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.
167 lines
100 KiB
Plaintext
167 lines
100 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "cb7dea7c",
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"metadata": {},
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"source": [
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"# 17 — MMD calibration loss"
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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": "8d6df02a",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2026-05-12T10:16:23.357071Z",
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"iopub.status.busy": "2026-05-12T10:16:23.356796Z",
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"iopub.status.idle": "2026-05-12T10:16:24.029739Z",
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"shell.execute_reply": "2026-05-12T10:16:24.028259Z"
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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": "code",
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"execution_count": 2,
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"id": "b8b76095",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2026-05-12T10:16:24.040309Z",
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"iopub.status.busy": "2026-05-12T10:16:24.039241Z",
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"iopub.status.idle": "2026-05-12T10:16:24.058710Z",
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"shell.execute_reply": "2026-05-12T10:16:24.057343Z"
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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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"MMD self = 0.0\n",
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"MMD at shift 6.0 = 0.9032217374045481\n"
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]
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}
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],
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"source": [
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"x = np.linspace(0.0, 5.0, 80)\n",
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"shifts = np.linspace(0.0, 6.0, 40)\n",
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"d = [opt.mmd_gaussian(x.tolist(), (x + s).tolist(), 1.0) for s in shifts]\n",
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"print('MMD self =', d[0])\n",
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"print('MMD at shift 6.0 =', d[-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": 3,
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"id": "e3457ca1",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2026-05-12T10:16:24.061731Z",
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"iopub.status.busy": "2026-05-12T10:16:24.061447Z",
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"iopub.status.idle": "2026-05-12T10:16:24.329477Z",
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"shell.execute_reply": "2026-05-12T10:16:24.328075Z"
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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(shifts, d, lw=2)\n",
|
||
"ax.set_xlabel('translation Δ'); ax.set_ylabel('MMD(P, P + Δ)')\n",
|
||
"ax.set_title('Gaussian-kernel MMD vs translation (σ = 1)')\n",
|
||
"ax.grid(alpha=0.3); fig.tight_layout(); plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4861ad77",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Bandwidth dependence"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"id": "7f3b6484",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-05-12T10:16:24.336277Z",
|
||
"iopub.status.busy": "2026-05-12T10:16:24.335914Z",
|
||
"iopub.status.idle": "2026-05-12T10:16:24.819175Z",
|
||
"shell.execute_reply": "2026-05-12T10:16:24.817306Z"
|
||
}
|
||
},
|
||
"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 sigma in [0.25, 0.5, 1.0, 2.0]:\n",
|
||
" d = [opt.mmd_gaussian(x.tolist(), (x + s).tolist(), sigma) for s in shifts]\n",
|
||
" ax.plot(shifts, d, label=f'σ = {sigma:g}')\n",
|
||
"ax.set_xlabel('translation Δ'); ax.set_ylabel('MMD'); ax.legend(); ax.grid(alpha=0.3)\n",
|
||
"ax.set_title('MMD as a function of kernel bandwidth')\n",
|
||
"fig.tight_layout(); plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fd37ad48",
|
||
"metadata": {},
|
||
"source": [
|
||
"**Verified:** `MMD(x, x) = 0`; metric is strictly monotonic in shift."
|
||
]
|
||
}
|
||
],
|
||
"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
|
||
}
|