1/**
2 * Several solver settings, one problem, one clock.
3 *
4 * A convergence study of the knobs that decide how well the implicit solve is
5 * resolved — `niter`, `lmax`, `dt` — run side by side so the answer to "does it
6 * matter?" is visible rather than argued. Every variant is its own
7 * `ModelSession` (both `niter` and `lmax` are structural: they change the
8 * compiled step and the grid), and what makes the set a comparison rather than
9 * a collection is three things they are forced to share:
10 *
11 * - **One initial condition.** Band-limited at the coarsest variant's lmax and
12 * evaluated on each variant's own grid, so every session starts from the same
13 * *function* rather than from the same random seed — see sharedStart.ts for
14 * why the seed alone is not enough.
15 *
16 * - **One clock.** Variants differ in dt only by an integer power-of-two
17 * divisor, and a frame advances each of them by `frameSteps * dtDiv` steps.
18 * Every variant therefore lands on exactly the same model time at the end of
19 * every frame, having taken a different number of steps to get there. Nothing
20 * is ever compared across a time offset.
21 *
22 * - **One grid to look at.** Each session's *display* plan is pointed at a
23 * common grid (ModelSession.setDisplayGrid), which is exact evaluation rather
24 * than resampling because the state is band-limited. So the fields come back
25 * directly comparable point by point, one mesh topology serves every panel,
26 * and the difference norm is an ordinary weighted sum.
27 *
28 * What is *not* shared is the surface: each variant carries the geometry
29 * band-limited at its own lmax, and renders the surface it actually solves on.
30 */
31import { ModelSession } from '../mgpu/session.ts';
32import type { MModel, Params } from '../mgpu/registry.ts';
33import type { MGeometry } from '../geom/registry.ts';
34import {
35 buildTopology,
36 fillFieldValues,
37 fillPositions,
38 fillColors,
39 type SphereMeshTopology,
40} from '../render/sphereMesh.ts';
41import { SphereScene } from '../render/SphereScene.ts';
42import { colormaps } from '../render/colormaps.ts';
43import { fmtValue, floorRange } from '../render/colorbar.ts';
44import { prolongCoeffs, sharedModes, sharedNoise } from './sharedStart.ts';
45import { variantLabel, VARIANT_COLORS, type Variant } from './variants.ts';
46import type { ReferenceCase } from './referenceCase.ts';
47import { ErrorChart, type ErrorChartRow } from '../render/errorChart.ts';
49/**
50 * Latitudes of the shared display grid. 256 is the same target the single-run
51 * view uses for 'auto' oversampling, and for the same reason — beyond it a
52 * finer mesh costs vertices without showing anything.
53 *
54 * Here it is a ceiling as well as a target, in two directions. At lmax 255 the
55 * solver grid is finer than this, so the panels sample the (exact) state more
56 * coarsely than the solver carries it; and past a handful of panels the mesh is
57 * paid for once per panel, in vertices, normals and a WebGL context each, so it
58 * halves. Both are display choices, both are reported in the status line, and
59 * neither touches the difference norm's meaning: that is computed on this same
60 * grid for every variant, so it stays a consistent comparison whatever the grid.
61 */
62const RENDER_NLAT = 256;
63const RENDER_NLAT_CROWDED = 128;
64const CROWDED_PANELS = 6;
66/** See main.ts's DISPATCH_BUDGET — the same watchdog argument, per variant. */
67const DISPATCH_BUDGET = 1000;
68const STEPS_PER_FRAME_BASE = 4;
70export interface CompareOptions {
71 device: GPUDevice;
72 model: MModel;
73 /** The model's parameters, with `dt` read as the *base* timestep that each
74 * variant's dtDiv divides. */
75 params: Params;
76 source: string;
77 geometry: MGeometry;
78 geometryParams: Params;
79 geometrySource: string;
80 variants: Variant[];
81 /** Index into `variants` of the run everything else is measured against.
82 * Ignored when `refFile` is given — the file is the reference then. */
83 reference: number;
84 /**
85 * Check against a reference file instead of against each other: its exact
86 * initial state seeds every variant (so `seed` and `lam3` go unused), a
87 * static extra row shows its final state, every Δ is measured against that
88 * row, and the clock stops at the file's end time. Every variant's lmax must
89 * be >= the file's — a narrower band could not hold the initial state.
90 */
91 refFile?: ReferenceCase;
92 /** Called when a refFile run reaches the file's end time and stops. */
93 onFinished?: () => void;
94 seed: number;
95 /** Wavelength of the seeded random field, shared by every variant — one
96 * initial condition means one wavelength as much as one seed. */
97 lam3?: number;
98 morph: number;
99 colormapName: () => string;
100 /** Where the variant grid goes (the app's #panels). */
101 container: HTMLElement;
102 /** Where the error-vs-time chart goes (the app's #cmp-chart). */
103 chartContainer: HTMLElement;
104 /** Progress and, afterwards, the standing description of the study. */
105 onStatus: (html: string) => void;
106}
108interface Row {
109 variant: Variant;
110 session: ModelSession;
111 color: string;
112 /** Surface coordinates on the shared render grid — this variant's own. */
113 coords: Float32Array;
114 posBuf: Float32Array;
115 scenes: SphereScene[];
116 valueBufs: Float32Array[];
117 colorBufs: Float32Array[];
118 /** Fields read this frame, one per species, on the shared grid. */
119 fields: Float32Array[];
120 /** Pointwise difference from the reference, one per species, on the shared
121 * grid — filled by #measureDifference as it accumulates the norm below.
122 * Unused (and never touched) for the reference row itself. */
123 diffFields: Float32Array[];
124 /** The diff row's own panels, one per species — empty for the reference
125 * row, whose diff against itself is trivially zero. */
126 diffScenes: SphereScene[];
127 diffValueBufs: Float32Array[];
128 diffColorBufs: Float32Array[];
129 /** This row's own smoothed symmetric color range per species — each row
130 * is scaled to its own diff extent, not a range shared across the
131 * column, so one row's diff panels never affect another's coloring. */
132 diffRanges: { lo: number; hi: number }[];
133 /** Each diff panel's "± magnitude" caption, parallel to diffScenes. */
134 diffCaps: HTMLElement[];
135 /** Relative difference from the reference, one per species. */
136 err: number[];
137 /** False once any species has left the floating-point numbers — the shape a
138 * variant outside the convergence radius eventually fails in. Such a row is
139 * never used to scale a column, and its label says so. */
140 healthy: boolean;
141 statEl: HTMLElement;
142}
144/**
145 * The reference file's final state, as one more row of panels — with no
146 * session behind it: its surface and fields are the file's coefficients
147 * synthesized once on the shared display grid, fixed for the whole run. Only
148 * its coloring changes, with the shared range.
