def test_regression_simulation(inputs):
init_dict = random_init(inputs)
df, unobs, utilities, num_states = simulate(init_dict["simulation"])
num_buses = init_dict["simulation"]["buses"]
num_periods = init_dict["simulation"]["periods"]
beta = init_dict["simulation"]["beta"]
params = np.array(init_dict["simulation"]["params"])
probs = np.array(init_dict["simulation"]["known probs"])
v_disc_ = [0.0, 0.0]
v_disc = discount_utility(
v_disc_, num_buses, num_periods, num_periods, utilities, beta
)
trans_mat = create_transition_matrix(num_states, probs)
costs = myopic_costs(num_states, lin_cost, params)
v_calc = calc_fixp(num_states, trans_mat, costs, beta)
un_ob_av = 0
for bus in range(num_buses):
un_ob_av += unobs[bus, 0, 0]
un_ob_av = un_ob_av / num_buses
assert_allclose(v_disc[1] / (v_calc[0] + un_ob_av), 1, rtol=1e-02)
def get_worst_trans(init_dict, roh, num_states, max_it=1000, min_state=0):
beta = init_dict["beta"]
x_0 = np.array(init_dict["known probs"])
dim = x_0.shape[0]
params = np.array(init_dict["params"])
costs = myopic_costs(num_states, lin_cost, params)
eq_constr = {"type": "eq", "fun": lambda x: 1 - np.sum(x)}
ineq_constr = {
"type": "ineq",
"fun": lambda x: roh - np.sum(np.multiply(x, np.log(np.divide(x, x_0)))),
}
res = opt.minimize(
select_fixp,
args=(min_state, num_states, costs, beta, max_it),
x0=x_0,
bounds=[(1e-6, 1)] * dim,
method="SLSQP",
constraints=[eq_constr, ineq_constr],
)
worst_trans = np.array(res["x"])
return worst_trans
def plot_convergence(init_dict):
beta = init_dict["simulation"]["beta"]
df, unobs, utilities, num_states = simulate(init_dict["simulation"])
costs = myopic_costs(num_states, lin_cost,
init_dict["simulation"]["params"])
trans_probs = np.array(init_dict["simulation"]["known probs"])
trans_mat = create_transition_matrix(num_states, trans_probs)
ev = calc_fixp(num_states, trans_mat, costs, beta)
num_buses = init_dict["simulation"]["buses"]
num_periods = init_dict["simulation"]["periods"]
gridsize = init_dict["plot"]["gridsize"]
num_points = int(num_periods / gridsize)
v_exp = np.full(num_points, calc_ev_0(ev, unobs, num_buses))
v_start = np.zeros(num_points)
v_disc = discount_utility(v_start, num_buses, gridsize, num_periods,
utilities, beta)
periods = np.arange(0, num_periods, gridsize)
ax = plt.figure(figsize=(14, 6))
ax1 = ax.add_subplot(111)
ax1.set_ylim([0, 1.3 * v_disc[-1]])
ax1.set_ylabel(r"Value at time 0")
ax1.set_xlabel(r"Periods")
ax1.plot(periods, v_disc, color="blue")
ax1.plot(periods, v_exp, color="orange")
plt.tight_layout()
os.makedirs("figures", exist_ok=True)
plt.savefig("figures/figure_1.png", dpi=300)
def test_myopic_costs(inputs, outputs):
assert_array_almost_equal(
myopic_costs(inputs["nstates"], inputs["cost_fct"], inputs["params"]),
outputs["myop_costs"],
)
beta = init_dict["simulation"]["beta"]
init_dict["simulation"]["states"] = 90
v_exp_known = []
v_exp_real = []
v_disc = []
roh_plot = []
for roh in np.arange(0, 4, 0.1):
roh_plot += [roh]
init_dict["simulation"]["roh"] = roh
worst_trans = get_worst_trans(init_dict["simulation"])
init_dict["simulation"]["real probs"] = worst_trans
df, unobs, utilities, num_states = simulate(init_dict["simulation"])
costs = myopic_costs(num_states, lin_cost, init_dict["simulation"]["params"])
num_buses = init_dict["simulation"]["buses"]
num_periods = init_dict["simulation"]["periods"]
gridsize = init_dict["plot"]["gridsize"]
real_trans_probs = np.array(init_dict["simulation"]["real probs"])
real_trans_mat = create_transition_matrix(num_states, real_trans_probs)
ev_real = calc_fixp(num_states, real_trans_mat, costs, beta)
known_trans_probs = np.array(init_dict["simulation"]["known probs"])
known_trans_mat = create_transition_matrix(num_states, known_trans_probs)
ev_known = calc_fixp(num_states, known_trans_mat, costs, beta)
v_calc = 0
for i in range(num_buses):
def simulate_strategy(known_trans, increments, num_buses, num_periods, params,
beta, unobs, maint_func):
"""
This function manages the simulation process. It initializes the auxiliary
variables and calls therefore the subfuctions from estimation auxiliary. It then
calls the decision loop, written for numba. As the state size of the fixed point
needs to be a lot larger than the actual state, the size is doubled, if the loop
hasn't run yet through all the periods.
