Interactive WALNUTS sampling of a 2D banana target
A numbl + React demo: the WALNUTS sampler (within-orbit adaptive leapfrog
No-U-Turn Sampler) draws from a banana target; the figure shows the density
heatmap with samples, live controls (sample count, leapfrog step, max error,
resample), and a step-by-step movie that traces the orbit-building leapfrog
trajectories. MATLAB port of Brian Ward's WALNUTS.js (chi-feng/mcmc-demo).
21 changed files+3339−0
.github/workflows/deploy.ymladded+61−0View file
@@ -0,0 +1,61 @@
1+name: Deploy numbl project to GitHub Pages
2+
3+# Builds the single-file web app, bundles this numbl project with the browser
4+# IDE, and publishes it to GitHub Pages on every push to main.
5+#
6+# One-time setup: Settings → Pages → "Build and deployment" → Source →
7+# "GitHub Actions".
8+
9+on:
10+ push:
11+ branches: [main]
12+ workflow_dispatch:
13+
14+permissions:
15+ contents: read
16+ pages: write
17+ id-token: write
18+
19+concurrency:
20+ group: pages
21+ cancel-in-progress: false
22+
23+jobs:
24+ build:
25+ runs-on: ubuntu-latest
26+ steps:
27+ - uses: actions/checkout@v4
28+
29+ - uses: actions/setup-node@v6
30+ with:
31+ node-version: 24
32+
33+ # Build the single-file figure app (app/dist/index.html) that
34+ # walnuts_sampler.m loads via uihtml. build-site then bundles
35+ # app/dist/index.html into the project (the rest of app/ is excluded via
36+ # .numblignore).
37+ - name: Build figure app
38+ run: |
39+ cd app
40+ npm ci
41+ npm run build
42+
43+ - uses: flatironinstitute/numbl/.github/actions/build-site@main
44+ with:
45+ project-dir: .
46+ # Build numbl from the main branch (development version, which includes
47+ # the uihtml two-way data/event bridge) rather than the npm release.
48+ numbl-ref: main
49+ # Keep the (mostly empty) output panel small so the interactive figure
50+ # panel below it gets most of the height on first load.
51+ max-initial-output-panel-height: 100
52+
53+ deploy:
54+ needs: build
55+ runs-on: ubuntu-latest
56+ environment:
57+ name: github-pages
58+ url: ${{ steps.deployment.outputs.page_url }}
59+ steps:
60+ - id: deployment
61+ uses: actions/deploy-pages@v4
.gitignoreadded+4−0View file
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1+# Local output from `numbl build-site`
2+/_site/
3+/dist/
4+node_modules/
.numblignoreadded+12−0View file
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1+# Files NOT to bundle into the deployed numbl project. Only the built
2+# single-file app (app/dist/index.html) is needed at runtime — exclude the web
3+# app's source and config. (node_modules, .git, .github, and agent instruction
4+# files like CLAUDE.md are excluded by default.)
5+.gitignore
6+app/.gitignore
7+app/src
8+app/index.html
9+app/package.json
10+app/package-lock.json
11+app/tsconfig.json
12+app/vite.config.ts
CLAUDE.mdadded+84−0View file
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1+# CLAUDE.md
2+
3+Tips for future agents. Patterned after the sibling `hitandrun-interactive`
4+project (same numbl + uihtml two-way bridge, 2D canvas figure).
5+
6+## Architecture
7+
8+- `app/` — React single-file widget (`npm run build` → `app/dist/index.html`).
9+- `*.m` at root — `walnuts_demo.m` (driver) and `walnuts_sampler.m` (figure plumbing).
10+- `helpers/` — `walnuts.m` (the sampler) and the target `log_density.m` / `grad_log_density.m`, put on the path by the driver via `addpath('helpers')`.
11+- `numbl-project.json` — project metadata; `entry` is the landing page.
12+
13+`addpath('helpers')` must be the **first statement** in the driver (numbl
14+resolves the search path before running, and addpath can't live inside a
15+function file). Run `walnuts_demo.m`, not the sampler directly.
16+
17+## Data flow (uihtml bridge)
18+
19+- **MATLAB → figure:** `uihtml(..., 'Data', struct)` / `sendEventToHTMLSource(src, name, data)`.
20+- **Figure → MATLAB:** `sendToMATLAB(name, value)` (see `app/src/bridge.ts`), received via `HTMLEventReceivedFcn`.
21+
22+The script sends the density grid + samples once, then handles two requests
23+(`walnuts_sampler.m` `on_event`):
24+
25+- `resample` `{n, dt, maxError}` → fresh chain → `samples` event. (Target is
26+ fixed, so the density is not re-sent.)
27+- `movie` `{dt, maxError}` → `walnuts(..., record=true)` for a few transitions →
28+ `movie` event carrying their orbit trajectories.
29+
30+The figure's controls (samples / Δt / max error sliders, Resample) drive
31+`resample`; the **▶ Movie** button drives `movie` and animates the returned
32+orbits (`App.tsx` + `DensityView.tsx`).
33+
34+### Trajectory recording
35+
36+`walnuts.m` records the orbit path only when called with `record=true`, via
37+globals (`WREC_*`): `macro_step` appends each *committed* macro-step's leapfrog
38+path (recomputed by `leapfrog_capture`), tagged with a segment id so the figure
39+breaks the polyline at orbit direction flips. Plain sampling (`record=false`)
40+takes the fast path with no recording overhead.
41+
42+## The algorithm
43+
44+`helpers/walnuts.m` is a direct port of Brian Ward's `algorithms/WALNUTS.js`
45+from chi-feng/mcmc-demo (based on Bob Carpenter's C++,
46+flatironinstitute/walnuts; paper arXiv:2506.18746). Spans carry both orbit
47+endpoints; `macro_step` does the within-orbit step halving; `build_span`
48+recurses (NUTS doubling); selection is Barker within sub-orbits, Metropolis at
49+the top. See README for full credits.
50+
51+## Performance
52+
53+Unlike the hitandrun kernel, WALNUTS uses **recursion + structs**, so it runs in
54+the numbl **interpreter** (it does not JS-JIT like a flat numeric loop). It's
55+still fine — banana orbits are shallow, ~1–2 ms/transition — so keep `N` modest
56+(the demo uses 1000 + 200 burn-in). Don't add a `%!numbl:assert_jit` guard here;
57+it would (correctly) fail.
58+
59+## Key files
60+
61+| File | Purpose |
62+|------|---------|
63+| `app/src/App.tsx` | Reads data, hosts the info panel |
64+| `app/src/render/DensityView.tsx` | Canvas: density heatmap + sample scatter |
65+| `app/src/bridge.ts` | `onData` / `onHostEvent` / `sendToMATLAB` (generic) |
66+| `helpers/walnuts.m` | The WALNUTS sampler |
67+| `helpers/log_density.m` / `grad_log_density.m` | Banana target |
68+| `walnuts_sampler.m` | Runs the chain, builds the density grid, opens the figure |
69+| `walnuts_demo.m` | Driver: addpath + seed + call the sampler |
70+
71+## Local iteration
72+
73+```
74+cd app && npm install && npm run build # → app/dist/index.html
75+cd ..
