Generated Code
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The raw code is available.
# Size of variable arrays: sizeAlgebraic = 16 sizeStates = 3 sizeConstants = 37 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 (hour)" legend_constants[0] = "T_a in component model_parameters (celsius)" legend_constants[1] = "T_b in component model_parameters (celsius)" legend_constants[2] = "delta_T in component model_parameters (celsius)" legend_constants[3] = "kinc in component model_parameters (W_per_kg_C2)" legend_constants[4] = "tdose1 in component model_parameters (hour)" legend_constants[5] = "tdose2 in component model_parameters (hour)" legend_constants[6] = "tdose3 in component model_parameters (hour)" legend_algebraic[5] = "M_c in component M_c (W_per_kg)" legend_constants[7] = "t_day in component M_c (hour)" legend_constants[8] = "t_night in component M_c (hour)" legend_algebraic[1] = "tprime in component M_c (second)" legend_constants[9] = "day_length in component M_c (second)" legend_constants[35] = "M_day in component M_day (W_per_kg)" legend_algebraic[3] = "M_night in component M_night (W_per_kg)" legend_states[0] = "M in component M (W_per_kg)" legend_constants[10] = "km in component M (per_hour)" legend_states[1] = "T in component T (celsius)" legend_constants[11] = "c in component T (kJ_per_kg_C)" legend_algebraic[0] = "k in component k (W_per_kg_C)" legend_states[2] = "BR in component k (dimensionless)" legend_constants[12] = "pEtot in component k (dimensionless)" legend_constants[13] = "kR in component k (per_day)" legend_constants[14] = "AMT_dose in component k (mg_per_kg)" legend_constants[15] = "pEf1 in component k (per_day)" legend_constants[16] = "pEs1 in component k (kg_per_day_mg)" legend_constants[17] = "pEf2 in component k (per_day)" legend_constants[18] = "pEs2 in component k (kg_per_day_mg)" legend_constants[19] = "pEf3 in component k (per_day)" legend_constants[20] = "pEs3 in component k (kg_per_day_mg)" legend_algebraic[13] = "E_slow in component k (per_day)" legend_algebraic[15] = "E_fast in component k (per_day)" legend_constants[30] = "f2_drug in component k (W_per_kg_C)" legend_constants[34] = "kb in component kb (W_per_kg_C)" legend_algebraic[2] = "f_prime in component M_night (dimensionless)" legend_algebraic[6] = "gNsTs1 in component gNT (dimensionless)" legend_algebraic[9] = "gNsTs2 in component gNT (dimensionless)" legend_algebraic[12] = "gNsTs3 in component gNT (dimensionless)" legend_algebraic[7] = "gNfTf1 in component gNT (dimensionless)" legend_algebraic[10] = "gNfTf2 in component gNT (dimensionless)" legend_algebraic[14] = "gNfTf3 in component gNT (dimensionless)" legend_constants[29] = "T_day in component T_day (celsius)" legend_constants[32] = "T_night in component T_night (celsius)" legend_constants[21] = "M_b in component kb (W_per_kg)" legend_constants[22] = "t_prime in component M_night (hour)" legend_constants[23] = "alpha in component M_night (per_hour)" legend_constants[24] = "delta_high_dose in component M_night (dimensionless)" legend_constants[36] = "M_night_baseline in component M_night (W_per_kg)" legend_constants[25] = "Ns in component gNT (dimensionless)" legend_constants[26] = "Nf in component gNT (dimensionless)" legend_constants[27] = "Ts in component gNT (day)" legend_constants[28] = "Tf in component gNT (day)" legend_algebraic[4] = "X1 in component gNT (day)" legend_algebraic[8] = "X2 in component gNT (day)" legend_algebraic[11] = "X3 in component gNT (day)" legend_constants[31] = "Kf in component gNT (per_day)" legend_constants[33] = "Ks in component gNT (per_day)" legend_rates[0] = "d/dt M in component M (W_per_kg)" legend_rates[1] = "d/dt T in component T (celsius)" legend_rates[2] = "d/dt BR in component k (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 21.0 constants[1] = 38.0 constants[2] = 1.57 constants[3] = 0.0258 constants[4] = 24.0 constants[5] = 72.0 constants[6] = 120.0 constants[7] = 17.5 constants[8] = 6.73 constants[9] = 86400 states[0] = 3.5 constants[10] = 1.1375 states[1] = 38.785 constants[11] = 3.47 states[2] = 0.0 constants[12] = 0.144 constants[13] = 5.35 constants[14] = 3.0 constants[15] = 1.0 constants[16] = 0.2 constants[17] = 3.57 constants[18] = 2.43 constants[19] = 8.0 constants[20] = 50.0 constants[21] = 3.0 constants[22] = 45.12 constants[23] = 0.2229166 constants[24] = 1.0 constants[25] = 4.0 constants[26] = 4.0 constants[27] = 2.45 constants[28] = 0.368 constants[29] = constants[1]+constants[2]/2.00000 constants[30] = 0.00000 constants[31] = constants[26]/constants[28] constants[32] = constants[1]-constants[2]/2.00000 