# Size of variable arrays:
sizeAlgebraic = 20
sizeStates = 10
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 (second)"
    legend_states[0] = "q_OH_i in component environment (fmol)"
    legend_states[1] = "q_OH_o in component environment (fmol)"
    legend_states[2] = "q_Cl_i in component environment (fmol)"
    legend_states[3] = "q_Cl_o in component environment (fmol)"
    legend_states[4] = "q_S1_CHE in component environment (fmol)"
    legend_states[5] = "q_S2_CHE in component environment (fmol)"
    legend_states[6] = "q_S3_CHE in component environment (fmol)"
    legend_states[7] = "q_S4_CHE in component environment (fmol)"
    legend_states[8] = "q_S5_CHE in component environment (fmol)"
    legend_states[9] = "q_S6_CHE in component environment (fmol)"
    legend_algebraic[14] = "v_R61_CHE in component CHE (fmol_per_sec)"
    legend_algebraic[15] = "v_R12_CHE in component CHE (fmol_per_sec)"
    legend_algebraic[16] = "v_R23_CHE in component CHE (fmol_per_sec)"
    legend_algebraic[17] = "v_R34_CHE in component CHE (fmol_per_sec)"
    legend_algebraic[18] = "v_R45_CHE in component CHE (fmol_per_sec)"
    legend_algebraic[19] = "v_R56_CHE in component CHE (fmol_per_sec)"
    legend_algebraic[3] = "pH_i in component environment (dimensionless)"
    legend_algebraic[4] = "pH_o in component environment (dimensionless)"
    legend_algebraic[0] = "cOH_i in component environment (mM)"
    legend_algebraic[1] = "cOH_o in component environment (mM)"
    legend_constants[0] = "w_i in component environment (pL)"
    legend_constants[1] = "w_o in component environment (pL)"
    legend_constants[2] = "kappa_R61_CHE in component CHE_parameters (fmol_per_sec)"
    legend_constants[3] = "kappa_R12_CHE in component CHE_parameters (fmol_per_sec)"
    legend_constants[4] = "kappa_R23_CHE in component CHE_parameters (fmol_per_sec)"
    legend_constants[5] = "kappa_R34_CHE in component CHE_parameters (fmol_per_sec)"
    legend_constants[6] = "kappa_R45_CHE in component CHE_parameters (fmol_per_sec)"
    legend_constants[7] = "kappa_R56_CHE in component CHE_parameters (fmol_per_sec)"
    legend_constants[8] = "K_OH_i in component CHE_parameters (per_fmol)"
    legend_constants[9] = "K_OH_o in component CHE_parameters (per_fmol)"
    legend_constants[10] = "K_Cl_i in component CHE_parameters (per_fmol)"
    legend_constants[11] = "K_Cl_o in component CHE_parameters (per_fmol)"
    legend_constants[12] = "K_S1_CHE in component CHE_parameters (per_fmol)"
    legend_constants[13] = "K_S2_CHE in component CHE_parameters (per_fmol)"
    legend_constants[14] = "K_S3_CHE in component CHE_parameters (per_fmol)"
    legend_constants[15] = "K_S4_CHE in component CHE_parameters (per_fmol)"
    legend_constants[16] = "K_S5_CHE in component CHE_parameters (per_fmol)"
    legend_constants[17] = "K_S6_CHE in component CHE_parameters (per_fmol)"
    legend_constants[18] = "R in component constants (J_per_K_per_mol)"
    legend_constants[19] = "T in component constants (kelvin)"
    legend_algebraic[2] = "mu_OH_i in component CHE (J_per_mol)"
    legend_algebraic[5] = "mu_OH_o in component CHE (J_per_mol)"
    legend_algebraic[6] = "mu_Cl_i in component CHE (J_per_mol)"
    legend_algebraic[7] = "mu_Cl_o in component CHE (J_per_mol)"
    legend_algebraic[8] = "mu_S1_CHE in component CHE (J_per_mol)"
    legend_algebraic[9] = "mu_S2_CHE in component CHE (J_per_mol)"
    legend_algebraic[10] = "mu_S3_CHE in component CHE (J_per_mol)"
    legend_algebraic[11] = "mu_S4_CHE in component CHE (J_per_mol)"
    legend_algebraic[12] = "mu_S5_CHE in component CHE (J_per_mol)"