76+npx tsx $NUMBL/src/cli.ts run walnuts_demo.m --plot # quick loop
77+# or preview the GitHub Pages bundle:
78+( cd $NUMBL && npm run build:site-viewer ) # one-time
79+npx tsx $NUMBL/src/cli.ts build-site . --out _site --base /
80+( cd _site && python3 -m http.server 8080 )
81+```
82+
83+`$NUMBL` is a local clone of flatironinstitute/numbl. The real target is GitHub
84+Pages, where the deploy builds numbl from `main`.
README.mdadded+53−0View file
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1+# Interactive WALNUTS sampling
2+
3+Runs in the browser via [numbl](https://numbl.org) — no install.
4+
5+## ▶ [Open `walnuts_demo.m`](walnuts_demo.m) and click **Run**
6+
7+Samples are drawn from a 2D "banana" target by **WALNUTS** (the within-orbit
8+adaptive leapfrog No-U-Turn Sampler). The figure shows the target density as a
9+heatmap with the samples scattered on top.
10+
11+WALNUTS is a NUTS variant that adapts the leapfrog step size *within* each
12+orbit: each macro-step halves the step (and doubles the count) until the energy
13+error is within tolerance, then grows the orbit by NUTS-style doubling until a
14+U-turn.
15+
16+Controls:
17+
18+- **Samples** / **Leapfrog Δt** / **Max error** — change a setting to re-run the
19+ sampler with it (lower Δt or max error → more, smaller leapfrog steps).
20+- **Resample** — a fresh chain with the current settings.
21+- **▶ Movie** — animate WALNUTS building orbits step by step: each transition
22+ traces its leapfrog path (amber), then circles the selected draw, which joins
23+ the chain and starts the next transition.
24+
25+## How it works
26+
27+- [`walnuts_demo.m`](walnuts_demo.m) — driver: `addpath('helpers')`, seed, call the sampler.
28+- [`walnuts_sampler.m`](walnuts_sampler.m) — runs the chain, evaluates the target on a grid, opens the figure.
29+- `helpers/` — [`walnuts.m`](helpers/walnuts.m) (the algorithm) and the target [`log_density.m`](helpers/log_density.m) / [`grad_log_density.m`](helpers/grad_log_density.m).
30+- `app/` — a single-file React app that draws the density heatmap + samples on a canvas.
31+
32+The script sends the density grid + samples via `uihtml(..., 'Data', ...)`. The
33+controls call back: `sendToMATLAB('resample', {n, dt, maxError})` re-runs the
34+chain, and `sendToMATLAB('movie', {dt, maxError})` records a few transitions'
35+orbit trajectories (`walnuts(..., record=true)`); the script replies with
36+`sendEventToHTMLSource`.
37+
38+## Credits
39+
40+- **Algorithm:** N. Bou-Rabee, B. Carpenter, T. S. Kleppe, and S. Liu, *The
41+ within-orbit adaptive leapfrog no-U-turn sampler*,
42+ [arXiv:2506.18746](https://arxiv.org/abs/2506.18746) (2025). Reference C++ at
43+ [flatironinstitute/walnuts](https://github.com/flatironinstitute/walnuts)
44+ (Bob Carpenter).
45+- **This MATLAB port** follows Brian Ward's JavaScript implementation in
46+ [WardBrian/mcmc-demo](https://github.com/WardBrian/mcmc-demo) (`algorithms/WALNUTS.js`).
47+- **Demo framework & banana target** from Chi Feng's
48+ [mcmc-demo](https://github.com/chi-feng/mcmc-demo).
49+
50+## Deploy
51+
52+Pushing to `main` builds the app and publishes the project to GitHub Pages via
53+the [deploy workflow](.github/workflows/deploy.yml).
app/.gitignoreadded+2−0View file
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1+node_modules/
2+dist/
app/index.htmladded+22−0View file
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1+<!DOCTYPE html>
2+<html lang="en">
3+ <head>
4+ <meta charset="UTF-8" />
5+ <meta name="viewport" content="width=device-width, initial-scale=1.0" />
6+ <title>WALNUTS sampler</title>
7+ <style>
8+ html,
9+ body,
10+ #root {
11+ margin: 0;
12+ height: 100%;
13+ width: 100%;
14+ overflow: hidden;
15+ }
16+ </style>
17+ </head>
18+ <body>
19+ <div id="root"></div>
20+ <script type="module" src="/src/main.tsx"></script>
21+ </body>
22+</html>
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app/package.jsonadded+23−0View file
@@ -0,0 +1,23 @@
1+{
2+ "name": "walnuts-interactive-app",
3+ "private": true,
4+ "version": "0.0.0",
5+ "type": "module",
6+ "scripts": {
7+ "dev": "vite",
8+ "build": "vite build",
9+ "preview": "vite preview"
10+ },
11+ "dependencies": {
12+ "react": "^18.3.1",
13+ "react-dom": "^18.3.1"
14+ },
15+ "devDependencies": {
16+ "@types/react": "^18.3.12",
17+ "@types/react-dom": "^18.3.1",
18+ "@vitejs/plugin-react": "^4.3.4",
19+ "typescript": "^5.6.3",
20+ "vite": "^6.0.7",
21+ "vite-plugin-singlefile": "^2.1.0"
22+ }
23+}
app/src/App.tsxadded+327−0View file
@@ -0,0 +1,327 @@
1+import { useEffect, useState, type CSSProperties } from "react";
2+import {
3+ DensityView,
4+ type Points,
5+ type DensityGrid,
6+ type OrbitPath,
7+ type Pt,
8+} from "./render/DensityView.js";
9+import { onData, onHostEvent, sendToMATLAB } from "./bridge.js";
10+
11+/** Payload from the numbl script: the target density (for the heatmap) plus the
12+ * WALNUTS samples. Mirrors what walnuts_sampler.m sends. */
13+interface WalnutsData {
14+ type: "walnuts";
15+ density: DensityGrid;
16+ samples: Points;
17+ n: number;
18+ dt: number;
19+ maxError: number;
20+}
21+
22+function isWalnutsData(d: unknown): d is WalnutsData {
23+ return (
24+ !!d &&
25+ typeof d === "object" &&
26+ (d as WalnutsData).type === "walnuts" &&
27+ !!(d as WalnutsData).density &&
28+ !!(d as WalnutsData).samples
29+ );
30+}
31+
32+interface SamplesEvent {
33+ x: number[];
34+ y: number[];
35+ n: number;
36+ dt: number;
37+ maxError: number;
38+}
39+
40+/** One recorded transition's orbit (from `walnuts(..., record=true)`). */
41+interface MovieStep {
42+ px: number[];
43+ py: number[];
44+ seg: number[];
45+ startX: number;
46+ startY: number;
47+ selX: number;
48+ selY: number;
49+}
50+
51+const SAMPLE_CHOICES = [100, 300, 1000, 3000];
52+const DEFAULT_N = 1000;
53+const DT_MIN = 0.05;
54+const DT_MAX = 1.2;
55+const ERR_MIN = 0.1;
56+const ERR_MAX = 4;
57+
58+// Movie pacing: reveal a couple of leapfrog points per tick, then linger on the
59+// selected draw before the next transition.
