# Size of variable arrays: sizeAlgebraic = 2 sizeStates = 4 sizeConstants = 12 from math import * from numpy import * def createLegends(): legend_states = [""] * sizeStates legend_rates = [""] * sizeStates legend_algebraic = [""] * sizeAlgebraic legend_voi = "" legend_constants = [""] * sizeConstants legend_constants[0] = "n1_initial in component component (dimensionless)" legend_constants[1] = "d1_initial in component component (dimensionless)" legend_constants[2] = "n2_initial in component component (dimensionless)" legend_constants[3] = "d2_initial in component component (dimensionless)" legend_states[0] = "n in component component (dimensionless)" legend_states[1] = "d in component component (dimensionless)" legend_states[2] = "n in component component (dimensionless)" legend_states[3] = "d in component component (dimensionless)" legend_algebraic[0] = "cell_1_neighbourhood_d_average in component component (dimensionless)" legend_algebraic[1] = "cell_2_neighbourhood_d_average in component component (dimensionless)" legend_constants[4] = "start_boundary_d in component component (dimensionless)" legend_constants[5] = "a in component component (dimensionless)" legend_constants[6] = "b in component component (dimensionless)" legend_constants[7] = "v in component component (dimensionless)" legend_constants[8] = "k in component component (dimensionless)" legend_constants[9] = "h in component component (dimensionless)" legend_voi = "time in component component (dimensionless)" legend_constants[10] = "start_boundary_d in component component (dimensionless)" legend_constants[11] = "end_boundary_d in component component (dimensionless)" legend_rates[0] = "d/dt n in component component (dimensionless)" legend_rates[1] = "d/dt d in component component (dimensionless)" legend_rates[2] = "d/dt n in component component (dimensionless)" legend_rates[3] = "d/dt d in component component (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 1.0 constants[1] = 1.0 constants[2] = 0.99 constants[3] = 0.99 constants[4] = 0.0 constants[5] = 0.01 constants[6] = 100 constants[7] = 1 constants[8] = 2 constants[9] = 2 constants[10] = 0.0 constants[11] = 0.0 states[0] = constants[0] states[1] = constants[1] states[2] = constants[2] states[3] = constants[3] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[1] = constants[7]*(1.00000/(1.00000+constants[6]*(power(states[0], constants[9])))-states[1]) rates[3] = constants[7]*(1.00000/(1.00000+constants[6]*(power(states[2], constants[9])))-states[3]) algebraic[0] = (states[3]+constants[4])*0.500000 rates[0] = (power(algebraic[0], constants[8]))/(constants[5]+power(algebraic[0], constants[8]))-states[0] algebraic[1] = (states[1]+constants[11])*0.500000 rates[2] = (power(algebraic[1], constants[8]))/(constants[5]+power(algebraic[1], constants[8]))-states[2] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = (states[3]+constants[4])*0.500000 algebraic[1] = (states[1]+constants[11])*0.500000 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)