# Size of variable arrays: sizeAlgebraic = 6 sizeStates = 6 sizeConstants = 21 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 AE1 (second)" legend_constants[0] = "RT in component param (kJ_per_mol)" legend_constants[1] = "K_Cl_o in component param (per_mol)" legend_constants[2] = "K_Cl_i in component param (per_mol)" legend_constants[3] = "K_HCO3_i in component param (per_mol)" legend_constants[4] = "K_HCO3_o in component param (per_mol)" legend_constants[5] = "K_E_o in component param (per_mol)" legend_constants[6] = "K_ECl_o in component param (per_mol)" legend_constants[7] = "K_ECl_i in component param (per_mol)" legend_constants[8] = "K_E_i in component param (per_mol)" legend_constants[9] = "K_EHCO3_i in component param (per_mol)" legend_constants[10] = "K_EHCO3_o in component param (per_mol)" legend_constants[11] = "K_Re1 in component param (mM_per_s)" legend_constants[12] = "K_Re2 in component param (mM_per_s)" legend_constants[13] = "K_Re3 in component param (mM_per_s)" legend_constants[14] = "K_Re4 in component param (mM_per_s)" legend_constants[15] = "K_Re5 in component param (mM_per_s)" legend_constants[16] = "K_Re6 in component param (mM_per_s)" legend_constants[17] = "q_Cl_o in component AE1 (mole)" legend_constants[18] = "q_Cl_i in component AE1 (mole)" legend_constants[19] = "q_HCO3_i in component AE1 (mole)" legend_constants[20] = "q_HCO3_o in component AE1 (mole)" legend_states[0] = "q_E_o in component AE1 (mole)" legend_states[1] = "q_ECl_o in component AE1 (mole)" legend_states[2] = "q_ECl_i in component AE1 (mole)" legend_states[3] = "q_E_i in component AE1 (mole)" legend_states[4] = "q_EHCO3_i in component AE1 (mole)" legend_states[5] = "q_EHCO3_o in component AE1 (mole)" legend_algebraic[0] = "v_Re1 in component AE1 (mM_per_s)" legend_algebraic[1] = "v_Re2 in component AE1 (mM_per_s)" legend_algebraic[2] = "v_Re3 in component AE1 (mM_per_s)" legend_algebraic[3] = "v_Re4 in component AE1 (mM_per_s)" legend_algebraic[4] = "v_Re5 in component AE1 (mM_per_s)" legend_algebraic[5] = "v_Re6 in component AE1 (mM_per_s)" legend_rates[0] = "d/dt q_E_o in component AE1 (mole)" legend_rates[1] = "d/dt q_ECl_o in component AE1 (mole)" legend_rates[2] = "d/dt q_ECl_i in component AE1 (mole)" legend_rates[3] = "d/dt q_E_i in component AE1 (mole)" legend_rates[4] = "d/dt q_EHCO3_i in component AE1 (mole)" legend_rates[5] = "d/dt q_EHCO3_o in component AE1 (mole)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 2.5 constants[1] = 1.34784535e+00 constants[2] = 1.34809503e+00 constants[3] = 8.37243345e-01 constants[4] = 8.37398440e-01 constants[5] = 3.42812779e+00 constants[6] = 2.30943735e+02 constants[7] = 2.50575623e+01 constants[8] = 3.71610024e-01 constants[9] = 6.15805309e+01 constants[10] = 5.68610961e+02 constants[11] = 2.16462852e+01 constants[12] = 2.43394395e+00 constants[13] = 1.99577523e+02 constants[14] = 3.21470643e+02 constants[15] = 2.19265742e+00 constants[16] = 3.48281500e+01 constants[17] = 114 constants[18] = 29 constants[19] = 0.0 constants[20] = 26 states[0] = 0.01738 states[1] = 0.0396 states[2] = 0.274 states[3] = 0.473 states[4] = 0.0621 states[5] = 0.00228 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = constants[11]*(constants[1]*constants[17]*constants[5]*states[0]-constants[6]*states[1]) algebraic[1] = constants[12]*(constants[6]*states[1]-constants[7]*states[2]) rates[1] = algebraic[0]-algebraic[1] algebraic[2] = constants[13]*(constants[7]*states[2]-constants[2]*constants[18]*constants[8]*states[3]) rates[2] = algebraic[1]-algebraic[2] algebraic[3] = constants[14]*(constants[3]*constants[19]*constants[8]*states[3]-constants[9]*states[4]) rates[3] = algebraic[2]-algebraic[3] algebraic[4] = constants[15]*(constants[9]*states[4]-constants[10]*states[5]) rates[4] = algebraic[3]-algebraic[4] algebraic[5] = constants[16]*(constants[10]*states[5]-constants[4]*constants[20]*constants[5]*states[0]) rates[0] = algebraic[5]-algebraic[0] rates[5] = algebraic[4]-algebraic[5] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[11]*(constants[1]*constants[17]*constants[5]*states[0]-constants[6]*states[1]) algebraic[1] = constants[12]*(constants[6]*states[1]-constants[7]*states[2]) algebraic[2] = constants[13]*(constants[7]*states[2]-constants[2]*constants[18]*constants[8]*states[3]) algebraic[3] = constants[14]*(constants[3]*constants[19]*constants[8]*states[3]-constants[9]*states[4]) algebraic[4] = constants[15]*(constants[9]*states[4]-constants[10]*states[5]) algebraic[5] = constants[16]*(constants[10]*states[5]-constants[4]*constants[20]*constants[5]*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)