60+const MOVIE_TICK_MS = 55;
61+const MOVIE_REVEAL = 2;
62+const MOVIE_HOLD = 14; // extra k-units to hold the selected point
63+
64+export function App() {
65+ const [data, setData] = useState<WalnutsData | null>(null);
66+ const [n, setN] = useState(DEFAULT_N);
67+ const [dt, setDt] = useState(0.4);
68+ const [maxError, setMaxError] = useState(0.8);
69+ const [busy, setBusy] = useState(false);
70+ const [movieData, setMovieData] = useState<MovieStep[] | null>(null);
71+ const [movie, setMovie] = useState<{ si: number; k: number } | null>(null);
72+
73+ useEffect(() => {
74+ const offData = onData(d => {
75+ if (isWalnutsData(d)) {
76+ setData(d);
77+ setN(d.n);
78+ setDt(d.dt);
79+ setMaxError(d.maxError);
80+ }
81+ });
82+ // Resample: same target, new draws.
83+ const offSamples = onHostEvent("samples", ev => {
84+ const s = ev as SamplesEvent;
85+ if (!s || !Array.isArray(s.x)) return;
86+ setData(prev =>
87+ prev
88+ ? { ...prev, samples: { x: s.x, y: s.y }, n: s.n, dt: s.dt, maxError: s.maxError }
89+ : prev
90+ );
91+ setBusy(false);
92+ });
93+ // Movie: an array of recorded transition orbits to animate.
94+ const offMovie = onHostEvent("movie", ev => {
95+ if (!Array.isArray(ev) || ev.length === 0) {
96+ setBusy(false);
97+ return;
98+ }
99+ setMovieData(ev as MovieStep[]);
100+ setMovie({ si: 0, k: 0 });
101+ setBusy(false);
102+ });
103+ return () => {
104+ offData();
105+ offSamples();
106+ offMovie();
107+ };
108+ }, []);
109+
110+ // Movie clock.
111+ useEffect(() => {
112+ if (!movie || !movieData) return;
113+ const id = setTimeout(() => {
114+ setMovie(m => {
115+ if (!m) return m;
116+ const step = movieData[m.si];
117+ const count = step.px.length;
118+ if (m.k < count + MOVIE_HOLD) return { si: m.si, k: m.k + MOVIE_REVEAL };
119+ const nextSi = m.si + 1;
120+ return nextSi >= movieData.length ? null : { si: nextSi, k: 0 };
121+ });
122+ }, MOVIE_TICK_MS);
123+ return () => clearTimeout(id);
124+ }, [movie, movieData]);
125+
126+ const stopMovie = () => {
127+ setMovie(null);
128+ setMovieData(null);
129+ };
130+
131+ const resample = (count: number, step: number, err: number) => {
132+ if (!data || busy) return;
133+ stopMovie();
134+ setBusy(true);
135+ sendToMATLAB("resample", { n: count, dt: step, maxError: err });
136+ };
137+
138+ const playMovie = () => {
139+ if (movie) {
140+ stopMovie();
141+ return;
142+ }
143+ if (!data || busy) return;
144+ setBusy(true); // until the trajectory arrives
145+ sendToMATLAB("movie", { dt, maxError });
146+ };
147+
148+ // ── derive the movie overlay for the current frame ──
149+ let cloud: Points = data ? data.samples : { x: [], y: [] };
150+ let orbit: OrbitPath | null = null;
151+ let start: Pt | null = null;
152+ let lead: Pt | null = null;
153+ let chainPts: Points | null = null;
154+ let selected: Pt | null = null;
155+ if (movie && movieData) {
156+ const step = movieData[movie.si];
157+ const count = step.px.length;
158+ const k = Math.min(movie.k, count);
159+ orbit = { x: step.px.slice(0, k), y: step.py.slice(0, k), seg: step.seg.slice(0, k) };
160+ start = { x: step.startX, y: step.startY };
161+ if (k > 0) lead = { x: step.px[k - 1], y: step.py[k - 1] };
162+ const cx: number[] = [];
163+ const cy: number[] = [];
164+ for (let j = 0; j < movie.si; j++) {
165+ cx.push(movieData[j].selX);
166+ cy.push(movieData[j].selY);
167+ }
168+ chainPts = { x: cx, y: cy };
169+ if (movie.k >= count) selected = { x: step.selX, y: step.selY };
170+ cloud = data ? data.samples : { x: [], y: [] };
171+ }
172+
173+ const controlsDisabled = !data || busy || !!movie;
174+ const status = busy
175+ ? "sampling…"
176+ : movie && movieData
177+ ? `movie · transition ${movie.si + 1}/${movieData.length}`
178+ : `${data ? data.n.toLocaleString() : "—"} samples`;
179+
180+ return (
181+ <div style={rootStyle}>
182+ {data ? (
183+ <DensityView
184+ density={data.density}
185+ samples={cloud}
186+ orbit={orbit}
187+ start={start}
188+ lead={lead}
189+ chainPts={chainPts}
190+ selected={selected}
191+ />
192+ ) : (
193+ <div style={waitingStyle}>Waiting for samples from the script…</div>
194+ )}
195+
196+ <div style={panelStyle}>
197+ <div style={{ fontWeight: 600, marginBottom: 4 }}>WALNUTS</div>
198+ <div style={{ fontSize: 11, color: "#475569", marginBottom: 8 }}>
199+ sampling a banana target
200+ </div>
201+
202+ <label style={labelStyle}>
203+ Samples: <b>{n.toLocaleString()}</b>
204+ <input
205+ type="range"
206+ min={0}
207+ max={SAMPLE_CHOICES.length - 1}
208+ step={1}
209+ value={Math.max(0, SAMPLE_CHOICES.indexOf(n))}
210+ disabled={controlsDisabled}
211+ onChange={e => setN(SAMPLE_CHOICES[Number(e.target.value)])}
212+ onPointerUp={e =>
213+ resample(SAMPLE_CHOICES[Number(e.currentTarget.value)], dt, maxError)
214+ }
215+ style={sliderStyle}
216+ />
217+ </label>
218+
219+ <label style={labelStyle}>
220+ Leapfrog Δt: <b>{dt.toFixed(2)}</b>
221+ <input
222+ type="range"
223+ min={DT_MIN}
224+ max={DT_MAX}
225+ step={0.05}
226+ value={dt}
227+ disabled={controlsDisabled}
228+ onChange={e => setDt(Number(e.target.value))}
229+ onPointerUp={e => resample(n, Number(e.currentTarget.value), maxError)}
230+ style={sliderStyle}
231+ />
232+ </label>
233+
234+ <label style={labelStyle}>
235+ Max error: <b>{maxError.toFixed(2)}</b>
236+ <input
237+ type="range"
238+ min={ERR_MIN}
239+ max={ERR_MAX}
240+ step={0.1}
241+ value={maxError}
242+ disabled={controlsDisabled}
243+ onChange={e => setMaxError(Number(e.target.value))}
244+ onPointerUp={e => resample(n, dt, Number(e.currentTarget.value))}
245+ style={sliderStyle}
246+ />
247+ </label>
248+
249+ <div style={{ display: "flex", gap: 6, marginTop: 8 }}>
250+ <button
251+ style={btnStyle}
252+ disabled={controlsDisabled}
253+ onClick={() => resample(n, dt, maxError)}
254+ title="Draw a fresh chain with these settings"
255+ >
256+ Resample
257+ </button>
258+ <button
259+ style={btnStyle}
260+ disabled={!data || busy}
261+ onClick={playMovie}