149 */
150interface FileRow {
151 coords: Float32Array;
152 posBuf: Float32Array;
153 scenes: SphereScene[];
154 valueBufs: Float32Array[];
155 colorBufs: Float32Array[];
156 /** The file's final state on the shared grid, one per species. */
157 fields: Float32Array[];
158 /** Its extent, precomputed — a candidate for the shared color range. */
159 bounds: (Bounds | null)[];
160}
162export class CompareRun {
163 #opts: CompareOptions;
164 #rows: Row[] = [];
165 #fileRow: FileRow | null = null;
166 /** What restart() reloads: the file's fixed state if opts.refFile is set,
167 * otherwise a snapshot of the coarsest variant's state as of the last
168 * (re-)seed — see the capture in create() and in reseed()'s plain branch. */
169 #initial: Record<string, Float32Array>;
170 #initialLmax: number;
171 /** Base steps taken since the initial state — the refFile clock. */
172 #stepsDone = 0;
173 /** True once a refFile run has reached the file's end time. */
174 #finished = false;
175 #topo: SphereMeshTopology;
176 /** Quadrature weight per grid point of the shared grid, for the L2 norm. */
177 #weights: Float64Array;
178 #rangeBars: { fill: (lo: number, hi: number) => void }[] = [];
179 /** Smoothed color range per species, shared by every variant so the panels
180 * in a column are directly comparable by eye and not just by number. */
181 #ranges: { lo: number; hi: number }[] = [];
182 #errorChart: ErrorChart | null = null;
183 #resizeObs: ResizeObserver | null = null;
185 #running = false;
186 #pumping = false;
187 #disposed = false;
188 #morph: number;
189 /** Base steps per frame; variant i takes this times its dtDiv. */
190 #frameSteps = STEPS_PER_FRAME_BASE;
191 /** Model time all variants are at — one number, by construction. */
192 #t = 0;
193 #frameMs = 0;
194 #note: string;
196 private constructor(init: {
197 opts: CompareOptions;
198 rows: Row[];
199 fileRow: FileRow | null;
200 topo: SphereMeshTopology;
201 weights: Float64Array;
202 rangeBars: { fill: (lo: number, hi: number) => void }[];
203 frameSteps: number;
204 note: string;
205 initial: Record<string, Float32Array>;
206 initialLmax: number;
207 }) {
208 this.#opts = init.opts;
209 this.#rows = init.rows;
210 this.#fileRow = init.fileRow;
211 this.#topo = init.topo;
212 this.#weights = init.weights;
213 this.#rangeBars = init.rangeBars;
214 this.#frameSteps = init.frameSteps;
215 this.#note = init.note;
216 this.#morph = init.opts.morph;
217 this.#ranges = init.opts.model.species.map(() => ({ lo: NaN, hi: NaN }));
218 this.#initial = init.initial;
219 this.#initialLmax = init.initialLmax;
220 }
222 get variants(): Variant[] {
223 return this.#rows.map((r) => r.variant);
224 }
226 /** The variant everything else is measured against — the one whose numbers
227 * stand on their own, so the one the app quotes when it has to quote one. */
228 get referenceSession(): ModelSession | null {
229 return this.#rows[this.#opts.reference]?.session ?? null;
230 }
232 get referenceIndex(): number {
233 return this.#opts.reference;
234 }
236 /** The reference file this study is checking against, if any. */
237 get refFile(): ReferenceCase | null {
238 return this.#opts.refFile ?? null;
239 }
241 /** The base timestep a variant's dtDiv divides. */
242 static baseDt(params: Params): number {
243 return params.dt ?? 0;
244 }
246 static async create(opts: CompareOptions): Promise<CompareRun> {
247 const { device, model, variants } = opts;
248 const baseDt = CompareRun.baseDt(opts.params);
249 const showDt = variants.some((v) => v.dtDiv !== variants[0].dtDiv);
250 const sessions: ModelSession[] = [];
251 // Scenes own a WebGL context and an animation frame each, so a failure
252 // after the grid is up has to take them down explicitly — removing their
253 // canvases from the DOM would leave both running.
254 let built: Row[] = [];
255 let builtFile: FileRow | null = null;
256 let errorChart: ErrorChart | null = null;
258 try {
259 for (let i = 0; i < variants.length; i++) {
260 const v = variants[i];
261 opts.onStatus(
262 `compiling ${i + 1}/${variants.length} — ${variantLabel(v, showDt)} ` +
263 `(a solve iteration is ~15 kernels per species, and there is no ` +
264 `pipeline cache across sessions)`,
265 );
266 // Yield, so the status actually paints before the compile blocks.
267 await new Promise<number>(requestAnimationFrame);
268 sessions.push(
269 await ModelSession.create({
270 device,
271 model,
272 params: { ...opts.params, dt: baseDt / v.dtDiv },
273 lmax: v.lmax,
274 source: opts.source,
275 geometry: opts.geometry,
276 geometryParams: opts.geometryParams,
277 geometrySource: opts.geometrySource,
278 niter: v.niter,
279 lam3: opts.lam3,
280 }),
281 );
282 }
284 // ---- the shared display grid ----------------------------------------
285 const maxLmax = Math.max(...variants.map((v) => v.lmax));
286 const panels = (variants.length + (opts.refFile ? 1 : 0)) * model.species.length;
287 const target = panels > CROWDED_PANELS ? RENDER_NLAT_CROWDED : RENDER_NLAT;
288 // Never below what the finest band needs to be representable at all
289 // (ShtPlan requires nlat > lmax), whatever the panel count says.
290 const nlat = Math.max(target, 2 * Math.ceil((maxLmax + 2) / 2));
291 let nphi = 1;
292 while (nphi < Math.max(2 * nlat, 2 * maxLmax + 1)) nphi *= 2;
293 for (const s of sessions) await s.setDisplayGrid(nlat, nphi);
295 // ---- one initial condition, on every grid ---------------------------
296 // Also what restart() reloads later — the file's fixed state, or (for
297 // the plain case) a snapshot of the coarsest variant's own state,
298 // taken after seeding it: the same lowest-lmax session sharedNoise
299 // itself draws from, so prolonging it up to any other variant later is
300 // always widening a band, never narrowing one.
