# Size of variable arrays:
sizeAlgebraic = 9
sizeStates = 7
sizeConstants = 35
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 (second)"
    legend_states[0] = "IP3 in component IP3_dynamics (micromolar)"
    legend_algebraic[0] = "j_IP3 in component IP3_dynamics (micromolar_micrometre_per_second)"
    legend_constants[0] = "J_IP3 in component IP3_dynamics (micromolar_micrometre_per_second)"
    legend_constants[1] = "k_0 in component IP3_dynamics (first_order_rate_constant)"
    legend_constants[2] = "k_degr in component IP3_dynamics (first_order_rate_constant)"
    legend_constants[3] = "IP3_0 in component IP3_dynamics (micromolar)"
    legend_constants[4] = "Ca_ER in component ER (micromolar)"
    legend_states[1] = "Ca in component Calcium_dynamics (micromolar)"
    legend_constants[5] = "alpha in component Calcium_dynamics (dimensionless)"
    legend_algebraic[1] = "J_channel in component Channel_kinetics (flux)"
    legend_algebraic[7] = "J_pump in component SERCA_pump_kinetics (flux)"
    legend_algebraic[8] = "J_leak in component Leak (flux)"
    legend_constants[27] = "R_buffering in component Calcium_buffering (flux)"
    legend_constants[6] = "J_max in component Channel_kinetics (flux)"
    legend_states[2] = "h in component Channel_kinetics (dimensionless)"
    legend_constants[7] = "K_act in component Channel_kinetics (micromolar)"
    legend_constants[8] = "K_IP3 in component Channel_kinetics (micromolar)"
    legend_constants[9] = "K_inh in component Channel_kinetics (micromolar)"
    legend_constants[10] = "k_on in component Channel_kinetics (second_order_rate_constant)"
    legend_constants[11] = "V_max in component SERCA_pump_kinetics (flux)"
    legend_constants[12] = "K_p in component SERCA_pump_kinetics (micromolar)"
    legend_constants[13] = "L in component Leak (flux)"
    legend_constants[14] = "R1 in component Calcium_buffering (flux)"
    legend_constants[15] = "R2 in component Calcium_buffering (flux)"
    legend_states[3] = "B1 in component Calcium_buffering (micromolar)"
    legend_states[4] = "B2 in component Calcium_buffering (micromolar)"
    legend_states[5] = "CaB1 in component Calcium_buffering (micromolar)"
    legend_states[6] = "CaB2 in component Calcium_buffering (micromolar)"
    legend_algebraic[2] = "k1_on in component Calcium_buffering (second_order_rate_constant)"
    legend_algebraic[3] = "k1_off in component Calcium_buffering (first_order_rate_constant)"
    legend_algebraic[4] = "k2_on in component Calcium_buffering (second_order_rate_constant)"
    legend_algebraic[5] = "k2_off in component Calcium_buffering (first_order_rate_constant)"
    legend_constants[16] = "K1 in component Calcium_buffering (micromolar)"
    legend_constants[17] = "K2 in component Calcium_buffering (micromolar)"
    legend_constants[18] = "soma_or_neurite in component Plasma_membrane_extrusion_mechanisms (dimensionless)"
    legend_algebraic[6] = "j_Ca in component Plasma_membrane_extrusion_mechanisms (micromolar_micrometre_per_second)"
    legend_constants[19] = "gamma_0 in component Plasma_membrane_extrusion_mechanisms (micrometre_per_second)"
    legend_constants[30] = "gamma in component Plasma_membrane_extrusion_mechanisms (micrometre_per_second)"
    legend_constants[28] = "gamma_s in component Plasma_membrane_extrusion_mechanisms (micrometre_per_second)"
    legend_constants[29] = "gamma_n in component Plasma_membrane_extrusion_mechanisms (micrometre_per_second)"
    legend_constants[20] = "delta in component Plasma_membrane_extrusion_mechanisms (dimensionless)"
    legend_constants[21] = "sigma in component Plasma_membrane_extrusion_mechanisms (per_micrometre)"
    legend_constants[22] = "w_n in component Plasma_membrane_extrusion_mechanisms (dimensionless)"
    legend_constants[23] = "w_s in component Plasma_membrane_extrusion_mechanisms (dimensionless)"
    legend_constants[24] = "sigma_soma_2D in component Plasma_membrane_extrusion_mechanisms (per_micrometre)"
    legend_constants[25] = "sigma_neurite_2D in component Plasma_membrane_extrusion_mechanisms (per_micrometre)"
    legend_constants[26] = "Ca_c in component Plasma_membrane_extrusion_mechanisms (micromolar)"
    legend_rates[0] = "d/dt IP3 in component IP3_dynamics (micromolar)"
    legend_rates[1] = "d/dt Ca in component Calcium_dynamics (micromolar)"
    legend_rates[2] = "d/dt h in component Channel_kinetics (dimensionless)"
    legend_rates[3] = "d/dt B1 in component Calcium_buffering (micromolar)"
    legend_rates[5] = "d/dt CaB1 in component Calcium_buffering (micromolar)"
    legend_rates[4] = "d/dt B2 in component Calcium_buffering (micromolar)"
    legend_rates[6] = "d/dt CaB2 in component Calcium_buffering (micromolar)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 3.0
    constants[0] = 20.86
    constants[1] = 1.188
    constants[2] = 0.14
    constants[3] = 0.16
    constants[4] = 400.0
    states[1] = 0.05
    constants[5] = 0.0
    constants[6] = 3500.0
    states[2] = 0.8
    constants[7] = 0.3
    constants[8] = 0.8
    constants[9] = 0.2
    constants[10] = 2.7
    constants[11] = 3.75
    constants[12] = 0.27
    constants[13] = 0.1
    constants[14] = 0.1
    constants[15] = 0.1
    states[3] = 450.0
    states[4] = 75.0
    states[5] = 0
    states[6] = 0
    constants[16] = 10.0
    constants[17] = 0.24
    constants[18] = -1
    constants[19] = 8.0
    constants[20] = 1.45
    constants[21] = 0.263
    constants[22] = 0.377
    constants[23] = 0.623
    constants[24] = 0.132
    constants[25] = 0.479
    constants[26] = 0.2
    constants[27] = constants[14]+constants[15]
    constants[28] = (constants[19]*constants[21])/(constants[20]*constants[25]*constants[22]+constants[24]*constants[23])
    constants[31] = constants[14]
    constants[32] = -constants[14]
    constants[33] = constants[15]
    constants[34] = -constants[15]
    constants[29] = (constants[19]*constants[21]*constants[20])/(constants[20]*constants[25]*constants[22]+constants[24]*constants[23])
    constants[30] = custom_piecewise([less_equal(constants[18] , 0.00000), constants[28] , True, constants[29]])
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[3] = constants[31]
    rates[5] = constants[32]
    rates[4] = constants[33]
    rates[6] = constants[34]
    rates[0] = -(constants[2]*(states[0]-constants[3]))
    rates[2] = constants[10]*(constants[9]-states[2]*(states[1]+constants[9]))
    algebraic[1] = constants[6]*(power((states[0]/(states[0]+constants[8]))*(states[1]/(states[1]+constants[7]))*states[2], 3.00000))*(1.00000-states[1]/constants[4])
    algebraic[7] = constants[11]*((power(states[1], 2.00000))/(power(states[1], 2.00000)+power(constants[12], 2.00000)))
    algebraic[8] = constants[13]*(1.00000-states[1]/constants[4])
    rates[1] = constants[5]*(algebraic[1]+-algebraic[7]+algebraic[8])+constants[27]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[1] = constants[6]*(power((states[0]/(states[0]+constants[8]))*(states[1]/(states[1]+constants[7]))*states[2], 3.00000))*(1.00000-states[1]/constants[4])
    algebraic[7] = constants[11]*((power(states[1], 2.00000))/(power(states[1], 2.00000)+power(constants[12], 2.00000)))
    algebraic[8] = constants[13]*(1.00000-states[1]/constants[4])
    algebraic[0] = constants[0]*exp(-constants[1]*voi)
    rootfind_0(voi, constants, rates, states, algebraic)
    rootfind_1(voi, constants, rates, states, algebraic)
    algebraic[6] = custom_piecewise([greater(states[1] , constants[26]), constants[30]*(states[1]-constants[26]) , True, 0.00000])
    return algebraic