262+ title="Animate WALNUTS building orbits step by step"
263+ >
264+ {movie ? "■ Stop" : "▶ Movie"}
265+ </button>
266+ </div>
267+
268+ <div style={{ fontSize: 10, color: "#64748b", marginTop: 8 }}>
269+ {status}
270+ </div>
271+ </div>
272+ </div>
273+ );
274+}
275+
276+const rootStyle: CSSProperties = {
277+ position: "absolute",
278+ inset: 0,
279+ overflow: "hidden",
280+ background: "#ffffff",
281+ fontFamily: "system-ui, -apple-system, Arial, sans-serif",
282+};
283+
284+const waitingStyle: CSSProperties = {
285+ position: "absolute",
286+ inset: 0,
287+ display: "flex",
288+ alignItems: "center",
289+ justifyContent: "center",
290+ color: "#94a3b8",
291+};
292+
293+const panelStyle: CSSProperties = {
294+ position: "absolute",
295+ top: 8,
296+ left: 8,
297+ width: 168,
298+ padding: "8px 10px",
299+ background: "rgba(255,255,255,0.92)",
300+ border: "1px solid #e2e8f0",
301+ borderRadius: 6,
302+ boxShadow: "0 1px 3px rgba(0,0,0,0.1)",
303+ color: "#0f172a",
304+};
305+
306+const labelStyle: CSSProperties = {
307+ display: "block",
308+ fontSize: 11,
309+ marginTop: 6,
310+};
311+
312+const sliderStyle: CSSProperties = {
313+ width: "100%",
314+ marginTop: 2,
315+};
316+
317+const btnStyle: CSSProperties = {
318+ flex: 1,
319+ padding: "4px 6px",
320+ fontSize: 11,
321+ whiteSpace: "nowrap",
322+ cursor: "pointer",
323+ background: "#f8fafc",
324+ border: "1px solid #cbd5e1",
325+ borderRadius: 5,
326+ color: "#0f172a",
327+};
app/src/bridge.tsadded+71−0View file
@@ -0,0 +1,71 @@
1+// Bridge to the numbl/MATLAB `uihtml` host. The host calls a global
2+// `setup(htmlComponent)` once the page loads; we expose small subscribe/send
3+// helpers so React components don't race that callback (latest Data is buffered,
4+// and host-event listeners attach whenever the component becomes available).
5+
6+interface HtmlComponent {
7+ Data: unknown;
8+ addEventListener(name: string, fn: (e: { Data?: unknown }) => void): void;
9+ sendEventToMATLAB(name: string, data: unknown): void;
10+}
11+
12+type DataListener = (data: unknown) => void;
13+type EventListener = (data: unknown) => void;
14+
15+let htmlComponent: HtmlComponent | null = null;
16+let latestData: unknown = undefined;
17+const dataListeners = new Set<DataListener>();
18+const eventListeners = new Map<string, Set<EventListener>>();
19+const attachedNames = new Set<string>();
20+
21+function deliverData(d: unknown): void {
22+ latestData = d;
23+ dataListeners.forEach(fn => fn(d));
24+}
25+
26+/** Attach a single host listener for `name` that fans out to our listener set. */
27+function attach(name: string): void {
28+ if (!htmlComponent || attachedNames.has(name)) return;
29+ attachedNames.add(name);
30+ htmlComponent.addEventListener(name, e => {
31+ const fns = eventListeners.get(name);
32+ if (fns) fns.forEach(fn => fn(e?.Data));
33+ });
34+}
35+
36+// Register the global the host calls after the page loads.
37+(window as unknown as { setup: (hc: HtmlComponent) => void }).setup = hc => {
38+ htmlComponent = hc;
39+ hc.addEventListener("DataChanged", () => deliverData(hc.Data));
40+ for (const name of eventListeners.keys()) attach(name);
41+ if (hc.Data != null) deliverData(hc.Data);
42+};
43+
44+/** Subscribe to the `Data` channel (script → page). Fires immediately with the
45+ * latest data if it has already arrived. */
46+export function onData(fn: DataListener): () => void {
47+ dataListeners.add(fn);
48+ if (latestData !== undefined) fn(latestData);
49+ return () => {
50+ dataListeners.delete(fn);
51+ };
52+}
53+
54+/** Subscribe to a named host event (from MATLAB `sendEventToHTMLSource`). */
55+export function onHostEvent(name: string, fn: EventListener): () => void {
56+ let set = eventListeners.get(name);
57+ if (!set) {
58+ set = new Set();
59+ eventListeners.set(name, set);
60+ }
61+ set.add(fn);
62+ attach(name);
63+ return () => {
64+ set!.delete(fn);
65+ };
66+}
67+
68+/** Send an event back to the interpreter (page → script). */
69+export function sendToMATLAB(name: string, data: unknown): void {
70+ htmlComponent?.sendEventToMATLAB(name, data);
71+}
app/src/main.tsxadded+12−0View file
@@ -0,0 +1,12 @@
1+import { StrictMode } from "react";
2+import { createRoot } from "react-dom/client";
3+// Import the bridge first so `window.setup` is defined before the host's
4+// bootstrap calls it (it defers to DOMContentLoaded, after module scripts run).
5+import "./bridge.js";
6+import { App } from "./App.js";
7+
8+createRoot(document.getElementById("root")!).render(
9+ <StrictMode>
10+ <App />
11+ </StrictMode>
12+);
app/src/render/DensityView.tsxadded+228−0View file
@@ -0,0 +1,228 @@
1+import { useEffect, useRef, type CSSProperties } from "react";
2+
3+export interface Points {
4+ x: number[];
5+ y: number[];
6+}
7+
8+export interface Pt {
9+ x: number;
10+ y: number;
11+}
12+
13+/** A recorded orbit path: positions x/y with a per-point macro-step id `seg`,
14+ * so the polyline breaks where the orbit direction flips. */
15+export interface OrbitPath {
16+ x: number[];
17+ y: number[];
18+ seg: number[];
19+}
20+
21+export interface DensityGrid {
22+ /** Row-major log-density: index (iy)*nx + ix, iy from ymin (0) to ymax. */
23+ values: number[];
24+ nx: number;
25+ ny: number;
26+ xmin: number;
27+ xmax: number;
28+ ymin: number;
29+ ymax: number;
30+}
31+
32+interface DensityViewProps {
33+ density: DensityGrid;
34+ samples: Points;
35+ // ── movie overlay (all optional) ──
36+ orbit?: OrbitPath | null; // revealed orbit path of the current transition
37+ start?: Pt | null; // start point of the current transition (ringed)
38+ lead?: Pt | null; // current frontier point of the revealed path
39+ chainPts?: Points | null; // accepted draws so far (the Markov chain)
40+ selected?: Pt | null; // the just-selected draw (circled)
41+}
42+
43+const DOT = "rgba(15, 23, 42, 0.5)";
44+const DOT_RADIUS = 1.5;
45+const MARGIN = 16;
46+// Heatmap colour ramp: white (low density) → blue (high density).
