# Size of variable arrays: sizeAlgebraic = 12 sizeStates = 6 sizeConstants = 9 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 (minute)" legend_algebraic[11] = "v1 in component v1 (per_minute)" legend_algebraic[10] = "l in component l (dimensionless)" legend_states[0] = "RI in component RI (dimensionless)" legend_states[1] = "RII in component RII (dimensionless)" legend_constants[0] = "ka in component model_parameters (per_minute)" legend_algebraic[0] = "v2 in component v2 (per_minute)" legend_states[2] = "l_RI_RII in component l_RI_RII (dimensionless)" legend_constants[1] = "kcd in component model_parameters (per_minute)" legend_algebraic[1] = "v3 in component v3 (per_minute)" legend_constants[2] = "klid in component model_parameters (per_minute)" legend_algebraic[2] = "v4 in component v4 (per_minute)" legend_constants[3] = "ki in component model_parameters (per_minute)" legend_constants[7] = "v5 in component v5 (per_minute)" legend_constants[4] = "p_RI in component model_parameters (per_minute)" legend_algebraic[3] = "v6 in component v6 (per_minute)" legend_algebraic[4] = "v7 in component v7 (per_minute)" legend_algebraic[5] = "v8 in component v8 (per_minute)" legend_states[3] = "RI_endo in component RI_endo (dimensionless)" legend_constants[5] = "kr in component model_parameters (per_minute)" legend_algebraic[6] = "v9 in component v9 (per_minute)" legend_states[4] = "l_RI_RII_endo in component l_RI_RII_endo (dimensionless)" legend_constants[8] = "v10 in component v10 (per_minute)" legend_constants[6] = "p_RII in component model_parameters (per_minute)" legend_algebraic[7] = "v11 in component v11 (per_minute)" legend_algebraic[8] = "v12 in component v12 (per_minute)" legend_algebraic[9] = "v13 in component v13 (per_minute)" legend_states[5] = "RII_endo in component RII_endo (dimensionless)" legend_rates[2] = "d/dt l_RI_RII in component l_RI_RII (dimensionless)" legend_rates[0] = "d/dt RI in component RI (dimensionless)" legend_rates[1] = "d/dt RII in component RII (dimensionless)" legend_rates[4] = "d/dt l_RI_RII_endo in component l_RI_RII_endo (dimensionless)" legend_rates[3] = "d/dt RI_endo in component RI_endo (dimensionless)" legend_rates[5] = "d/dt RII_endo in component RII_endo (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 20.0 states[1] = 20.0 constants[0] = 1 states[2] = 0.0 constants[1] = 0.0277777778 constants[2] = 0.25 constants[3] = 0.333333333 constants[4] = 8 states[3] = 0.0 constants[5] = 0.033333333 states[4] = 40.0 constants[6] = 4 states[5] = 0.0 constants[7] = constants[4] constants[8] = constants[6] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[4] = constants[3]*states[0] algebraic[5] = constants[5]*states[3] rates[3] = algebraic[4]-algebraic[5] algebraic[2] = constants[3]*states[2] algebraic[6] = constants[5]*states[4] rates[4] = algebraic[2]-algebraic[6] algebraic[8] = constants[3]*states[1] algebraic[9] = constants[5]*states[5] rates[5] = algebraic[8]-algebraic[9] algebraic[10] = custom_piecewise([greater_equal(voi , 2500.00), 0.0100000 , True, 3.00000e-05]) algebraic[11] = constants[0]*algebraic[10]*states[0]*states[1] algebraic[0] = constants[1]*states[2] algebraic[1] = constants[2]*states[2] rates[2] = algebraic[11]-(algebraic[0]+algebraic[1]+algebraic[2]) algebraic[3] = constants[1]*states[0] rates[0] = (constants[7]+algebraic[5]+algebraic[6])-(algebraic[11]+algebraic[3]+algebraic[4]) algebraic[7] = constants[1]*states[1] rates[1] = (algebraic[6]+constants[8]+algebraic[9])-(algebraic[11]+algebraic[7]+algebraic[8]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[4] = constants[3]*states[0] algebraic[5] = constants[5]*states[3] algebraic[2] = constants[3]*states[2] algebraic[6] = constants[5]*states[4] algebraic[8] = constants[3]*states[1] algebraic[9] = constants[5]*states[5] algebraic[10] = custom_piecewise([greater_equal(voi , 2500.00), 0.0100000 , True, 3.00000e-05]) algebraic[11] = constants[0]*algebraic[10]*states[0]*states[1] algebraic[0] = constants[1]*states[2] algebraic[1] = constants[2]*states[2] algebraic[3] = constants[1]*states[0] algebraic[7] = constants[1]*states[1] 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)