# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 8 sizeConstants = 17 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] = "C1 in component C1 (dimensionless)" legend_constants[0] = "C1C2 in component reaction_constants (second_order_rate_constant)" legend_constants[1] = "C2C1 in component reaction_constants (first_order_rate_constant)" legend_states[1] = "C2 in component C2 (dimensionless)" legend_constants[2] = "Ca in component reaction_constants (micromolar)" legend_constants[3] = "C2C3 in component reaction_constants (second_order_rate_constant)" legend_constants[4] = "C3C2 in component reaction_constants (first_order_rate_constant)" legend_constants[5] = "C2C5 in component reaction_constants (first_order_rate_constant)" legend_constants[6] = "C5C2 in component reaction_constants (first_order_rate_constant)" legend_states[2] = "C3 in component C3 (dimensionless)" legend_states[3] = "C5 in component C5 (dimensionless)" legend_constants[7] = "O1C3 in component reaction_constants (first_order_rate_constant)" legend_constants[8] = "C3O1 in component reaction_constants (first_order_rate_constant)" legend_constants[9] = "O2C3 in component reaction_constants (first_order_rate_constant)" legend_constants[10] = "C3O2 in component reaction_constants (first_order_rate_constant)" legend_constants[11] = "O3C3 in component reaction_constants (first_order_rate_constant)" legend_constants[12] = "C3O3 in component reaction_constants (first_order_rate_constant)" legend_states[4] = "O1 in component O1 (dimensionless)" legend_states[5] = "O2 in component O2 (dimensionless)" legend_states[6] = "O3 in component O3 (dimensionless)" legend_states[7] = "C4 in component C4 (dimensionless)" legend_constants[13] = "O2C4 in component reaction_constants (first_order_rate_constant)" legend_constants[14] = "C4O2 in component reaction_constants (first_order_rate_constant)" legend_constants[15] = "O3C4 in component reaction_constants (first_order_rate_constant)" legend_constants[16] = "C4O3 in component reaction_constants (first_order_rate_constant)" legend_rates[0] = "d/dt C1 in component C1 (dimensionless)" legend_rates[1] = "d/dt C2 in component C2 (dimensionless)" legend_rates[2] = "d/dt C3 in component C3 (dimensionless)" legend_rates[7] = "d/dt C4 in component C4 (dimensionless)" legend_rates[3] = "d/dt C5 in component C5 (dimensionless)" legend_rates[4] = "d/dt O1 in component O1 (dimensionless)" legend_rates[5] = "d/dt O2 in component O2 (dimensionless)" legend_rates[6] = "d/dt O3 in component O3 (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.125 constants[0] = 2.5 constants[1] = 13.3 states[1] = 0.125 constants[2] = 20.0 constants[3] = 68.0 constants[4] = 8000.0 constants[5] = 0.13 constants[6] = 3.6 states[2] = 0.125 states[3] = 0.125 constants[7] = 3400.0 constants[8] = 1100.0 constants[9] = 92.0 constants[10] = 17.0 constants[11] = 138.0 constants[12] = 14.0 states[4] = 0.125 states[5] = 0.125 states[6] = 0.125 states[7] = 0.125 constants[13] = 1900.0 constants[14] = 520.0 constants[15] = 300.0 constants[16] = 46.0 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[1]*states[1]-constants[0]*constants[2]*states[1] rates[1] = (constants[0]*constants[2]*states[0]+constants[4]*states[2]+constants[6]*states[3])-(constants[1]*states[1]+constants[3]*constants[2]*states[1]+constants[5]*states[1]) rates[2] = (constants[3]*constants[2]*states[1]+constants[7]*states[4]+constants[11]*states[6]+constants[9]*states[5])-(constants[4]*states[2]+constants[8]*states[2]+constants[10]*states[2]+constants[12]*states[2]) rates[7] = (constants[13]*states[5]+constants[15]*states[6])-(constants[14]*states[7]+constants[16]*states[7]) rates[3] = constants[5]*states[1]-constants[6]*states[3] rates[4] = constants[8]*states[2]-constants[7]*states[4] rates[5] = (constants[10]*states[2]+constants[14]*states[7])-(constants[9]*states[5]+constants[13]*states[5]) rates[6] = (constants[12]*states[2]+constants[16]*states[7])-(constants[11]*states[6]+constants[15]*states[6]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) 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)