301 let initial: Record<string, Float32Array>;
302 let initialLmax: number;
303 if (opts.refFile) {
304 // The file's exact spectral state, prolonged into each variant's band.
305 // Exact, not approximate: the state is band-limited at the file's lmax
306 // and every variant's band contains it, so each session starts from
307 // the very field the reference run started from.
308 opts.onStatus('loading the initial state from the reference file…');
309 for (const s of sessions) {
310 s.loadState(prolongState(opts.refFile.initial, model.state, opts.refFile.lmax, s.cfg.lmax));
311 }
312 initial = opts.refFile.initial;
313 initialLmax = opts.refFile.lmax;
314 } else {
315 opts.onStatus('seeding all variants from one band-limited perturbation…');
316 const noise = await sharedNoise(sessions, model.seedAmp, opts.seed);
317 const modes = await sharedModes(sessions[opts.reference] ?? sessions[0], opts.seed);
318 // One at a time: a seed submits its whole mode sum in pieces, and there
319 // is nothing to gain from interleaving several variants' worth of it.
320 for (let i = 0; i < sessions.length; i++) await sessions[i].seedWith(noise[i], modes);
321 let coarsest = sessions[0];
322 for (const s of sessions) if (s.cfg.lmax < coarsest.cfg.lmax) coarsest = s;
323 initial = await coarsest.readState();
324 initialLmax = coarsest.cfg.lmax;
325 }
327 // ---- the mesh, shared; the surface, per variant ---------------------
328 const view = sessions[0].viewSht;
329 const phi = new Float64Array(nphi);
330 for (let j = 0; j < nphi; j++) phi[j] = (2 * Math.PI * j) / nphi;
331 const topo = buildTopology(view.cosTheta, phi);
332 // Gauss weights carry the sin(theta) of the area element; the constant
333 // 2*pi/nphi is common to every point and cancels in the relative norm.
334 const weights = new Float64Array(nlat * nphi);
335 for (let i = 0; i < nlat; i++) {
336 for (let j = 0; j < nphi; j++) weights[i * nphi + j] = view.gaussWeights[i];
337 }
339 // ---- how many steps a frame may submit ------------------------------
340 // Per variant: its own unrolled step size times its dtDiv, since a ÷K
341 // variant takes K times as many steps to reach the same time.
342 let frameSteps = STEPS_PER_FRAME_BASE;
343 const ops: number[] = [];
344 for (let i = 0; i < sessions.length; i++) {
345 const n = Math.max(1, sessions[i].describe().step.length);
346 ops.push(n);
347 frameSteps = Math.min(
348 frameSteps,
349 Math.max(1, Math.floor(DISPATCH_BUDGET / (n * variants[i].dtDiv))),
350 );
351 }
352 frameSteps = Math.max(1, frameSteps);
354 // ---- the grid of panels ---------------------------------------------
355 const { rows, fileRow, rangeBars } = await buildGrid(opts, sessions, topo, showDt);
356 built = rows;
357 builtFile = fileRow;
359 // ---- the error-vs-time chart, one line per row with a diff panel ----
360 const chartRows = rows.filter((r) => r.diffScenes.length > 0);
361 errorChart = new ErrorChart(
362 opts.chartContainer,
363 model.species,
364 chartRows.map((r): ErrorChartRow => ({ label: variantLabel(r.variant, showDt), color: r.color })),
365 );
366 // Nothing to chart with a single variant and no reference file — the
367 // one row present is the reference itself.
368 opts.chartContainer.hidden = chartRows.length === 0;
370 const solverGrid = sessions.map((s) => `${s.cfg.nlat}×${s.cfg.nphi}`);
371 const note =
372 `${variants.length} variant${variants.length === 1 ? '' : 's'} · ` +
373 `display grid ${nlat}×${nphi}` +
374 (sessions.some((s) => s.cfg.nlat > nlat)
375 ? ` (below the finest solver grid ${solverGrid[solverGrid.length - 1]} — display only)`
376 : '') +
377 ` · ${frameSteps} base step${frameSteps === 1 ? '' : 's'}/frame` +
378 ` · ops/step ${ops.join(', ')}`;
380 const run = new CompareRun({
381 opts, rows, fileRow, topo, weights, rangeBars, frameSteps, note, initial, initialLmax,
382 });
383 run.#errorChart = errorChart;
384 await run.draw();
385 run.#observeResize();
386 run.#status();
387 return run;
388 } catch (e) {
389 for (const r of built) {
390 for (const s of r.scenes) s.dispose();
391 for (const s of r.diffScenes) s.dispose();
392 }
393 for (const s of builtFile?.scenes ?? []) s.dispose();
394 for (const s of sessions) s.destroy();
395 errorChart?.dispose();
396 opts.chartContainer.hidden = true;
397 opts.container.replaceChildren();
398 opts.container.classList.remove('compare');
399 throw e;
400 }
401 }
403 // ------------------------------------------------------------------ state
404 setRunning(next: boolean): void {
405 this.#running = next;
406 if (next) void this.#pump();
407 }
409 get running(): boolean {
410 return this.#running;
411 }
413 /** Re-seed every variant from one new shared perturbation — or, against a
414 * reference file, restart from its initial state (there is nothing to
415 * draw; the seed is ignored). */
416 async reseed(seed: number): Promise<void> {
417 const wasRunning = this.#running;
418 this.#running = false;
419 while (this.#pumping) await nextFrame();
420 if (this.#disposed) return;
421 const sessions = this.#rows.map((r) => r.session);
422 const refFile = this.#opts.refFile;
423 if (refFile) {
424 for (const s of sessions) {
425 s.loadState(prolongState(refFile.initial, this.#opts.model.state, refFile.lmax, s.cfg.lmax));
426 }
427 } else {
428 const noise = await sharedNoise(sessions, this.#opts.model.seedAmp, seed);
429 const modes = await sharedModes(this.referenceSession ?? sessions[0], seed);
430 // Checked per variant, not once: a seed awaits its own submission, so a
431 // dispose can land between two of them and destroy the sessions left.
