# Size of variable arrays:
sizeAlgebraic = 0
sizeStates = 7
sizeConstants = 11
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 (hour)"
    legend_states[0] = "T in component T (cell_ml)"
    legend_constants[0] = "k1 in component model_parameters (cell_per_ml_molecule2_hour)"
    legend_states[1] = "Lm in component Lm (molecule_cell)"
    legend_states[2] = "RT in component RT (molecule_cell)"
    legend_states[3] = "m in component m (cell_ml)"
    legend_states[4] = "LT in component LT (molecule_cell)"
    legend_constants[1] = "k2 in component model_parameters (molecule_ml2_per_cell3_hour)"
    legend_constants[2] = "k3 in component model_parameters (per_hour)"
    legend_constants[3] = "k4 in component model_parameters (per_hour)"
    legend_constants[4] = "k5 in component model_parameters (ml2_per_cell_molecule_hour)"
    legend_states[5] = "Rm in component Rm (molecule_cell)"
    legend_constants[5] = "k6 in component model_parameters (molecule_per_cell_hour)"
    legend_constants[6] = "k7 in component model_parameters (per_hour)"
    legend_constants[7] = "k8 in component model_parameters (per_molar_per_minute)"
    legend_states[6] = "SL in component SL (molecule_ml)"
    legend_constants[8] = "k10 in component model_parameters (molecule_per_cell_hour)"
    legend_constants[9] = "k11 in component model_parameters (per_hour)"
    legend_constants[10] = "k9 in component model_parameters (per_molar_per_minute)"
    legend_rates[0] = "d/dt T in component T (cell_ml)"
    legend_rates[4] = "d/dt LT in component LT (molecule_cell)"
    legend_rates[2] = "d/dt RT in component RT (molecule_cell)"
    legend_rates[3] = "d/dt m in component m (cell_ml)"
    legend_rates[1] = "d/dt Lm in component Lm (molecule_cell)"
    legend_rates[5] = "d/dt Rm in component Rm (molecule_cell)"
    legend_rates[6] = "d/dt SL in component SL (molecule_ml)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 500.0
    constants[0] = 8.38E-10
    states[1] = 1E3
    states[2] = 1E4
    states[3] = 500.0
    states[4] = 0.0
    constants[1] = 6E-3
    constants[2] = 5.9413
    constants[3] = 0.35
    constants[4] = 2.52E-9
    states[5] = 1E3
    constants[5] = 2.244E3
    constants[6] = 0.35
    constants[7] = 1.92E10
    states[6] = 0.0
    constants[8] = 3.11E3
    constants[9] = 13.9
    constants[10] = 87.3E8
    return (states, constants)

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

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(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)