# Size of variable arrays:
sizeAlgebraic = 7
sizeStates = 3
sizeConstants = 10
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_constants[0] = "q_Cai_init in component environment (fmol)"
    legend_constants[1] = "q_TRPN_init in component environment (fmol)"
    legend_constants[2] = "q_Ca_TRPN_init in component environment (fmol)"
    legend_algebraic[0] = "q_Cai in component environment (fmol)"
    legend_algebraic[1] = "q_TRPN in component environment (fmol)"
    legend_algebraic[2] = "q_Ca_TRPN in component environment (fmol)"
    legend_states[0] = "q_Cai in component TRPN (fmol)"
    legend_states[1] = "q_TRPN in component TRPN (fmol)"
    legend_states[2] = "q_Ca_TRPN in component TRPN (fmol)"
    legend_constants[3] = "kappa_R_TRPNCa in component TRPN_parameters (fmol_per_sec)"
    legend_constants[4] = "K_Cai in component TRPN_parameters (per_fmol)"
    legend_constants[5] = "K_TRPN in component TRPN_parameters (per_fmol)"
    legend_constants[6] = "K_Ca_TRPN in component TRPN_parameters (per_fmol)"
    legend_constants[7] = "R in component constants (J_per_K_per_mol)"
    legend_constants[8] = "T in component constants (kelvin)"
    legend_algebraic[3] = "mu_Cai in component TRPN (J_per_mol)"
    legend_algebraic[4] = "mu_TRPN in component TRPN (J_per_mol)"
    legend_algebraic[5] = "mu_Ca_TRPN in component TRPN (J_per_mol)"
    legend_algebraic[6] = "v_R_TRPNCa in component TRPN (fmol_per_sec)"
    legend_constants[9] = "F in component constants (C_per_mol)"
    legend_rates[0] = "d/dt q_Cai in component TRPN (fmol)"
    legend_rates[1] = "d/dt q_TRPN in component TRPN (fmol)"
    legend_rates[2] = "d/dt q_Ca_TRPN in component TRPN (fmol)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 6.82e-1
    constants[1] = 2.57
    constants[2] = 1e-16
    states[0] = 1e-16
    states[1] = 1e-16
    states[2] = 1e-16
    constants[3] = 83.2553
    constants[4] = 1.00748
    constants[5] = 1.00748
    constants[6] = 0.0698328
    constants[7] = 8.31
    constants[8] = 310
    constants[9] = 96485
    return (states, constants)

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

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = states[0]+constants[0]
    algebraic[3] = constants[7]*constants[8]*log(constants[4]*algebraic[0])
    algebraic[1] = states[1]+constants[1]
    algebraic[4] = constants[7]*constants[8]*log(constants[5]*algebraic[1])
    algebraic[2] = states[2]+constants[2]
    algebraic[5] = constants[7]*constants[8]*log(constants[6]*algebraic[2])
    algebraic[6] = constants[3]*(exp((algebraic[3]+algebraic[4])/(constants[7]*constants[8]))-exp(algebraic[5]/(constants[7]*constants[8])))
    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)