# Size of variable arrays:
sizeAlgebraic = 22
sizeStates = 11
sizeConstants = 25
from math import *
from numpy import *

def createLegends():
    legend_states = [""] * sizeStates
    legend_rates = [""] * sizeStates
    legend_algebraic = [""] * sizeAlgebraic
    legend_voi = ""
    legend_constants = [""] * sizeConstants
    legend_constants[0] = "kappa_R_1a_cGMP in component BG_parameters (fmol_per_sec)"
    legend_constants[1] = "kappa_R_1b_cGMP in component BG_parameters (fmol_per_sec)"
    legend_constants[2] = "kappa_R_2a_cGMP in component BG_parameters (fmol_per_sec)"
    legend_constants[3] = "kappa_R_2b_cGMP in component BG_parameters (fmol_per_sec)"
    legend_constants[4] = "kappa_R_1_sGC in component BG_parameters (fmol_per_sec)"
    legend_constants[5] = "kappa_R_2_sGC in component BG_parameters (fmol_per_sec)"
    legend_constants[6] = "kappa_R_3_sGC in component BG_parameters (fmol_per_sec)"
    legend_constants[7] = "kappa_R_4_sGC in component BG_parameters (fmol_per_sec)"
    legend_constants[8] = "kappa_R_DNO_sGC in component BG_parameters (fmol_per_sec)"
    legend_constants[9] = "K_GTP in component BG_parameters (per_fmol)"
    legend_constants[10] = "K_E5c in component BG_parameters (per_fmol)"
    legend_constants[11] = "K_cGMP in component BG_parameters (per_fmol)"
    legend_constants[12] = "K_PDE in component BG_parameters (per_fmol)"
    legend_constants[13] = "K_GTP_E5c in component BG_parameters (per_fmol)"
    legend_constants[14] = "K_cGMP_PDE in component BG_parameters (per_fmol)"
    legend_constants[15] = "K_GMP in component BG_parameters (per_fmol)"
    legend_constants[16] = "K_Eb in component BG_parameters (per_fmol)"
    legend_constants[17] = "K_NO in component BG_parameters (per_fmol)"
    legend_constants[18] = "K_E6c in component BG_parameters (per_fmol)"
    legend_constants[19] = "K_NO_product in component BG_parameters (per_fmol)"
    legend_voi = "t in component environment (second)"
    legend_constants[20] = "vol_myo in component environment (pL)"
    legend_states[0] = "q_cGMP in component environment (fmol)"
    legend_states[1] = "q_GTP in component environment (fmol)"
    legend_states[2] = "q_E5c in component environment (fmol)"
    legend_states[3] = "q_PDE in component environment (fmol)"
    legend_states[4] = "q_GTP_E5c in component environment (fmol)"
    legend_states[5] = "q_cGMP_PDE in component environment (fmol)"
    legend_states[6] = "q_GMP in component environment (fmol)"
    legend_states[7] = "q_Eb in component environment (fmol)"
    legend_states[8] = "q_NO in component environment (fmol)"
    legend_states[9] = "q_E6c in component environment (fmol)"
    legend_states[10] = "q_NO_product in component environment (fmol)"
    legend_algebraic[7] = "v_R_1a_cGMP in component cGMP (fmol_per_sec)"
    legend_algebraic[8] = "v_R_1b_cGMP in component cGMP (fmol_per_sec)"
    legend_algebraic[9] = "v_R_2a_cGMP in component cGMP (fmol_per_sec)"
    legend_algebraic[10] = "v_R_2b_cGMP in component cGMP (fmol_per_sec)"
    legend_algebraic[17] = "v_R_1_sGC in component sGC (fmol_per_sec)"
    legend_algebraic[18] = "v_R_2_sGC in component sGC (fmol_per_sec)"
    legend_algebraic[19] = "v_R_3_sGC in component sGC (fmol_per_sec)"
    legend_algebraic[20] = "v_R_4_sGC in component sGC (fmol_per_sec)"
    legend_algebraic[21] = "v_R_DNO_sGC in component sGC (fmol_per_sec)"
    legend_constants[21] = "v_NO_generation in component environment (fmol_per_sec)"
    legend_constants[22] = "R in component constants (J_per_K_per_mol)"
    legend_constants[23] = "T in component constants (kelvin)"
    legend_constants[24] = "F in component constants (C_per_mol)"
    legend_algebraic[0] = "mu_GTP in component cGMP (J_per_mol)"
    legend_algebraic[1] = "mu_E5c in component cGMP (J_per_mol)"
    legend_algebraic[2] = "mu_cGMP in component cGMP (J_per_mol)"
