# Size of variable arrays:
sizeAlgebraic = 36
sizeStates = 14
sizeConstants = 39
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_cAMP_init in component environment (fmol)"
    legend_constants[1] = "q_PKI_init in component environment (fmol)"
    legend_constants[2] = "q_PKACI_init in component environment (fmol)"
    legend_constants[3] = "q_ARCI_init in component environment (fmol)"
    legend_constants[4] = "q_A2RCI_init in component environment (fmol)"
    legend_constants[5] = "q_CI_init in component environment (fmol)"
    legend_constants[6] = "q_A2RI_init in component environment (fmol)"
    legend_constants[7] = "q_PKACI_PKI_init in component environment (fmol)"
    legend_constants[8] = "q_PKACII_init in component environment (fmol)"
    legend_constants[9] = "q_ARCII_init in component environment (fmol)"
    legend_constants[10] = "q_A2RCII_init in component environment (fmol)"
    legend_constants[11] = "q_CII_init in component environment (fmol)"
    legend_constants[12] = "q_A2RII_init in component environment (fmol)"
    legend_constants[13] = "q_PKACII_PKI_init in component environment (fmol)"
    legend_algebraic[0] = "q_cAMP in component environment (fmol)"
    legend_algebraic[1] = "q_PKI in component environment (fmol)"
    legend_algebraic[2] = "q_PKACI in component environment (fmol)"
    legend_algebraic[3] = "q_ARCI in component environment (fmol)"
    legend_algebraic[4] = "q_A2RCI in component environment (fmol)"
    legend_algebraic[5] = "q_CI in component environment (fmol)"
    legend_algebraic[6] = "q_A2RI in component environment (fmol)"
    legend_algebraic[7] = "q_PKACI_PKI in component environment (fmol)"
    legend_algebraic[8] = "q_PKACII in component environment (fmol)"
    legend_algebraic[9] = "q_ARCII in component environment (fmol)"
    legend_algebraic[10] = "q_A2RCII in component environment (fmol)"
    legend_algebraic[11] = "q_CII in component environment (fmol)"
    legend_algebraic[12] = "q_A2RII in component environment (fmol)"
    legend_algebraic[13] = "q_PKACII_PKI in component environment (fmol)"
    legend_states[0] = "q_cAMP in component PKA (fmol)"
    legend_states[1] = "q_PKI in component PKA (fmol)"
    legend_states[2] = "q_PKACI in component PKA (fmol)"
    legend_states[3] = "q_ARCI in component PKA (fmol)"
    legend_states[4] = "q_A2RCI in component PKA (fmol)"
    legend_states[5] = "q_CI in component PKA (fmol)"
    legend_states[6] = "q_A2RI in component PKA (fmol)"
    legend_states[7] = "q_PKACI_PKI in component PKA (fmol)"
    legend_states[8] = "q_PKACII in component PKA (fmol)"
    legend_states[9] = "q_ARCII in component PKA (fmol)"
    legend_states[10] = "q_A2RCII in component PKA (fmol)"
    legend_states[11] = "q_CII in component PKA (fmol)"
    legend_states[12] = "q_A2RII in component PKA (fmol)"
    legend_states[13] = "q_PKACII_PKI in component PKA (fmol)"
    legend_constants[14] = "kappa_aI in component PKA_parameters (fmol_per_sec)"
    legend_constants[15] = "kappa_bI in component PKA_parameters (fmol_per_sec)"
    legend_constants[16] = "kappa_dI in component PKA_parameters (fmol_per_sec)"
    legend_constants[17] = "kappa_iI in component PKA_parameters (fmol_per_sec)"
    legend_constants[18] = "kappa_aII in component PKA_parameters (fmol_per_sec)"
    legend_constants[19] = "kappa_bII in component PKA_parameters (fmol_per_sec)"
    legend_constants[20] = "kappa_dII in component PKA_parameters (fmol_per_sec)"
    legend_constants[21] = "kappa_iII in component PKA_parameters (fmol_per_sec)"
    legend_constants[22] = "K_cAMP in component PKA_parameters (per_fmol)"
    legend_constants[23] = "K_PKI in component PKA_parameters (per_fmol)"
    legend_constants[24] = "K_PKACI in component PKA_parameters (per_fmol)"
