# Size of variable arrays: sizeAlgebraic = 2 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 = "time in component Environment (s)" legend_constants[0] = "HR in component Environment (ratepm)" legend_constants[5] = "hrf in component Environment (Hz)" legend_constants[1] = "PRint in component LVTiming (s)" legend_algebraic[0] = "beattime in component LVTiming (s)" legend_constants[2] = "Esys in component LVElastanceFunction (elastance)" legend_constants[3] = "Edia in component LVElastanceFunction (elastance)" legend_constants[4] = "TsK in component LVElastanceFunction (s)" legend_constants[6] = "Ts in component LVElastanceFunction (s)" legend_algebraic[1] = "E_LV in component LVElastanceFunction (elastance)" legend_states[0] = "dummy in component dummy (dimensionless)" legend_rates[0] = "d/dt dummy in component dummy (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 70 constants[1] = 0.00012 constants[2] = 5.6 constants[3] = 0.19 constants[4] = 0.35 states[0] = 10 constants[5] = constants[0]/60.0000 constants[6] = constants[4]*(power(1.00000*constants[5], 1.0/2)) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = states[0]*-3.00000 return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = (voi-floor(voi/constants[5])*constants[5])-constants[1] algebraic[1] = custom_piecewise([greater_equal(algebraic[0] , 0.00000) & less_equal(algebraic[0] , constants[6]), constants[3]+((constants[2]-constants[3])*(1.00000-cos(( pi*algebraic[0])/constants[6])))/2.00000 , less(algebraic[0] , 1.50000*constants[6]) & greater_equal(algebraic[0] , constants[6]), constants[3]+((constants[2]-constants[3])*(1.00000+cos((2.00000* pi*(algebraic[0]-constants[6]))/constants[6])))/2.00000 , True, constants[3]]) 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)