47+const LO: [number, number, number] = [255, 255, 255];
48+const HI: [number, number, number] = [37, 99, 235];
49+const ORBIT = "#f59e0b"; // amber: the leapfrog orbit path
50+const START = "#334155"; // slate ring: where the transition started
51+const SELECTED = "#0f172a"; // near-black: the selected draw (circled)
52+
53+/** Renders the target density as a heatmap with samples scattered on top, plus
54+ * an optional orbit overlay for the step-by-step movie. Fits the density's
55+ * world bounds to the canvas (aspect preserved, y up). DPR-aware; redraws on
56+ * data change and resize. */
57+export function DensityView({
58+ density,
59+ samples,
60+ orbit,
61+ start,
62+ lead,
63+ chainPts,
64+ selected,
65+}: DensityViewProps) {
66+ const canvasRef = useRef<HTMLCanvasElement>(null);
67+ const containerRef = useRef<HTMLDivElement>(null);
68+
69+ useEffect(() => {
70+ const canvas = canvasRef.current;
71+ const container = containerRef.current;
72+ if (!canvas || !container) return;
73+
74+ const draw = () => {
75+ const ctx = canvas.getContext("2d");
76+ if (!ctx) return;
77+
78+ const dpr = window.devicePixelRatio || 1;
79+ const cssW = container.clientWidth;
80+ const cssH = container.clientHeight;
81+ if (cssW === 0 || cssH === 0) return;
82+
83+ canvas.width = Math.round(cssW * dpr);
84+ canvas.height = Math.round(cssH * dpr);
85+ canvas.style.width = `${cssW}px`;
86+ canvas.style.height = `${cssH}px`;
87+ ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
88+ ctx.clearRect(0, 0, cssW, cssH);
89+
90+ const { nx, ny, xmin, xmax, ymin, ymax, values } = density;
91+ if (!nx || !ny) return;
92+
93+ const worldW = xmax - xmin || 1;
94+ const worldH = ymax - ymin || 1;
95+ const scale = Math.min(
96+ (cssW - 2 * MARGIN) / worldW,
97+ (cssH - 2 * MARGIN) / worldH
98+ );
99+ const destW = worldW * scale;
100+ const destH = worldH * scale;
101+ const destX = (cssW - destW) / 2;
102+ const destY = (cssH - destH) / 2;
103+ const toPx = (x: number) => destX + (x - xmin) * scale;
104+ const toPy = (y: number) => destY + (ymax - y) * scale; // y up
105+
106+ // Heatmap: paint the grid into an offscreen nx×ny image, then scale it in.
107+ let maxLp = -Infinity;
108+ for (let i = 0; i < values.length; i++) {
109+ if (values[i] > maxLp) maxLp = values[i];
110+ }
111+ const off = document.createElement("canvas");
112+ off.width = nx;
113+ off.height = ny;
114+ const offCtx = off.getContext("2d");
115+ if (offCtx) {
116+ const img = offCtx.createImageData(nx, ny);
117+ for (let r = 0; r < ny; r++) {
118+ const iy = ny - 1 - r; // image row 0 = top = ymax
119+ for (let c = 0; c < nx; c++) {
120+ const t = Math.pow(Math.exp(values[iy * nx + c] - maxLp), 0.4);
121+ const p = (r * nx + c) * 4;
122+ img.data[p] = LO[0] + t * (HI[0] - LO[0]);
123+ img.data[p + 1] = LO[1] + t * (HI[1] - LO[1]);
124+ img.data[p + 2] = LO[2] + t * (HI[2] - LO[2]);
125+ img.data[p + 3] = 255;
126+ }
127+ }
128+ offCtx.putImageData(img, 0, 0);
129+ ctx.imageSmoothingEnabled = true;
130+ ctx.drawImage(off, destX, destY, destW, destH);
131+ }
132+
133+ ctx.strokeStyle = "rgba(15,23,42,0.15)";
134+ ctx.lineWidth = 1;
135+ ctx.strokeRect(destX, destY, destW, destH);
136+
137+ // Sample cloud (dimmed when the movie overlay is active).
138+ ctx.fillStyle = orbit || chainPts ? "rgba(15,23,42,0.18)" : DOT;
139+ const n = Math.min(samples.x.length, samples.y.length);
140+ for (let i = 0; i < n; i++) {
141+ ctx.beginPath();
142+ ctx.arc(toPx(samples.x[i]), toPy(samples.y[i]), DOT_RADIUS, 0, 2 * Math.PI);
143+ ctx.fill();
144+ }
145+
146+ // Accepted draws so far (the Markov chain).
147+ if (chainPts) {
148+ ctx.fillStyle = SELECTED;
149+ const m = Math.min(chainPts.x.length, chainPts.y.length);
150+ for (let i = 0; i < m; i++) {
151+ ctx.beginPath();
152+ ctx.arc(toPx(chainPts.x[i]), toPy(chainPts.y[i]), 2, 0, 2 * Math.PI);
153+ ctx.fill();
154+ }
155+ }
156+
157+ // The orbit being traced: polyline (broken at segment changes) + a dot at
158+ // each leapfrog step, so the discrete steps and step-size are visible.
159+ if (orbit && orbit.x.length > 0) {
160+ ctx.strokeStyle = ORBIT;
161+ ctx.lineWidth = 1.5;
162+ ctx.beginPath();
163+ for (let i = 0; i < orbit.x.length; i++) {
164+ const px = toPx(orbit.x[i]);
165+ const py = toPy(orbit.y[i]);
166+ if (i === 0 || orbit.seg[i] !== orbit.seg[i - 1]) ctx.moveTo(px, py);
167+ else ctx.lineTo(px, py);
168+ }
169+ ctx.stroke();
170+ ctx.fillStyle = ORBIT;
171+ for (let i = 0; i < orbit.x.length; i++) {
172+ ctx.beginPath();
173+ ctx.arc(toPx(orbit.x[i]), toPy(orbit.y[i]), 1.7, 0, 2 * Math.PI);
174+ ctx.fill();
175+ }
176+ }
177+
178+ // Start of the current transition (open ring).
179+ if (start) {
180+ ctx.strokeStyle = START;
181+ ctx.lineWidth = 1.5;
182+ ctx.beginPath();
183+ ctx.arc(toPx(start.x), toPy(start.y), 4, 0, 2 * Math.PI);
184+ ctx.stroke();
185+ }
186+
187+ // Current frontier of the orbit.
188+ if (lead) {
189+ ctx.fillStyle = ORBIT;
190+ ctx.beginPath();
191+ ctx.arc(toPx(lead.x), toPy(lead.y), 3, 0, 2 * Math.PI);
192+ ctx.fill();
193+ }
194+
195+ // The selected draw: a circled black point.
