# Size of variable arrays:
sizeAlgebraic = 13
sizeStates = 8
sizeConstants = 17
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] = "vol in component environment (pL)"
    legend_states[0] = "q_A in component environment (fmol)"
    legend_states[1] = "q_M in component environment (fmol)"
    legend_states[2] = "q_Mp in component environment (fmol)"
    legend_states[3] = "q_AM in component environment (fmol)"
    legend_states[4] = "q_AMp in component environment (fmol)"
    legend_states[5] = "q_Pi in component environment (fmol)"
    legend_states[6] = "q_Ca_i in component environment (fmol)"
    legend_states[7] = "q_cGMP in component environment (fmol)"
    legend_algebraic[9] = "v_R_12 in component HaiMurphy (fmol_per_sec)"
    legend_algebraic[10] = "v_R_34 in component HaiMurphy (fmol_per_sec)"
    legend_algebraic[11] = "v_R_56 in component HaiMurphy (fmol_per_sec)"
    legend_algebraic[12] = "v_R_78 in component HaiMurphy (fmol_per_sec)"
    legend_constants[1] = "n_Cai_SM in component environment (dimensionless)"
    legend_algebraic[1] = "stress in component environment (dimensionless)"
    legend_constants[2] = "kappa_R_12 in component HaiMurphy_parameters (fmol_per_sec)"
    legend_constants[3] = "kappa_R_34 in component HaiMurphy_parameters (fmol_per_sec)"
    legend_constants[4] = "kappa_R_56 in component HaiMurphy_parameters (fmol_per_sec)"
    legend_constants[5] = "kappa_R_78 in component HaiMurphy_parameters (fmol_per_sec)"
    legend_constants[6] = "K_A in component HaiMurphy_parameters (per_fmol)"
    legend_constants[7] = "K_M in component HaiMurphy_parameters (per_fmol)"
    legend_constants[8] = "K_Mp in component HaiMurphy_parameters (per_fmol)"
    legend_constants[9] = "K_AM in component HaiMurphy_parameters (per_fmol)"
    legend_constants[10] = "K_AMp in component HaiMurphy_parameters (per_fmol)"
    legend_constants[11] = "K_Pi in component HaiMurphy_parameters (per_fmol)"
    legend_constants[12] = "K_Ca_i in component HaiMurphy_parameters (per_fmol)"
    legend_constants[13] = "K_cGMP in component HaiMurphy_parameters (per_fmol)"
    legend_constants[14] = "R in component constants (J_per_K_per_mol)"
    legend_constants[15] = "T in component constants (kelvin)"
    legend_algebraic[0] = "mu_A in component HaiMurphy (J_per_mol)"
    legend_algebraic[2] = "mu_M in component HaiMurphy (J_per_mol)"
    legend_algebraic[3] = "mu_Mp in component HaiMurphy (J_per_mol)"
    legend_algebraic[4] = "mu_AM in component HaiMurphy (J_per_mol)"
    legend_algebraic[5] = "mu_AMp in component HaiMurphy (J_per_mol)"
    legend_algebraic[6] = "mu_Pi in component HaiMurphy (J_per_mol)"
    legend_algebraic[7] = "mu_Ca_i in component HaiMurphy (J_per_mol)"
    legend_algebraic[8] = "mu_cGMP in component HaiMurphy (J_per_mol)"
    legend_constants[16] = "F in component constants (C_per_mol)"
    legend_rates[0] = "d/dt q_A in component environment (fmol)"
    legend_rates[1] = "d/dt q_M in component environment (fmol)"
    legend_rates[2] = "d/dt q_Mp in component environment (fmol)"
    legend_rates[3] = "d/dt q_AM in component environment (fmol)"
    legend_rates[4] = "d/dt q_AMp in component environment (fmol)"
    legend_rates[5] = "d/dt q_Pi in component environment (fmol)"
    legend_rates[6] = "d/dt q_Ca_i in component environment (fmol)"
    legend_rates[7] = "d/dt q_cGMP in component environment (fmol)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 1
    states[0] = 1e-6
    states[1] = 1e-6
    states[2] = 0
    states[3] = 0
    states[4] = 0
    states[5] = 15
    states[6] = 1e-3
    states[7] = 1e-6
    constants[1] = 1.66
    constants[2] = 0.117606
    constants[3] = 6.98167
    constants[4] = 2.11691
    constants[5] = 0.0270688
    constants[6] = 0.532601
    constants[7] = 4.08193
    constants[8] = 0.0351692
    constants[9] = 0.448094
    constants[10] = 0.0038607
    constants[11] = 250.692
    constants[12] = 0.145785
    constants[13] = 0.0971738
    constants[14] = 8.31
    constants[15] = 310
    constants[16] = 96485
    return (states, constants)

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

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