# Size of variable arrays: sizeAlgebraic = 4 sizeStates = 5 sizeConstants = 22 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 (day)" legend_states[0] = "R in component R (nanomolar)" legend_constants[0] = "delta_R in component R (first_order_rate_constant)" legend_algebraic[0] = "f1 in component f1 (flux)" legend_states[1] = "U in component U (nanomolar)" legend_constants[1] = "delta_U in component U (first_order_rate_constant)" legend_constants[2] = "alpha0 in component model_parameters (per_nanomolar_day)" legend_constants[3] = "alpha1 in component model_parameters (per_nanomolar_day)" legend_constants[4] = "d01 in component model_parameters (first_order_rate_constant)" legend_constants[5] = "d12 in component model_parameters (first_order_rate_constant)" legend_states[2] = "B1 in component B1 (nanomolar)" legend_states[3] = "B2 in component B2 (nanomolar)" legend_algebraic[2] = "P in component P (nanomolar)" legend_algebraic[3] = "f2 in component f2 (flux)" legend_constants[6] = "delta_b1 in component B1 (first_order_rate_constant)" legend_constants[7] = "delta_b2 in component B2 (first_order_rate_constant)" legend_constants[8] = "PE in component P (nanomolar)" legend_algebraic[1] = "q in component P (dimensionless)" legend_constants[9] = "G in component P (first_order_rate_constant)" legend_constants[10] = "ti in component P (day)" legend_constants[11] = "T in component P (day)" legend_constants[12] = "P0 in component model_parameters (nanomolar)" legend_constants[13] = "a in component f1 (flux)" legend_constants[14] = "a0 in component f1 (flux)" legend_constants[15] = "b in component f1 (nanomolar)" legend_constants[16] = "b0 in component f1 (nanomolar)" legend_states[4] = "x in component x (flux)" legend_constants[17] = "P1 in component x (nanomolar)" legend_constants[18] = "s in component x (nanomolar_day2)" legend_constants[19] = "delta_x in component x (first_order_rate_constant)" legend_constants[20] = "kappa in component f2 (flux)" legend_constants[21] = "kappa0 in component f2 (nanomolar)" legend_rates[0] = "d/dt R in component R (nanomolar)" legend_rates[1] = "d/dt U in component U (nanomolar)" legend_rates[2] = "d/dt B1 in component B1 (nanomolar)" legend_rates[3] = "d/dt B2 in component B2 (nanomolar)" legend_rates[4] = "d/dt x in component x (flux)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 1.0 constants[0] = 1.905 states[1] = 1.0 constants[1] = 7.5 constants[2] = 4.15 constants[3] = 3.02 constants[4] = 13.0 constants[5] = 4.72E3 states[2] = 1.0 states[3] = 1.0 constants[6] = 7.5 constants[7] = 50.0 constants[8] = 20.55 constants[9] = 35.6 constants[10] = 1.0 constants[11] = 9.0 constants[12] = 0.25 constants[13] = 3.58E5 constants[14] = 2.33E4 constants[15] = 100.0 constants[16] = 263.0 states[4] = 1.0 constants[17] = 20.0 constants[18] = 3.71E5 constants[19] = 0.207 constants[20] = 2.4E5 constants[21] = 6.55E3 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[3] = constants[3]*states[2]*states[1]-(constants[5]*states[3]+constants[7]*states[3]) algebraic[0] = constants[14]*(1.00000-states[3]/(constants[15]+states[3]))+(states[4]*(1.00000-exp(-states[4]/constants[13]))*states[3])/(constants[16]+states[3]) rates[0] = algebraic[0]-constants[0]*states[0] algebraic[1] = custom_piecewise([less(voi , constants[10]), 0.00000 , less(voi , constants[11]+constants[10]) & greater_equal(voi , constants[10]), 1.00000-exp(-constants[9]*(voi-constants[10])) , True, exp(constants[9]*constants[11]-1.00000)*exp(constants[9]*(voi-constants[10]))]) algebraic[2] = constants[12]+constants[8]*algebraic[1] rates[2] = (constants[2]*algebraic[2]*states[1]+constants[5]*states[3])-(constants[4]*states[2]+constants[6]*states[2]+constants[3]*states[2]*states[1]) rates[4] = (constants[18]*(algebraic[2]-constants[12]))/(algebraic[2]+constants[17])-constants[19]*states[4] algebraic[3] = (constants[20]*states[0])/(constants[21]+states[0]) rates[1] = (algebraic[3]+constants[4]*states[2]+constants[5]*states[3])-(constants[1]*states[1]+constants[2]*algebraic[2]*states[1]+constants[3]*states[2]*states[1]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[14]*(1.00000-states[3]/(constants[15]+states[3]))+(states[4]*(1.00000-exp(-states[4]/constants[13]))*states[3])/(constants[16]+states[3]) algebraic[1] = custom_piecewise([less(voi , constants[10]), 0.00000 , less(voi , constants[11]+constants[10]) & greater_equal(voi , constants[10]), 1.00000-exp(-constants[9]*(voi-constants[10])) , True, exp(constants[9]*constants[11]-1.00000)*exp(constants[9]*(voi-constants[10]))]) algebraic[2] = constants[12]+constants[8]*algebraic[1] algebraic[3] = (constants[20]*states[0])/(constants[21]+states[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)