196+ if (selected) {
197+ const cx = toPx(selected.x);
198+ const cy = toPy(selected.y);
199+ ctx.strokeStyle = SELECTED;
200+ ctx.lineWidth = 1.5;
201+ ctx.beginPath();
202+ ctx.arc(cx, cy, 6.5, 0, 2 * Math.PI);
203+ ctx.stroke();
204+ ctx.fillStyle = SELECTED;
205+ ctx.beginPath();
206+ ctx.arc(cx, cy, 3.2, 0, 2 * Math.PI);
207+ ctx.fill();
208+ }
209+ };
210+
211+ draw();
212+ const ro = new ResizeObserver(draw);
213+ ro.observe(container);
214+ return () => ro.disconnect();
215+ }, [density, samples, orbit, start, lead, chainPts, selected]);
216+
217+ return (
218+ <div ref={containerRef} style={containerStyle}>
219+ <canvas ref={canvasRef} style={{ display: "block" }} />
220+ </div>
221+ );
222+}
223+
224+const containerStyle: CSSProperties = {
225+ position: "absolute",
226+ inset: 0,
227+ overflow: "hidden",
228+};
app/tsconfig.jsonadded+20−0View file
@@ -0,0 +1,20 @@
1+{
2+ "compilerOptions": {
3+ "target": "ESNext",
4+ "useDefineForClassFields": true,
5+ "lib": ["ESNext", "DOM", "DOM.Iterable"],
6+ "module": "ESNext",
7+ "skipLibCheck": true,
8+ "moduleResolution": "bundler",
9+ "allowImportingTsExtensions": true,
10+ "resolveJsonModule": true,
11+ "isolatedModules": true,
12+ "noEmit": true,
13+ "jsx": "react-jsx",
14+ "strict": true,
15+ "noUnusedLocals": false,
16+ "noUnusedParameters": false,
17+ "noFallthroughCasesInSwitch": true
18+ },
19+ "include": ["src"]
20+}
app/vite.config.tsadded+16−0View file
@@ -0,0 +1,16 @@
1+import { defineConfig } from "vite";
2+import react from "@vitejs/plugin-react";
3+import { viteSingleFile } from "vite-plugin-singlefile";
4+
5+// Builds the whole app (JS + CSS) inlined into a single dist/index.html, so the
6+// numbl `.m` can read it with `fileread` and pass it to uihtml (HTMLSource) —
7+// no supporting files, works in numbl (browser and CLI) and real MATLAB.
8+export default defineConfig({
9+ plugins: [react(), viteSingleFile()],
10+ build: {
11+ target: "esnext",
12+ cssCodeSplit: false,
13+ assetsInlineLimit: 100_000_000,
14+ chunkSizeWarningLimit: 100_000_000,
15+ },
16+});
helpers/grad_log_density.madded+18−0View file
@@ -0,0 +1,18 @@
1+function g = grad_log_density(theta)
2+%GRAD_LOG_DENSITY Gradient of the banana log density (see log_density.m).
3+a = 2;
4+b = 0.2;
5+x1 = theta(1);
6+x2 = theta(2);
7+y1 = x1 / a;
8+y2 = x2 * a + a * b * (x1.^2 + a.^2);
9+d1 = y1 - 0;
10+d2 = y2 - 4;
11+% Gradient w.r.t. y of the Gaussian log density is -inv(Sigma)*d.
12+gy1 = -((4 / 3) * d1 - (2 / 3) * d2);
13+gy2 = -(-(2 / 3) * d1 + (4 / 3) * d2);
14+% Chain rule back through the twist y(x).
15+gx1 = gy1 / a + gy2 * a * b * 2 * x1;
16+gx2 = gy2 * a;
17+g = [gx1; gx2];
18+end
helpers/log_density.madded+19−0View file
@@ -0,0 +1,19 @@
1+function lp = log_density(theta)
2+%LOG_DENSITY Unnormalized log density of the "banana" target.
3+% The standard banana from chi-feng's mcmc-demo: a correlated Gaussian
4+% (mean [0; 4], covariance [1 0.5; 0.5 1]) pulled into a banana shape by a
5+% quadratic twist. theta is a 2x1 column vector. The normalizing constant is
6+% dropped (irrelevant for sampling and for the heatmap).
7+a = 2;
8+b = 0.2;
9+x1 = theta(1);
10+x2 = theta(2);
11+% Twist x -> y, then evaluate the Gaussian at y.
12+y1 = x1 / a;
13+y2 = x2 * a + a * b * (x1.^2 + a.^2);
14+d1 = y1 - 0;
15+d2 = y2 - 4;
16+% Q = d' * inv(Sigma) * d, with inv([1 .5; .5 1]) = [4/3 -2/3; -2/3 4/3].
17+Q = (4 / 3) * (d1.^2 + d2.^2) - (4 / 3) * d1 .* d2;
18+lp = -0.5 * Q;
19+end
helpers/walnuts.madded+275−0View file
@@ -0,0 +1,275 @@
1+function [chain, traj] = walnuts(theta0, n_samples, dt, max_error, record)
2+%WALNUTS Within-orbit adaptive No-U-Turn Sampler.
3+% CHAIN = WALNUTS(THETA0, N_SAMPLES, DT, MAX_ERROR) runs N_SAMPLES WALNUTS
4+% transitions starting from column vector THETA0 and returns CHAIN, a
5+% dim-by-N_SAMPLES matrix of draws. DT is the base leapfrog step and MAX_ERROR
6+% the per-macro-step energy-error tolerance that drives the within-orbit step
7+% halving.
8+%
9+% [CHAIN, TRAJ] = WALNUTS(..., true) additionally records, per transition, the
10+% leapfrog path of the orbit it builds (for the figure's step-by-step movie).
11+% TRAJ{i} has fields px/py (orbit positions), seg (per-point macro-step id, so
12+% the path breaks at direction flips), startX/startY and selX/selY. Recording
13+% adds overhead, so leave it off for plain sampling.
14+%
15+% This is a direct port of Brian Ward's JavaScript implementation in
16+% chi-feng/mcmc-demo (algorithms/WALNUTS.js), itself based on Bob Carpenter's
17+% C++ (flatironinstitute/walnuts) for the paper arXiv:2506.18746. The target
18+% density is supplied by log_density.m / grad_log_density.m on the path.
19+%
20+% A Span carries the two orbit endpoints (backward "_bk", forward "_fw"),
21+% each with position/momentum/gradient/joint-logp, plus a selected draw
22+% theta_select and the log of the summed orbit weight (logp).
23+
24+if nargin < 5 || isempty(record)
25+ record = false;
26+end
27+% Trajectory recorder (used only when record is true). macro_step appends each
28+% committed leapfrog path to these as it grows the orbit.
29+global WREC_ON WREC_X WREC_Y WREC_SEG WREC_SEGID
30+WREC_ON = record;
31+
32+dim = numel(theta0);
33+chain = zeros(dim, n_samples);
34+traj = {};
35+theta = theta0;
36+for i = 1:n_samples
37+ if record
38+ start_pt = theta;
39+ WREC_X = [];
40+ WREC_Y = [];
41+ WREC_SEG = [];
42+ WREC_SEGID = 0;
43+ end
44+ theta = transition(theta, dt, max_error);
45+ chain(:, i) = theta;
46+ if record
47+ traj{i} = struct('px', WREC_X, 'py', WREC_Y, 'seg', WREC_SEG, ...
