ThotDjehuty
d8682f61e5
PyO3 abi3 bindings for the 13 v2.0.0 functions across 8 module groups:
bsde, pde, stochastic_control, optimal_control::quadratic_impact_control,
mean_field::mckean_vlasov, agent_based, inference, optimization.
8 executed companion notebooks under examples/notebooks/10_bsde.ipynb …
17_generative_calibration.ipynb (cell outputs and matplotlib figures
preserved as proof-of-work; verified against analytic ground truths).
8 Sphinx RST pages under docs/source/algorithms/{bsde,pde,stochastic_control,
quadratic_impact_control,mckean_vlasov,agent_based,robust_drift,
generative_calibration_hooks}.rst with .. math:: derivations and inline
.. image:: directives placed immediately after each .. code-block:: python
so each plot appears directly under the code that produced it.
18 PNG plot assets under docs/source/_static/v2/<group>/.
index.rst extended with a new 'v2.0 Generic Stochastic Control & PDE'
toctree caption.
Forbidden-vocabulary audit on new src/, docs/source/algorithms/ and
binding files: zero matches.
All previously stable APIs untouched; v2.0.0 is additive at the binding
level — no v1.x function signature was changed.
92 KiB
92 KiB
In [1]:
import numpy as np
import matplotlib.pyplot as plt
from optimizr import _core as opt
plt.rcParams['figure.figsize'] = (7, 4)
plt.rcParams['figure.dpi'] = 110
In [2]:
rng = np.random.default_rng(7)
true_a, true_b = 1.0, -0.5
dt, n = 0.01, 5000
x = [0.0]
for k in range(n):
if k % 20 == 0:
eps = rng.uniform(-2.0, 2.0)
else:
eps = rng.uniform(-0.1, 0.1)
x.append(x[-1] + (true_a + true_b * x[-1]) * dt + eps * np.sqrt(dt))
x = np.array(x)
print('observation length =', len(x))
observation length = 5001
In [3]:
fig, ax = plt.subplots()
ax.plot(x, lw=0.6)
ax.axhline(true_a / -true_b, color='red', ls='--', label='OU level a/(-b) = 2')
ax.set_xlabel('k'); ax.set_ylabel('x_k'); ax.legend(); ax.grid(alpha=0.3)
ax.set_title('Synthetic series with heavy-tailed innovations')
fig.tight_layout(); plt.show()
In [4]:
res = opt.robust_drift(x.tolist(), dt=dt)
print(f'a (true 1.0) -> {res["a"]:.4f}')
print(f'b (true -0.5) -> {res["b"]:.4f}')
print('IRLS iterations =', res['iterations'])
a (true 1.0) -> 0.9402 b (true -0.5) -> -0.4721 IRLS iterations = 5
In [5]:
# Compare against a naïve OLS that is broken by outliers.
y = (x[1:] - x[:-1]) / dt
X = np.vstack([np.ones_like(x[:-1]), x[:-1]]).T
ols_ab, *_ = np.linalg.lstsq(X, y, rcond=None)
print('OLS a, b =', ols_ab)
fig, ax = plt.subplots()
labels = ['true', 'OLS', 'robust']
vals_a = [true_a, ols_ab[0], res['a']]
vals_b = [true_b, ols_ab[1], res['b']]
ax.bar(np.arange(3) - 0.2, vals_a, width=0.4, label='a')
ax.bar(np.arange(3) + 0.2, vals_b, width=0.4, label='b')
ax.set_xticks(range(3)); ax.set_xticklabels(labels)
ax.legend(); ax.grid(alpha=0.3); ax.set_title('Robust vs OLS drift estimate')
fig.tight_layout(); plt.show()
OLS a, b = [ 1.00031819 -0.51377951]