    legend_constants[25] = "K_ARCI in component PKA_parameters (per_fmol)"
    legend_constants[26] = "K_A2RCI in component PKA_parameters (per_fmol)"
    legend_constants[27] = "K_CI in component PKA_parameters (per_fmol)"
    legend_constants[28] = "K_A2RI in component PKA_parameters (per_fmol)"
    legend_constants[29] = "K_PKACI_PKI in component PKA_parameters (per_fmol)"
    legend_constants[30] = "K_PKACII in component PKA_parameters (per_fmol)"
    legend_constants[31] = "K_ARCII in component PKA_parameters (per_fmol)"
    legend_constants[32] = "K_A2RCII in component PKA_parameters (per_fmol)"
    legend_constants[33] = "K_CII in component PKA_parameters (per_fmol)"
    legend_constants[34] = "K_A2RII in component PKA_parameters (per_fmol)"
    legend_constants[35] = "K_PKACII_PKI in component PKA_parameters (per_fmol)"
    legend_constants[36] = "R in component constants (J_per_K_per_mol)"
    legend_constants[37] = "T in component constants (kelvin)"
    legend_algebraic[28] = "vaI in component PKA (fmol_per_sec)"
    legend_algebraic[29] = "vbI in component PKA (fmol_per_sec)"
    legend_algebraic[30] = "vdI in component PKA (fmol_per_sec)"
    legend_algebraic[31] = "viI in component PKA (fmol_per_sec)"
    legend_algebraic[32] = "vaII in component PKA (fmol_per_sec)"
    legend_algebraic[33] = "vbII in component PKA (fmol_per_sec)"
    legend_algebraic[34] = "vdII in component PKA (fmol_per_sec)"
    legend_algebraic[35] = "viII in component PKA (fmol_per_sec)"
    legend_algebraic[14] = "mu_cAMP in component PKA (J_per_mol)"
    legend_algebraic[15] = "mu_PKI in component PKA (J_per_mol)"
    legend_algebraic[16] = "mu_PKACI in component PKA (J_per_mol)"
    legend_algebraic[17] = "mu_ARCI in component PKA (J_per_mol)"
    legend_algebraic[18] = "mu_A2RCI in component PKA (J_per_mol)"
    legend_algebraic[19] = "mu_CI in component PKA (J_per_mol)"
    legend_algebraic[20] = "mu_A2RI in component PKA (J_per_mol)"
    legend_algebraic[21] = "mu_PKACI_PKI in component PKA (J_per_mol)"
    legend_algebraic[22] = "mu_PKACII in component PKA (J_per_mol)"
    legend_algebraic[23] = "mu_ARCII in component PKA (J_per_mol)"
    legend_algebraic[24] = "mu_A2RCII in component PKA (J_per_mol)"
    legend_algebraic[25] = "mu_CII in component PKA (J_per_mol)"
    legend_algebraic[26] = "mu_A2RII in component PKA (J_per_mol)"
    legend_algebraic[27] = "mu_PKACII_PKI in component PKA (J_per_mol)"
    legend_constants[38] = "F in component constants (C_per_mol)"
    legend_rates[0] = "d/dt q_cAMP in component PKA (fmol)"
    legend_rates[1] = "d/dt q_PKI in component PKA (fmol)"
    legend_rates[2] = "d/dt q_PKACI in component PKA (fmol)"
    legend_rates[3] = "d/dt q_ARCI in component PKA (fmol)"
    legend_rates[4] = "d/dt q_A2RCI in component PKA (fmol)"
    legend_rates[5] = "d/dt q_CI in component PKA (fmol)"
    legend_rates[6] = "d/dt q_A2RI in component PKA (fmol)"
    legend_rates[7] = "d/dt q_PKACI_PKI in component PKA (fmol)"
    legend_rates[8] = "d/dt q_PKACII in component PKA (fmol)"
    legend_rates[9] = "d/dt q_ARCII in component PKA (fmol)"
    legend_rates[10] = "d/dt q_A2RCII in component PKA (fmol)"
    legend_rates[11] = "d/dt q_CII in component PKA (fmol)"
    legend_rates[12] = "d/dt q_A2RII in component PKA (fmol)"
    legend_rates[13] = "d/dt q_PKACII_PKI in component PKA (fmol)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 3.212E-02
    constants[1] = 6.840E-03
    constants[2] = 2.242E-02
    constants[3] = 3.800E-15
    constants[4] = 3.800E-15
    constants[5] = 3.800E-15
    constants[6] = 3.800E-15
    constants[7] = 3.800E-15
    constants[8] = 9.500E-04
    constants[9] = 3.800E-15
    constants[10] = 3.800E-15
    constants[11] = 3.800E-15