    legend_algebraic[3] = "mu_PDE in component cGMP (J_per_mol)"
    legend_algebraic[4] = "mu_GTP_E5c in component cGMP (J_per_mol)"
    legend_algebraic[5] = "mu_cGMP_PDE in component cGMP (J_per_mol)"
    legend_algebraic[6] = "mu_GMP in component cGMP (J_per_mol)"
    legend_algebraic[11] = "mu_Eb in component sGC (J_per_mol)"
    legend_algebraic[12] = "mu_NO in component sGC (J_per_mol)"
    legend_algebraic[13] = "mu_E6c in component sGC (J_per_mol)"
    legend_algebraic[14] = "mu_E5c in component sGC (J_per_mol)"
    legend_algebraic[15] = "mu_cGMP in component sGC (J_per_mol)"
    legend_algebraic[16] = "mu_NO_product in component sGC (J_per_mol)"
    legend_rates[0] = "d/dt q_cGMP in component environment (fmol)"
    legend_rates[1] = "d/dt q_GTP in component environment (fmol)"
    legend_rates[2] = "d/dt q_E5c in component environment (fmol)"
    legend_rates[3] = "d/dt q_PDE in component environment (fmol)"
    legend_rates[4] = "d/dt q_GTP_E5c in component environment (fmol)"
    legend_rates[5] = "d/dt q_cGMP_PDE in component environment (fmol)"
    legend_rates[6] = "d/dt q_GMP in component environment (fmol)"
    legend_rates[7] = "d/dt q_Eb in component environment (fmol)"
    legend_rates[8] = "d/dt q_NO in component environment (fmol)"
    legend_rates[9] = "d/dt q_E6c in component environment (fmol)"
    legend_rates[10] = "d/dt q_NO_product 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] = 192.663
    constants[1] = 0.00328297
    constants[2] = 56591.2
    constants[3] = 0.0110353
    constants[4] = 3.61127e+06
    constants[5] = 0.00328297
    constants[6] = 4.92446
    constants[7] = 0.0361127
    constants[8] = 0.01
    constants[9] = 17040
    constants[10] = 0.304602
    constants[11] = 1
    constants[12] = 17.6706
    constants[13] = 5190.42
    constants[14] = 35.3412
    constants[15] = 0.0051282
    constants[16] = 0.0276911
    constants[17] = 1
    constants[18] = 30.4602
    constants[19] = 0.1
    constants[20] = 1
    states[0] = 1e-6
    states[1] = 0.0005
    states[2] = 1e-16
    states[3] = 1e-10
    states[4] = 1e-16
    states[5] = 1e-16
    states[6] = 1e-16
    states[7] = 1e-6
    states[8] = 0.00836
    states[9] = 1e-16
    states[10] = 1e-16
    constants[21] = 0.000114
    constants[22] = 8.31
    constants[23] = 310
    constants[24] = 96485
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = constants[22]*constants[23]*log(constants[9]*states[1])
    algebraic[1] = constants[22]*constants[23]*log(constants[10]*states[2])
    algebraic[4] = constants[22]*constants[23]*log(constants[13]*states[4])
    algebraic[7] = constants[0]*(exp((algebraic[0]+algebraic[1])/(constants[22]*constants[23]))-exp(algebraic[4]/(constants[22]*constants[23])))
    rates[1] = -algebraic[7]
    algebraic[2] = constants[22]*constants[23]*log(constants[11]*states[0])
    algebraic[8] = constants[1]*(exp(algebraic[4]/(constants[22]*constants[23]))-exp((algebraic[2]+algebraic[1])/(constants[22]*constants[23])))
    rates[4] = algebraic[7]-algebraic[8]
    algebraic[3] = constants[22]*constants[23]*log(constants[12]*states[3])
    algebraic[5] = constants[22]*constants[23]*log(constants[14]*states[5])
    algebraic[9] = constants[2]*(exp((algebraic[2]+algebraic[3])/(constants[22]*constants[23]))-exp(algebraic[5]/(constants[22]*constants[23])))
    algebraic[6] = constants[22]*constants[23]*log(constants[15]*states[6])
    algebraic[10] = constants[3]*(exp((algebraic[5]+algebraic[2])/(constants[22]*constants[23]))-exp((algebraic[6]+algebraic[3])/(constants[22]*constants[23])))
    rates[3] = -algebraic[9]+algebraic[10]
    rates[5] = algebraic[9]-algebraic[10]
    rates[6] = algebraic[10]
    algebraic[11] = constants[22]*constants[23]*log(constants[16]*states[7])
    algebraic[12] = constants[22]*constants[23]*log(constants[17]*states[8])
