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.
272 lines
150 KiB
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272 lines
150 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "1c737c8c",
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"metadata": {},
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"source": [
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"# 12 — Stochastic control"
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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": "2538d7df",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2026-05-12T10:16:06.244193Z",
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"iopub.status.busy": "2026-05-12T10:16:06.243690Z",
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"iopub.status.idle": "2026-05-12T10:16:07.005639Z",
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"shell.execute_reply": "2026-05-12T10:16:07.003895Z"
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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": "24eca7d5",
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"metadata": {},
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"source": [
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"## Optimal switching (Snell envelope)\n",
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"\n",
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"Two modes; only mode 1 pays a unit reward. Free switching should give `V_0(0) = N - 1` and `V_0(1) = 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": 2,
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"id": "7add7040",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2026-05-12T10:16:07.009088Z",
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"iopub.status.busy": "2026-05-12T10:16:07.008716Z",
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"iopub.status.idle": "2026-05-12T10:16:07.018949Z",
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"shell.execute_reply": "2026-05-12T10:16:07.015673Z"
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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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"V_0 = [4. 5.]\n",
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"Optimal next mode at each (k, i):\n",
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"[[1 1]\n",
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" [1 1]\n",
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" [1 1]\n",
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" [1 1]\n",
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" [0 0]\n",
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" [0 1]]\n"
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]
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}
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],
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"source": [
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"n_steps, n_modes = 5, 2\n",
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"stage = np.zeros((n_steps, n_modes)); stage[:, 1] = 1.0\n",
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"cost = [0.0] * (n_modes * n_modes)\n",
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"res = opt.optimal_switching_dp(stage.flatten().tolist(),\n",
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" [0.0] * n_modes, cost,\n",
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" n_modes, n_steps)\n",
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"value = np.array(res['value']).reshape(n_steps + 1, n_modes)\n",
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"policy = np.array(res['policy']).reshape(n_steps + 1, n_modes)\n",
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"print('V_0 =', value[0])\n",
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"print('Optimal next mode at each (k, i):'); print(policy)\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": "1bf3fb78",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2026-05-12T10:16:07.022668Z",
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"iopub.status.busy": "2026-05-12T10:16:07.022382Z",
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"iopub.status.idle": "2026-05-12T10:16:07.321635Z",
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"shell.execute_reply": "2026-05-12T10:16:07.320449Z"
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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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",
|
||
"text/plain": [
|
||
"<Figure size 770x440 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"fig, ax = plt.subplots()\n",
|
||
"ax.step(range(n_steps + 1), value[:, 0], where='post', label='V_k(mode 0)')\n",
|
||
"ax.step(range(n_steps + 1), value[:, 1], where='post', label='V_k(mode 1)')\n",
|
||
"ax.set_xlabel('k'); ax.set_ylabel('value'); ax.legend(); ax.grid(alpha=0.3)\n",
|
||
"ax.set_title('Snell envelope — free switching')\n",
|
||
"fig.tight_layout(); plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b439b794",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Pontryagin 1-D LQR\n",
|
||
"\n",
|
||
"Closed-form Riccati for $a=q=0$, $b=r=s_T=1$, $T=1$ is $P(t) = 1/(1 + (T - t))$, hence $P(0) = 0.5$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"id": "6d27157f",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-05-12T10:16:07.324766Z",
|
||
"iopub.status.busy": "2026-05-12T10:16:07.324457Z",
|
||
"iopub.status.idle": "2026-05-12T10:16:07.333897Z",
|
||
"shell.execute_reply": "2026-05-12T10:16:07.331408Z"
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"P(0) = 0.499913334323088 analytic = 0.5\n",
|
||
"cost = 0.5000000041705193\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"res = opt.pontryagin_lqr(a=0.0, b=1.0, q=0.0, r=1.0,\n",
|
||
" s_terminal=1.0, x0=1.0,\n",
|
||
" t_horizon=1.0, n_steps=2000)\n",
|
||
"tg = np.array(res['time_grid'])\n",
|
||
"P = np.array(res['riccati'])\n",
|
||
"x = np.array(res['state']); u = np.array(res['control'])\n",
|
||
"P_an = 1.0 / (1.0 + (1.0 - tg))\n",
|
||
"print('P(0) =', P[0], ' analytic =', P_an[0])\n",
|
||
"print('cost =', res['cost'])\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"id": "0dc4a80a",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-05-12T10:16:07.337718Z",
|
||
"iopub.status.busy": "2026-05-12T10:16:07.337376Z",
|
||
"iopub.status.idle": "2026-05-12T10:16:08.271548Z",
|
||
"shell.execute_reply": "2026-05-12T10:16:08.269696Z"
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1430x440 with 3 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"fig, axes = plt.subplots(1, 3, figsize=(13, 4))\n",
|
||
"axes[0].plot(tg, P, label='numeric'); axes[0].plot(tg, P_an, '--', label='analytic')\n",
|
||
"axes[0].set_title('Riccati P(t)'); axes[0].set_xlabel('t'); axes[0].legend(); axes[0].grid(alpha=0.3)\n",
|
||
"axes[1].plot(tg, x); axes[1].set_title('state x(t)'); axes[1].set_xlabel('t'); axes[1].grid(alpha=0.3)\n",
|
||
"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)\n",
|
||
"fig.tight_layout(); plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6c10852e",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Two-sided intensity control\n",
|
||
"\n",
|
||
"Affine premium $δ_±(λ) = α_± + κ_± λ$. First-order condition: $\\lambda^*_\\pm = \\max(0, (α_\\pm - ΔV_\\pm) / (2 κ_\\pm))$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"id": "61395265",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-05-12T10:16:08.275395Z",
|
||
"iopub.status.busy": "2026-05-12T10:16:08.274998Z",
|
||
"iopub.status.idle": "2026-05-12T10:16:08.557818Z",
|
||
"shell.execute_reply": "2026-05-12T10:16:08.555785Z"
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 770x440 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"deltas = np.linspace(-2.0, 2.0, 41)\n",
|
||
"lam_plus = []\n",
|
||
"for dv in deltas:\n",
|
||
" r = opt.two_sided_intensities(1.0, 1.0, 0.5, 0.5, dv, -dv)\n",
|
||
" lam_plus.append(r['lambda_plus'])\n",
|
||
"lam_plus = np.array(lam_plus)\n",
|
||
"fig, ax = plt.subplots()\n",
|
||
"ax.plot(deltas, lam_plus, lw=2)\n",
|
||
"ax.set_xlabel('ΔV_+'); ax.set_ylabel('λ*_+')\n",
|
||
"ax.set_title('Optimal upward intensity vs value-function gradient')\n",
|
||
"ax.grid(alpha=0.3); fig.tight_layout(); plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "09d2a422",
|
||
"metadata": {},
|
||
"source": [
|
||
"**Verified:** switching `V_0` matches analytic recursion exactly; Pontryagin `P(0) = 0.4999` against analytic `0.5`."
|
||
]
|
||
}
|
||
],
|
||
"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
|
||
}
|