# Size of variable arrays: sizeAlgebraic = 9 sizeStates = 5 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 = "time in component environment (dimensionless)" legend_algebraic[0] = "f in component f (dimensionless)" legend_constants[0] = "a in component f (dimensionless)" legend_states[0] = "r in component r (dimensionless)" legend_constants[1] = "p in component model_parameters (dimensionless)" legend_constants[2] = "beta in component r (dimensionless)" legend_constants[3] = "alpha in component r (dimensionless)" legend_algebraic[5] = "ur0 in component ur0 (dimensionless)" legend_algebraic[3] = "m in component m (dimensionless)" legend_constants[4] = "r0 in component model_parameters (dimensionless)" legend_algebraic[4] = "y in component y (dimensionless)" legend_constants[5] = "r1 in component model_parameters (dimensionless)" legend_algebraic[2] = "ur1 in component ur1 (dimensionless)" legend_algebraic[6] = "z in component z (dimensionless)" legend_constants[6] = "t1 in component model_parameters (dimensionless)" legend_states[1] = "x1 in component x1 (dimensionless)" legend_algebraic[8] = "q in component q (dimensionless)" legend_constants[7] = "d in component q (dimensionless)" legend_constants[8] = "k in component q (dimensionless)" legend_algebraic[7] = "uz in component uz (dimensionless)" legend_states[2] = "x2 in component x2 (dimensionless)" legend_constants[9] = "t2 in component model_parameters (dimensionless)" legend_states[3] = "x3 in component x3 (dimensionless)" legend_algebraic[1] = "phi in component phi (dimensionless)" legend_states[4] = "h in component h (dimensionless)" legend_constants[10] = "t4 in component model_parameters (dimensionless)" legend_rates[0] = "d/dt r in component r (dimensionless)" legend_rates[1] = "d/dt x1 in component x1 (dimensionless)" legend_rates[2] = "d/dt x2 in component x2 (dimensionless)" legend_rates[3] = "d/dt x3 in component x3 (dimensionless)" legend_rates[4] = "d/dt h in component h (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 1.0 states[0] = 0.5 constants[1] = 1.05 constants[2] = 1.0 constants[3] = 1.0 constants[4] = 0.5 constants[5] = 1.2 constants[6] = 0.1 states[1] = 0.0 constants[7] = 5.0 constants[8] = 10.5 states[2] = 0.0 constants[9] = 0.5 states[3] = 0.0 states[4] = 0.0 constants[10] = 20.0 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[3] = (states[2]-states[3])/constants[9] algebraic[0] = constants[0]*constants[1]*(power(states[0], 4.00000)) rates[4] = (algebraic[0]-states[4])/constants[10] algebraic[2] = custom_piecewise([greater(states[0] , constants[5]), 1.00000 , True, 0.00000]) algebraic[4] = (states[0]-constants[5])*algebraic[2] rates[1] = (algebraic[4]-states[1])/constants[6] algebraic[5] = custom_piecewise([greater(states[0] , constants[4]), 1.00000 , True, 0.00000]) algebraic[1] = custom_piecewise([less(states[0] , 0.250000), 0.00000 , greater(states[0] , 2.00000), 0.00000 , True, 1.00000-1.30612*(states[0]-1.12500)*(states[0]-1.12500)]) algebraic[3] = states[3]*algebraic[1] rates[0] = constants[2]*(constants[1]*states[0]-(constants[3]*(power(states[0]-constants[4], 2.00000))*algebraic[5]+algebraic[3])) algebraic[6] = (algebraic[4]-states[1])/constants[6] algebraic[7] = custom_piecewise([greater(algebraic[6] , 0.00000), 1.00000 , True, 0.00000]) algebraic[8] = constants[8]*(1.00000-exp(-(constants[7]*algebraic[6])))*algebraic[7] rates[2] = (algebraic[8]-states[2])/constants[9] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[0]*constants[1]*(power(states[0], 4.00000)) algebraic[2] = custom_piecewise([greater(states[0] , constants[5]), 1.00000 , True, 0.00000]) algebraic[4] = (states[0]-constants[5])*algebraic[2] algebraic[5] = custom_piecewise([greater(states[0] , constants[4]), 1.00000 , True, 0.00000]) algebraic[1] = custom_piecewise([less(states[0] , 0.250000), 0.00000 , greater(states[0] , 2.00000), 0.00000 , True, 1.00000-1.30612*(states[0]-1.12500)*(states[0]-1.12500)]) algebraic[3] = states[3]*algebraic[1] algebraic[6] = (algebraic[4]-states[1])/constants[6] algebraic[7] = custom_piecewise([greater(algebraic[6] , 0.00000), 1.00000 , True, 0.00000]) algebraic[8] = constants[8]*(1.00000-exp(-(constants[7]*algebraic[6])))*algebraic[7] 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)