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.
150 KiB
150 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]:
n_steps, n_modes = 5, 2
stage = np.zeros((n_steps, n_modes)); stage[:, 1] = 1.0
cost = [0.0] * (n_modes * n_modes)
res = opt.optimal_switching_dp(stage.flatten().tolist(),
[0.0] * n_modes, cost,
n_modes, n_steps)
value = np.array(res['value']).reshape(n_steps + 1, n_modes)
policy = np.array(res['policy']).reshape(n_steps + 1, n_modes)
print('V_0 =', value[0])
print('Optimal next mode at each (k, i):'); print(policy)
V_0 = [4. 5.] Optimal next mode at each (k, i): [[1 1] [1 1] [1 1] [1 1] [0 0] [0 1]]
In [3]:
fig, ax = plt.subplots()
ax.step(range(n_steps + 1), value[:, 0], where='post', label='V_k(mode 0)')
ax.step(range(n_steps + 1), value[:, 1], where='post', label='V_k(mode 1)')
ax.set_xlabel('k'); ax.set_ylabel('value'); ax.legend(); ax.grid(alpha=0.3)
ax.set_title('Snell envelope — free switching')
fig.tight_layout(); plt.show()
In [4]:
res = opt.pontryagin_lqr(a=0.0, b=1.0, q=0.0, r=1.0,
s_terminal=1.0, x0=1.0,
t_horizon=1.0, n_steps=2000)
tg = np.array(res['time_grid'])
P = np.array(res['riccati'])
x = np.array(res['state']); u = np.array(res['control'])
P_an = 1.0 / (1.0 + (1.0 - tg))
print('P(0) =', P[0], ' analytic =', P_an[0])
print('cost =', res['cost'])
P(0) = 0.499913334323088 analytic = 0.5 cost = 0.5000000041705193
In [5]:
fig, axes = plt.subplots(1, 3, figsize=(13, 4))
axes[0].plot(tg, P, label='numeric'); axes[0].plot(tg, P_an, '--', label='analytic')
axes[0].set_title('Riccati P(t)'); axes[0].set_xlabel('t'); axes[0].legend(); axes[0].grid(alpha=0.3)
axes[1].plot(tg, x); axes[1].set_title('state x(t)'); axes[1].set_xlabel('t'); axes[1].grid(alpha=0.3)
axes[2].plot(tg[:-1], u); axes[2].set_title('feedback u(t) = -(b/r) P(t) x(t)'); axes[2].set_xlabel('t'); axes[2].grid(alpha=0.3)
fig.tight_layout(); plt.show()
In [6]:
deltas = np.linspace(-2.0, 2.0, 41)
lam_plus = []
for dv in deltas:
r = opt.two_sided_intensities(1.0, 1.0, 0.5, 0.5, dv, -dv)
lam_plus.append(r['lambda_plus'])
lam_plus = np.array(lam_plus)
fig, ax = plt.subplots()
ax.plot(deltas, lam_plus, lw=2)
ax.set_xlabel('ΔV_+'); ax.set_ylabel('λ*_+')
ax.set_title('Optimal upward intensity vs value-function gradient')
ax.grid(alpha=0.3); fig.tight_layout(); plt.show()
