# Size of variable arrays:
sizeAlgebraic = 3
sizeStates = 4
sizeConstants = 23
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 (minute)"
    legend_states[0] = "RA in component RA (nanomolar)"
    legend_constants[21] = "v_s1 in component v_s1 (flux)"
    legend_constants[0] = "k_d1 in component model_parameters (second_order_rate_constant)"
    legend_constants[1] = "C in component RA (nanomolar)"
    legend_constants[2] = "k_d5 in component RA (first_order_rate_constant)"
    legend_states[1] = "M_C in component M_C (nanomolar)"
    legend_constants[3] = "V_0 in component M_C (flux)"
    legend_constants[4] = "V_sC in component M_C (flux)"
    legend_states[2] = "F in component F (nanomolar)"
    legend_constants[5] = "n in component M_C (dimensionless)"
    legend_constants[6] = "K_A in component M_C (nanomolar)"
    legend_constants[7] = "k_d3 in component model_parameters (first_order_rate_constant)"
    legend_states[3] = "C in component C (nanomolar)"
    legend_constants[8] = "k_s2 in component model_parameters (first_order_rate_constant)"
    legend_constants[9] = "k_d2 in component model_parameters (first_order_rate_constant)"
    legend_constants[10] = "k_s3 in component model_parameters (first_order_rate_constant)"
    legend_constants[22] = "M_F in component M_F (nanomolar)"
    legend_constants[11] = "m in component F (dimensionless)"
    legend_constants[12] = "K_I in component F (nanomolar)"
    legend_constants[13] = "k_d4 in component model_parameters (first_order_rate_constant)"
    legend_constants[14] = "k_s1 in component model_parameters (first_order_rate_constant)"
    legend_constants[15] = "RALDH2_0 in component model_parameters (nanomolar)"
    legend_constants[16] = "x in component model_parameters (dimensionless)"
    legend_constants[17] = "L in component model_parameters (dimensionless)"
    legend_constants[18] = "M_0 in component model_parameters (nanomolar)"
    legend_algebraic[0] = "alpha_1 in component alpha_1 (dimensionless)"
    legend_constants[19] = "K_r1 in component model_parameters (nanomolar)"
    legend_algebraic[1] = "alpha_2 in component alpha_2 (dimensionless)"
    legend_constants[20] = "K_r2 in component model_parameters (nanomolar)"
    legend_algebraic[2] = "rho in component rho (dimensionless)"
    legend_rates[0] = "d/dt RA in component RA (nanomolar)"
    legend_rates[1] = "d/dt M_C in component M_C (nanomolar)"
    legend_rates[3] = "d/dt C in component C (nanomolar)"
    legend_rates[2] = "d/dt F in component F (nanomolar)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 0.1
    constants[0] = 1
    constants[1] = 0.1
    constants[2] = 0
    states[1] = 0.1
    constants[3] = 0.365
    constants[4] = 7.1
    states[2] = 0.0001
    constants[5] = 2
    constants[6] = 0.2
    constants[7] = 1
    states[3] = 0.1
    constants[8] = 1
    constants[9] = 0.28
    constants[10] = 1
    constants[11] = 2
    constants[12] = 0.2
    constants[13] = 1
    constants[14] = 1
    constants[15] = 7.1
    constants[16] = 15
    constants[17] = 50
    constants[18] = 5
    constants[19] = 1
    constants[20] = 1
    constants[21] = constants[14]*constants[15]*(1.00000-constants[16]/constants[17])
    constants[22] = (constants[18]*constants[16])/constants[17]
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[0] = (constants[21]-constants[0]*constants[1]*states[0])-constants[2]*states[0]
    rates[1] = (constants[3]+(constants[4]*(power(states[2], constants[5])))/(power(constants[6], constants[5])+power(states[2], constants[5])))-constants[7]*states[1]
    rates[3] = constants[8]*states[1]-constants[9]*states[3]
    rates[2] = (constants[10]*constants[22]*(power(constants[12], constants[11])))/(power(constants[12], constants[11])+power(states[0], constants[11]))-constants[13]*states[2]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = states[0]/(states[0]+constants[19])
    algebraic[1] = states[2]/(states[2]+constants[20])
    algebraic[2] = algebraic[1]/algebraic[0]
    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)