Toby
ad8b889437
- femap/: planar best-effort solver, build, result and page (fe-map.aethercosmology.com) - satellites/: The Sync Test build, ISS elements, SatNOGS timings and page (iss.aethercosmology.com) - src/handoff/The_Shape_of_Distance_PRESENTATION.html: inputs for both - CONTRIBUTING.md; README and LICENSE-DATA cover all four sites; GitHub mirror for issues and pull requests Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
346 lines
18 KiB
Python
346 lines
18 KiB
Python
"""The Best Flat Map: every measured length and limit laid out on one plane, then released into 3D.
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Data (all published earlier on distance.aethercosmology.com and pingstats.aethercosmology.com):
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flights The Measured Sphere, "each flight's own speed": 219 cities, 1,344 routes flown both ways.
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Length = aircraft cruise speed x mean airborne time, less 15 min for climb and descent.
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limits The Measured Sphere's cable, rail, road and satellite-ranging limits, every WonderNetwork
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2020 round trip and every live round trip (RIPE Atlas, Globalping, Vultr) between servers
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in these cities.
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triangles The Triangle Test's 935 surveyed triangles (scored, not solved: a plane gives every
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triangle exactly 180 degrees).
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Coordinates are used to label cities, draw the start maps, match servers to cities and score the
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globe for comparison. The solver (fit.py) sees only lengths and limits.
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../.venv/bin/python build.py -> data/femap.json, site/index.html
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"""
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import base64, datetime as dt, importlib.util, json, math, os, pickle, re, sys, time
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for _v in ("OPENBLAS_NUM_THREADS", "OMP_NUM_THREADS", "MKL_NUM_THREADS"):
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os.environ.setdefault(_v, "1")
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from multiprocessing import Pool
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import numpy as np
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HERE = os.path.dirname(os.path.abspath(__file__))
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SRC = os.path.join(HERE, "..", "src")
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sys.path.insert(0, SRC)
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_spec = importlib.util.spec_from_file_location("pingstats_build", os.path.join(SRC, "build.py"))
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_pb = importlib.util.module_from_spec(_spec); _spec.loader.exec_module(_pb)
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live, land = _pb.live, _pb.land # src/build.py
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from models import R, C_FIBER, globe as gc, ae_xy, dualpole_xy, mercator_xy
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from fit import Problem, sphere_fit
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PRES = os.path.join(SRC, "handoff", "The_Shape_of_Distance_PRESENTATION.html")
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KM_PER_MS = C_FIBER / 2 / 1000 # one-way km per ms of round trip, light in glass
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END_SLACK = 25.0 # km allowed at each end of a round trip
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MATCH_KM = 80.0 # a server belongs to a city if it is this close to its airport
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LO, HI = 0.25, 0.10 # default flight band: [0.75 L, 1.10 L]
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BANDS = [(0.25, 0.10), (0.25, 0.25), (0.40, 0.10), (0.50, 0.10)]
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N_RANDOM = 300
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FAST = os.environ.get("FAST") == "1" # quick preview: one start, one 3D seed, one band -> data/preview.json, site/preview.html
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SEED = 20261030
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FA_PREFIX = "https://www.flightaware.com/live/flight/"
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def pages():
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s = open(PRES, encoding="utf-8").read()
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out = []
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for b in re.findall(r"[A-Za-z0-9+/]{20000,}={0,2}", s):
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out.append(base64.b64decode(b).decode("utf-8", "ignore"))
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return out
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def page_const(html, name):
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js = next(x for x in re.findall(r"<script[^>]*>(.*?)</script>", html, flags=re.S) if f"const {name}=" in x)
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i = js.index(f"const {name}=") + len(name) + 7
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return json.JSONDecoder().raw_decode(js[i:])[0]
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def aeq(lat, lon, lat0, lon0):
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"""Azimuthal equidistant map centred on (lat0, lon0), km. North-pole AE is (90, 0); dual-pole is (0, 0)."""
