def exercise1(clargs):
""" Exercise 1 """
# Setup
pylog.info("Running exercise 1")
# Setup
time_max = 5 # Maximum simulation time
time_step = 0.2 # Time step for ODE integration in simulation
x0 = np.array([1.]) # Initial state
# Integration methods (Exercises 1.a - 1.d)
pylog.info("Running function integration using different methods")
# Example
pylog.debug("Running example plot for integration (remove)")
example = example_integrate(x0, time_max, time_step)
example.plot_state(figure="Example", label="Example", marker=".")
# Analytical (1.a)
time = np.arange(0, time_max, time_step) # Time vector
x_a = analytic_function(time)
analytical = Result(x_a, time) if x_a is not None else None
# Euler (1.b)
euler = euler_integrate(function, x0, time_max, time_step)
# ODE (1.c)
ode = ode_integrate(function, x0, time_max, time_step)
# ODE Runge-Kutta (1.c)
ode_rk = ode_integrate_rk(function_rk, x0, time_max, time_step)
# Euler with lower time step (1.d)
pylog.warning("Euler with smaller ts must be implemented")
euler_time_step = None
euler_ts_small = (euler_integrate(function, x0, time_max, euler_time_step)
if euler_time_step is not None else None)
# Plot integration results
plot_integration_methods(analytical=analytical,
euler=euler,
ode=ode,
ode_rk=ode_rk,
euler_ts_small=euler_ts_small,
euler_timestep=time_step,
euler_timestep_small=euler_time_step)
# Error analysis (Exercise 1.e)
pylog.warning("Error analysis must be implemented")
# Show plots of all results
if not clargs.save_figures:
plt.show()
return
def exercise1(clargs):
""" Exercise 1 """
# Setup
pylog.info("Running exercise 1")
# Setup
time_max = 5 # Maximum simulation time
time_step = 0.2 # Time step for ODE integration in simulation
x0 = np.array([1.]) # Initial state
# Integration methods (Exercises 1.a - 1.d)
pylog.info("Running function integration using different methods")
# Analytical (1.a)
time = np.arange(0, time_max, time_step) # Time vector
x_a = analytic_function(time)
analytical = Result(x_a, time) if x_a is not None else None
# Euler (1.b)
euler = euler_integrate(function, x0, time_max, time_step)
error(euler.state, analytical.state, "Euler")
# ODE (1.c)
ode = ode_integrate(function, x0, time_max, time_step)
error(ode.state, analytical.state, "LSODA")
# ODE Runge-Kutta (1.c)
ode_rk = ode_integrate_rk(function_rk, x0, time_max, time_step)
error(ode_rk.state, analytical.state, "Runge-Kutta")
# Euler with lower time step (1.d)
euler_time_step = 0.05
time_small = np.arange(0, time_max, euler_time_step) # Time vector
x_a = analytic_function(time_small)
analytical_ts_small = Result(x_a, time_small)
euler_ts_small = (euler_integrate(function, x0, time_max, euler_time_step)
if euler_time_step is not None else None)
error(euler_ts_small.state, analytical_ts_small.state,
"Euler (smaller ts)")
# Plot integration results
plot_integration_methods(analytical=analytical,
euler=euler,
ode=ode,
ode_rk=ode_rk,
euler_ts_small=euler_ts_small,
euler_timestep=time_step,
euler_timestep_small=euler_time_step)
# Error analysis (Exercise 1.e)
pylog.info("Studying integration error using different methods")
dt_list = np.logspace(-3, 0, 20) # List of timesteps (powers of 10)
integration_errors = [["L1", 1], ["L2", 2], ["Linf", 0]]
methods = [["Euler", euler_integrate, function],
["Lsoda", ode_integrate, function],
["RK", ode_integrate_rk, function_rk]]
for error_name, error_index in integration_errors:
for name, integration_function, f in methods:
compute_error(f,
analytic_function,
integration_function,
x0,
dt_list,
time_max=time_max,
figure=error_name,
label=name,
n=error_index)
# Show plots of all results
if not clargs.save_figures:
plt.show()
return