# Size of variable arrays:
sizeAlgebraic = 0
sizeStates = 9
sizeConstants = 40
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] = "pRB in component pRB (CONC)"
    legend_constants[0] = "k1 in component model_parameters (dimensionless)"
    legend_states[1] = "E2F1 in component E2F1 (CONC)"
    legend_constants[1] = "km1 in component model_parameters (dimensionless)"
    legend_constants[2] = "j11 in component model_parameters (dimensionless)"
    legend_constants[3] = "j61 in component model_parameters (dimensionless)"
    legend_constants[4] = "k16 in component model_parameters (dimensionless)"
    legend_states[2] = "CycDa in component CycDa (CONC)"
    legend_constants[5] = "k61 in component model_parameters (dimensionless)"
    legend_states[3] = "pRBp in component pRBp (CONC)"
    legend_constants[6] = "phi_pRB in component model_parameters (dimensionless)"
    legend_constants[7] = "kp in component model_parameters (dimensionless)"
    legend_constants[8] = "k2 in component model_parameters (dimensionless)"
    legend_constants[9] = "a in component model_parameters (dimensionless)"
    legend_constants[10] = "km2 in component model_parameters (dimensionless)"
    legend_constants[11] = "j12 in component model_parameters (dimensionless)"
    legend_constants[12] = "j62 in component model_parameters (dimensionless)"
    legend_constants[13] = "phi_E2F1 in component model_parameters (dimensionless)"
    legend_constants[14] = "k34 in component model_parameters (dimensionless)"
    legend_states[4] = "CycDi in component CycDi (CONC)"
    legend_constants[15] = "km4 in component model_parameters (dimensionless)"
    legend_constants[16] = "k43 in component model_parameters (dimensionless)"
    legend_constants[17] = "phi_CycDa in component model_parameters (dimensionless)"
    legend_constants[18] = "k3 in component model_parameters (dimensionless)"
    legend_states[5] = "AP1 in component AP1 (CONC)"
    legend_constants[19] = "k23 in component model_parameters (dimensionless)"
    legend_constants[20] = "j13 in component model_parameters (dimensionless)"
    legend_constants[21] = "j63 in component model_parameters (dimensionless)"
    legend_constants[22] = "phi_CycDi in component model_parameters (dimensionless)"
    legend_constants[23] = "Fm in component model_parameters (dimensionless)"
    legend_constants[24] = "k25 in component model_parameters (dimensionless)"
    legend_constants[25] = "j15 in component model_parameters (dimensionless)"
    legend_constants[26] = "j65 in component model_parameters (dimensionless)"
    legend_constants[27] = "phi_AP1 in component model_parameters (dimensionless)"
    legend_constants[28] = "k67 in component model_parameters (dimensionless)"
    legend_states[6] = "CycEa in component CycEa (CONC)"
    legend_constants[29] = "k76 in component model_parameters (dimensionless)"
    legend_states[7] = "pRBpp in component pRBpp (CONC)"
    legend_constants[30] = "phi_pRBp in component model_parameters (dimensionless)"
    legend_constants[31] = "phi_pRBpp in component model_parameters (dimensionless)"
    legend_states[8] = "CycEi in component CycEi (CONC)"
    legend_constants[32] = "k28 in component model_parameters (dimensionless)"
    legend_constants[33] = "j18 in component model_parameters (dimensionless)"
    legend_constants[34] = "j68 in component model_parameters (dimensionless)"
    legend_constants[35] = "k98 in component model_parameters (dimensionless)"
    legend_constants[36] = "k89 in component model_parameters (dimensionless)"
    legend_constants[37] = "km9 in component model_parameters (dimensionless)"