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p1, l1, p0, l0 = map(np.radians, (np.asarray(lat), np.asarray(lon), lat0, lon0))
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cc = np.sin(p0) * np.sin(p1) + np.cos(p0) * np.cos(p1) * np.cos(l1 - l0)
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c = np.arccos(np.clip(cc, -1, 1)); k = np.where(c < 1e-9, 1.0, c / np.sin(np.maximum(c, 1e-9)))
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x = R * k * np.cos(p1) * np.sin(l1 - l0)
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y = R * k * (np.cos(p0) * np.sin(p1) - np.sin(p0) * np.cos(p1) * np.cos(l1 - l0))
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return np.c_[x, y]
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def plane_d(f, a, b):
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x1, y1 = f(*a); x2, y2 = f(*b)
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return math.hypot(x2 - x1, y2 - y1)
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def shortest_on_any(a, b):
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"""Shortest distance between two places on the globe or any of the three flat maps used elsewhere."""
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return min(gc(*a, *b), plane_d(ae_xy, a, b), plane_d(dualpole_xy, a, b), plane_d(mercator_xy, a, b))
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def load():
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P = pages()
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ms = page_const(P[6], "DATA")["own"]
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tri = page_const(P[7], "FIN")["tri"]
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cities = ms["cities"]
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C = [(c[1], c[2]) for c in cities]
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n = len(C)
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fl = []
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for f in ms["flights"]:
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a, b, x = f[0], f[1], f[8]
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ab, ba = x["ab"], x["ba"]
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fl.append(dict(a=a, b=b, L=x["km"], airline=f[4], fa=f[5], fb=f[6], page=f[7],
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ab=[ab["ident"], ab["ac"], ab["air"], ab["n"], round(ab["v"]), ab["src"]],
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ba=[ba["ident"], ba["ac"], ba["air"], ba["n"], round(ba["v"]), ba["src"]]))
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lim = {} # (a, b, kind) -> record; round trips keep the tightest per pair
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def add(a, b, U, kind, note, label="", url=""):
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if a == b:
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return
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a, b = min(a, b), max(a, b)
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k = (a, b, kind)
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if k not in lim or U < lim[k]["U"]:
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lim[k] = dict(a=a, b=b, U=round(U, 1), kind=kind, note=note, label=label, url=url)
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kinds = {"cable": "rt", "rail": "rail", "road": "road", "satellite": "sat"}
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for l in ms["limits"]:
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add(l[0], l[1], l[2], kinds[l[3]], l[4].replace("round trip ", ""), l[5], l[6] if len(l) > 6 else "")
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def nearest(p):
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d = [gc(*p, *q) for q in C]; i = int(np.argmin(d)); return i, d[i]
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dropped = []
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wn = json.load(open(os.path.join(SRC, "data", "wn_clean.json")))
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srv = wn["servers"]; wm = {k: nearest((s["lat"], s["lon"])) for k, s in srv.items()}
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n_wn = 0
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# A round trip shorter than every surface allows means a server is not where it is listed. A server
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# caught in two or more such pairs is treated as mislocated and all its pairs are left out.
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reach_of = lambda p: KM_PER_MS * p["rtt"] + 2 * END_SLACK
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bad = [p for p in wn["pairs"] if reach_of(p) < min(p["globe"], p["ae"], p["dualpole"], p["mercator"])]
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hits = {}
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for p in bad:
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for s in (p["a"], p["b"]):
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hits[s] = hits.get(s, 0) + 1
