# Size of variable arrays: sizeAlgebraic = 1 sizeStates = 1 sizeConstants = 6 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 y_channel (millisecond)" legend_states[0] = "y in component y_channel (dimensionless)" legend_constants[0] = "V in component y_channel (millivolt)" legend_constants[1] = "E_y in component y_channel (millivolt)" legend_algebraic[0] = "i_y in component y_channel (microA_per_cm2)" legend_constants[2] = "g_y in component y_channel (milliS_per_cm2)" legend_constants[3] = "gamma in component y_channel (dimensionless)" legend_constants[4] = "alpha_y in component y_channel (per_millisecond)" legend_constants[5] = "beta_y in component y_channel (per_millisecond)" legend_rates[0] = "d/dt y in component y_channel (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0 constants[0] = 0 constants[1] = -85 constants[2] = 36 constants[3] = 4 constants[4] = 1 constants[5] = 2 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[4]*(1.00000-states[0])-constants[5]*states[0] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[2]*(power(states[0], constants[3]))*(constants[0]-constants[1]) 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)