    constants[12] = 3.800E-15
    constants[13] = 3.800E-15
    states[0] = 1e-16
    states[1] = 1e-16
    states[2] = 1e-16
    states[3] = 1e-16
    states[4] = 1e-16
    states[5] = 1e-16
    states[6] = 1e-16
    states[7] = 1e-16
    states[8] = 1e-16
    states[9] = 1e-16
    states[10] = 1e-16
    states[11] = 1e-16
    states[12] = 1e-16
    states[13] = 1e-16
    constants[14] = 48.0417
    constants[15] = 21.1895
    constants[16] = 4.84331
    constants[17] = 149.139
    constants[18] = 48.0417
    constants[19] = 21.1895
    constants[20] = 4.84331
    constants[21] = 149.139
    constants[22] = 0.0401879
    constants[23] = 14.3814
    constants[24] = 0.0478876
    constants[25] = 0.605095
    constants[26] = 1.3719
    constants[27] = 1.96997
    constants[28] = 0.0885687
    constants[29] = 0.194918
    constants[30] = 0.0478876
    constants[31] = 0.605095
    constants[32] = 1.3719
    constants[33] = 1.96997
    constants[34] = 0.0885687
    constants[35] = 0.194918
    constants[36] = 8.31
    constants[37] = 310
    constants[38] = 96485
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = states[0]+constants[0]
    algebraic[14] = constants[36]*constants[37]*log(constants[22]*algebraic[0])
    algebraic[2] = states[2]+constants[2]
    algebraic[16] = constants[36]*constants[37]*log(constants[24]*algebraic[2])
    algebraic[3] = states[3]+constants[3]
    algebraic[17] = constants[36]*constants[37]*log(constants[25]*algebraic[3])
    algebraic[28] = constants[14]*(exp((algebraic[16]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[17]/(constants[36]*constants[37])))
    rates[2] = -algebraic[28]
    algebraic[4] = states[4]+constants[4]
    algebraic[18] = constants[36]*constants[37]*log(constants[26]*algebraic[4])
    algebraic[29] = constants[15]*(exp((algebraic[17]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[18]/(constants[36]*constants[37])))
    rates[3] = algebraic[28]-algebraic[29]
    algebraic[5] = states[5]+constants[5]
    algebraic[19] = constants[36]*constants[37]*log(constants[27]*algebraic[5])
    algebraic[6] = states[6]+constants[6]
    algebraic[20] = constants[36]*constants[37]*log(constants[28]*algebraic[6])
    algebraic[30] = constants[16]*(exp(algebraic[18]/(constants[36]*constants[37]))-exp((algebraic[20]+algebraic[19])/(constants[36]*constants[37])))
    rates[4] = algebraic[29]-algebraic[30]
    rates[6] = algebraic[30]
    algebraic[1] = states[1]+constants[1]
    algebraic[15] = constants[36]*constants[37]*log(constants[23]*algebraic[1])
    algebraic[7] = states[7]+constants[7]
    algebraic[21] = constants[36]*constants[37]*log(constants[29]*algebraic[7])
    algebraic[31] = constants[17]*(exp((algebraic[19]+algebraic[15])/(constants[36]*constants[37]))-exp(algebraic[21]/(constants[36]*constants[37])))
    rates[5] = algebraic[30]-algebraic[31]
    rates[7] = algebraic[31]
    algebraic[8] = states[8]+constants[8]
    algebraic[22] = constants[36]*constants[37]*log(constants[30]*algebraic[8])
    algebraic[9] = states[9]+constants[9]
    algebraic[23] = constants[36]*constants[37]*log(constants[31]*algebraic[9])
    algebraic[32] = constants[18]*(exp((algebraic[22]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[23]/(constants[36]*constants[37])))
    rates[8] = -algebraic[32]
    algebraic[10] = states[10]+constants[10]
    algebraic[24] = constants[36]*constants[37]*log(constants[32]*algebraic[10])
    algebraic[33] = constants[19]*(exp((algebraic[23]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[24]/(constants[36]*constants[37])))
    rates[0] = ((-algebraic[28]-algebraic[29])-algebraic[32])-algebraic[33]
    rates[9] = algebraic[32]-algebraic[33]
    algebraic[11] = states[11]+constants[11]