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mislocated = {s for s, k in hits.items() if k >= 2}
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for p in bad:
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dropped.append(f'{srv[p["a"]]["name"]} - {srv[p["b"]]["name"]} ({p["rtt"]} ms)')
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for p in wn["pairs"]:
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a, b = wm[p["a"]], wm[p["b"]]
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if a[1] > MATCH_KM or b[1] > MATCH_KM or p in bad or p["a"] in mislocated or p["b"] in mislocated:
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continue
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reach = reach_of(p)
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n_wn += 1
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add(a[0], b[0], reach + a[1] + b[1], "rt",
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f'{p["rtt"]:.2f} ms, WonderNetwork 2020 archive ({p["n"]} samples)',
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f'WonderNetwork servers {srv[p["a"]]["name"]} and {srv[p["b"]]["name"]}', "https://wondernetwork.com/pings")
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lv = live(); sites = lv["sites"]; sm = [nearest((s[2], s[3])) for s in sites]
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n_live = 0
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for c in lv["cells"]:
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a, b = sm[c[0]], sm[c[1]]
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if a[1] > MATCH_KM or b[1] > MATCH_KM:
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continue
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sa, sb = sites[c[0]], sites[c[1]]
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reach = KM_PER_MS * c[2] + 2 * END_SLACK
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if reach < shortest_on_any((sa[2], sa[3]), (sb[2], sb[3])):
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dropped.append(f"{sa[0]} - {sb[0]} ({c[2]} ms)")
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continue
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n_live += 1
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add(a[0], b[0], reach + a[1] + b[1], "rt", f"{c[2]:.1f} ms, live measurement 2026 ({c[5]})",
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f"{sa[0]} probe to {sb[0]} anchor", "https://pingstats.aethercosmology.com/")
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lim = sorted(lim.values(), key=lambda r: (r["kind"], r["a"], r["b"]))
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tri_fail = dict(n=len(tri), flat=sum(abs(t[3]) > 4 for t in tri), globe=sum(abs(t[2]) > 4 for t in tri))
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return dict(cities=cities, C=np.array(C), fl=fl, lim=lim, tri=tri_fail, dropped=dropped, n_wn=n_wn, n_live=n_live,
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mislocated=sorted(f'{srv[s]["name"]} ({srv[s]["country"]})' for s in mislocated))
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def mds_start(prob, C):
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"""Classical multidimensional scaling of the shortest flight-path lengths, turned and mirrored
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(no stretching) to sit as close as possible to the North-pole AE layout for drawing."""
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n = prob.n; D = np.full((n, n), np.inf); np.fill_diagonal(D, 0)
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for a, b, L in zip(prob.fa, prob.fb, prob.fl):
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D[a, b] = D[b, a] = min(D[a, b], L)
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for k in range(n):
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D = np.minimum(D, D[:, k:k + 1] + D[k:k + 1, :])
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J = np.eye(n) - 1 / n; B = -0.5 * J @ (D ** 2) @ J
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w, V = np.linalg.eigh(B); X = V[:, -2:] * np.sqrt(np.maximum(w[-2:], 0))
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T = aeq(C[:, 0], C[:, 1], 90, 0)
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Xc, Tc = X - X.mean(0), T - T.mean(0)
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U, _, Vt = np.linalg.svd(Xc.T @ Tc)
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return Xc @ (U @ Vt) + T.mean(0)
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_PROB = None
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def _init(prob):
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global _PROB
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_PROB = prob
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def _run(job):
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label, centre, X0, lo, hi = job[:5]
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k, X = _PROB.best_effort(X0, lo, hi, **(job[5] if len(job) > 5 else {}))
