[robustness] Execution Error
mmcky opened this issue · comments
Matt McKay commented
@Smit-create can you please review the robustness
lecture
AttributeError: module 'quantecon' has no attribute 'lqcontrol'
due to this code block
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# Model parameters
a_0 = 100
a_1 = 0.5
ρ = 0.9
σ_d = 0.05
β = 0.95
c = 2
γ = 50.0
θ = 0.002
ac = (a_0 - c) / 2.0
# Define LQ matrices
R = np.array([[0., ac, 0.],
[ac, -a_1, 0.5],
[0., 0.5, 0.]])
R = -R # For minimization
Q = γ / 2
A = np.array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., ρ]])
B = np.array([[0.],
[1.],
[0.]])
C = np.array([[0.],
[0.],
[σ_d]])
# ----------------------------------------------------------------------- #
# Functions
# ----------------------------------------------------------------------- #
def evaluate_policy(θ, F):
"""
Given θ (scalar, dtype=float) and policy F (array_like), returns the
value associated with that policy under the worst case path for {w_t},
as well as the entropy level.
"""
rlq = qe.robustlq.RBLQ(Q, R, A, B, C, β, θ)
K_F, P_F, d_F, O_F, o_F = rlq.evaluate_F(F)
x0 = np.array([[1.], [0.], [0.]])
value = - x0.T @ P_F @ x0 - d_F
entropy = x0.T @ O_F @ x0 + o_F
return list(map(float, (value, entropy)))
def value_and_entropy(emax, F, bw, grid_size=1000):
"""
Compute the value function and entropy levels for a θ path
increasing until it reaches the specified target entropy value.
Parameters
==========
emax: scalar
The target entropy value
F: array_like
The policy function to be evaluated
bw: str
A string specifying whether the implied shock path follows best
or worst assumptions. The only acceptable values are 'best' and
'worst'.
Returns
=======
df: pd.DataFrame
A pandas DataFrame containing the value function and entropy
values up to the emax parameter. The columns are 'value' and
'entropy'.
"""
if bw == 'worst':
θs = 1 / np.linspace(1e-8, 1000, grid_size)
else:
θs = -1 / np.linspace(1e-8, 1000, grid_size)
df = pd.DataFrame(index=θs, columns=('value', 'entropy'))
for θ in θs:
df.loc[θ] = evaluate_policy(θ, F)
if df.loc[θ, 'entropy'] >= emax:
break
df = df.dropna(how='any')
return df
# ------------------------------------------------------------------------ #
# Main
# ------------------------------------------------------------------------ #
# Compute the optimal rule
optimal_lq = qe.lqcontrol.LQ(Q, R, A, B, C, beta=β)
Po, Fo, do = optimal_lq.stationary_values()
# Compute a robust rule given θ
baseline_robust = qe.robustlq.RBLQ(Q, R, A, B, C, β, θ)
Fb, Kb, Pb = baseline_robust.robust_rule()
# Check the positive definiteness of worst-case covariance matrix to
# ensure that θ exceeds the breakdown point
test_matrix = np.identity(Pb.shape[0]) - (C.T @ Pb @ C) / θ
eigenvals, eigenvecs = eig(test_matrix)
assert (eigenvals >= 0).all(), 'θ below breakdown point.'
emax = 1.6e6
optimal_best_case = value_and_entropy(emax, Fo, 'best')
robust_best_case = value_and_entropy(emax, Fb, 'best')
optimal_worst_case = value_and_entropy(emax, Fo, 'worst')
robust_worst_case = value_and_entropy(emax, Fb, 'worst')
fig, ax = plt.subplots()
ax.set_xlim(0, emax)
ax.set_ylabel("Value")
ax.set_xlabel("Entropy")
ax.grid()
for axis in 'x', 'y':
plt.ticklabel_format(style='sci', axis=axis, scilimits=(0, 0))
plot_args = {'lw': 2, 'alpha': 0.7}
colors = 'r', 'b'
df_pairs = ((optimal_best_case, optimal_worst_case),
(robust_best_case, robust_worst_case))
class Curve:
def __init__(self, x, y):
self.x, self.y = x, y
def __call__(self, z):
return np.interp(z, self.x, self.y)
for c, df_pair in zip(colors, df_pairs):
curves = []
for df in df_pair:
# Plot curves
x, y = df['entropy'], df['value']
x, y = (np.asarray(a, dtype='float') for a in (x, y))
egrid = np.linspace(0, emax, 100)
curve = Curve(x, y)
print(ax.plot(egrid, curve(egrid), color=c, **plot_args))
curves.append(curve)
# Color fill between curves
ax.fill_between(egrid,
curves[0](egrid),
curves[1](egrid),
color=c, alpha=0.1)
plt.show()
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