constants[33] = constants[25]/constants[27] constants[34] = constants[21]/(constants[1]-constants[0]) constants[35] = (constants[34]+constants[3]*(constants[29]-constants[1]))*(constants[29]-constants[0]) constants[36] = (constants[34]+constants[3]*(constants[32]-constants[1]))*(constants[32]-constants[0]) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = constants[34]+constants[3]*(states[1]-constants[1]*(1.00000+constants[12]*states[2]))+constants[30] rates[1] = (power(constants[11], -1.00000))*(states[0]-algebraic[0]*(states[1]-constants[0])) algebraic[1] = voi*3600.00*1.00000 % constants[9] algebraic[2] = constants[24]*(power(1.00000+exp(-constants[23]*(voi-(constants[4]+constants[22]))), -1.00000)) algebraic[3] = (1.00000-algebraic[2])*constants[36]+algebraic[2]*constants[35] algebraic[5] = custom_piecewise([greater_equal(algebraic[1]/3600.00 , constants[8]) & less(algebraic[1]/3600.00 , constants[7]), algebraic[3] , True, constants[35]]) rates[0] = -constants[10]*(states[0]-algebraic[5]) algebraic[4] = (voi-constants[4])/24.0000 algebraic[6] = custom_piecewise([greater(algebraic[4] , 0.00000), ((power(constants[33], constants[25]))/6.00000)*exp(-constants[33]*algebraic[4])*(power(algebraic[4], constants[25]-1.00000)) , True, 0.00000]) algebraic[8] = (voi-constants[5])/24.0000 algebraic[9] = custom_piecewise([greater(algebraic[8] , 0.00000), ((power(constants[33], constants[25]))/6.00000)*exp(-constants[33]*algebraic[8])*(power(algebraic[8], constants[25]-1.00000)) , True, 0.00000]) algebraic[11] = (voi-constants[6])/24.0000 algebraic[12] = custom_piecewise([greater(algebraic[11] , 0.00000), ((power(constants[33], constants[25]))/6.00000)*exp(-constants[33]*algebraic[11])*(power(algebraic[11], constants[25]-1.00000)) , True, 0.00000]) algebraic[13] = constants[14]*constants[18]*(algebraic[6]+algebraic[9]+algebraic[12]) algebraic[7] = custom_piecewise([greater(algebraic[4] , 0.00000), ((power(constants[31], constants[26]))/6.00000)*exp(-constants[31]*algebraic[4])*(power(algebraic[4], constants[26]-1.00000)) , True, 0.00000]) algebraic[10] = custom_piecewise([greater(algebraic[8] , 0.00000), ((power(constants[31], constants[26]))/6.00000)*exp(-constants[31]*algebraic[8])*(power(algebraic[8], constants[26]-1.00000)) , True, 0.00000]) algebraic[14] = custom_piecewise([greater(algebraic[11] , 0.00000), ((power(constants[31], constants[26]))/6.00000)*exp(-constants[31]*algebraic[11])*(power(algebraic[11], constants[26]-1.00000)) , True, 0.00000]) algebraic[15] = constants[17]*(algebraic[7]+algebraic[10]+algebraic[14]) rates[2] = (algebraic[2]*(algebraic[13]+algebraic[15]))*(1.00000-states[2])-constants[13]*states[2] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[34]+constants[3]*(states[1]-constants[1]*(1.00000+constants[12]*states[2]))+constants[30] algebraic[1] = voi*3600.00*1.00000 % constants[9] algebraic[2] = constants[24]*(power(1.00000+exp(-constants[23]*(voi-(constants[4]+constants[22]))), -1.00000)) algebraic[3] = (1.00000-algebraic[2])*constants[36]+algebraic[2]*constants[35] algebraic[5] = custom_piecewise([greater_equal(algebraic[1]/3600.00 , constants[8]) & less(algebraic[1]/3600.00 , constants[7]), algebraic[3] , True, constants[35]]) algebraic[4] = (voi-constants[4])/24.0000 algebraic[6] = custom_piecewise([greater(algebraic[4] , 0.00000), ((power(constants[33], constants[25]))/6.00000)*exp(-constants[33]*algebraic[4])*(power(algebraic[4], constants[25]-1.00000)) , True, 0.00000]) algebraic[8] = (voi-constants[5])/24.0000 algebraic[9] = custom_piecewise([greater(algebraic[8] , 0.00000), ((power(constants[33], constants[25]))/6.00000)*exp(-constants[33]*algebraic[8])*(power(algebraic[8], constants[25]-1.00000)) , True, 0.00000]) algebraic[11] = (voi-constants[6])/24.0000 algebraic[12] = custom_piecewise([greater(algebraic[11] , 0.00000), ((power(constants[33], constants[25]))/6.00000)*exp(-constants[33]*algebraic[11])*(power(algebraic[11], constants[25]-1.00000)) , True, 0.00000]) algebraic[13] = constants[14]*constants[18]*(algebraic[6]+algebraic[9]+algebraic[12]) algebraic[7] = custom_piecewise([greater(algebraic[4] , 0.00000), ((power(constants[31], constants[26]))/6.00000)*exp(-constants[31]*algebraic[4])*(power(algebraic[4], constants[26]-1.00000)) , True, 0.00000]) algebraic[10] = custom_piecewise([greater(algebraic[8] , 0.00000), ((power(constants[31], constants[26]))/6.00000)*exp(-constants[31]*algebraic[8])*(power(algebraic[8], constants[26]-1.00000)) , True, 0.00000]) algebraic[14] = custom_piecewise([greater(algebraic[11] , 0.00000), ((power(constants[31], constants[26]))/6.00000)*exp(-constants[31]*algebraic[11])*(power(algebraic[11], constants[26]-1.00000)) , True, 0.00000]) algebraic[15] = constants[17]*(algebraic[7]+algebraic[10]+algebraic[14]) 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)