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r = _PROB.dists(X)[0] / _PROB.fl
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return dict(label=label, centre=centre, broken=k, meanlog=float(np.abs(np.log(r)).mean()), X=X)
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def counts(prob, X, lo, hi):
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dd, ld = prob.dists(X); r = dd / prob.fl
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return dict(short=int((r < 1 - lo).sum()), long=int((r > 1 + hi).sum()), limits=int((ld > prob.lu * 1.0005).sum()))
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def main():
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t0 = time.time()
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D = load(); C = D["C"]; fl, lim = D["fl"], D["lim"]
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prob = Problem(len(C), [f["a"] for f in fl], [f["b"] for f in fl], [f["L"] for f in fl],
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[l["a"] for l in lim], [l["b"] for l in lim], [l["U"] for l in lim])
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GF = np.array([gc(*C[f["a"]], *C[f["b"]]) for f in fl]); GL = np.array([gc(*C[l["a"]], *C[l["b"]]) for l in lim])
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print(f"{len(C)} cities, {len(fl)} flights, {len(lim)} limits ({D['n_wn']} WonderNetwork pairs, {D['n_live']} live cells, "
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f"{len(D['dropped'])} round trips dropped as mislocated)", flush=True)
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starts = {"ae": ("North-pole AE", [90, 0], aeq(C[:, 0], C[:, 1], 90, 0)),
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"dp": ("Dual-pole AE", [0, 0], aeq(C[:, 0], C[:, 1], 0, 0)),
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"mds": ("Flight times only", [90, 0], mds_start(prob, C))}
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rng = np.random.default_rng(SEED)
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jobs = [(v[0], v[1], v[2], LO, HI) for v in starts.values()]
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named = [(0, 90), (0, -90), (0, 180), (-90, 0), (45, 100), (60, -30), (30, 60), (-30, 150)]
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rand = [(round(math.degrees(math.asin(rng.uniform(-1, 1))), 1), round(rng.uniform(-180, 180), 1)) for _ in range(N_RANDOM)]
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jobs += [(f"AE centred on {la}, {lo}", [la, lo], aeq(C[:, 0], C[:, 1], la, lo), LO, HI) for la, lo in named + rand]
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if FAST:
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jobs = jobs[:1]
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cache = os.path.join(HERE, "data", "search_fast.pkl" if FAST else "search.pkl")
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sig = (len(C), len(fl), len(lim), LO, HI, len(jobs))
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pool = Pool(7, initializer=_init, initargs=(prob,))
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if os.path.exists(cache) and pickle.load(open(cache, "rb"))["sig"] == sig:
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res = pickle.load(open(cache, "rb"))["res"]
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print("search: cached", flush=True)
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else:
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res = pool.map(_run, jobs, chunksize=1)
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pickle.dump(dict(sig=sig, res=res), open(cache, "wb"))
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res.sort(key=lambda r: (r["broken"], r["meanlog"]))
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# Refine the 20 best layouts: twelve rounds, shorter solves, two reweighting floors.
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if not FAST:
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ref = pool.map(_run, [(r["label"], r["centre"], r["X"], LO, HI, dict(rounds=12, maxiter=3000, eps=e))
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for r in res[:20] for e in (0.02, 0.05)], chunksize=1)
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for r in ref:
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r["refined"] = True
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print("refined:", sorted(r["broken"] for r in ref)[:10], flush=True)
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res = sorted(res + ref, key=lambda r: (r["broken"], r["meanlog"]))
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best = res[0]
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print(f"search: {len(res)} starts in {time.time() - t0:.0f}s; best {best['broken']} broken from {best['label']}; "
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f"worst start {res[-1]['broken']}", flush=True)
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for r in res[:5]:
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print(" ", r["broken"], round(r["meanlog"], 4), r["label"])