:param known_trans: A numpy array containing the transition probabilities the agent
assumes.
:param increments: A two dimensional numpy array containing for each bus in each
period a random drawn state increase as integer.
:param num_buses: The number of buses to be simulated.
:type num_buses: int
:param num_periods: The number of periods to be simulated.
:type num_periods: int
:param params: A numpy array containing the parameters shaping the cost
function.
:param beta: The discount factor.
:type beta: float
:param unobs: A three dimensional numpy array containing for each bus,
for each period for the decision to maintain or replace the
bus engine a random drawn utility as float.
:param maint_func: The maintenance cost function. Only linear implemented so
far.
:return: The function returns the following objects:
:states: : A two dimensional numpy array containing for each bus in
each period the state as an integer.
:decisions: : A two dimensional numpy array containing for each bus in
each period the decision as an integer.
:utilities: : A two dimensional numpy array containing for each bus in
each period the utility as a float.
:num_states: (int) : The size of the state space.
"""
num_states = int(200)
start_period = int(0)
states = np.zeros((num_buses, num_periods), dtype=int)
decisions = np.zeros((num_buses, num_periods), dtype=int)
utilities = np.zeros((num_buses, num_periods), dtype=float)
while start_period < num_periods - 1:
num_states = 2 * num_states
known_trans_mat = create_transition_matrix(num_states, known_trans)
costs = myopic_costs(num_states, maint_func, params)
ev = calc_fixp(num_states, known_trans_mat, costs, beta)
states, decisions, utilities, start_period = simulate_strategy_loop(
num_buses,
states,
decisions,
utilities,
costs,
ev,
increments,
num_states,
start_period,
num_periods,
beta,
unobs,
)
return states, decisions, utilities, num_states
def simulate(init_dict):
"""
The main function to simulate a decision process in the theoretical framework of
John Rust's 1987 paper. It reads the inputs from the initiation dictionary and
draws the random variables. It then calls the main subfunction with all the
relevant parameters. So far, the feature of a agent's misbelief on the underlying
transition probabilities is not implemented.
:param init_dict: A dictionary containing the following variables as keys:
:seed: (Digits) : The seed determines random draws.
:buses: (int) : Number of buses to be simulated.
:beta: (float) : Discount factor.
:periods: (int) : Number of periods to be simulated.
:probs: : A list or array of the true underlying transition
probabilities.
:params: : A list or array of the cost parameters shaping the cost
function.
:maint_func: (string): The type of cost function, as string. Only linear
implemented so far.
:return: The function returns the following objects:
:df: : A pandas dataframe containing for each observation the period,
state, decision and a Bus ID.
:unobs: : A three dimensional numpy array containing for each bus,
for each period random drawn utility for the decision to
maintain or replace the bus engine.
:utilities: : A two dimensional numpy array containing for each bus in each
period the utility as a float.
:num_states: : A integer documenting the size of the state space.
"""
np.random.seed(init_dict["seed"])
num_buses = init_dict["buses"]
beta = init_dict["beta"]
num_periods = init_dict["periods"]
if "real probs" in init_dict.keys():
real_trans = np.array(init_dict["real probs"])
else:
real_trans = np.array(init_dict["known probs"])
known_trans = np.array(init_dict["known probs"])
params = np.array(init_dict["params"])
if init_dict["maint_func"] == "linear":
maint_func = lin_cost
else:
maint_func = lin_cost
unobs = np.random.gumbel(loc=-mp.euler, size=[num_buses, num_periods, 2])
increments = np.random.choice(len(real_trans),
size=(num_buses, num_periods),
p=real_trans)
if "ev_known" in init_dict.keys():
# If there is already ev given, the auxiliary function is skipped and the
# simulation is executed with no further increases of the state space. This
# option is perfect if only one parameter in the setting is varied and
# therefore the highest achievable state can be guessed.
ev_known = np.array(init_dict["ev_known"])
num_states = int(len(ev_known))
costs = myopic_costs(num_states, lin_cost, params)
states = np.zeros((num_buses, num_periods), dtype=int)
decisions = np.zeros((num_buses, num_periods), dtype=int)
utilities = np.zeros((num_buses, num_periods), dtype=float)
states, decisions, utilities = simulate_strategy_loop_known(
num_buses,
states,
decisions,
utilities,
costs,
ev_known,
increments,
num_periods,
beta,
unobs,
)
else:
states, decisions, utilities, num_states = simulate_strategy(
known_trans,
increments,
num_buses,
num_periods,
params,
beta,
unobs,
maint_func,
)
df = pd.DataFrame({
"state": states.flatten(),
"decision": decisions.flatten()
})
df["period"] = np.arange(num_periods).repeat(num_buses).astype(int)
bus_id = np.array([])
for i in range(1, num_buses + 1):
bus_id = np.append(bus_id, np.full(num_periods, i, dtype=int))
df["Bus_ID"] = bus_id
return df, unobs, utilities, num_states