# Size of variable arrays: sizeAlgebraic = 13 sizeStates = 3 sizeConstants = 3 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 main (second)" legend_states[0] = "q_C in component main (coulomb)" legend_algebraic[2] = "v_C in component main (C_per_s)" legend_algebraic[0] = "v_R in component main (C_per_s)" legend_states[1] = "v_L in component main (C_per_s)" legend_algebraic[8] = "a_L in component main (C_per_s2)" legend_algebraic[4] = "u_C in component main (J_per_C)" legend_algebraic[6] = "u_R in component main (J_per_C)" legend_algebraic[7] = "u_L in component main (J_per_C)" legend_constants[0] = "C in component main (C2_per_J)" legend_constants[1] = "R in component main (Js_per_C2)" legend_constants[2] = "L in component main (Js2_per_C2)" legend_algebraic[9] = "P_C in component main (watt)" legend_algebraic[10] = "P_R in component main (watt)" legend_algebraic[11] = "P_L in component main (watt)" legend_algebraic[12] = "P_tot in component main (watt)" legend_algebraic[1] = "E_C in component main (joule)" legend_states[2] = "E_R in component main (joule)" legend_algebraic[3] = "E_L in component main (joule)" legend_algebraic[5] = "E_tot in component main (joule)" legend_rates[1] = "d/dt v_L in component main (C_per_s)" legend_rates[0] = "d/dt q_C in component main (coulomb)" legend_rates[2] = "d/dt E_R in component main (joule)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 1 states[1] = 0 constants[0] = 20 constants[1] = 2 constants[2] = 10 states[2] = 0 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = states[1] algebraic[2] = -algebraic[0] rates[0] = algebraic[2] algebraic[4] = states[0]/constants[0] algebraic[6] = algebraic[0]*constants[1] rootfind_0(voi, constants, rates, states, algebraic) rootfind_1(voi, constants, rates, states, algebraic) rates[1] = algebraic[8] algebraic[10] = algebraic[6]*algebraic[0] rates[2] = algebraic[10] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = states[1] algebraic[2] = -algebraic[0] algebraic[4] = states[0]/constants[0] algebraic[6] = algebraic[0]*constants[1] algebraic[10] = algebraic[6]*algebraic[0] algebraic[1] = ((0.500000*1.00000)/constants[0])*(power(states[0], 2.00000)) algebraic[3] = 0.500000*constants[2]*(power(states[1], 2.00000)) algebraic[5] = algebraic[1]+algebraic[3]+states[2] algebraic[9] = algebraic[4]*algebraic[2] algebraic[11] = algebraic[7]*states[1] algebraic[12] = algebraic[9]+algebraic[10]+algebraic[11] return algebraic initialGuess0 = None def rootfind_0(voi, constants, states, algebraic): """Calculate value of algebraic variable for DAE""" from scipy.optimize import fsolve global initialGuess0 if initialGuess0 is None: initialGuess0 = 0.1 if not iterable(voi): algebraic[7] = fsolve(residualSN_0, initialGuess0, args=(algebraic, voi, constants, rates, states), xtol=1E-6) initialGuess0 = algebraic[7] else: for (i,t) in enumerate(voi): algebraic[7][i] = fsolve(residualSN_0, initialGuess0, args=(algebraic[:,i], voi[i], constants, rates, states[:,i]), xtol=1E-6) initialGuess0 = algebraic[7][i] def residualSN_0(algebraicCandidate, algebraic, voi, constants, rates, states): algebraic[7] = algebraicCandidate return (algebraic[4]) - (algebraic[6]+algebraic[7]) initialGuess1 = None def rootfind_1(voi, constants, states, algebraic): """Calculate value of algebraic variable for DAE""" from scipy.optimize import fsolve global initialGuess1 if initialGuess1 is None: initialGuess1 = 0.1 if not iterable(voi): algebraic[8] = fsolve(residualSN_1, initialGuess1, args=(algebraic, voi, constants, rates, states), xtol=1E-6) initialGuess1 = algebraic[8] else: for (i,t) in enumerate(voi): algebraic[8][i] = fsolve(residualSN_1, initialGuess1, args=(algebraic[:,i], voi[i], constants, rates, states[:,i]), xtol=1E-6) initialGuess1 = algebraic[8][i] def residualSN_1(algebraicCandidate, algebraic, voi, constants, rates, states): algebraic[8] = algebraicCandidate return (algebraic[7]) - (algebraic[8]*constants[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)