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# Release the best flat layout into free 3D space: same data, same solver, the plane rule removed.
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# In the same pool: the band table (each band solved from the best layout and from North-pole AE).
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seeds = 1 if FAST else 6
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rel = [("3D", None, np.c_[best["X"], np.random.default_rng(SEED + s).normal(0, 50, len(C))], LO, HI) for s in range(seeds)]
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seeds_b = [r["X"] for r in res[:5]] + [starts["ae"][2]]
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NB = len(seeds_b)
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bjobs = [(f"band {lo} {hi}", None, X0, lo, hi) for lo, hi in (BANDS[:1] if FAST else BANDS) for X0 in seeds_b]
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out_jobs = pool.map(_run, rel + bjobs, chunksize=1)
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pool.close()
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X3s = out_jobs[:seeds]
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b3 = min(X3s, key=lambda t: t["broken"]); k3, X3 = b3["broken"], b3["X"]
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sph = sphere_fit(X3)
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print(f"3D: {k3} broken, radius {sph['radius']:.0f} km, wrap {sph['wrap']:.0f} deg, offset {sph['offset']:.3f}", flush=True)
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bands = []
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for j, (lo, hi) in enumerate(BANDS[:1] if FAST else BANDS):
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cand = out_jobs[seeds + NB * j: seeds + NB * (j + 1)]
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cand = cand + [dict(broken=prob.broken(best["X"], lo, hi), X=best["X"])]
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X = min(cand, key=lambda t: t["broken"])["X"]; r = prob.dists(X)[0] / prob.fl; gr = GF / prob.fl
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bands.append(dict(lo=lo, hi=hi, flat=dict(**counts(prob, X, lo, hi), below75=int((r < 0.75).sum()), below60=int((r < 0.6).sum())),
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globe=dict(short=int((gr < 1 - lo).sum()), long=int((gr > 1 + hi).sum()), limits=int((GL > prob.lu * 1.0005).sum()),
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below75=int((gr < 0.75).sum()), below60=int((gr < 0.6).sum())),
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flat_long=[[int(prob.fa[i]), int(prob.fb[i]), round(float(r[i]), 3)] for i in np.where(r > 1 + hi)[0]]))
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print("band", lo, hi, bands[-1]["flat"], bands[-1]["globe"], flush=True)
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r = prob.dists(best["X"])[0] / prob.fl; gr = GF / prob.fl
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stats = dict(
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n_cities=len(C), n_flights=len(fl), n_limits=len(lim),
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n_kind={k: sum(l["kind"] == k for l in lim) for k in ("rt", "rail", "road", "sat")},
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n_wn=D["n_wn"], n_live=D["n_live"], dropped=D["dropped"], mislocated=D["mislocated"], n_starts=len(jobs),
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best=dict(label=best["label"], centre=best["centre"], broken=best["broken"], **counts(prob, best["X"], LO, HI),
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below80=int((r < 0.8).sum()), below85=int((r < 0.85).sum()), meanlog=best["meanlog"]),
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globe=dict(**{k: int(v) for k, v in dict(short=(gr < 1 - LO).sum(), long=(gr > 1 + HI).sum(),
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limits=(GL > prob.lu * 1.0005).sum()).items()},
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below80=int((gr < 0.8).sum()), below85=int((gr < 0.85).sum()), meanlog=float(np.abs(np.log(gr)).mean())),
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starts_broken=[[x["label"], x["broken"]] for x in res if "refined" not in x],
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n_best=sum(x["broken"] == best["broken"] for x in res),
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three=dict(broken=k3, **counts(prob, X3, LO, HI), **sph),
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globe_long=[[int(prob.fa[i]), int(prob.fb[i]), round(float(gr[i]), 3)] for i in np.where(gr > 1 + HI)[0]],
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globe_short=[[int(prob.fa[i]), int(prob.fb[i]), round(float(gr[i]), 3)] for i in np.where(gr < 1 - LO)[0]],
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tri=D["tri"], lo=LO, hi=HI, km_per_ms=KM_PER_MS, end_slack=END_SLACK, match_km=MATCH_KM,
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built=dt.datetime.now(dt.timezone.utc).strftime("%Y-%m-%d %H:%M UTC"))
