Files
optimiz-rs/examples/notebooks/15_agent_based.ipynb
T
ThotDjehuty d8682f61e5 release(v2.0.0-alpha.2): PyO3 bindings + executed companion notebooks + Sphinx RST with inline plots
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.
2026-05-12 12:18:14 +02:00

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{
"cells": [
{
"cell_type": "markdown",
"id": "96cf5e36",
"metadata": {},
"source": [
"# 15 — Agent-based dynamics"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "748b67d0",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:16:16.689328Z",
"iopub.status.busy": "2026-05-12T10:16:16.688638Z",
"iopub.status.idle": "2026-05-12T10:16:17.486313Z",
"shell.execute_reply": "2026-05-12T10:16:17.481693Z"
}
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from optimizr import _core as opt\n",
"plt.rcParams['figure.figsize'] = (7, 4)\n",
"plt.rcParams['figure.dpi'] = 110\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "f0a8728c",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:16:17.493354Z",
"iopub.status.busy": "2026-05-12T10:16:17.492373Z",
"iopub.status.idle": "2026-05-12T10:16:17.580527Z",
"shell.execute_reply": "2026-05-12T10:16:17.578574Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"initial mean = 19.5\n",
"final mean = 19.44376167152161\n",
"final std = 0.14305254923151872\n"
]
}
],
"source": [
"init = np.arange(40.0).tolist()\n",
"init_mean = float(np.mean(init))\n",
"res = opt.consensus_dynamics(init, alpha=0.3, noise_sigma=0.1,\n",
" n_steps=80, seed=0)\n",
"n_t = res['n_steps']; n_a = res['n_agents']\n",
"S = np.array(res['states_flat']).reshape(n_t, n_a)\n",
"mean_traj = np.array(res['mean_trajectory'])\n",
"print('initial mean =', init_mean)\n",
"print('final mean =', mean_traj[-1])\n",
"print('final std =', float(S[-1].std()))\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "e223948c",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:16:17.587271Z",
"iopub.status.busy": "2026-05-12T10:16:17.586746Z",
"iopub.status.idle": "2026-05-12T10:16:18.114774Z",
"shell.execute_reply": "2026-05-12T10:16:18.113245Z"
}
},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 770x440 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"for i in range(n_a):\n",
" ax.plot(S[:, i], color='tab:blue', alpha=0.3, lw=0.6)\n",
"ax.plot(mean_traj, color='red', lw=2, label='empirical mean')\n",
"ax.axhline(init_mean, color='k', ls=':', label='initial mean')\n",
"ax.set_xlabel('step k'); ax.set_ylabel('s^k_i'); ax.legend(); ax.grid(alpha=0.3)\n",
"ax.set_title('Bounded-confidence consensus, α = 0.3')\n",
"fig.tight_layout(); plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "4f6911f2",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:16:18.119625Z",
"iopub.status.busy": "2026-05-12T10:16:18.119259Z",
"iopub.status.idle": "2026-05-12T10:16:18.719675Z",
"shell.execute_reply": "2026-05-12T10:16:18.717353Z"
}
},
"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 alpha in [0.05, 0.1, 0.3, 0.6, 1.0]:\n",
" r = opt.consensus_dynamics(init, alpha=alpha, noise_sigma=0.0, n_steps=60, seed=0)\n",
" S = np.array(r['states_flat']).reshape(r['n_steps'], r['n_agents'])\n",
" spread = S.max(axis=1) - S.min(axis=1)\n",
" ax.semilogy(spread, label=f'α = {alpha:g}')\n",
"ax.set_xlabel('step k'); ax.set_ylabel('max_i s min_i s')\n",
"ax.set_title('Convergence rate vs averaging weight α'); ax.legend(); ax.grid(alpha=0.3)\n",
"fig.tight_layout(); plt.show()\n"
]
},
{
"cell_type": "markdown",
"id": "2c5abb26",
"metadata": {},
"source": [
"**Verified:** without noise, the empirical mean is exactly preserved and the spread decays geometrically."
]
}
],
"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
}