# Size of variable arrays: sizeAlgebraic = 3 sizeStates = 1 sizeConstants = 7 from math import * from numpy import * def createLegends(): legend_states = [""] * sizeStates legend_rates = [""] * sizeStates legend_algebraic = [""] * sizeAlgebraic legend_voi = "" legend_constants = [""] * sizeConstants legend_voi = "x in component main (dimensionless)" legend_algebraic[0] = "sin in component sin (dimensionless)" legend_states[0] = "sin in component sin (dimensionless)" legend_constants[0] = "deriv_approx_initial_value in component main (dimensionless)" legend_algebraic[2] = "sin in component sin (dimensionless)" legend_constants[2] = "k2_oPi in component sin (dimensionless)" legend_constants[3] = "k2Pi in component sin (dimensionless)" legend_constants[4] = "kPi_2 in component sin (dimensionless)" legend_constants[5] = "kPi in component sin (dimensionless)" legend_constants[6] = "kPi_32 in component sin (dimensionless)" legend_algebraic[1] = "z in component sin (dimensionless)" legend_constants[1] = "C in component sin (dimensionless)" legend_rates[0] = "d/dt sin in component sin (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 0 constants[1] = 0.75 constants[2] = 2.00000/ pi constants[3] = 2.00000* pi constants[4] = pi/2.00000 constants[5] = pi constants[6] = (3.00000* pi)/2.00000 states[0] = constants[0] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = cos(voi) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = sin(voi) algebraic[1] = custom_piecewise([less(voi , constants[4]), voi*constants[2]-0.500000 , less(voi , constants[5]), ( pi-voi)*constants[2]-0.500000 , less(voi , constants[6]), (voi- pi)*constants[2]-0.500000 , True, (constants[3]-voi)*constants[2]-0.500000]) algebraic[2] = custom_piecewise([less(voi , constants[4]), -(algebraic[1]*algebraic[1])+constants[1]+algebraic[1] , less(voi , constants[5]), -(algebraic[1]*algebraic[1])+constants[1]+algebraic[1] , less(voi , constants[6]), (algebraic[1]*algebraic[1]-constants[1])-algebraic[1] , True, (algebraic[1]*algebraic[1]-constants[1])-algebraic[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)