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def strip(u):
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return u[len(FA_PREFIX):] if u.startswith(FA_PREFIX) else u
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out = dict(
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cities=D["cities"],
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fl=[[f["a"], f["b"], round(f["L"], 1), f["airline"], f["fa"], f["fb"], f["page"],
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f["ab"][:5] + [strip(f["ab"][5])], f["ba"][:5] + [strip(f["ba"][5])]] for f in fl],
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lim=[[l["a"], l["b"], l["U"], l["kind"], l["note"], l["label"], l["url"]] for l in lim],
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gf=[round(float(x), 1) for x in GF], gl=[round(float(x), 1) for x in GL],
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land=land(),
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starts={k: dict(label=v[0], centre=v[1], X=np.round(v[2], 1).tolist()) for k, v in starts.items()},
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best=dict(label=best["label"], centre=best["centre"], X=np.round(best["X"], 1).tolist()),
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best3=dict(X=np.round(X3, 1).tolist()),
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bands=bands, stats=stats, fa_prefix=FA_PREFIX)
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os.makedirs(os.path.join(HERE, "data"), exist_ok=True)
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with open(os.path.join(HERE, "data", "preview.json" if FAST else "femap.json"), "w") as fh:
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json.dump(out, fh, separators=(",", ":"))
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print(json.dumps(stats, indent=1)[:4000])
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render(out)
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print(f"done in {time.time() - t0:.0f}s")
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def render(out):
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tpl = os.path.join(HERE, "template.html")
|
||
if not os.path.exists(tpl):
|
||
return
|
||
html = open(tpl, encoding="utf-8").read()
|
||
s = out["stats"]
|
||
vals = copy_values(out)
|
||
for k, v in vals.items():
|
||
html = html.replace("{{" + k + "}}", v)
|
||
left = sorted(set(re.findall(r"\{\{(\w+)\}\}", html)))
|
||
assert not left, left
|
||
html = html.replace("/*DATA*/null", json.dumps(out, separators=(",", ":")))
|
||
os.makedirs(os.path.join(HERE, "site"), exist_ok=True)
|
||
name = "preview.html" if FAST else "index.html"
|
||
open(os.path.join(HERE, "site", name), "w", encoding="utf-8").write(html)
|
||
print("site/" + name, round(len(html) / 1e6, 2), "MB")
|
||
|
||
|
||
def fmt(n):
|
||
return f"{n:,}"
|
||
|
||
|
||
def copy_values(out):
|
||
s = out["stats"]; b, g, t3 = s["best"], s["globe"], s["three"]
|
||
names = [c[0] for c in out["cities"]]
|
||
long_ = sorted(out["bands"][0]["flat_long"], key=lambda x: -x[2])
|
||
v = dict(
|
||
N_CITIES=fmt(s["n_cities"]), N_FLIGHTS=fmt(s["n_flights"]), N_LIMITS=fmt(s["n_limits"]),
|
||
N_RT=fmt(s["n_kind"]["rt"]), N_RAIL=fmt(s["n_kind"]["rail"] + s["n_kind"]["road"]), N_SAT=fmt(s["n_kind"]["sat"]),
|
||
N_STARTS=fmt(s["n_starts"]), N_TRI=fmt(s["tri"]["n"]), TRI_FLAT=fmt(s["tri"]["flat"]), TRI_GLOBE=fmt(s["tri"]["globe"]),
|
||
BEST_LONG=fmt(b["long"]), BEST_SHORT=fmt(b["short"]), BEST_LIM=fmt(b["limits"]), BEST_BROKEN=fmt(b["broken"]),
|
||
BEST_B80=fmt(b["below80"]), GLOBE_B80=fmt(g["below80"]), GLOBE_LONG=fmt(g["long"]), GLOBE_SHORT=fmt(g["short"]),
|
||
GLOBE_LIM=fmt(g["limits"]),
|
||
WORST_PAIR=f"{names[long_[0][0]]}–{names[long_[0][1]]}" if long_ else "–",
|
||
WORST_X=f"{long_[0][2]:.2f}" if long_ else "–",
|
||
LONG_LIST=", ".join(f"{names[a]}–{names[bb]} ×{x:.2f}" for a, bb, x in long_[:8]),
|
||
R3=fmt(round(t3["radius"])), WRAP3=f"{t3['wrap']:.0f}", OFF3=f"{t3['offset'] * 100:.1f}", BROKEN3=fmt(t3["broken"]),
|
||
LO_PCT=f"{round((1 - s['lo']) * 100)}", HI_PCT=f"{round((1 + s['hi']) * 100)}",
|
||
BUILT=s["built"], N_DROPPED=fmt(len(s["dropped"])), N_STARTS_AE=fmt(s["n_starts"] - 3), KM_PER_MS=f"{s['km_per_ms']:.1f}",
|
||
FIT_LO=next((f"{round((1 - x['lo']) * 100)}" for x in out["bands"] if x["flat"]["short"] + x["flat"]["long"] + x["flat"]["limits"] == 0), "–"),
|
||
FIT_B75=next((fmt(x["flat"]["below75"]) for x in out["bands"] if x["flat"]["short"] + x["flat"]["long"] + x["flat"]["limits"] == 0), "–"),
|
||
FIT_B60=next((fmt(x["flat"]["below60"]) for x in out["bands"] if x["flat"]["short"] + x["flat"]["long"] + x["flat"]["limits"] == 0), "–"),
|
||
GLOBE_B75=fmt(out["bands"][0]["globe"]["below75"]), GLOBE_B60=fmt(out["bands"][0]["globe"]["below60"]),
|
||
GLOBE_SHORT_LIST=", ".join(f"{names[a]}–{names[bb]}" for a, bb, x in sorted(s["globe_short"], key=lambda t: t[2])[:4]),
|
||
)
|
||
return v
|
||
|
||
|
||
if __name__ == "__main__":
|
||
main()
|