    algebraic[13] = constants[22]*constants[23]*log(constants[18]*states[9])
    algebraic[17] = constants[4]*(exp((algebraic[11]+algebraic[12])/(constants[22]*constants[23]))-exp(algebraic[13]/(constants[22]*constants[23])))
    algebraic[14] = constants[22]*constants[23]*log(constants[10]*states[2])
    algebraic[18] = constants[5]*(exp(algebraic[13]/(constants[22]*constants[23]))-exp(algebraic[14]/(constants[22]*constants[23])))
    algebraic[19] = constants[6]*(exp((algebraic[13]+algebraic[12])/(constants[22]*constants[23]))-exp((algebraic[14]+algebraic[12])/(constants[22]*constants[23])))
    rates[9] = (algebraic[17]-algebraic[18])-algebraic[19]
    algebraic[15] = constants[22]*constants[23]*log(constants[11]*states[0])
    algebraic[20] = constants[7]*(exp((algebraic[14]+algebraic[15]*2.00000)/(constants[22]*constants[23]))-exp((algebraic[11]+algebraic[12])/(constants[22]*constants[23])))
    rates[0] = ((algebraic[8]-algebraic[9])-algebraic[10])-2.00000*algebraic[20]
    rates[2] = (-algebraic[7]+algebraic[8]+algebraic[18]+algebraic[19])-algebraic[20]
    rates[7] = -algebraic[17]+algebraic[20]
    algebraic[16] = constants[22]*constants[23]*log(constants[19]*states[10])
    algebraic[21] = constants[8]*(exp(algebraic[12]/(constants[22]*constants[23]))-exp(algebraic[16]/(constants[22]*constants[23])))
    rates[8] = ((-algebraic[17]+algebraic[20])-algebraic[21])+constants[21]
    rates[10] = algebraic[21]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = constants[22]*constants[23]*log(constants[9]*states[1])
    algebraic[1] = constants[22]*constants[23]*log(constants[10]*states[2])
    algebraic[4] = constants[22]*constants[23]*log(constants[13]*states[4])
    algebraic[7] = constants[0]*(exp((algebraic[0]+algebraic[1])/(constants[22]*constants[23]))-exp(algebraic[4]/(constants[22]*constants[23])))
    algebraic[2] = constants[22]*constants[23]*log(constants[11]*states[0])
    algebraic[8] = constants[1]*(exp(algebraic[4]/(constants[22]*constants[23]))-exp((algebraic[2]+algebraic[1])/(constants[22]*constants[23])))
    algebraic[3] = constants[22]*constants[23]*log(constants[12]*states[3])
    algebraic[5] = constants[22]*constants[23]*log(constants[14]*states[5])
    algebraic[9] = constants[2]*(exp((algebraic[2]+algebraic[3])/(constants[22]*constants[23]))-exp(algebraic[5]/(constants[22]*constants[23])))
    algebraic[6] = constants[22]*constants[23]*log(constants[15]*states[6])
    algebraic[10] = constants[3]*(exp((algebraic[5]+algebraic[2])/(constants[22]*constants[23]))-exp((algebraic[6]+algebraic[3])/(constants[22]*constants[23])))
    algebraic[11] = constants[22]*constants[23]*log(constants[16]*states[7])
    algebraic[12] = constants[22]*constants[23]*log(constants[17]*states[8])
    algebraic[13] = constants[22]*constants[23]*log(constants[18]*states[9])
    algebraic[17] = constants[4]*(exp((algebraic[11]+algebraic[12])/(constants[22]*constants[23]))-exp(algebraic[13]/(constants[22]*constants[23])))
    algebraic[14] = constants[22]*constants[23]*log(constants[10]*states[2])
    algebraic[18] = constants[5]*(exp(algebraic[13]/(constants[22]*constants[23]))-exp(algebraic[14]/(constants[22]*constants[23])))
    algebraic[19] = constants[6]*(exp((algebraic[13]+algebraic[12])/(constants[22]*constants[23]))-exp((algebraic[14]+algebraic[12])/(constants[22]*constants[23])))
    algebraic[15] = constants[22]*constants[23]*log(constants[11]*states[0])
    algebraic[20] = constants[7]*(exp((algebraic[14]+algebraic[15]*2.00000)/(constants[22]*constants[23]))-exp((algebraic[11]+algebraic[12])/(constants[22]*constants[23])))
    algebraic[16] = constants[22]*constants[23]*log(constants[19]*states[10])
    algebraic[21] = constants[8]*(exp(algebraic[12]/(constants[22]*constants[23]))-exp(algebraic[16]/(constants[22]*constants[23])))
    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)