48+ 'startX', start_pt(1), 'startY', start_pt(2), ...
49+ 'selX', theta(1), 'selY', theta(2));
50+ end
51+end
52+WREC_ON = false;
53+end
54+
55+function theta_select = transition(theta, dt, max_error)
56+% One WALNUTS transition: sample momentum, grow the orbit by repeated doubling
57+% in random directions until a U-turn (or a failed step / max depth), choosing
58+% the draw by a Metropolis update against the growing orbit.
59+rho = randn(numel(theta), 1);
60+grad = grad_log_density(theta);
61+logp = log_density(theta) - sum(rho.^2) / 2;
62+span_accum = make_leaf_span(theta, rho, grad, logp);
63+
64+for depth = 0:11
65+ if rand < 0.5
66+ direction = -1;
67+ else
68+ direction = 1;
69+ end
70+ [ok, next_span] = build_span(span_accum, direction, depth, dt, max_error);
71+ if ~ok
72+ break
73+ end
74+ combined_uturn = uturn(span_accum, next_span, direction);
75+ % Top-level selection is a Metropolis update (use_barker = false).
76+ span_accum = combine(span_accum, next_span, false, direction);
77+ if combined_uturn
78+ break
79+ end
80+end
81+theta_select = span_accum.theta_select;
82+end
83+
84+function [ok, span] = build_span(span_in, direction, depth, dt, max_error)
85+% Recursively build a balanced orbit of 2^depth macro-steps. Returns ok=false
86+% if any macro-step fails or a sub-orbit U-turns.
87+if depth == 0
88+ [ok, span] = build_leaf(span_in, direction, dt, max_error);
89+ return
90+end
91+[ok, left] = build_span(span_in, direction, depth - 1, dt, max_error);
92+if ~ok
93+ span = left;
94+ return
95+end
96+[ok, right] = build_span(left, direction, depth - 1, dt, max_error);
97+if ~ok
98+ span = right;
99+ return
100+end
101+if uturn(left, right, direction)
102+ ok = false;
103+ span = left;
104+ return
105+end
106+% Sub-orbit selection is a Barker update (use_barker = true).
107+span = combine(left, right, true, direction);
108+ok = true;
109+end
110+
111+function [ok, span] = build_leaf(span_in, direction, dt, max_error)
112+[success, theta_next, rho_next, grad_next, logp_next] = ...
113+ macro_step(span_in, direction, dt, max_error);
114+if ~success
115+ ok = false;
116+ span = span_in;
117+ return
118+end
119+span = make_leaf_span(theta_next, rho_next, grad_next, logp_next);
120+ok = true;
121+end
122+
123+function [success, theta_next, rho_next, grad_next, logp_next] = ...
124+ macro_step(span, direction, dt, max_error)
125+% Take one macro-step off the orbit's leading endpoint, adaptively halving the
126+% leapfrog step (and doubling the count) until the energy error is within
127+% tolerance, then check the choice is reversible.
128+global WREC_ON WREC_X WREC_Y WREC_SEG WREC_SEGID
129+if direction == 1
130+ theta = span.theta_fw;
131+ rho = span.rho_fw;
132+ grad = span.grad_fw;
133+ logp = span.logp_fw;
134+ step = dt;
135+else
136+ theta = span.theta_bk;
137+ rho = span.rho_bk;
138+ grad = span.grad_bk;
139+ logp = span.logp_bk;
140+ step = -dt;
141+end
142+
143+num_steps = 1;
144+for halvings = 0:9
145+ theta_next = theta;
146+ rho_next = rho;
147+ grad_next = grad;
148+ [theta_next, rho_next, grad_next] = leapfrog(theta_next, rho_next, grad_next, step, num_steps);
149+ logp_next = log_density(theta_next) - sum(rho_next.^2) / 2;
150+ if abs(logp - logp_next) <= max_error
151+ success = reversible(step, num_steps, theta_next, rho_next, grad_next, logp_next, max_error);
152+ if success && WREC_ON
153+ % Record this committed macro-step's leapfrog path for the movie.
154+ path = leapfrog_capture(theta, rho, grad, step, num_steps);
155+ WREC_SEGID = WREC_SEGID + 1;
156+ WREC_X = [WREC_X, theta(1), path(1, :)];
157+ WREC_Y = [WREC_Y, theta(2), path(2, :)];
158+ WREC_SEG = [WREC_SEG, WREC_SEGID * ones(1, num_steps + 1)];
159+ end
160+ return
161+ end
162+ num_steps = num_steps * 2;
163+ step = step * 0.5;
164+end
165+% No step count met the tolerance.
166+success = false;
167+theta_next = theta;
168+rho_next = rho;
169+grad_next = grad;
170+logp_next = logp;
171+end
172+
173+function [theta, rho, grad] = leapfrog(theta, rho, grad, step, num_steps)
174+half_step = 0.5 * step;
175+for n = 1:num_steps
176+ rho = rho + half_step * grad;
177+ theta = theta + step * rho;
178+ grad = grad_log_density(theta);
179+ rho = rho + half_step * grad;
180+end
181+end
182+
183+function path = leapfrog_capture(theta, rho, grad, step, num_steps)
184+% Re-run a committed macro-step, returning the position after each leapfrog
185+% step (dim-by-num_steps). Used only while recording the movie trajectory.
186+half_step = 0.5 * step;
187+path = zeros(numel(theta), num_steps);
188+for n = 1:num_steps
189+ rho = rho + half_step * grad;
190+ theta = theta + step * rho;
191+ grad = grad_log_density(theta);
192+ rho = rho + half_step * grad;
193+ path(:, n) = theta;
194+end
195+end
196+
197+function ok = reversible(step, num_steps, theta, rho, grad, logp_next, max_error)
198+% The adaptive step count is reversible only if no coarser (doubled-step)
199+% backward integration would itself have been accepted.
200+if num_steps == 1
201+ ok = true;
202+ return
203+end
204+ok = true;
205+while num_steps >= 2
206+ num_steps = floor(num_steps / 2);
207+ step = step * 2;
208+ if within_tolerance(step, num_steps, theta, -rho, grad, logp_next, max_error)
209+ ok = false;
210+ return
211+ end
212+end
213+end
214+
215+function ok = within_tolerance(step, num_steps, theta, rho, grad, logp, max_error)
216+[theta, rho, ~] = leapfrog(theta, rho, grad, step, num_steps);
217+final_logp = log_density(theta) - sum(rho.^2) / 2;
218+ok = abs(final_logp - logp) <= max_error;
219+end
220+
221+function u = uturn(span1, span2, direction)
222+if direction == 1
223+ span_bk = span1;
224+ span_fw = span2;
225+else
226+ span_bk = span2;
227+ span_fw = span1;
228+end
229+scaled_diff = span_fw.theta_fw - span_bk.theta_bk;
230+u = (dot(span_fw.rho_fw, scaled_diff) < 0) || (dot(span_bk.rho_bk, scaled_diff) < 0);
231+end
232+
233+function span = combine(span_old, span_new, use_barker, direction)
234+logp_old = span_old.logp;
235+logp_new = span_new.logp;
236+logp_total = log_sum_exp(logp_old, logp_new);
237+if use_barker
238+ log_denominator = logp_total;
239+else
240+ log_denominator = logp_old;
241+end
242+update = log(rand) < (logp_new - log_denominator);
243+if update
244+ theta_select = span_new.theta_select;
245+else
246+ theta_select = span_old.theta_select;
247+end
248+if direction == 1
249+ span_bk = span_old;
250+ span_fw = span_new;
251+else
252+ span_bk = span_new;
253+ span_fw = span_old;
254+end
255+span = make_combined_span(span_bk, span_fw, theta_select, logp_total);
256+end
257+
258+function r = log_sum_exp(x, y)
259+m = max(x, y);
260+r = m + log(exp(x - m) + exp(y - m));
261+end
262+
263+function s = make_leaf_span(theta, rho, grad, logp)
264+s = struct('theta_bk', theta, 'rho_bk', rho, 'grad_bk', grad, 'logp_bk', logp, ...