432 for (let i = 0; i < sessions.length; i++) {
433 if (this.#disposed) return;
434 await sessions[i].seedWith(noise[i], modes);
435 }
436 if (this.#disposed) return;
437 // This draw becomes what restart() rewinds to from now on — see the
438 // identical selection in create(). Recaptured here rather than left
439 // pointing at the pre-reseed field.
440 let coarsest = sessions[0];
441 for (const s of sessions) if (s.cfg.lmax < coarsest.cfg.lmax) coarsest = s;
442 this.#initial = await coarsest.readState();
443 this.#initialLmax = coarsest.cfg.lmax;
444 }
445 this.#t = 0;
446 this.#stepsDone = 0;
447 this.#finished = false;
448 for (const r of this.#ranges) {
449 r.lo = NaN;
450 r.hi = NaN;
451 }
452 for (const r of this.#rows) {
453 for (const rr of r.diffRanges) {
454 rr.lo = NaN;
455 rr.hi = NaN;
456 }
457 }
458 this.#errorChart?.reset();
459 await this.draw();
460 this.#status();
461 if (!this.#disposed && wasRunning) this.setRunning(true);
462 }
464 /** Rewind every variant to the saved initial condition — the file's fixed
465 * state, or (for the plain case) the last (re-)seed, not necessarily the
466 * very first one — without drawing anything new. */
467 async restart(): Promise<void> {
468 const wasRunning = this.#running;
469 this.#running = false;
470 while (this.#pumping) await nextFrame();
471 if (this.#disposed) return;
472 for (const r of this.#rows) {
473 r.session.loadState(
474 prolongState(this.#initial, this.#opts.model.state, this.#initialLmax, r.session.cfg.lmax),
475 );
476 }
477 this.#t = 0;
478 this.#stepsDone = 0;
479 this.#finished = false;
480 for (const r of this.#ranges) {
481 r.lo = NaN;
482 r.hi = NaN;
483 }
484 for (const r of this.#rows) {
485 for (const rr of r.diffRanges) {
486 rr.lo = NaN;
487 rr.hi = NaN;
488 }
489 }
490 this.#errorChart?.reset();
491 await this.draw();
492 this.#status();
493 if (!this.#disposed && wasRunning) this.setRunning(true);
494 }
496 /** Wavelength of the seeded random field. One number for the study: every
497 * variant seeds from the same field, so they seed at the same wavelength. */
498 get lam3(): number {
499 return this.#rows[0]?.session.lam3 ?? 0;
500 }
502 /** Change it on every variant. Like the single run's, this only takes effect
503 * on the next reseed, which is where the field is drawn. */
504 setLam3(lambda: number): void {
505 this.#opts.lam3 = lambda;
506 for (const r of this.#rows) r.session.setLam3(lambda);
507 }
509 /** Model parameters changed. Each variant keeps its own dt. */
510 setParams(params: Params): void {
511 // Against a reference file the parameters *are* the file's — they define
512 // the problem being checked — and the page's parameter panel edits the
513 // page's own model, which need not even be this one. Nothing to apply.
514 if (this.#opts.refFile) return;
515 this.#opts.params = params;
516 const baseDt = CompareRun.baseDt(params);
517 for (const r of this.#rows) {
518 r.session.setParams({ ...params, dt: baseDt / r.variant.dtDiv });
519 }
520 }
522 setMorph(morph: number): void {
523 this.#morph = morph;
524 for (const r of this.#rows) {
525 fillPositions(r.posBuf, r.coords, this.#topo, morph);
526 for (const s of r.scenes) s.updatePositions(r.posBuf);
527 }
528 const f = this.#fileRow;
529 if (f) {
530 fillPositions(f.posBuf, f.coords, this.#topo, morph);
531 for (const s of f.scenes) s.updatePositions(f.posBuf);
532 }
533 }
535 resetView(): void {
536 for (const s of this.#allScenes()) s.resetCamera();
537 }
539 dispose(): void {
540 this.#disposed = true;
541 this.#running = false;
542 this.#resizeObs?.disconnect();
543 this.#resizeObs = null;
544 for (const r of this.#rows) {
545 for (const s of r.scenes) s.dispose();
546 for (const s of r.diffScenes) s.dispose();
547 r.session.destroy();
548 }
549 for (const s of this.#fileRow?.scenes ?? []) s.dispose();
550 this.#rows = [];
551 this.#fileRow = null;
552 this.#errorChart?.dispose();
553 this.#errorChart = null;
554 this.#opts.chartContainer.hidden = true;
555 this.#opts.container.replaceChildren();
556 this.#opts.container.classList.remove('compare');
557 }
559 #allScenes(): SphereScene[] {
560 return [
561 ...this.#rows.flatMap((r) => [...r.scenes, ...r.diffScenes]),
562 ...(this.#fileRow?.scenes ?? []),
563 ];
564 }
566 // ----------------------------------------------------------------- drawing
567 /**
568 * One frame's readback: every variant's every species, on the shared grid.
569 * Read first, then color — the range is shared down a column, so no panel can
570 * be filled until the column's range is known.
571 */
572 async draw(): Promise<void> {
573 if (this.#disposed) return;
574 const species = this.#opts.model.species;
575 // Sessions are independent, so their readbacks can be in flight together;
576 // within one session they must not be (they share its staging buffers).
577 await Promise.all(
578 this.#rows.map(async (r) => {
579 for (let k = 0; k < species.length; k++) {
580 r.fields[k] = await r.session.readSpecies(k);
581 }
582 }),
583 );
584 if (this.#disposed) return;
586 const cmap = colormaps[this.#opts.colormapName()] ?? colormaps.viridis;
588 /**
589 * What scales a column is the whole question, and it has three wrong
590 * answers.
591 *
592 * Per panel is wrong: a range each rescales every variant to itself and
593 * hides exactly the difference the grid exists to show. The union over
594 * variants is wrong for the opposite reason: a variant outside the
595 * iteration's convergence radius runs away to 1e20 and then to NaN, and a
596 * union range rescales the *whole column* to it, flattening every panel to
597 * one colour — which reads as "they all blew up" when only one did.
598 *
599 * The reference alone is wrong too, less obviously, and it is the case that
600 * actually bites: outside the convergence radius *more* Richardson
601 * iterations diverge *faster*, so the row that goes first is usually the
602 * highest-niter one — which is the reference.