    legend_algebraic[13] = "mu_S6_CHE in component CHE (J_per_mol)"
    legend_constants[20] = "F in component constants (C_per_mol)"
    legend_rates[0] = "d/dt q_OH_i in component environment (fmol)"
    legend_rates[1] = "d/dt q_OH_o in component environment (fmol)"
    legend_rates[2] = "d/dt q_Cl_i in component environment (fmol)"
    legend_rates[3] = "d/dt q_Cl_o in component environment (fmol)"
    legend_rates[4] = "d/dt q_S1_CHE in component environment (fmol)"
    legend_rates[5] = "d/dt q_S2_CHE in component environment (fmol)"
    legend_rates[6] = "d/dt q_S3_CHE in component environment (fmol)"
    legend_rates[7] = "d/dt q_S4_CHE in component environment (fmol)"
    legend_rates[8] = "d/dt q_S5_CHE in component environment (fmol)"
    legend_rates[9] = "d/dt q_S6_CHE in component environment (fmol)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 5.36764E-06
    states[1] = 1.30166E-06
    states[2] = 824.6
    states[3] = 725.48
    states[4] = 1.666e-7
    states[5] = 1.666e-7
    states[6] = 1.666e-7
    states[7] = 1.666e-7
    states[8] = 1.666e-7
    states[9] = 1.666e-7
    constants[0] = 38
    constants[1] = 5.182
    constants[2] = 8.77838
    constants[3] = 0.031295
    constants[4] = 50940.7
    constants[5] = 0.000192726
    constants[6] = 2.96501e+06
    constants[7] = 1.82153e+06
    constants[8] = 0.0253475
    constants[9] = 7203.46
    constants[10] = 0.015572
    constants[11] = 0.00442538
    constants[12] = 28.479
    constants[13] = 856.026
    constants[14] = 353352
    constants[15] = 6070.81
    constants[16] = 0.569962
    constants[17] = 0.4887
    constants[18] = 8.31
    constants[19] = 310
    constants[20] = 96485
    return (states, constants)

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

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[5] = constants[18]*constants[19]*log(constants[9]*states[1])
    algebraic[8] = constants[18]*constants[19]*log(constants[12]*states[4])
    algebraic[9] = constants[18]*constants[19]*log(constants[13]*states[5])
    algebraic[15] = constants[3]*(exp(algebraic[8]/(constants[18]*constants[19]))-exp((algebraic[9]+algebraic[5])/(constants[18]*constants[19])))
    algebraic[13] = constants[18]*constants[19]*log(constants[17]*states[9])
    algebraic[14] = constants[2]*(exp(algebraic[13]/(constants[18]*constants[19]))-exp(algebraic[8]/(constants[18]*constants[19])))
    algebraic[7] = constants[18]*constants[19]*log(constants[11]*states[3])
    algebraic[10] = constants[18]*constants[19]*log(constants[14]*states[6])
    algebraic[16] = constants[4]*(exp((algebraic[9]+algebraic[7])/(constants[18]*constants[19]))-exp(algebraic[10]/(constants[18]*constants[19])))
    algebraic[11] = constants[18]*constants[19]*log(constants[15]*states[7])
    algebraic[17] = constants[5]*(exp(algebraic[10]/(constants[18]*constants[19]))-exp(algebraic[11]/(constants[18]*constants[19])))
    algebraic[6] = constants[18]*constants[19]*log(constants[10]*states[2])
    algebraic[12] = constants[18]*constants[19]*log(constants[16]*states[8])
    algebraic[18] = constants[6]*(exp(algebraic[11]/(constants[18]*constants[19]))-exp((algebraic[12]+algebraic[6])/(constants[18]*constants[19])))
    algebraic[2] = constants[18]*constants[19]*log(constants[8]*states[0])
    algebraic[19] = constants[7]*(exp((algebraic[12]+algebraic[2])/(constants[18]*constants[19]))-exp(algebraic[13]/(constants[18]*constants[19])))
    algebraic[0] = states[0]/constants[0]
    algebraic[1] = states[1]/constants[1]
    algebraic[3] = 14.0000+log(algebraic[0], 10)
    algebraic[4] = 14.0000+log(algebraic[1], 10)
    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)