# Size of variable arrays:
sizeAlgebraic = 0
sizeStates = 8
sizeConstants = 12
from math import *
from numpy import *

def createLegends():
    legend_states = [""] * sizeStates
    legend_rates = [""] * sizeStates
    legend_algebraic = [""] * sizeAlgebraic
    legend_voi = ""
    legend_constants = [""] * sizeConstants
    legend_voi = "t in component environment (s)"
    legend_constants[0] = "km2 in component PIPtoDAG (um)"
    legend_constants[1] = "km6 in component PIPtoDAG (um)"
    legend_constants[2] = "Vmax2 in component PIPtoDAG (per_s)"
    legend_constants[3] = "Vmax6 in component PIPtoDAG (per_s)"
    legend_states[0] = "PIP2 in component PIPtoDAG (um)"
    legend_states[1] = "DAG in component PIPtoDAG (um)"
    legend_states[2] = "IP3 in component PIPtoDAG (um)"
    legend_states[3] = "CaPLCg in component PLC (um)"
    legend_states[4] = "CaPLCg_star in component PLC (um)"
    legend_constants[4] = "kf1 in component PLC (per_um_s)"
    legend_constants[5] = "kb1 in component PLC (per_s)"
    legend_constants[6] = "kf3 in component PLC (per_s)"
    legend_constants[7] = "kf5 in component PLC (per_um_s)"
    legend_constants[8] = "kb5 in component PLC (per_s)"
    legend_constants[9] = "km4 in component PLC (um)"
    legend_constants[10] = "Vmax4 in component PLC (per_s)"
    legend_states[5] = "PLCg in component PLC (um)"
    legend_states[6] = "PLCg_star in component PLC (um)"
    legend_constants[11] = "EGF_EGFR in component UndefinedVariables (um)"
    legend_states[7] = "Ca in component PLC (um)"
    legend_rates[0] = "d/dt PIP2 in component PIPtoDAG (um)"
    legend_rates[1] = "d/dt DAG in component PIPtoDAG (um)"
    legend_rates[2] = "d/dt IP3 in component PIPtoDAG (um)"
    legend_rates[5] = "d/dt PLCg in component PLC (um)"
    legend_rates[3] = "d/dt CaPLCg in component PLC (um)"
    legend_rates[4] = "d/dt CaPLCg_star in component PLC (um)"
    legend_rates[6] = "d/dt PLCg_star in component PLC (um)"
    legend_rates[7] = "d/dt Ca in component PLC (um)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 97
    constants[1] = 19.79166667
    constants[2] = 14
    constants[3] = 57
    states[0] = 10
    states[1] = 0
    states[2] = 0
    states[3] = 0
    states[4] = 0
    constants[4] = 0.0003
    constants[5] = 10
    constants[6] = 0.05
    constants[7] = 0.00002
    constants[8] = 10
    constants[9] = 0.33333333333
    constants[10] = 0.2
    states[5] = 0.82
    states[6] = 0
    constants[11] = 0.1
    states[7] = 0.1
    return (states, constants)

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