Generated Code

# Size of variable arrays:
sizeAlgebraic = 9
sizeStates = 5
sizeConstants = 11
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 (dimensionless)"
    legend_algebraic[0] = "f in component f (dimensionless)"
    legend_constants[0] = "a in component f (dimensionless)"
    legend_states[0] = "r in component r (dimensionless)"
    legend_constants[1] = "p in component model_parameters (dimensionless)"
    legend_constants[2] = "beta in component r (dimensionless)"
    legend_constants[3] = "alpha in component r (dimensionless)"
    legend_algebraic[5] = "ur0 in component ur0 (dimensionless)"
    legend_algebraic[3] = "m in component m (dimensionless)"
    legend_constants[4] = "r0 in component model_parameters (dimensionless)"
    legend_algebraic[4] = "y in component y (dimensionless)"
    legend_constants[5] = "r1 in component model_parameters (dimensionless)"
    legend_algebraic[2] = "ur1 in component ur1 (dimensionless)"
    legend_algebraic[6] = "z in component z (dimensionless)"
    legend_constants[6] = "t1 in component model_parameters (dimensionless)"
    legend_states[1] = "x1 in component x1 (dimensionless)"
    legend_algebraic[8] = "q in component q (dimensionless)"
    legend_constants[7] = "d in component q (dimensionless)"
    legend_constants[8] = "k in component q (dimensionless)"
    legend_algebraic[7] = "uz in component uz (dimensionless)"
    legend_states[2] = "x2 in component x2 (dimensionless)"
    legend_constants[9] = "t2 in component model_parameters (dimensionless)"
    legend_states[3] = "x3 in component x3 (dimensionless)"
    legend_algebraic[1] = "phi in component phi (dimensionless)"
    legend_states[4] = "h in component h (dimensionless)"
    legend_constants[10] = "t4 in component model_parameters (dimensionless)"
    legend_rates[0] = "d/dt r in component r (dimensionless)"
    legend_rates[1] = "d/dt x1 in component x1 (dimensionless)"
    legend_rates[2] = "d/dt x2 in component x2 (dimensionless)"
    legend_rates[3] = "d/dt x3 in component x3 (dimensionless)"
    legend_rates[4] = "d/dt h in component h (dimensionless)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 1.0
    states[0] = 0.5
    constants[1] = 1.05
    constants[2] = 1.0
    constants[3] = 1.0
    constants[4] = 0.5
    constants[5] = 1.2
    constants[6] = 0.1
    states[1] = 0.0
    constants[7] = 5.0
    constants[8] = 10.5
    states[2] = 0.0
    constants[9] = 0.5
    states[3] = 0.0
    states[4] = 0.0
    constants[10] = 20.0
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[3] = (states[2]-states[3])/constants[9]
    algebraic[0] = constants[0]*constants[1]*(power(states[0], 4.00000))
    rates[4] = (algebraic[0]-states[4])/constants[10]
    algebraic[2] = custom_piecewise([greater(states[0] , constants[5]), 1.00000 , True, 0.00000])
    algebraic[4] = (states[0]-constants[5])*algebraic[2]
    rates[1] = (algebraic[4]-states[1])/constants[6]
    algebraic[5] = custom_piecewise([greater(states[0] , constants[4]), 1.00000 , True, 0.00000])
    algebraic[1] = custom_piecewise([less(states[0] , 0.250000), 0.00000 , greater(states[0] , 2.00000), 0.00000 , True, 1.00000-1.30612*(states[0]-1.12500)*(states[0]-1.12500)])
    algebraic[3] = states[3]*algebraic[1]
    rates[0] = constants[2]*(constants[1]*states[0]-(constants[3]*(power(states[0]-constants[4], 2.00000))*algebraic[5]+algebraic[3]))
    algebraic[6] = (algebraic[4]-states[1])/constants[6]
    algebraic[7] = custom_piecewise([greater(algebraic[6] , 0.00000), 1.00000 , True, 0.00000])
    algebraic[8] = constants[8]*(1.00000-exp(-(constants[7]*algebraic[6])))*algebraic[7]
    rates[2] = (algebraic[8]-states[2])/constants[9]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = constants[0]*constants[1]*(power(states[0], 4.00000))
    algebraic[2] = custom_piecewise([greater(states[0] , constants[5]), 1.00000 , True, 0.00000])
    algebraic[4] = (states[0]-constants[5])*algebraic[2]
    algebraic[5] = custom_piecewise([greater(states[0] , constants[4]), 1.00000 , True, 0.00000])
    algebraic[1] = custom_piecewise([less(states[0] , 0.250000), 0.00000 , greater(states[0] , 2.00000), 0.00000 , True, 1.00000-1.30612*(states[0]-1.12500)*(states[0]-1.12500)])
    algebraic[3] = states[3]*algebraic[1]
    algebraic[6] = (algebraic[4]-states[1])/constants[6]
    algebraic[7] = custom_piecewise([greater(algebraic[6] , 0.00000), 1.00000 , True, 0.00000])
    algebraic[8] = constants[8]*(1.00000-exp(-(constants[7]*algebraic[6])))*algebraic[7]
    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)