# Size of variable arrays:
sizeAlgebraic = 31
sizeStates = 12
sizeConstants = 32
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_algebraic[0] = "q_L_B1_init in component environment (fmol)"
    legend_constants[0] = "q_R_B1_init in component environment (fmol)"
    legend_constants[1] = "q_Gs_init in component environment (fmol)"
    legend_constants[2] = "q_LR_B1_init in component environment (fmol)"
    legend_constants[3] = "q_LR_B1Gs_init in component environment (fmol)"
    legend_constants[4] = "q_B1d_init in component environment (fmol)"
    legend_constants[5] = "q_BARK_init in component environment (fmol)"
    legend_constants[6] = "q_LR_B1_BARK_init in component environment (fmol)"
    legend_constants[7] = "q_LR_B1Gs_BARK_init in component environment (fmol)"
    legend_constants[8] = "q_B1p_init in component environment (fmol)"
    legend_constants[9] = "q_PKACI_init in component environment (fmol)"
    legend_constants[10] = "q_R_PKACI_init in component environment (fmol)"
    legend_algebraic[2] = "q_L_B1 in component environment (fmol)"
    legend_algebraic[1] = "q_R_B1 in component environment (fmol)"
    legend_algebraic[4] = "q_Gs in component environment (fmol)"
    legend_algebraic[6] = "q_LR_B1 in component environment (fmol)"
    legend_algebraic[8] = "q_LR_B1Gs in component environment (fmol)"
    legend_algebraic[10] = "q_B1d in component environment (fmol)"
    legend_algebraic[12] = "q_BARK in component environment (fmol)"
    legend_algebraic[14] = "q_LR_B1_BARK in component environment (fmol)"
    legend_algebraic[17] = "q_LR_B1Gs_BARK in component environment (fmol)"
    legend_algebraic[3] = "q_B1p in component environment (fmol)"
    legend_algebraic[5] = "q_PKACI in component environment (fmol)"
    legend_algebraic[7] = "q_R_PKACI in component environment (fmol)"
    legend_states[0] = "q_L_B1 in component B1AR (fmol)"
    legend_states[1] = "q_R_B1 in component B1AR (fmol)"
    legend_states[2] = "q_Gs in component B1AR (fmol)"
    legend_states[3] = "q_LR_B1 in component B1AR (fmol)"
    legend_states[4] = "q_LR_B1Gs in component B1AR (fmol)"
    legend_states[5] = "q_B1d in component B1AR (fmol)"
    legend_states[6] = "q_BARK in component B1AR (fmol)"
    legend_states[7] = "q_LR_B1_BARK in component B1AR (fmol)"
    legend_states[8] = "q_LR_B1Gs_BARK in component B1AR (fmol)"
    legend_states[9] = "q_B1p in component B1AR (fmol)"
    legend_states[10] = "q_PKACI in component B1AR (fmol)"
    legend_states[11] = "q_R_PKACI in component B1AR (fmol)"
    legend_constants[11] = "kappa_B11 in component B1AR_parameters (fmol_per_sec)"
    legend_constants[12] = "kappa_B12 in component B1AR_parameters (fmol_per_sec)"
    legend_constants[13] = "kappa_B21 in component B1AR_parameters (fmol_per_sec)"
    legend_constants[14] = "kappa_B22 in component B1AR_parameters (fmol_per_sec)"
    legend_constants[15] = "kappa_P1 in component B1AR_parameters (fmol_per_sec)"
    legend_constants[16] = "kappa_P2 in component B1AR_parameters (fmol_per_sec)"
    legend_constants[17] = "K_L_B1 in component B1AR_parameters (per_fmol)"
    legend_constants[18] = "K_R_B1 in component B1AR_parameters (per_fmol)"
    legend_constants[19] = "K_Gs in component B1AR_parameters (per_fmol)"
    legend_constants[20] = "K_LR_B1 in component B1AR_parameters (per_fmol)"
    legend_constants[21] = "K_LR_B1Gs in component B1AR_parameters (per_fmol)"
    legend_constants[22] = "K_B1d in component B1AR_parameters (per_fmol)"
    legend_constants[23] = "K_BARK in component B1AR_parameters (per_fmol)"
    legend_constants[24] = "K_LR_B1_BARK in component B1AR_parameters (per_fmol)"
    legend_constants[25] = "K_LR_B1Gs_BARK in component B1AR_parameters (per_fmol)"
    legend_constants[26] = "K_B1p in component B1AR_parameters (per_fmol)"
    legend_constants[27] = "K_PKACI in component B1AR_parameters (per_fmol)"
    legend_constants[28] = "K_R_PKACI in component B1AR_parameters (per_fmol)"
    legend_constants[29] = "R in component constants (J_per_K_per_mol)"
    legend_constants[30] = "T in component constants (kelvin)"
    legend_algebraic[27] = "vB11 in component B1AR (fmol_per_sec)"
    legend_algebraic[28] = "vB12 in component B1AR (fmol_per_sec)"
    legend_algebraic[29] = "vB21 in component B1AR (fmol_per_sec)"
