# Size of variable arrays: sizeAlgebraic = 12 sizeStates = 3 sizeConstants = 19 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_states[0] = "C in component C (dimensionless)" legend_constants[0] = "gamma in component C (dimensionless)" legend_algebraic[5] = "Vs in component Vs (dimensionless)" legend_algebraic[0] = "V1 in component V1 (dimensionless)" legend_algebraic[10] = "V2 in component V2 (dimensionless)" legend_algebraic[6] = "Vd in component Vd (dimensionless)" legend_states[1] = "K in component K (dimensionless)" legend_states[2] = "RP in component RP (dimensionless)" legend_algebraic[11] = "V3 in component V3 (dimensionless)" legend_algebraic[1] = "V4 in component V4 (dimensionless)" legend_algebraic[2] = "E in component E (dimensionless)" legend_constants[1] = "sigma in component E (dimensionless)" legend_algebraic[3] = "RE in component RE (dimensionless)" legend_algebraic[7] = "KP in component KP (dimensionless)" legend_algebraic[8] = "KPI in component KPI (dimensionless)" legend_constants[2] = "thetaI in component KPI (dimensionless)" legend_algebraic[9] = "I in component I (dimensionless)" legend_constants[3] = "lambda in component I (dimensionless)" legend_constants[4] = "thetaE in component RE (dimensionless)" legend_algebraic[4] = "R in component R (dimensionless)" legend_constants[5] = "VCs in component Vs (dimensionless)" legend_constants[6] = "Vsm in component Vs (dimensionless)" legend_constants[7] = "KsE in component Vs (dimensionless)" legend_constants[8] = "V1m in component V1 (dimensionless)" legend_constants[9] = "K1C in component V1 (dimensionless)" legend_constants[10] = "K1 in component V1 (dimensionless)" legend_constants[11] = "V2m in component V2 (dimensionless)" legend_constants[12] = "K2 in component V2 (dimensionless)" legend_constants[13] = "V3m in component V3 (dimensionless)" legend_constants[14] = "K3 in component V3 (dimensionless)" legend_constants[15] = "V4m in component V4 (dimensionless)" legend_constants[16] = "K4 in component V4 (dimensionless)" legend_constants[17] = "VdEm in component Vd (dimensionless)" legend_constants[18] = "KdC in component Vd (dimensionless)" legend_rates[0] = "d/dt C in component C (dimensionless)" legend_rates[1] = "d/dt K in component K (dimensionless)" legend_rates[2] = "d/dt RP in component RP (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.38 constants[0] = 1.0 states[1] = 0.1 states[2] = 1.0 constants[1] = 10 constants[2] = 1.0 constants[3] = 1.0 constants[4] = 0.01 constants[5] = 1.0 constants[6] = 1.0 constants[7] = 0.1 constants[8] = 50.0 constants[9] = 0.1 constants[10] = 0.0001 constants[11] = 40 constants[12] = 0.0001 constants[13] = 3000 constants[14] = 0.0001 constants[15] = 3.0 constants[16] = 0.0001 constants[17] = 1000.0 constants[18] = 0.005 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rootfind_0(voi, constants, rates, states, algebraic) algebraic[5] = constants[5]+constants[6]*(algebraic[2]/(constants[7]+algebraic[2])) algebraic[0] = constants[8]*(states[0]/(constants[9]+states[0]))*(states[1]/(constants[10]+states[1])) rootfind_1(voi, constants, rates, states, algebraic) algebraic[10] = constants[11]*(algebraic[7]/(constants[12]+algebraic[7])) algebraic[6] = states[0]+constants[17]*algebraic[2]*(states[0]/(constants[18]+states[0])) rates[0] = (algebraic[5]+constants[0]*algebraic[10])-(constants[0]*algebraic[0]+algebraic[6]) rates[1] = algebraic[10]-algebraic[0] algebraic[11] = constants[13]*algebraic[7]*(algebraic[3]/(constants[14]+algebraic[3])) algebraic[1] = constants[15]*(states[2]/(constants[16]+states[2])) rates[2] = algebraic[11]-algebraic[1] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[5] = constants[5]+constants[6]*(algebraic[2]/(constants[7]+algebraic[2])) algebraic[0] = constants[8]*(states[0]/(constants[9]+states[0]))*(states[1]/(constants[10]+states[1])) algebraic[10] = constants[11]*(algebraic[7]/(constants[12]+algebraic[7])) algebraic[6] = states[0]+constants[17]*algebraic[2]*(states[0]/(constants[18]+states[0])) algebraic[11] = constants[13]*algebraic[7]*(algebraic[3]/(constants[14]+algebraic[3])) algebraic[1] = constants[15]*(states[2]/(constants[16]+states[2])) return algebraic initialGuess0 = None def rootfind_0(voi, constants, rates, states, algebraic): """Calculate values of algebraic variables for DAE""" from scipy.optimize import fsolve global initialGuess0 if initialGuess0 is None: initialGuess0 = ones(3)*0.1 if not iterable(voi): soln = fsolve(residualSN_0, initialGuess0, args=(algebraic, voi, constants, rates, states), xtol=1E-6) initialGuess0 = soln algebraic[2] = soln[0] algebraic[3] = soln[1] algebraic[4] = soln[2] else: for (i,t) in enumerate(voi): soln = fsolve(residualSN_0, initialGuess0, args=(algebraic[:,i], voi[i], constants, rates[:i], states[:,i]), xtol=1E-6) initialGuess0 = soln algebraic[2][i] = soln[0] algebraic[3][i] = soln[1] algebraic[4][i] = soln[2] def residualSN_0(algebraicCandidate, algebraic, voi, constants, rates, states): resid = array([0.0] * 3) algebraic[2] = algebraicCandidate[0] algebraic[3] = algebraicCandidate[1] algebraic[4] = algebraicCandidate[2] resid[0] = (algebraic[2]-(1.00000-constants[1]*algebraic[3])) resid[1] = (algebraic[3]-constants[4]*algebraic[4]*algebraic[2]) resid[2] = (algebraic[4]-(1.00000-(states[2]+algebraic[3]))) return resid initialGuess1 = None def rootfind_1(voi, constants, rates, states, algebraic): """Calculate values of algebraic variables for DAE""" from scipy.optimize import fsolve global initialGuess1 if initialGuess1 is None: initialGuess1 = ones(3)*0.1 if not iterable(voi): soln = fsolve(residualSN_1, initialGuess1, args=(algebraic, voi, constants, rates, states), xtol=1E-6) initialGuess1 = soln algebraic[7] = soln[0] algebraic[8] = soln[1] algebraic[9] = soln[2] else: for (i,t) in enumerate(voi): soln = fsolve(residualSN_1, initialGuess1, args=(algebraic[:,i], voi[i], constants, rates[:i], states[:,i]), xtol=1E-6) initialGuess1 = soln algebraic[7][i] = soln[0] algebraic[8][i] = soln[1] algebraic[9][i] = soln[2] def residualSN_1(algebraicCandidate, algebraic, voi, constants, rates, states): resid = array([0.0] * 3) algebraic[7] = algebraicCandidate[0] algebraic[8] = algebraicCandidate[1] algebraic[9] = algebraicCandidate[2] resid[0] = (algebraic[7]-(1.00000-(algebraic[8]+states[1]))) resid[1] = (algebraic[8]-constants[2]*algebraic[7]*algebraic[9]) resid[2] = (algebraic[9]-(1.00000-constants[3]*algebraic[8])) return resid 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)