initialGuess0 = None
def rootfind_0(voi, constants, rates, states, algebraic):
    """Calculate values of algebraic variables for DAE"""
    from scipy.optimize import fsolve
    global initialGuess0
    if initialGuess0 is None: initialGuess0 = ones(2)*0.1
    if not iterable(voi):
        soln = fsolve(residualSN_0, initialGuess0, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
        initialGuess0 = soln
        algebraic[2] = soln[0]
        algebraic[3] = soln[1]
    else:
        for (i,t) in enumerate(voi):
            soln = fsolve(residualSN_0, initialGuess0, args=(algebraic[:,i], voi[i], constants, rates[:i], states[:,i]), xtol=1E-6)
            initialGuess0 = soln
            algebraic[2][i] = soln[0]
            algebraic[3][i] = soln[1]

def residualSN_0(algebraicCandidate, algebraic, voi, constants, rates, states):
    resid = array([0.0] * 2)
    algebraic[2] = algebraicCandidate[0]
    algebraic[3] = algebraicCandidate[1]
    resid[0] = (constants[14]-(-(algebraic[2]*states[1]*states[3])+algebraic[3]*states[5]))
    resid[1] = (constants[16]-algebraic[3]/algebraic[2])
    return resid

initialGuess1 = None
def rootfind_1(voi, constants, rates, states, algebraic):
    """Calculate values of algebraic variables for DAE"""
    from scipy.optimize import fsolve
    global initialGuess1
    if initialGuess1 is None: initialGuess1 = ones(2)*0.1
    if not iterable(voi):
        soln = fsolve(residualSN_1, initialGuess1, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
        initialGuess1 = soln
        algebraic[4] = soln[0]
        algebraic[5] = soln[1]
    else:
        for (i,t) in enumerate(voi):
            soln = fsolve(residualSN_1, initialGuess1, args=(algebraic[:,i], voi[i], constants, rates[:i], states[:,i]), xtol=1E-6)
            initialGuess1 = soln
            algebraic[4][i] = soln[0]
            algebraic[5][i] = soln[1]

def residualSN_1(algebraicCandidate, algebraic, voi, constants, rates, states):
    resid = array([0.0] * 2)
    algebraic[4] = algebraicCandidate[0]
    algebraic[5] = algebraicCandidate[1]
    resid[0] = (constants[15]-(-(algebraic[4]*states[1]*states[4])+algebraic[5]*states[6]))
    resid[1] = (constants[17]-algebraic[5]/algebraic[4])
    return resid

def custom_piecewise(cases):
    """Compute result of a piecewise function"""
    return select(cases[0::2],cases[1::2])

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)