    legend_constants[38] = "phi_CycEi in component model_parameters (dimensionless)"
    legend_constants[39] = "phi_CycEa in component model_parameters (dimensionless)"
    legend_rates[0] = "d/dt pRB in component pRB (CONC)"
    legend_rates[1] = "d/dt E2F1 in component E2F1 (CONC)"
    legend_rates[2] = "d/dt CycDa in component CycDa (CONC)"
    legend_rates[4] = "d/dt CycDi in component CycDi (CONC)"
    legend_rates[5] = "d/dt AP1 in component AP1 (CONC)"
    legend_rates[3] = "d/dt pRBp in component pRBp (CONC)"
    legend_rates[7] = "d/dt pRBpp in component pRBpp (CONC)"
    legend_rates[8] = "d/dt CycEi in component CycEi (CONC)"
    legend_rates[6] = "d/dt CycEa in component CycEa (CONC)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 0
    constants[0] = 1
    states[1] = 0
    constants[1] = 0.5
    constants[2] = 0.5
    constants[3] = 5
    constants[4] = 0.4
    states[2] = 0
    constants[5] = 0.3
    states[3] = 0
    constants[6] = 0.005
    constants[7] = 0.05
    constants[8] = 1.6
    constants[9] = 0.04
    constants[10] = 4
    constants[11] = 5
    constants[12] = 8
    constants[13] = 0.1
    constants[14] = 0.04
    states[4] = 0
    constants[15] = 0.3
    constants[16] = 0.01
    constants[17] = 0.03
    constants[18] = 0.05
    states[5] = 0
    constants[19] = 0.3
    constants[20] = 0.002
    constants[21] = 2
    constants[22] = 0.023
    constants[23] = 0
    constants[24] = 0.9
    constants[25] = 0.001
    constants[26] = 6
    constants[27] = 0.01
    constants[28] = 0.7
    states[6] = 0
    constants[29] = 0.1
    states[7] = 0
    constants[30] = 0.06
    constants[31] = 0.04
    states[8] = 0
    constants[32] = 0.06
    constants[33] = 0.6
    constants[34] = 7
    constants[35] = 0.01
    constants[36] = 0.07
    constants[37] = 0.005
    constants[38] = 0.06
    constants[39] = 0.05
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[0] = ((constants[0]*(states[1]/(constants[1]+states[1]))*(constants[2]/(constants[2]*states[0]))*(constants[3]/(constants[3]*states[3]))-constants[4]*states[0]*states[2])+constants[5]*states[3])-constants[6]*states[0]
    rates[1] = (constants[7]+constants[8]*((power(constants[9], 2.00000)+power(states[1], 2.00000))/(power(constants[10], 2.00000)+power(states[1], 2.00000)))*(constants[11]/(constants[11]+states[3]))*(constants[12]/(constants[12]+states[3])))-constants[13]*states[1]
    rates[2] = ((constants[14]*states[4]*states[2])/(constants[15]+states[2])-constants[14]*states[2])-constants[17]*states[2]
    rates[4] = ((constants[18]*states[5]+constants[19]*states[1]*(constants[20]/(constants[20]+states[0]))*(constants[21]/(constants[21]+states[3]))+constants[16]*states[2])-constants[14]*states[4]*(states[2]/(constants[15]+states[2])))-constants[22]*states[4]
    rates[5] = (constants[23]+constants[24]*states[1]*(constants[25]/(constants[25]+states[0]))*(constants[26]/(constants[26]+states[3])))-constants[27]*states[5]
    rates[3] = (((constants[4]*states[0]*states[2]-constants[5]*states[3])-constants[28]*states[3]*states[6])+constants[29]*states[7])-constants[30]*states[3]
    rates[7] = (constants[28]*states[3]*states[6]-constants[29]*states[7])-constants[31]*states[7]
    rates[8] = ((constants[32]*states[1]*(constants[33]/(constants[33]+states[0]))*(constants[34]/(constants[34]+states[3]))+constants[35]*states[6])-constants[36]*states[8]*(states[6]/(constants[37]+states[6])))-constants[38]*states[8]
    rates[6] = (constants[36]*states[8]*(states[6]/(constants[37]+states[6]))-constants[35]*states[6])-constants[39]*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)