12] = 1
    return (states, constants)

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

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = (states[0]/(constants[10]+states[0]))*constants[11]
    algebraic[1] = states[2]*constants[12]
    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)