    legend_algebraic[30] = "vB22 in component B1AR (fmol_per_sec)"
    legend_algebraic[16] = "vP1 in component B1AR (fmol_per_sec)"
    legend_algebraic[18] = "vP2 in component B1AR (fmol_per_sec)"
    legend_algebraic[19] = "mu_L_B1 in component B1AR (J_per_mol)"
    legend_algebraic[9] = "mu_R_B1 in component B1AR (J_per_mol)"
    legend_algebraic[20] = "mu_Gs in component B1AR (J_per_mol)"
    legend_algebraic[21] = "mu_LR_B1 in component B1AR (J_per_mol)"
    legend_algebraic[22] = "mu_LR_B1Gs in component B1AR (J_per_mol)"
    legend_algebraic[23] = "mu_B1d in component B1AR (J_per_mol)"
    legend_algebraic[24] = "mu_BARK in component B1AR (J_per_mol)"
    legend_algebraic[25] = "mu_LR_B1_BARK in component B1AR (J_per_mol)"
    legend_algebraic[26] = "mu_LR_B1Gs_BARK in component B1AR (J_per_mol)"
    legend_algebraic[11] = "mu_B1p in component B1AR (J_per_mol)"
    legend_algebraic[13] = "mu_PKACI in component B1AR (J_per_mol)"
    legend_algebraic[15] = "mu_R_PKACI in component B1AR (J_per_mol)"
    legend_constants[31] = "F in component constants (C_per_mol)"
    legend_rates[0] = "d/dt q_L_B1 in component B1AR (fmol)"
    legend_rates[1] = "d/dt q_R_B1 in component B1AR (fmol)"
    legend_rates[2] = "d/dt q_Gs in component B1AR (fmol)"
    legend_rates[3] = "d/dt q_LR_B1 in component B1AR (fmol)"
    legend_rates[5] = "d/dt q_B1d in component B1AR (fmol)"
    legend_rates[6] = "d/dt q_BARK in component B1AR (fmol)"
    legend_rates[7] = "d/dt q_LR_B1_BARK in component B1AR (fmol)"
    legend_rates[4] = "d/dt q_LR_B1Gs in component B1AR (fmol)"
    legend_rates[8] = "d/dt q_LR_B1Gs_BARK in component B1AR (fmol)"
    legend_rates[9] = "d/dt q_B1p in component B1AR (fmol)"
    legend_rates[10] = "d/dt q_PKACI in component B1AR (fmol)"
    legend_rates[11] = "d/dt q_R_PKACI in component B1AR (fmol)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 0.00005
    constants[1] = 0.00015
    constants[2] = 0
    constants[3] = 0.0000508778
    constants[4] = 0
    constants[5] = 0.0228
    constants[6] = 0.0000508778
    constants[7] = 0.0000508778
    constants[8] = 0
    constants[9] = 0.000221209
    constants[10] = 0.008778
    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
    constants[11] = 0.000282928
    constants[12] = 128604
    constants[13] = 0.000200356
    constants[14] = 91071.1
    constants[15] = 2.28764e-05
    constants[16] = 10398.4
    constants[17] = 2.90698e-08
    constants[18] = 1849.44
    constants[19] = 0.0410501
    constants[20] = 0.0242248
    constants[21] = 0.0342084
    constants[22] = 2.90698e-08
    constants[23] = 0.226042
    constants[24] = 0.226042
    constants[25] = 0.319199
    constants[26] = 1.13021e-09
    constants[27] = 7.19049e-05
    constants[28] = 2.79561
    constants[29] = 8.31
    constants[30] = 310
    constants[31] = 96485
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[1] = states[1]+constants[0]
    algebraic[9] = constants[29]*constants[30]*log(constants[18]*algebraic[1])
    algebraic[5] = states[10]+constants[9]
    algebraic[13] = constants[29]*constants[30]*log(constants[27]*algebraic[5])
    algebraic[7] = states[11]+constants[10]
    algebraic[15] = constants[29]*constants[30]*log(constants[28]*algebraic[7])
    algebraic[16] = constants[15]*(exp((algebraic[9]+algebraic[13])/(constants[29]*constants[30]))-exp(algebraic[15]/(constants[29]*constants[30])))
    rates[1] = -algebraic[16]
    rates[9] = -algebraic[16]
    algebraic[3] = states[9]+constants[8]
    algebraic[11] = constants[29]*constants[30]*log(constants[26]*algebraic[3])
    algebraic[18] = constants[16]*(exp(algebraic[15]/(constants[29]*constants[30]))-exp((algebraic[13]+algebraic[11])/(constants[29]*constants[30])))
    rates[10] = algebraic[18]-algebraic[16]
    rates[11] = algebraic[16]-algebraic[18]
    algebraic[6] = states[3]+constants[2]
    algebraic[21] = constants[29]*constants[30]*log(constants[20]*algebraic[6])
    algebraic[12] = states[6]+constants[5]
    algebraic[24] = constants[29]*constants[30]*log(constants[23]*algebraic[12])
    algebraic[14] = states[7]+constants[6]
    algebraic[25] = constants[29]*constants[30]*log(constants[24]*algebraic[14])
