# Size of variable arrays:
sizeAlgebraic = 10
sizeStates = 5
sizeConstants = 21
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] = "Ca_m in component Ca_m (micromolar)"
    legend_algebraic[0] = "J_min in component J_min (micromolar)"
    legend_algebraic[3] = "J_mout in component J_mout (micromolar)"
    legend_constants[0] = "k_min in component J_min (micromolar)"
    legend_states[1] = "Ca_cyt in component Ca_cyt (micromolar)"
    legend_constants[1] = "K_m in component J_min (micromolar)"
    legend_constants[2] = "n in component J_min (micromolar)"
    legend_constants[3] = "k_mout in component J_mout (micromolar)"
    legend_algebraic[6] = "J_ERch in component J_ERch (micromolar)"
    legend_algebraic[7] = "J_ERpump in component J_ERpump (micromolar)"
    legend_algebraic[8] = "J_in in component J_in (micromolar)"
    legend_algebraic[9] = "J_out in component J_out (micromolar)"
    legend_states[2] = "Ca_ER in component Ca_ER (micromolar)"
    legend_states[3] = "PLC in component PLC (micromolar)"
    legend_algebraic[1] = "J_PLCact in component J_PLCact (micromolar)"
    legend_algebraic[4] = "J_PLCinact in component J_PLCinact (micromolar)"
    legend_states[4] = "G_alpha in component G_alpha (micromolar)"
    legend_algebraic[2] = "J_actG_alpha in component J_actG_alpha (micromolar)"
    legend_algebraic[5] = "J_inactG_alpha in component J_inactG_alpha (micromolar)"
    legend_constants[4] = "k_10 in component J_ERch (dimensionless)"
    legend_constants[5] = "K_11 in component J_ERch (dimensionless)"
    legend_constants[6] = "K_17 in component J_ERpump (dimensionless)"
    legend_constants[7] = "k_16 in component J_ERpump (dimensionless)"
    legend_constants[8] = "K_12 in component J_in (dimensionless)"
    legend_constants[9] = "k_13 in component J_in (dimensionless)"
    legend_constants[10] = "k_14 in component J_out (dimensionless)"
    legend_constants[11] = "K_15 in component J_out (dimensionless)"
    legend_constants[12] = "k_7 in component J_PLCact (dimensionless)"
    legend_constants[13] = "k_8 in component J_PLCinact (dimensionless)"
    legend_constants[14] = "K_9 in component J_PLCinact (dimensionless)"
    legend_constants[15] = "k_1 in component J_actG_alpha (dimensionless)"
    legend_constants[16] = "k_2 in component J_actG_alpha (dimensionless)"
    legend_constants[17] = "k_3 in component J_inactG_alpha (dimensionless)"
    legend_constants[18] = "K_4 in component J_inactG_alpha (dimensionless)"
    legend_constants[19] = "k_5 in component J_inactG_alpha (dimensionless)"
    legend_constants[20] = "K_6 in component J_inactG_alpha (dimensionless)"
    legend_rates[0] = "d/dt Ca_m in component Ca_m (micromolar)"
    legend_rates[1] = "d/dt Ca_cyt in component Ca_cyt (micromolar)"
    legend_rates[2] = "d/dt Ca_ER in component Ca_ER (micromolar)"
    legend_rates[3] = "d/dt PLC in component PLC (micromolar)"
    legend_rates[4] = "d/dt G_alpha in component G_alpha (micromolar)"
    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] = 330
    states[1] = 0.01
    constants[1] = 1.6
    constants[2] = 8
    constants[3] = 0.5
    states[2] = 20
    states[3] = 0.01
    states[4] = 0.01
    constants[4] = 5
    constants[5] = 3
    constants[6] = 0.05
    constants[7] = 5.37
    constants[8] = 2.8
    constants[9] = 13.4
    constants[10] = 153
    constants[11] = 0.16
    constants[12] = 2.08
    constants[13] = 32.24
    constants[14] = 29.09
    constants[15] = 0.01
    constants[16] = 0.1
    constants[17] = 0.64
    constants[18] = 0.09
    constants[19] = 4.88
    constants[20] = 1.18
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = (constants[0]*(power(states[1], constants[2])))/(power(constants[1], constants[2])+power(states[1], constants[2]))
    algebraic[3] = (constants[3]*states[0])/1.00000
    rates[0] = algebraic[0]-algebraic[3]
    algebraic[1] = constants[12]*states[4]
    algebraic[4] = constants[13]*(states[3]/(constants[14]+states[3]))
    rates[3] = (algebraic[1]-algebraic[4])*1.00000
    algebraic[2] = constants[15]+constants[16]*states[4]
    algebraic[5] = constants[17]*states[3]*(states[4]/(constants[18]+states[4]))+constants[19]*states[1]*(states[4]/(constants[20]+states[4]))
    rates[4] = (algebraic[2]-algebraic[5])*1.00000
    algebraic[6] = constants[4]*states[1]*states[3]*(states[2]/(constants[5]+states[2]))
    algebraic[7] = constants[7]*(states[1]/(constants[6]+states[2]))
    rates[2] = (algebraic[7]-algebraic[6])*1.00000
    algebraic[8] = constants[8]*states[3]+constants[9]*states[4]
    algebraic[9] = constants[10]*(states[1]/(constants[11]+states[1]))
    rates[1] = (((((algebraic[6]-algebraic[7])+algebraic[8])-algebraic[9])+algebraic[3])-algebraic[0])*1.00000
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = (constants[0]*(power(states[1], constants[2])))/(power(constants[1], constants[2])+power(states[1], constants[2]))
    algebraic[3] = (constants[3]*states[0])/1.00000
    algebraic[1] = constants[12]*states[4]
    algebraic[4] = constants[13]*(states[3]/(constants[14]+states[3]))
    algebraic[2] = constants[15]+constants[16]*states[4]
    algebraic[5] = constants[17]*states[3]*(states[4]/(constants[18]+states[4]))+constants[19]*states[1]*(states[4]/(constants[20]+states[4]))
    algebraic[6] = constants[4]*states[1]*states[3]*(states[2]/(constants[5]+states[2]))
    algebraic[7] = constants[7]*(states[1]/(constants[6]+states[2]))
    algebraic[8] = constants[8]*states[3]+constants[9]*states[4]
    algebraic[9] = constants[10]*(states[1]/(constants[11]+states[1]))
    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)