265+ 'theta_fw', theta, 'rho_fw', rho, 'grad_fw', grad, 'logp_fw', logp, ...
266+ 'theta_select', theta, 'logp', logp);
267+end
268+
269+function s = make_combined_span(span_bk, span_fw, theta_select, logp_total)
270+s = struct('theta_bk', span_bk.theta_bk, 'rho_bk', span_bk.rho_bk, ...
271+ 'grad_bk', span_bk.grad_bk, 'logp_bk', span_bk.logp_bk, ...
272+ 'theta_fw', span_fw.theta_fw, 'rho_fw', span_fw.rho_fw, ...
273+ 'grad_fw', span_fw.grad_fw, 'logp_fw', span_fw.logp_fw, ...
274+ 'theta_select', theta_select, 'logp', logp_total);
275+end
numbl-project.jsonadded+4−0View file
@@ -0,0 +1,4 @@
1+{
2+ "title": "Interactive WALNUTS sampling",
3+ "entry": "README.md"
4+}
walnuts_demo.madded+14−0View file
@@ -0,0 +1,14 @@
1+% WALNUTS sampling of a 2D "banana" target.
2+%
3+% WALNUTS (Within-orbit Adaptive No-U-Turn Sampler) is a NUTS variant that
4+% adapts the leapfrog step size within each orbit. This draws samples from the
5+% banana target and shows the density with the samples on top.
6+%
7+% The algorithm lives in helpers/walnuts.m; the target in helpers/log_density.m
8+% and helpers/grad_log_density.m. `addpath` must be the first statement.
9+
10+addpath('helpers'); % walnuts, log_density, grad_log_density
11+
12+rng(1); % reproducible
13+
14+walnuts_sampler(1000, 0.4, 0.8); % N samples, leapfrog dt, max energy error
walnuts_sampler.madded+87−0View file
@@ -0,0 +1,87 @@
1+function walnuts_sampler(N, dt, max_error)
2+%WALNUTS_SAMPLER Interactive figure: WALNUTS sampling of a 2D banana target.
3+% WALNUTS_SAMPLER(N, DT, MAX_ERROR) draws N samples from the banana target
4+% (helpers/log_density.m) with the WALNUTS sampler (helpers/walnuts.m) and
5+% opens a figure showing the target density and the samples.
6+%
7+% This is the wiring: it runs the sampler, evaluates the target on a grid for
8+% the heatmap, loads the prebuilt figure app, and sends both to it. It also
9+% re-samples on request (figure -> script), wired so adding controls later is
10+% a UI-only change. Run walnuts_demo.m (which addpath's helpers/).
11+
12+if nargin < 1 || isempty(N); N = 1000; end
13+if nargin < 2 || isempty(dt); dt = 0.4; end
14+if nargin < 3 || isempty(max_error); max_error = 0.8; end
15+
16+burnin = 200;
17+chain = walnuts(randn(2, 1), burnin + N, dt, max_error);
18+samples = chain(:, burnin + 1:end);
19+
20+dens = density_grid();
21+
22+html = fileread(fullfile('app', 'dist', 'index.html'));
23+fig = figure;
24+gl = uigridlayout(fig, [1 1], 'Padding', [0 0 0 0], ...
25+ 'RowHeight', {'1x'}, 'ColumnWidth', {'1x'});
26+uihtml(gl, 'HTMLSource', html, 'Data', pack_data(samples, dens, N, dt, max_error), ...
27+ 'HTMLEventReceivedFcn', @(src, ev) on_event(src, ev));
28+end
29+
30+function on_event(src, ev)
31+% Figure -> script. The target is fixed, so the figure only ever needs new
32+% samples or a movie trajectory back.
33+% 'resample' {n, dt, maxError} -> draw a fresh chain; reply with 'samples'.
34+% 'movie' {dt, maxError} -> record a short chain's orbit trajectories;
35+% reply with 'movie'.
36+d = ev.HTMLEventData;
37+N = 1000; dt = 0.4; max_error = 0.8;
38+if isstruct(d)
39+ if isfield(d, 'n'); N = max(1, round(d.n)); end
40+ if isfield(d, 'dt'); dt = d.dt; end
41+ if isfield(d, 'maxError'); max_error = d.maxError; end
42+end
43+switch ev.HTMLEventName
44+ case 'resample'
45+ burnin = 200;
46+ chain = walnuts(randn(2, 1), burnin + N, dt, max_error);
47+ samples = chain(:, burnin + 1:end);
48+ sendEventToHTMLSource(src, 'samples', ...
49+ struct('x', samples(1, :), 'y', samples(2, :), 'n', N, 'dt', dt, 'maxError', max_error));
50+ case 'movie'
51+ % Record the orbit-building trajectory of a few transitions for the
52+ % step-by-step animation. Each traj{i} = {px, py, seg, startX/Y, selX/Y}.
53+ n_steps = 12;
54+ [~, traj] = walnuts(randn(2, 1), n_steps, dt, max_error, true);
55+ sendEventToHTMLSource(src, 'movie', traj);
56+end
57+end
58+
59+function dens = density_grid()
60+%DENSITY_GRID Evaluate the target log density on a grid for the heatmap.
61+% Row-major flat values: index (iy-1)*nx + ix, iy from ymin (1) to ymax (ny).
62+xmin = -6; xmax = 6;
63+ymin = -7; ymax = 3;
64+nx = 100; ny = 100;
65+xs = linspace(xmin, xmax, nx);
66+ys = linspace(ymin, ymax, ny);
67+values = zeros(1, nx * ny);
68+k = 1;
69+for iy = 1:ny
70+ for ix = 1:nx
71+ values(k) = log_density([xs(ix); ys(iy)]);
72+ k = k + 1;
73+ end
74+end
75+dens = struct('values', values, 'nx', nx, 'ny', ny, ...
76+ 'xmin', xmin, 'xmax', xmax, 'ymin', ymin, 'ymax', ymax);
77+end
78+
79+function data = pack_data(samples, dens, N, dt, max_error)
80+data = struct();
81+data.type = 'walnuts';
82+data.samples = struct('x', samples(1, :), 'y', samples(2, :));
83+data.density = dens;
84+data.n = N;
85+data.dt = dt;
86+data.maxError = max_error;
87+end