# Size of variable arrays: sizeAlgebraic = 2 sizeStates = 4 sizeConstants = 14 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 (second)" legend_states[0] = "M in component M (dimensionless)" legend_states[1] = "AM in component AM (dimensionless)" legend_states[2] = "Mp in component Mp (dimensionless)" legend_algebraic[0] = "k1 in component model_parameters (first_order_rate_constant)" legend_constants[0] = "k2 in component model_parameters (first_order_rate_constant)" legend_constants[12] = "gx in component model_parameters (first_order_rate_constant)" legend_states[3] = "AMp in component AMp (dimensionless)" legend_constants[7] = "fp in component model_parameters (first_order_rate_constant)" legend_constants[13] = "gp in component model_parameters (first_order_rate_constant)" legend_constants[1] = "k5 in component model_parameters (first_order_rate_constant)" legend_algebraic[1] = "k6 in component model_parameters (first_order_rate_constant)" legend_constants[2] = "fp1 in component model_parameters (first_order_rate_constant)" legend_constants[3] = "gp1 in component model_parameters (first_order_rate_constant)" legend_constants[4] = "g1 in component model_parameters (first_order_rate_constant)" legend_constants[10] = "gp3 in component model_parameters (first_order_rate_constant)" legend_constants[11] = "g3 in component model_parameters (first_order_rate_constant)" legend_constants[8] = "g2 in component model_parameters (first_order_rate_constant)" legend_constants[9] = "gp2 in component model_parameters (first_order_rate_constant)" legend_constants[5] = "x in component model_parameters (nanometre)" legend_constants[6] = "h in component model_parameters (nanometre)" legend_rates[0] = "d/dt M in component M (dimensionless)" legend_rates[2] = "d/dt Mp in component Mp (dimensionless)" legend_rates[3] = "d/dt AMp in component AMp (dimensionless)" legend_rates[1] = "d/dt AM in component AM (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.97 states[1] = 0.01 states[2] = 0.01 constants[0] = 0.1 states[3] = 0.01 constants[1] = 0.1 constants[2] = 0.88 constants[3] = 0.22 constants[4] = 0.01 constants[5] = 2200.0 constants[6] = 15.6 constants[7] = custom_piecewise([less(constants[5] , 0.00000), 0.00000 , greater_equal(constants[5] , 0.00000) & greater_equal(constants[5] , constants[6]), constants[2]*(constants[5]/constants[6]) , less(constants[6] , constants[5]), 0.00000 , True, float('nan')]) constants[8] = 20.0000*constants[4] constants[9] = 4.00000*(constants[2]+constants[3]) constants[10] = 3.00000*constants[3] constants[11] = 3.00000*constants[4] constants[12] = custom_piecewise([less(constants[5] , 0.00000), constants[8] , greater_equal(constants[5] , 0.00000) & greater_equal(constants[5] , constants[6]), constants[4]*(constants[5]/constants[6]) , less(constants[6] , constants[5]), (constants[4]+constants[11])*(constants[5]/constants[6]) , True, float('nan')]) constants[13] = custom_piecewise([less(constants[5] , 0.00000), constants[9] , greater_equal(constants[5] , 0.00000) & greater_equal(constants[5] , constants[6]), constants[3]*(constants[5]/constants[6]) , less(constants[6] , constants[5]), (constants[3]+constants[10])*(constants[5]/constants[6]) , True, float('nan')]) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = custom_piecewise([less(voi , 0.00000) & less(voi , 5.00000), 0.350000 , True, 0.0600000]) rates[0] = -algebraic[0]*states[0]+constants[0]*states[2]+constants[12]*states[1] rates[2] = algebraic[0]*states[0]+(-constants[0]-constants[7])*states[2]+constants[13]*states[3] algebraic[1] = algebraic[0] rates[3] = constants[7]*states[2]+(-constants[1]-constants[13])*states[3]+algebraic[1]*states[1] rates[1] = constants[1]*states[3]+(-algebraic[1]-constants[12])*states[1] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = custom_piecewise([less(voi , 0.00000) & less(voi , 5.00000), 0.350000 , True, 0.0600000]) algebraic[1] = algebraic[0] 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)