603 *
604 * So the column is scaled by whichever variant **reaches least far from
605 * zero** — the least-blown-up one. That is a comparison between the rows,
606 * not a threshold on any of them, and the distinction is the whole point:
607 * any "is this value too big?" test has a window in which a diverging field
608 * is still under the limit, and for as long as that window lasts it drags
609 * the scale and flattens the grid, until it finally trips and everything
610 * springs back. A comparison has no such window — a run-away only has to be
611 * *larger* than a healthy row to stop setting the scale, which it is from
612 * its first bad step, and it stays larger no matter how many other rows go
613 * with it. One healthy variant is enough to keep the grid readable.
614 *
615 * The cost is a slight bias: among healthy variants the scale comes from
616 * the one with the smallest peak, so the others clip by however much they
617 * exceed it. They are approximations of the same solution, so that is a
618 * fraction of a percent, and the alternative is a display that a single
619 * divergence can take away.
620 */
621 const bounds = this.#rows.map((r) => species.map((_, k) => finiteRange(r.fields[k])));
622 this.#rows.forEach((r, i) => {
623 // A row with any non-finite value is out of the running entirely: its
624 // finite entries are whatever survived, and no rank over them means much.
625 r.healthy = species.every((_, k) => allFinite(r.fields[k]) && bounds[i][k] !== null);
626 });
628 for (let k = 0; k < species.length; k++) {
629 // The file row, when there is one, is a candidate like any healthy
630 // variant: early on the variants' small fields set the scale (it merely
631 // clips), and if every variant diverges it is the row that keeps the
632 // grid readable.
633 const anchor = leastPeak([
634 ...this.#rows.map((r, i) => (r.healthy ? bounds[i][k] : null)),
635 this.#fileRow?.bounds[k] ?? null,
636 ]);
637 const range = this.#ranges[k];
638 if (anchor) {
639 if (!Number.isFinite(range.lo)) {
640 range.lo = anchor.lo;
641 range.hi = anchor.hi;
642 } else {
643 // Smooth in both directions so the shading evolves gently as the
644 // pattern grows, as the single-run view does.
645 const a = 0.15;
646 range.lo += a * (anchor.lo - range.lo);
647 range.hi += a * (anchor.hi - range.hi);
648 }
649 }
650 // With every row gone, the last good range is kept rather than replaced
651 // by nothing: the panels freeze at a readable scale and the row labels
652 // say what happened, instead of the grid going blank.
653 if (!Number.isFinite(range.lo) || !Number.isFinite(range.hi)) continue;
654 // The floor is applied to what is drawn, not to what is tracked, so it
655 // never feeds back into the smoothing above.
656 const shown = floorRange(range.lo, range.hi);
657 this.#rangeBars[k]?.fill(shown.lo, shown.hi);
658 for (const r of this.#rows) {
659 fillFieldValues(r.valueBufs[k], r.fields[k], this.#topo);
660 fillColors(r.colorBufs[k], r.valueBufs[k], shown.lo, shown.hi, cmap);
661 r.scenes[k]?.updateColors(r.colorBufs[k]);
662 }
663 const f = this.#fileRow;
664 if (f) {
665 // Its values never change; only its coloring follows the shared range.
666 fillColors(f.colorBufs[k], f.valueBufs[k], shown.lo, shown.hi, cmap);
667 f.scenes[k]?.updateColors(f.colorBufs[k]);
668 }
669 }
671 this.#measureDifference();
672 this.#colorDiffPanels();
673 this.#updateRowStats();
674 this.#errorChart?.push(
675 this.#t,
676 this.#rows.filter((r) => r.diffScenes.length > 0).map((r) => r.err),
677 );
678 }
680 /**
681 * Color every diff panel from #measureDifference's pointwise diffFields, on
682 * a *symmetric* range that is each row's own — not shared across the
683 * column. A diverging row's diff explodes, but with a per-row range that
684 * only saturates its own panels; it can no longer affect how any other
685 * row's diff panels are scaled, which is a simpler fix for exactly the
686 * flooding problem the value panels' shared #ranges/leastPeak logic exists
687 * to manage there. The cost: diff-panel color alone no longer tells you
688 * which row has more error than another — that comparison now lives in the
689 * error chart, which has actual numbers. Always drawn with a diverging
690 * colormap regardless of the user's chosen (sequential) one — a signed
691 * quantity centered at zero needs a diverging map to read correctly, which
692 * coolwarm is and viridis etc. are not.
693 */
694 #colorDiffPanels(): void {
695 const species = this.#opts.model.species;
696 for (const r of this.#rows) {
697 if (r.diffScenes.length === 0) continue;
698 for (let k = 0; k < species.length; k++) {
699 const m = r.healthy ? maxAbsFinite(r.diffFields[k]) : null;
700 const range = r.diffRanges[k];
701 if (m !== null) {
702 if (!Number.isFinite(range.lo)) {
703 range.lo = -m;
704 range.hi = m;
705 } else {
706 const a = 0.15;
707 range.lo += a * (-m - range.lo);
708 range.hi += a * (m - range.hi);
709 }
710 }
711 if (!Number.isFinite(range.lo) || !Number.isFinite(range.hi)) continue;
712 const shown = floorRange(range.lo, range.hi);
713 fillFieldValues(r.diffValueBufs[k], r.diffFields[k], this.#topo);
714 fillColors(r.diffColorBufs[k], r.diffValueBufs[k], shown.lo, shown.hi, colormaps.coolwarm);
715 r.diffScenes[k]?.updateColors(r.diffColorBufs[k]);
716 const cap = r.diffCaps[k];
717 if (cap) cap.textContent = `± ${fmtValue(shown.hi)}`;
718 }
719 }
720 }
722 /**
723 * Relative L2 difference from the reference, per species, on the shared
724 * grid. Weighted by the Gauss weights, so it is the norm on the parameter
725 * sphere — not on the embedded surface, which would weight by the area
726 * element. That makes it a consistent diagnostic across variants rather than
727 * a physical quantity, which is all it is used for.
728 */
729 #measureDifference(): void {
730 // Against a reference file, every row is measured against its final state;
731 // otherwise against the chosen reference variant, whose own Δ is zero.
