# Size of variable arrays:
sizeAlgebraic = 3
sizeStates = 3
sizeConstants = 19
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 (s)"
    legend_states[0] = "Z in component Ca (uM)"
    legend_states[1] = "Y in component Ca (uM)"
    legend_constants[0] = "v_0 in component Ca (uM_per_s)"
    legend_constants[1] = "v_1 in component Ca (uM_per_s)"
    legend_algebraic[0] = "v_2 in component v_2 (uM_per_s)"
    legend_algebraic[2] = "v_3 in component v_3 (uM_per_s)"
    legend_constants[2] = "k in component Ca (per_s)"
    legend_constants[3] = "k_f in component Ca (per_s)"
    legend_constants[4] = "beta in component Ca (dimensionless)"
    legend_constants[5] = "V_M2 in component v_2 (uM_per_s)"
    legend_constants[6] = "K_2 in component v_2 (uM)"
    legend_constants[7] = "n in component v_2 (dimensionless)"
    legend_constants[8] = "V_M3 in component v_3 (uM_per_s)"
    legend_constants[9] = "K_R in component v_3 (uM)"
    legend_constants[10] = "K_A in component v_3 (uM)"
    legend_constants[11] = "m in component v_3 (dimensionless)"
    legend_constants[12] = "p in component v_3 (dimensionless)"
    legend_states[2] = "W_star in component W_star (dimensionless)"
    legend_constants[13] = "W_T in component W_star (uM)"
    legend_constants[14] = "v_P in component W_star (uM_per_s)"
    legend_algebraic[1] = "v_K in component v_K (uM_per_s)"
    legend_constants[15] = "K_1 in component W_star (dimensionless)"
    legend_constants[16] = "K_2 in component W_star (dimensionless)"
    legend_constants[17] = "V_MK in component v_K (uM_per_s)"
    legend_constants[18] = "K_a in component v_K (uM)"
    legend_rates[0] = "d/dt Z in component Ca (uM)"
    legend_rates[1] = "d/dt Y in component Ca (uM)"
    legend_rates[2] = "d/dt W_star in component W_star (dimensionless)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 0.5
    states[1] = 1.75
    constants[0] = 1
    constants[1] = 7.3
    constants[2] = 10
    constants[3] = 1
    constants[4] = 0.301
    constants[5] = 65
    constants[6] = 1
    constants[7] = 2
    constants[8] = 500
    constants[9] = 2
    constants[10] = 0.9
    constants[11] = 2
    constants[12] = 4
    states[2] = 0
    constants[13] = 1
    constants[14] = 5
    constants[15] = 0.1
    constants[16] = 0.1
    constants[17] = 40
    constants[18] = 2.5
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[1] = constants[17]*(states[0]/(constants[18]+states[0]))
    rates[2] = (constants[14]/constants[13])*((algebraic[1]/constants[14])*((1.00000-states[2])/(constants[15]+1.00000+-states[2]))-states[2]/(constants[16]+states[2]))
    algebraic[0] = constants[5]*((power(states[0], constants[7]))/(power(constants[6], constants[7])+power(states[0], constants[7])))
    algebraic[2] = constants[8]*((power(states[1], constants[11]))/(power(constants[9], constants[11])+power(states[1], constants[11])))*((power(states[0], constants[12]))/(power(constants[10], constants[12])+power(states[0], constants[12])))
    rates[0] = constants[0]+constants[1]*constants[4]+-algebraic[0]+algebraic[2]+constants[3]*states[1]+-(constants[2]*states[0])
    rates[1] = algebraic[0]+-algebraic[2]+-(constants[3]*states[1])
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[1] = constants[17]*(states[0]/(constants[18]+states[0]))
    algebraic[0] = constants[5]*((power(states[0], constants[7]))/(power(constants[6], constants[7])+power(states[0], constants[7])))
    algebraic[2] = constants[8]*((power(states[1], constants[11]))/(power(constants[9], constants[11])+power(states[1], constants[11])))*((power(states[0], constants[12]))/(power(constants[10], constants[12])+power(states[0], 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)