# Size of variable arrays:
sizeAlgebraic = 13
sizeStates = 6
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 (second)"
    legend_states[0] = "D in component equations (dimensionless)"
    legend_states[1] = "A_1 in component equations (dimensionless)"
    legend_states[2] = "A_2 in component equations (dimensionless)"
    legend_algebraic[0] = "R_off in component equations (dimensionless)"
    legend_constants[0] = "x_0 in component equations (dimensionless)"
    legend_states[3] = "x_1 in component equations (dimensionless)"
    legend_states[4] = "x_2 in component equations (dimensionless)"
    legend_algebraic[7] = "g in component equations (per_second)"
    legend_algebraic[11] = "f in component equations (per_second)"
    legend_algebraic[8] = "h in component equations (per_second)"
    legend_algebraic[3] = "lambda_A1 in component equations (dimensionless)"
    legend_algebraic[5] = "lambda_A2 in component equations (dimensionless)"
    legend_algebraic[4] = "F_t in component equations (dimensionless)"
    legend_algebraic[1] = "E_1 in component equations (dimensionless)"
    legend_algebraic[2] = "E_2 in component equations (dimensionless)"
    legend_algebraic[12] = "dSL_dt in component equations (per_second)"
    legend_states[5] = "SL in component equations (dimensionless)"
    legend_constants[1] = "k_on in component equations (per_second)"
    legend_constants[2] = "k_off in component equations (per_second)"
    legend_constants[3] = "f_r in component equations (per_second)"
    legend_algebraic[9] = "f_prime in component equations (per_second)"
    legend_constants[4] = "f_prime_0 in component equations (per_second)"
    legend_constants[5] = "h_0 in component equations (per_second)"
    legend_algebraic[10] = "h_prime in component equations (per_second)"
    legend_constants[6] = "h_prime_0 in component equations (per_second)"
    legend_constants[7] = "g_0 in component equations (per_second)"
    legend_constants[8] = "nu in component equations (dimensionless)"
    legend_algebraic[6] = "sigma in component equations (dimensionless)"
    legend_constants[9] = "sigma_minus in component equations (dimensionless)"
    legend_constants[10] = "sigma_plus in component equations (dimensionless)"
    legend_constants[11] = "R_T in component equations (dimensionless)"
    legend_constants[12] = "e_cb in component equations (dimensionless)"
    legend_rates[0] = "d/dt D in component equations (dimensionless)"
    legend_rates[1] = "d/dt A_1 in component equations (dimensionless)"
    legend_rates[2] = "d/dt A_2 in component equations (dimensionless)"
    legend_rates[4] = "d/dt x_2 in component equations (dimensionless)"
    legend_rates[3] = "d/dt x_1 in component equations (dimensionless)"
    legend_rates[5] = "d/dt SL in component equations (dimensionless)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 0.005
    states[1] = 0.005
    states[2] = 0.005
    constants[0] = 1e-16
    states[3] = 1e-16
    states[4] = 1e-16
    states[5] = 2
    constants[1] = 120
    constants[2] = 50
    constants[3] = 50
    constants[4] = 400
    constants[5] = 8
    constants[6] = 6
    constants[7] = 4
    constants[8] = 3
    constants[9] = 1
    constants[10] = 8
    constants[11] = 1
    constants[12] = 1.5
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[6] = custom_piecewise([greater(states[4] , constants[0]), constants[10] , less(states[4] , constants[0]), constants[9] , True, 0.00000])
    algebraic[7] = constants[7]*exp(algebraic[6]*(power(states[4]-constants[0], 2.00000)))
    algebraic[8] = constants[5]*exp(algebraic[6]*(power(states[3], 2.00000)))
    algebraic[10] = constants[6]*exp(algebraic[6]*(power(states[4], 2.00000)-power(states[3], 2.00000)))
    rates[2] = algebraic[8]*states[1]-(algebraic[10]+algebraic[7])*states[2]
    algebraic[0] = ((constants[11]-states[0])-states[1])-states[2]
    algebraic[3] = states[1]/constants[11]
    algebraic[5] = states[2]/constants[11]
    algebraic[11] = constants[3]*(power(1.00000+algebraic[3]*(exp((states[3]/constants[0])*(constants[8]-1.00000))-1.00000)+algebraic[5]*(exp((states[4]/constants[0])*(constants[8]-1.00000))-1.00000), 2.00000))
    algebraic[9] = constants[4]*exp(algebraic[6]*(power(states[3], 2.00000)))
    rates[0] = (constants[1]*algebraic[0]+algebraic[9]*states[1]+algebraic[7]*states[2])-(constants[2]+algebraic[11])*states[0]
    rates[1] = (algebraic[11]*states[0]+algebraic[10]*states[2])-(algebraic[9]+algebraic[8])*states[1]
    algebraic[12] = custom_piecewise([greater(voi , 0.00100000) & less(voi , 0.00200000), 21.2000 , True, 0.00000])
    rates[4] = custom_piecewise([equal(states[2] , 0.00000), algebraic[12] , True, ((-algebraic[8]*states[1])/states[2])*(states[4]-constants[0])+algebraic[12]])
    rates[3] = custom_piecewise([equal(states[1] , 0.00000), algebraic[12] , True, -((algebraic[11]*states[0])/states[1]+(algebraic[10]*states[2])/states[1])*states[3]+algebraic[12]])
    rates[5] = algebraic[12]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[6] = custom_piecewise([greater(states[4] , constants[0]), constants[10] , less(states[4] , constants[0]), constants[9] , True, 0.00000])
    algebraic[7] = constants[7]*exp(algebraic[6]*(power(states[4]-constants[0], 2.00000)))
    algebraic[8] = constants[5]*exp(algebraic[6]*(power(states[3], 2.00000)))
    algebraic[10] = constants[6]*exp(algebraic[6]*(power(states[4], 2.00000)-power(states[3], 2.00000)))
    algebraic[0] = ((constants[11]-states[0])-states[1])-states[2]
    algebraic[3] = states[1]/constants[11]
    algebraic[5] = states[2]/constants[11]
    algebraic[11] = constants[3]*(power(1.00000+algebraic[3]*(exp((states[3]/constants[0])*(constants[8]-1.00000))-1.00000)+algebraic[5]*(exp((states[4]/constants[0])*(constants[8]-1.00000))-1.00000), 2.00000))
    algebraic[9] = constants[4]*exp(algebraic[6]*(power(states[3], 2.00000)))
    algebraic[12] = custom_piecewise([greater(voi , 0.00100000) & less(voi , 0.00200000), 21.2000 , True, 0.00000])
    algebraic[1] = constants[12]*states[1]
    algebraic[2] = constants[12]*states[2]
    algebraic[4] = algebraic[1]*states[3]+algebraic[2]*states[4]
    return algebraic

def custom_piecewise(cases):
    """Compute result of a piecewise function"""
    return select(cases[0::2],cases[1::2])

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)