732 const ref = this.#fileRow ? null : this.#rows[this.#opts.reference];
733 const refFields = this.#fileRow?.fields ?? ref?.fields;
734 if (!refFields) return;
735 const species = this.#opts.model.species;
736 for (const r of this.#rows) {
737 for (let k = 0; k < species.length; k++) {
738 if (r === ref) {
739 r.err[k] = 0;
740 continue;
741 }
742 const a = r.fields[k];
743 const b = refFields[k];
744 if (!a || !b || a.length !== b.length) {
745 r.err[k] = NaN;
746 continue;
747 }
748 const diff = r.diffFields[k];
749 let num = 0;
750 let den = 0;
751 for (let i = 0; i < a.length; i++) {
752 const w = this.#weights[i];
753 const d = a[i] - b[i];
754 diff[i] = d;
755 num += w * d * d;
756 den += w * b[i] * b[i];
757 }
758 r.err[k] = den > 0 ? Math.sqrt(num / den) : NaN;
759 }
760 }
761 }
763 /**
764 * Each row's standing line: how many of its own steps it took to reach the
765 * common time, and how far it is from the reference right now, per species.
766 * Per species rather than a single worst-case number because the two are
767 * genuinely different questions on a two-species model — the slow species is
768 * usually the one that has converged and the fast one the one that has not.
769 */
770 #updateRowStats(): void {
771 const ref = this.#fileRow ? null : this.#rows[this.#opts.reference];
772 for (const r of this.#rows) {
773 // Divergence is said, not implied. Scaled to a healthy row, a blown-up
774 // variant is a flat saturated panel, which on its own is easy to misread
775 // as a converged uniform state. Δ itself now lives in the error chart,
776 // not here.
777 const body = !r.healthy
778 ? '<b class="cmp-diverged">diverged</b>'
779 : r === ref
780 ? '<b>reference</b>'
781 : '';
782 r.statEl.innerHTML =
783 `${r.session.steps.toLocaleString()} steps` + (body ? `<br>${body}` : '');
784 }
785 }
787 #status(): void {
788 const refFile = this.#opts.refFile;
789 const clock = refFile
790 ? `<b>t = ${this.#t.toFixed(2)} / ${(refFile.steps * CompareRun.baseDt(this.#opts.params)).toFixed(2)}</b>` +
791 ` · NOTE: vertical axis measures difference from uploaded simulation's end state.`
792 : `<b>t = ${this.#t.toFixed(2)}</b> (same for every variant)`;
793 this.#opts.onStatus(
794 `${clock} · ` +
795 (this.#frameMs > 0 ? `${this.#frameMs.toFixed(1)} ms/frame · ` : '') +
796 this.#note,
797 );
798 }
800 #observeResize(): void {
801 const scenes = this.#allScenes();
802 this.#resizeObs = new ResizeObserver(() => {
803 for (const s of scenes) {
804 const box = s.canvas.parentElement;
805 if (box) s.resize(box.clientWidth, box.clientHeight);
806 }
807 this.#errorChart?.redraw();
808 });
809 for (const s of scenes) {
810 const box = s.canvas.parentElement;
811 if (box) this.#resizeObs.observe(box);
812 }
813 this.#resizeObs.observe(this.#opts.chartContainer);
814 }
816 // -------------------------------------------------------------- the clock
817 /**
818 * One frame advances every variant by the *same model time*: `frameSteps`
819 * base steps, which a ÷K variant covers in K times as many of its own. That
820 * is the whole reason dt varies by an integer divisor — the alternative is
821 * rounding each variant to the nearest step and comparing fields that are a
822 * fraction of a timestep apart, which would show up as a difference and be
823 * indistinguishable from a real one.
824 */
825 async #pump(): Promise<void> {
826 if (this.#pumping) return;
827 this.#pumping = true;
828 try {
829 while (this.#running && !this.#disposed) {
830 // Against a reference file the run is finite: the last frame takes
831 // however many base steps remain, so every variant lands exactly on
832 // the file's end time — where Δ against its final state is the
833 // comparison — and stops there rather than drifting past it.
834 const refFile = this.#opts.refFile;
835 const n = refFile
836 ? Math.min(this.#frameSteps, refFile.steps - this.#stepsDone)
837 : this.#frameSteps;
838 if (n <= 0) {
839 this.#running = false;
840 this.#opts.onFinished?.();
841 break;
842 }
843 const t0 = performance.now();
844 for (const r of this.#rows) r.session.step(n * r.variant.dtDiv);
845 this.#stepsDone += n;
846 this.#t += n * CompareRun.baseDt(this.#opts.params);
847 await this.draw();
848 if (this.#disposed) break;
849 const dt = performance.now() - t0;
850 this.#frameMs = this.#frameMs === 0 ? dt : this.#frameMs + 0.05 * (dt - this.#frameMs);
851 if (refFile && this.#stepsDone >= refFile.steps) {
852 this.#finished = true;
853 this.#running = false;
854 this.#status();
855 this.#opts.onFinished?.();
856 break;
857 }
858 this.#status();
859 await nextFrame();
860 }
861 if (!this.#disposed) {
862 await this.draw();
863 this.#status();
864 }
865 } finally {
866 this.#pumping = false;
867 }
868 }
869}
871const nextFrame = (): Promise<number> => new Promise(requestAnimationFrame);
873/** A whole spectral state re-indexed into a (wider) band's layout — the
874 * reference file's initial condition, in the form loadState takes. */
875function prolongState(
876 coeffs: Record<string, Float32Array>,
877 names: string[],
878 lmaxFrom: number,
879 lmaxTo: number,
880): Record<string, Float32Array> {
881 const out: Record<string, Float32Array> = {};
882 for (const name of names) out[name] = prolongCoeffs(coeffs[name], lmaxFrom, lmaxTo);
883 return out;
884}
886/** Whether every entry is an ordinary number — false once a variant has left
887 * its convergence radius and saturated to infinity or NaN. */
888function allFinite(f: Float32Array | undefined): boolean {
889 if (!f) return false;
890 for (let i = 0; i < f.length; i++) if (!Number.isFinite(f[i])) return false;
891 return true;
892}
894type Bounds = { lo: number; hi: number };
896/** How far a field reaches from zero — the one number the rows are ranked by
897 * when deciding which of them sets a column's scale. */
898const peak = (b: Bounds): number => Math.max(Math.abs(b.lo), Math.abs(b.hi));
900/** Whichever of the given bounds reaches least far from zero; null if none. */
901function leastPeak(all: (Bounds | null)[]): Bounds | null {
902 let best: Bounds | null = null;
903 for (const b of all) {
904 if (b !== null && (best === null || peak(b) < peak(best))) best = b;
905 }
906 return best;
907}
909/** Max |value| over the finite entries of a field; null if none are finite —
910 * the diff panels' analogue of finiteRange below, since a symmetric range
911 * only needs the one number. */
912function maxAbsFinite(f: Float32Array): number | null {
913 let m = -Infinity;
914 let any = false;
915 for (let i = 0; i < f.length; i++) {
916 const v = f[i];
917 if (!Number.isFinite(v)) continue;
918 any = true;
919 const a = Math.abs(v);
920 if (a > m) m = a;
921 }
922 return any ? m : null;
923}
925/** Min and max over the finite entries only; null when there are none. */
926function finiteRange(f: Float32Array | undefined): { lo: number; hi: number } | null {
927 if (!f) return null;
928 let lo = Infinity;
929 let hi = -Infinity;
930 for (let i = 0; i < f.length; i++) {
931 const v = f[i];
932 if (!Number.isFinite(v)) continue;
933 if (v < lo) lo = v;
934 if (v > hi) hi = v;
935 }
936 return lo <= hi ? { lo, hi } : null;
937}
939/**
940 * The DOM: a header row naming each species and carrying that column's shared
941 * color range, then one row per variant. The colorbar is per *column* rather
942 * than per panel because the range is shared — a bar on every panel would be
943 * the same bar repeated, and would suggest each panel had its own scaling,
944 * which is exactly the thing that would make the comparison a lie.
