# Size of variable arrays: sizeAlgebraic = 7 sizeStates = 5 sizeConstants = 23 from math import * from numpy import * def createLegends(): legend_states = [""] * sizeStates legend_rates = [""] * sizeStates legend_algebraic = [""] * sizeAlgebraic legend_voi = "" legend_constants = [""] * sizeConstants legend_voi = "t in component main (second)" legend_states[0] = "q_1 in component main (mole)" legend_states[1] = "q_2 in component main (mole)" legend_states[2] = "q_3 in component main (mole)" legend_states[3] = "q_4 in component main (mole)" legend_states[4] = "q_5 in component main (mole)" legend_algebraic[0] = "q_6 in component main (mole)" legend_constants[0] = "q_tot in component main (mole)" legend_algebraic[3] = "v_1 in component main (mol_per_s)" legend_algebraic[4] = "v_2 in component main (mol_per_s)" legend_algebraic[5] = "v_3 in component main (mol_per_s)" legend_algebraic[6] = "v_4 in component main (mol_per_s)" legend_constants[1] = "kappa_1 in component main (mol_per_s)" legend_constants[2] = "kappa_2 in component main (mol_per_s)" legend_constants[3] = "kappa_3 in component main (mol_per_s)" legend_constants[4] = "kappa_4 in component main (mol_per_s)" legend_constants[5] = "K_1 in component main (per_mol)" legend_constants[6] = "K_2 in component main (per_mol)" legend_constants[7] = "K_s in component main (per_mol)" legend_constants[8] = "K_3 in component main (per_mol)" legend_constants[9] = "K_4 in component main (per_mol)" legend_constants[10] = "K_5 in component main (per_mol)" legend_constants[11] = "K_6 in component main (per_mol)" legend_constants[12] = "K_m in component main (per_mol)" legend_constants[13] = "k_m in component main (mole)" legend_constants[14] = "v_max in component main (mol_per_s)" legend_constants[15] = "k_f_1 in component main (per_mol_per_s)" legend_constants[16] = "k_r_1 in component main (per_s)" legend_constants[17] = "k_f_2 in component main (per_s)" legend_constants[18] = "k_r_2 in component main (per_mol_per_s)" legend_constants[19] = "k_f_3 in component main (per_s)" legend_constants[20] = "k_r_3 in component main (per_s)" legend_constants[21] = "k_f_4 in component main (per_s)" legend_constants[22] = "k_r_4 in component main (per_s)" legend_algebraic[1] = "v_SF in component main (mol_per_s)" legend_algebraic[2] = "v_MM in component main (mol_per_s)" legend_rates[0] = "d/dt q_1 in component main (mole)" legend_rates[1] = "d/dt q_2 in component main (mole)" legend_rates[2] = "d/dt q_3 in component main (mole)" legend_rates[3] = "d/dt q_4 in component main (mole)" legend_rates[4] = "d/dt q_5 in component main (mole)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 100 states[1] = 0 states[2] = 0 states[3] = 0 states[4] = 0 constants[0] = 1 constants[1] = 100 constants[2] = 100 constants[3] = 1 constants[4] = 0.1 constants[5] = 0.1 constants[6] = 0.1 constants[7] = 0.1 constants[8] = 1 constants[9] = 1 constants[10] = 1 constants[11] = 1 constants[12] = 1 constants[13] = 2.00000/(constants[7]*(1.00000+constants[3]/constants[4])) constants[14] = (constants[0]*constants[3]*constants[12])/(1.00000+constants[3]/constants[4]) constants[15] = constants[1]*constants[5]*constants[11] constants[16] = constants[1]*constants[8] constants[17] = constants[2]*constants[9] constants[18] = constants[2]*constants[6]*constants[10] constants[19] = constants[3]*constants[8] constants[20] = constants[3]*constants[9] constants[21] = constants[4]*constants[10] constants[22] = constants[4]*constants[11] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = ((constants[0]-states[2])-states[3])-states[4] algebraic[3] = constants[15]*states[0]*algebraic[0]-constants[16]*states[2] rates[0] = -algebraic[3] algebraic[4] = constants[17]*states[3]-constants[18]*states[1]*states[4] rates[1] = algebraic[4]-1000.00*states[1] algebraic[5] = constants[19]*states[2]-constants[20]*states[3] rates[2] = algebraic[3]-algebraic[5] rates[3] = algebraic[5]-algebraic[4] algebraic[6] = constants[21]*states[4]-constants[22]*algebraic[0] rates[4] = algebraic[4]-algebraic[6] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = ((constants[0]-states[2])-states[3])-states[4] algebraic[3] = constants[15]*states[0]*algebraic[0]-constants[16]*states[2] algebraic[4] = constants[17]*states[3]-constants[18]*states[1]*states[4] algebraic[5] = constants[19]*states[2]-constants[20]*states[3] algebraic[6] = constants[21]*states[4]-constants[22]*algebraic[0] algebraic[1] = (constants[0]*constants[3]*constants[4]*constants[12]*constants[7]*(states[0]-states[1]))/(2.00000*constants[4]+(constants[3]+constants[4])*constants[7]*(states[0]+states[1])+2.00000*constants[3]*constants[7]*constants[7]*states[0]*states[1]) algebraic[2] = (constants[14]*states[0])/(constants[13]+states[0]) 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)