# Size of variable arrays: sizeAlgebraic = 16 sizeStates = 6 sizeConstants = 11 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_constants[0] = "RT in component main (J_per_mol)" 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_e0 in component main (mole)" legend_states[5] = "q_e1 in component main (mole)" legend_algebraic[14] = "v_1 in component main (mol_per_s)" legend_algebraic[15] = "v_2 in component main (mol_per_s)" legend_algebraic[0] = "u_1 in component main (J_per_mol)" legend_algebraic[2] = "u_2 in component main (J_per_mol)" legend_algebraic[4] = "u_3 in component main (J_per_mol)" legend_algebraic[6] = "u_4 in component main (J_per_mol)" legend_algebraic[8] = "u_e0 in component main (J_per_mol)" legend_algebraic[11] = "u_e1 in component main (J_per_mol)" legend_algebraic[9] = "u_f_1 in component main (J_per_mol)" legend_algebraic[12] = "u_r_1 in component main (J_per_mol)" legend_algebraic[13] = "u_f_2 in component main (J_per_mol)" legend_algebraic[10] = "u_r_2 in component main (J_per_mol)" legend_constants[1] = "K_q_1 in component main (per_mol)" legend_constants[2] = "K_q_2 in component main (per_mol)" legend_constants[3] = "K_q_3 in component main (per_mol)" legend_constants[4] = "K_q_4 in component main (per_mol)" legend_constants[5] = "K_q_e0 in component main (per_mol)" legend_constants[6] = "K_q_e1 in component main (per_mol)" legend_constants[7] = "kappa_1 in component main (mol_per_s)" legend_constants[8] = "kappa_2 in component main (mol_per_s)" legend_algebraic[1] = "q_e_tot in component main (mole)" legend_algebraic[3] = "A_f in component main (per_mol3_per_s)" legend_algebraic[5] = "A_r in component main (per_mol3_per_s)" legend_constants[9] = "B_f in component main (per_mol3)" legend_constants[10] = "B_r in component main (per_mol3)" legend_algebraic[7] = "v_SS 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_e0 in component main (mole)" legend_rates[5] = "d/dt q_e1 in component main (mole)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 2578.73058 states[0] = 3 states[1] = 1 states[2] = 0 states[3] = 0 states[4] = 1 states[5] = 1 constants[1] = 2 constants[2] = 2 constants[3] = 2 constants[4] = 2 constants[5] = 2 constants[6] = 2 constants[7] = 0.20 constants[8] = 0.1 constants[9] = (((constants[5]/constants[6])*constants[7])/(constants[7]+constants[8]))*constants[1]*(power(constants[2], 2.00000)) constants[10] = (((constants[5]/constants[6])*constants[7])/(constants[7]+constants[8]))*constants[3]*(power(constants[4], 2.00000)) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = constants[0]*log(constants[1]*states[0]) algebraic[2] = constants[0]*log(constants[2]*states[1]) algebraic[8] = constants[0]*log(constants[5]*states[4]) algebraic[9] = algebraic[0]+2.00000*algebraic[2]+algebraic[8] algebraic[11] = constants[0]*log(constants[6]*states[5]) algebraic[12] = algebraic[11] algebraic[14] = constants[7]*(exp(algebraic[9]/constants[0])-exp(algebraic[12]/constants[0])) rates[0] = -algebraic[14] rates[1] = -2.00000*algebraic[14] algebraic[13] = algebraic[11] algebraic[4] = constants[0]*log(constants[3]*states[2]) algebraic[6] = constants[0]*log(constants[4]*states[3]) algebraic[10] = algebraic[4]+2.00000*algebraic[6]+algebraic[8] algebraic[15] = constants[8]*(exp(algebraic[13]/constants[0])-exp(algebraic[10]/constants[0])) rates[2] = algebraic[15] rates[3] = 2.00000*algebraic[15] rates[4] = algebraic[15]-algebraic[14] rates[5] = algebraic[14]-algebraic[15] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[0]*log(constants[1]*states[0]) algebraic[2] = constants[0]*log(constants[2]*states[1]) algebraic[8] = constants[0]*log(constants[5]*states[4]) algebraic[9] = algebraic[0]+2.00000*algebraic[2]+algebraic[8] algebraic[11] = constants[0]*log(constants[6]*states[5]) algebraic[12] = algebraic[11] algebraic[14] = constants[7]*(exp(algebraic[9]/constants[0])-exp(algebraic[12]/constants[0])) algebraic[13] = algebraic[11] algebraic[4] = constants[0]*log(constants[3]*states[2]) algebraic[6] = constants[0]*log(constants[4]*states[3]) algebraic[10] = algebraic[4]+2.00000*algebraic[6]+algebraic[8] algebraic[15] = constants[8]*(exp(algebraic[13]/constants[0])-exp(algebraic[10]/constants[0])) algebraic[1] = states[4]+states[5] algebraic[3] = ((algebraic[1]*constants[5]*constants[7]*constants[8])/(constants[7]+constants[8]))*constants[1]*(power(constants[2], 2.00000)) algebraic[5] = ((algebraic[1]*constants[5]*constants[7]*constants[8])/(constants[7]+constants[8]))*constants[3]*(power(constants[4], 2.00000)) algebraic[7] = (algebraic[3]*states[0]*(power(states[1], 2.00000))-algebraic[5]*states[2]*(power(states[3], 2.00000)))/(1.00000+constants[9]*states[0]*(power(states[1], 2.00000))+constants[10]*states[2]*(power(states[3], 2.00000))) 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)