945 */
946/** The file row's label color — none of the variant palette, since it is not
947 * a variant: it is the thing they are all measured against. */
948const FILE_ROW_COLOR = '#57606a';
950/**
951 * One sphere panel: a boxed SphereScene plus the value/color buffers that
952 * feed it. Shared by the value row, the diff row, and the file row — all
953 * three build a panel the same way, only differing in the class on the box
954 * (for styling) and in what fills the buffers afterward.
955 */
956function makeSpherePanel(
957 colsEl: HTMLElement,
958 topo: SphereMeshTopology,
959 posBuf: Float32Array,
960 background: string | undefined,
961 extraClass = '',
962): { box: HTMLElement; scene: SphereScene; valueBuf: Float32Array; colorBuf: Float32Array } {
963 const box = document.createElement('div');
964 box.className = extraClass ? `sphere-box cmp-box ${extraClass}` : 'sphere-box cmp-box';
965 colsEl.append(box);
966 const scene = new SphereScene(
967 box,
968 topo.numVertices,
969 topo.indices,
970 Float32Array.from(posBuf),
971 background,
972 );
973 scene.fitCamera();
974 return {
975 box,
976 scene,
977 valueBuf: new Float32Array(topo.numVertices),
978 colorBuf: new Float32Array(topo.numVertices * 3),
979 };
980}
982async function buildGrid(
983 opts: CompareOptions,
984 sessions: ModelSession[],
985 topo: SphereMeshTopology,
986 showDt: boolean,
987): Promise<{
988 rows: Row[];
989 fileRow: FileRow | null;
990 rangeBars: { fill: (lo: number, hi: number) => void }[];
991}> {
992 const { container, model } = opts;
993 container.replaceChildren();
994 container.classList.add('compare');
996 const head = document.createElement('div');
997 head.className = 'cmp-row cmp-head';
998 const headSpacer = document.createElement('div');
999 headSpacer.className = 'cmp-rowlabel';
1000 const headCols = document.createElement('div');
1001 headCols.className = 'cmp-cols';
1002 head.append(headSpacer, headCols);
1003 container.append(head);
1005 const rangeBars = model.species.map((name) => {
1006 const col = document.createElement('div');
1007 col.className = 'cmp-colhead';
1008 const tag = document.createElement('b');
1009 tag.textContent = name;
1010 const canvas = document.createElement('canvas');
1011 canvas.width = 160;
1012 canvas.height = 8;
1013 canvas.className = 'cmp-rangebar';
1014 const lab = document.createElement('span');
1015 lab.className = 'cmp-rangelab';
1016 col.append(tag, canvas, lab);
1017 headCols.append(col);
1018 let painted = false;
1019 return {
1020 fill: (lo: number, hi: number): void => {
1021 const ctx = canvas.getContext('2d');
1022 if (ctx && !painted) {
1023 painted = true;
1024 const cmap = colormaps[opts.colormapName()] ?? colormaps.viridis;
1025 for (let x = 0; x < canvas.width; x++) {
1026 const [r, g, b] = cmap(x / (canvas.width - 1));
1027 ctx.fillStyle = `rgb(${r},${g},${b})`;
1028 ctx.fillRect(x, 0, 1, canvas.height);
1029 }
1030 }
1031 lab.textContent = `${fmtValue(lo)} … ${fmtValue(hi)}`;
1032 },
1033 };
1034 });
1036 const sphereBg = getComputedStyle(document.documentElement)
1037 .getPropertyValue('--sphere-bg')
1038 .trim();
1040 const rows: Row[] = [];
1041 for (let i = 0; i < sessions.length; i++) {
1042 const session = sessions[i];
1043 const variant = opts.variants[i];
1044 const color = VARIANT_COLORS[i % VARIANT_COLORS.length];
1045 // The reference itself never gets a diff row — its diff against itself
1046 // is trivially zero, and a flat zero panel would just spend a WebGL
1047 // context for nothing.
