Files
optimiz-rs/examples/notebooks/10_bsde.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": "7b032b6b",
"metadata": {},
"source": [
"# 10 — BSDE θ-scheme\n",
"\n",
"Generic CPU-only CrankNicolson scheme for linear backward stochastic differential equations. Reference doc page: [bsde.rst](../../docs/source/algorithms/bsde.rst)."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "9e253922",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:15:57.439545Z",
"iopub.status.busy": "2026-05-12T10:15:57.439220Z",
"iopub.status.idle": "2026-05-12T10:15:58.354185Z",
"shell.execute_reply": "2026-05-12T10:15:58.352587Z"
}
},
"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": "markdown",
"id": "afd86cb2",
"metadata": {},
"source": [
"## Exponential ground-truth check\n",
"\n",
"With $a(t) \\equiv -\\rho$, $b = c = 0$ and $Y_T = 1$ the analytic deterministic solution is $Y_t = e^{-\\rho (T-t)}$."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "b2abb764",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:15:58.357829Z",
"iopub.status.busy": "2026-05-12T10:15:58.357449Z",
"iopub.status.idle": "2026-05-12T10:15:58.364151Z",
"shell.execute_reply": "2026-05-12T10:15:58.363092Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Y0 = 0.740818179010676 exp(-rho T) = 0.7408182206817179\n",
"max abs error = 4.167104183938619e-08\n"
]
}
],
"source": [
"rho = 0.3\n",
"T = 1.0\n",
"res = opt.linear_bsde_constant_coeffs(\n",
" a_const=-rho, b_const=0.0, c_const=0.0,\n",
" terminal=1.0, n_steps=200, t_horizon=T, theta=0.5,\n",
")\n",
"tg = np.array(res['time_grid'])\n",
"yg = np.array(res['y'])\n",
"analytic = np.exp(-rho * (T - tg))\n",
"print('Y0 =', yg[0], ' exp(-rho T) =', analytic[0])\n",
"print('max abs error =', float(np.max(np.abs(yg - analytic))))\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "6d088c15",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:15:58.373282Z",
"iopub.status.busy": "2026-05-12T10:15:58.372923Z",
"iopub.status.idle": "2026-05-12T10:15:58.766339Z",
"shell.execute_reply": "2026-05-12T10:15:58.762616Z"
}
},
"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",
"ax.plot(tg, yg, label='θ-scheme', lw=2)\n",
"ax.plot(tg, analytic, '--', label='analytic exp(-ρ(T-t))')\n",
"ax.set_xlabel('t'); ax.set_ylabel('Y_t')\n",
"ax.set_title('Linear BSDE — CrankNicolson vs analytic')\n",
"ax.legend(); ax.grid(alpha=0.3)\n",
"fig.tight_layout(); plt.show()\n"
]
},
{
"cell_type": "markdown",
"id": "8f7263bb",
"metadata": {},
"source": [
"## Convergence rate study\n",
"\n",
"CrankNicolson is second-order in `Δt`."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "ee119e84",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:15:58.776028Z",
"iopub.status.busy": "2026-05-12T10:15:58.775538Z",
"iopub.status.idle": "2026-05-12T10:15:58.792909Z",
"shell.execute_reply": "2026-05-12T10:15:58.789105Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[(25, np.float64(2.666998401679166e-06)), (50, np.float64(6.667396952320104e-07)), (100, np.float64(1.6668430979915883e-07)), (200, np.float64(4.167104183938619e-08)), (400, np.float64(1.0417760876180182e-08)), (800, np.float64(2.6044438827810268e-09))]\n"
]
}
],
"source": [
"errs = []\n",
"ns = [25, 50, 100, 200, 400, 800]\n",
"for n in ns:\n",
" r = opt.linear_bsde_constant_coeffs(-rho, 0.0, 0.0, 1.0, n, T, 0.5)\n",
" errs.append(abs(r['y'][0] - np.exp(-rho * T)))\n",
"print(list(zip(ns, errs)))\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "b5e30db2",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-12T10:15:58.804359Z",
"iopub.status.busy": "2026-05-12T10:15:58.799015Z",
"iopub.status.idle": "2026-05-12T10:15:59.662120Z",
"shell.execute_reply": "2026-05-12T10:15:59.660888Z"
}
},
"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",
"ax.loglog(ns, errs, 'o-')\n",
"ax.loglog(ns, [errs[0] * (ns[0] / n) ** 2 for n in ns],\n",
" ':', label='O(Δt²) reference')\n",
"ax.set_xlabel('n_steps'); ax.set_ylabel('|Y0 analytic|')\n",
"ax.set_title('CrankNicolson convergence'); ax.grid(which='both', alpha=0.3); ax.legend()\n",
"fig.tight_layout(); plt.show()\n"
]
},
{
"cell_type": "markdown",
"id": "771765c7",
"metadata": {},
"source": [
"**Verified against analytic ground truth:** `Y_t = exp(-ρ (T - t))` — relative error at `t = 0` below `1e-3` for `n_steps = 200`."
]
}
],
"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
}