    algebraic[27] = constants[11]*(exp((algebraic[21]+algebraic[24])/(constants[29]*constants[30]))-exp(algebraic[25]/(constants[29]*constants[30])))
    rates[3] = -algebraic[27]
    algebraic[0] = custom_piecewise([greater(sin(2.00000* pi*voi) , 0.100000), 0.000100000 , True, 1.00000e-06])
    algebraic[2] = states[0]+algebraic[0]
    algebraic[19] = constants[29]*constants[30]*log(constants[17]*algebraic[2])
    algebraic[10] = states[5]+constants[4]
    algebraic[23] = constants[29]*constants[30]*log(constants[22]*algebraic[10])
    algebraic[28] = constants[12]*(exp(algebraic[25]/(constants[29]*constants[30]))-exp((algebraic[24]+algebraic[23]+algebraic[19])/(constants[29]*constants[30])))
    rates[7] = algebraic[27]-algebraic[28]
    algebraic[8] = states[4]+constants[3]
    algebraic[22] = constants[29]*constants[30]*log(constants[21]*algebraic[8])
    algebraic[17] = states[8]+constants[7]
    algebraic[26] = constants[29]*constants[30]*log(constants[25]*algebraic[17])
    algebraic[29] = constants[13]*(exp((algebraic[22]+algebraic[24])/(constants[29]*constants[30]))-exp(algebraic[26]/(constants[29]*constants[30])))
    rates[4] = -algebraic[29]
    algebraic[4] = states[2]+constants[1]
    algebraic[20] = constants[29]*constants[30]*log(constants[19]*algebraic[4])
    algebraic[30] = constants[14]*(exp(algebraic[26]/(constants[29]*constants[30]))-exp((algebraic[24]+algebraic[23]+algebraic[19]+algebraic[20])/(constants[29]*constants[30])))
    rates[0] = algebraic[28]+algebraic[30]
    rates[2] = algebraic[30]
    rates[5] = algebraic[28]+algebraic[30]
    rates[6] = ((algebraic[28]+algebraic[30])-algebraic[27])-algebraic[29]
    rates[8] = algebraic[29]-algebraic[30]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[1] = states[1]+constants[0]
    algebraic[9] = constants[29]*constants[30]*log(constants[18]*algebraic[1])
    algebraic[5] = states[10]+constants[9]
    algebraic[13] = constants[29]*constants[30]*log(constants[27]*algebraic[5])
    algebraic[7] = states[11]+constants[10]
    algebraic[15] = constants[29]*constants[30]*log(constants[28]*algebraic[7])
    algebraic[16] = constants[15]*(exp((algebraic[9]+algebraic[13])/(constants[29]*constants[30]))-exp(algebraic[15]/(constants[29]*constants[30])))
    algebraic[3] = states[9]+constants[8]
    algebraic[11] = constants[29]*constants[30]*log(constants[26]*algebraic[3])
    algebraic[18] = constants[16]*(exp(algebraic[15]/(constants[29]*constants[30]))-exp((algebraic[13]+algebraic[11])/(constants[29]*constants[30])))
    algebraic[6] = states[3]+constants[2]
    algebraic[21] = constants[29]*constants[30]*log(constants[20]*algebraic[6])
    algebraic[12] = states[6]+constants[5]
    algebraic[24] = constants[29]*constants[30]*log(constants[23]*algebraic[12])
    algebraic[14] = states[7]+constants[6]
    algebraic[25] = constants[29]*constants[30]*log(constants[24]*algebraic[14])
    algebraic[27] = constants[11]*(exp((algebraic[21]+algebraic[24])/(constants[29]*constants[30]))-exp(algebraic[25]/(constants[29]*constants[30])))
    algebraic[0] = custom_piecewise([greater(sin(2.00000* pi*voi) , 0.100000), 0.000100000 , True, 1.00000e-06])
    algebraic[2] = states[0]+algebraic[0]
    algebraic[19] = constants[29]*constants[30]*log(constants[17]*algebraic[2])
    algebraic[10] = states[5]+constants[4]
    algebraic[23] = constants[29]*constants[30]*log(constants[22]*algebraic[10])
    algebraic[28] = constants[12]*(exp(algebraic[25]/(constants[29]*constants[30]))-exp((algebraic[24]+algebraic[23]+algebraic[19])/(constants[29]*constants[30])))
    algebraic[8] = states[4]+constants[3]
    algebraic[22] = constants[29]*constants[30]*log(constants[21]*algebraic[8])
    algebraic[17] = states[8]+constants[7]
    algebraic[26] = constants[29]*constants[30]*log(constants[25]*algebraic[17])
    algebraic[29] = constants[13]*(exp((algebraic[22]+algebraic[24])/(constants[29]*constants[30]))-exp(algebraic[26]/(constants[29]*constants[30])))
    algebraic[4] = states[2]+constants[1]
    algebraic[20] = constants[29]*constants[30]*log(constants[19]*algebraic[4])
    algebraic[30] = constants[14]*(exp(algebraic[26]/(constants[29]*constants[30]))-exp((algebraic[24]+algebraic[23]+algebraic[19]+algebraic[20])/(constants[29]*constants[30])))
    return algebraic

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)