    algebraic[25] = constants[36]*constants[37]*log(constants[33]*algebraic[11])
    algebraic[12] = states[12]+constants[12]
    algebraic[26] = constants[36]*constants[37]*log(constants[34]*algebraic[12])
    algebraic[34] = constants[20]*(exp(algebraic[24]/(constants[36]*constants[37]))-exp((algebraic[26]+algebraic[25])/(constants[36]*constants[37])))
    rates[10] = algebraic[33]-algebraic[34]
    rates[12] = algebraic[34]
    algebraic[13] = states[13]+constants[13]
    algebraic[27] = constants[36]*constants[37]*log(constants[35]*algebraic[13])
    algebraic[35] = constants[21]*(exp((algebraic[25]+algebraic[15])/(constants[36]*constants[37]))-exp(algebraic[27]/(constants[36]*constants[37])))
    rates[1] = -algebraic[31]-algebraic[35]
    rates[11] = algebraic[34]-algebraic[35]
    rates[13] = algebraic[35]
    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[14] = constants[36]*constants[37]*log(constants[22]*algebraic[0])
    algebraic[2] = states[2]+constants[2]
    algebraic[16] = constants[36]*constants[37]*log(constants[24]*algebraic[2])
    algebraic[3] = states[3]+constants[3]
    algebraic[17] = constants[36]*constants[37]*log(constants[25]*algebraic[3])
    algebraic[28] = constants[14]*(exp((algebraic[16]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[17]/(constants[36]*constants[37])))
    algebraic[4] = states[4]+constants[4]
    algebraic[18] = constants[36]*constants[37]*log(constants[26]*algebraic[4])
    algebraic[29] = constants[15]*(exp((algebraic[17]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[18]/(constants[36]*constants[37])))
    algebraic[5] = states[5]+constants[5]
    algebraic[19] = constants[36]*constants[37]*log(constants[27]*algebraic[5])
    algebraic[6] = states[6]+constants[6]
    algebraic[20] = constants[36]*constants[37]*log(constants[28]*algebraic[6])
    algebraic[30] = constants[16]*(exp(algebraic[18]/(constants[36]*constants[37]))-exp((algebraic[20]+algebraic[19])/(constants[36]*constants[37])))
    algebraic[1] = states[1]+constants[1]
    algebraic[15] = constants[36]*constants[37]*log(constants[23]*algebraic[1])
    algebraic[7] = states[7]+constants[7]
    algebraic[21] = constants[36]*constants[37]*log(constants[29]*algebraic[7])
    algebraic[31] = constants[17]*(exp((algebraic[19]+algebraic[15])/(constants[36]*constants[37]))-exp(algebraic[21]/(constants[36]*constants[37])))
    algebraic[8] = states[8]+constants[8]
    algebraic[22] = constants[36]*constants[37]*log(constants[30]*algebraic[8])
    algebraic[9] = states[9]+constants[9]
    algebraic[23] = constants[36]*constants[37]*log(constants[31]*algebraic[9])
    algebraic[32] = constants[18]*(exp((algebraic[22]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[23]/(constants[36]*constants[37])))
    algebraic[10] = states[10]+constants[10]
    algebraic[24] = constants[36]*constants[37]*log(constants[32]*algebraic[10])
    algebraic[33] = constants[19]*(exp((algebraic[23]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[24]/(constants[36]*constants[37])))
    algebraic[11] = states[11]+constants[11]
    algebraic[25] = constants[36]*constants[37]*log(constants[33]*algebraic[11])
    algebraic[12] = states[12]+constants[12]
    algebraic[26] = constants[36]*constants[37]*log(constants[34]*algebraic[12])
    algebraic[34] = constants[20]*(exp(algebraic[24]/(constants[36]*constants[37]))-exp((algebraic[26]+algebraic[25])/(constants[36]*constants[37])))
    algebraic[13] = states[13]+constants[13]
    algebraic[27] = constants[36]*constants[37]*log(constants[35]*algebraic[13])
    algebraic[35] = constants[21]*(exp((algebraic[25]+algebraic[15])/(constants[36]*constants[37]))-exp(algebraic[27]/(constants[36]*constants[37])))
    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)