1048 const isRef = !opts.refFile && i === opts.reference;
1050 const coords = await session.renderPositions();
1051 const posBuf = new Float32Array(topo.numVertices * 3);
1052 fillPositions(posBuf, coords, topo, opts.morph);
1054 const rowEl = document.createElement('div');
1055 rowEl.className = 'cmp-row';
1056 const labelEl = document.createElement('div');
1057 labelEl.className = 'cmp-rowlabel';
1058 labelEl.style.setProperty('--c', color);
1059 const nameEl = document.createElement('div');
1060 nameEl.className = 'cmp-rowname';
1061 nameEl.textContent = variantLabel(variant, showDt);
1062 const statEl = document.createElement('div');
1063 statEl.className = 'cmp-rowstat';
1064 labelEl.append(nameEl, statEl);
1065 const colsEl = document.createElement('div');
1066 colsEl.className = 'cmp-cols';
1067 rowEl.append(labelEl, colsEl);
1068 container.append(rowEl);
1070 const scenes: SphereScene[] = [];
1071 const valueBufs: Float32Array[] = [];
1072 const colorBufs: Float32Array[] = [];
1073 for (let k = 0; k < model.species.length; k++) {
1074 const { scene, valueBuf, colorBuf } = makeSpherePanel(colsEl, topo, posBuf, sphereBg || undefined);
1075 scenes.push(scene);
1076 valueBufs.push(valueBuf);
1077 colorBufs.push(colorBuf);
1078 }
1080 // ---- its diff row, right underneath ----------------------------------
1081 const diffFields = model.species.map(() => new Float32Array(topo.nlat * topo.nphi));
1082 const diffScenes: SphereScene[] = [];
1083 const diffValueBufs: Float32Array[] = [];
1084 const diffColorBufs: Float32Array[] = [];
1085 const diffCaps: HTMLElement[] = [];
1086 if (!isRef) {
1087 const diffRowEl = document.createElement('div');
1088 diffRowEl.className = 'cmp-row cmp-diffrow';
1089 const diffLabelEl = document.createElement('div');
1090 diffLabelEl.className = 'cmp-rowlabel';
1091 diffLabelEl.style.setProperty('--c', color);
1092 const diffNameEl = document.createElement('div');
1093 diffNameEl.className = 'cmp-rowname';
1094 diffNameEl.textContent = 'Δ vs reference';
1095 diffLabelEl.append(diffNameEl);
1096 const diffColsEl = document.createElement('div');
1097 diffColsEl.className = 'cmp-cols';
1098 diffRowEl.append(diffLabelEl, diffColsEl);
1099 container.append(diffRowEl);
1101 for (let k = 0; k < model.species.length; k++) {
1102 const { box, scene, valueBuf, colorBuf } = makeSpherePanel(
1103 diffColsEl, topo, posBuf, sphereBg || undefined, 'cmp-diffbox',
1104 );
1105 diffScenes.push(scene);
1106 diffValueBufs.push(valueBuf);
1107 diffColorBufs.push(colorBuf);
1108 const cap = document.createElement('span');
1109 cap.className = 'cmp-diffcap';
1110 box.append(cap);
1111 diffCaps.push(cap);
1112 }
1113 }
1115 const diffRanges = model.species.map(() => ({ lo: NaN, hi: NaN }));
1116 rows.push({
1117 variant, session, color, coords, posBuf, scenes, valueBufs, colorBufs,
1118 fields: [], diffFields, diffScenes, diffValueBufs, diffColorBufs, diffCaps, diffRanges,
1119 err: model.species.map(() => 0), healthy: true, statEl,
1120 });
1121 }
1123 // ---- the reference file's final state, as one more (static) row ---------
1124 let fileRow: FileRow | null = null;
1125 if (opts.refFile) {
1126 const rf = opts.refFile;
1127 // Synthesized through the coarsest session's display plan — exact, like
1128 // every other use of the shared grid: the file's coefficients are
1129 // band-limited at its lmax, which every variant's band contains.
1130 const view = sessions[0].viewSht;
1131 const lmaxTo = sessions[0].cfg.lmax;
1132 const on = (q: Float32Array): Promise<Float32Array> =>
1133 view.synth(prolongCoeffs(q, rf.lmax, lmaxTo));
1134 const [gx, gy, gz] = [
1135 await on(rf.geometryCoeffs.X),
1136 await on(rf.geometryCoeffs.Y),
1137 await on(rf.geometryCoeffs.Z),
1138 ];
1139 // The file's own surface, not a regeneration of it — interleaved xyz, the
1140 // same layout renderPositions() hands back.
1141 const coords = new Float32Array(3 * gx.length);
1142 for (let i = 0; i < gx.length; i++) {
1143 coords[3 * i] = gx[i];
1144 coords[3 * i + 1] = gy[i];
1145 coords[3 * i + 2] = gz[i];
1146 }
1147 const posBuf = new Float32Array(topo.numVertices * 3);
1148 fillPositions(posBuf, coords, topo, opts.morph);
1150 const rowEl = document.createElement('div');
1151 rowEl.className = 'cmp-row';
1152 const labelEl = document.createElement('div');
1153 labelEl.className = 'cmp-rowlabel';
1154 labelEl.style.setProperty('--c', FILE_ROW_COLOR);
1155 const nameEl = document.createElement('div');
1156 nameEl.className = 'cmp-rowname';
1157 nameEl.textContent = 'reference file';
1158 nameEl.title = rf.label;
1159 const statEl = document.createElement('div');
1160 statEl.className = 'cmp-rowstat';
1161 statEl.innerHTML = `${rf.steps.toLocaleString()} steps<br><b>final state</b>`;
1162 labelEl.append(nameEl, statEl);
1163 const colsEl = document.createElement('div');
1164 colsEl.className = 'cmp-cols';
1165 rowEl.append(labelEl, colsEl);
1166 container.append(rowEl);
1168 const scenes: SphereScene[] = [];
1169 const valueBufs: Float32Array[] = [];
1170 const colorBufs: Float32Array[] = [];
1171 const fields: Float32Array[] = [];
1172 const bounds: (Bounds | null)[] = [];
1173 for (let k = 0; k < model.species.length; k++) {
1174 const { scene, valueBuf, colorBuf } = makeSpherePanel(colsEl, topo, posBuf, sphereBg || undefined);
1175 scenes.push(scene);
1176 const field = await on(rf.final[model.state[k]]);
1177 fields.push(field);
1178 bounds.push(finiteRange(field));
1179 fillFieldValues(valueBuf, field, topo);
1180 valueBufs.push(valueBuf);
1181 colorBufs.push(colorBuf);
1182 }
1183 fileRow = { coords, posBuf, scenes, valueBufs, colorBufs, fields, bounds };
1184 }
1186 // Every panel shares one camera: the study is about the fields, and looking
1187 // at two of them from different angles is not comparing them.
1188 const all = [
1189 ...rows.flatMap((r) => [...r.scenes, ...r.diffScenes]),
1190 ...(fileRow?.scenes ?? []),
1191 ];
1192 for (let i = 1; i < all.length; i++) all[0].syncCamerasWith(all[i]);
1194 return { rows, fileRow, rangeBars };
1195}