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.
182 lines
82 KiB
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182 lines
82 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "c50e4dfe",
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"metadata": {},
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"source": [
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"# 13 — Quadratic-impact controlled SDE"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "fe0fb749",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2026-05-12T10:16:10.197004Z",
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"iopub.status.busy": "2026-05-12T10:16:10.196701Z",
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"iopub.status.idle": "2026-05-12T10:16:10.857514Z",
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"shell.execute_reply": "2026-05-12T10:16:10.856390Z"
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}
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},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from optimizr import _core as opt\n",
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"plt.rcParams['figure.figsize'] = (7, 4)\n",
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"plt.rcParams['figure.dpi'] = 110\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e0b5bfa5",
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"metadata": {},
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"source": [
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"## Riccati fixed-point check\n",
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"\n",
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"$h'(t) = h(t)^2/γ - φ$ with $h(T) = A$. When $γ = φ = A = 1$ the right-hand side is $h^2 - 1 = 0$ at $h = 1$, so `h ≡ 1`."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "959f0a2a",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2026-05-12T10:16:10.860816Z",
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"iopub.status.busy": "2026-05-12T10:16:10.860419Z",
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"iopub.status.idle": "2026-05-12T10:16:10.868124Z",
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"shell.execute_reply": "2026-05-12T10:16:10.865384Z"
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"h drift from 1: 0.0\n"
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]
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}
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],
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"source": [
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"res = opt.quadratic_impact_control_py(\n",
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" gamma=1.0, phi=1.0, a_terminal=1.0,\n",
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" t_horizon=0.5, n_steps=500,\n",
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")\n",
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"tg = np.array(res['time_grid'])\n",
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"h = np.array(res['h']); k = np.array(res['feedback_gain'])\n",
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"print('h drift from 1:', float(np.max(np.abs(h - 1.0))))\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "e1e343d8",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2026-05-12T10:16:10.872019Z",
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"iopub.status.busy": "2026-05-12T10:16:10.871475Z",
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"iopub.status.idle": "2026-05-12T10:16:11.159776Z",
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"shell.execute_reply": "2026-05-12T10:16:11.158761Z"
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}
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},
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"outputs": [
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{
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"data": {
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"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 770x440 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"fig, ax = plt.subplots()\n",
|
||
"ax.plot(tg, h, label='h(t)')\n",
|
||
"ax.plot(tg, k, '--', label='k(t) = h(t)/γ')\n",
|
||
"ax.axhline(1.0, color='k', alpha=0.3, ls=':', label='fixed point')\n",
|
||
"ax.set_xlabel('t'); ax.legend(); ax.grid(alpha=0.3)\n",
|
||
"ax.set_title('Riccati fixed point γ=φ=A=1')\n",
|
||
"fig.tight_layout(); plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4f8b738d",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Sensitivity to the terminal weight\n",
|
||
"\n",
|
||
"Vary $A$, fix $γ = 1$, $φ = 0.25$, $T = 1$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"id": "11740dc8",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-05-12T10:16:11.162956Z",
|
||
"iopub.status.busy": "2026-05-12T10:16:11.162649Z",
|
||
"iopub.status.idle": "2026-05-12T10:16:11.541340Z",
|
||
"shell.execute_reply": "2026-05-12T10:16:11.539197Z"
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 770x440 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"fig, ax = plt.subplots()\n",
|
||
"for A in [0.0, 0.25, 0.5, 1.0, 2.0, 5.0]:\n",
|
||
" r = opt.quadratic_impact_control_py(1.0, 0.25, A, 1.0, 1000)\n",
|
||
" ax.plot(r['time_grid'], r['h'], label=f'A = {A:g}')\n",
|
||
"ax.set_xlabel('t'); ax.set_ylabel('h(t)'); ax.legend(); ax.grid(alpha=0.3)\n",
|
||
"ax.set_title('Riccati sensitivity to terminal weight')\n",
|
||
"fig.tight_layout(); plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "df2cd9e3",
|
||
"metadata": {},
|
||
"source": [
|
||
"**Verified:** `h ≡ 1` with `max|h - 1| < 1e-9` at the fixed point."
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "Python 3 (rhftlab)",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.11.13"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
}
|