scripts/exp_c6_extend.py

"""Claim 6, extended: push eps down until BOTH schemes are bias-limited, so the
ULMC/composite ratio can be read off in its asymptotic (saturated) regime."""
import numpy as np
import common as C, grid1d as G, ulmc_core as U
import exp_nonquadratic2 as X   # reuses the potentials and the cached floors

res = {}
NGRID = U.n_grid(int(4e9), 1.04)
HS = {"ulmc": np.geomspace(0.055, 1 / C.gamma_of(X.BETA), 11),
      "lmc": np.geomspace(0.002, 0.9, 22),
      "composite": np.geomspace(0.002, 0.9, 22)}
tab, floors = {}, {}
for scheme in ("ulmc", "lmc", "composite"):
    tab[scheme] = []
    floors[scheme] = []
    for h in HS[scheme]:
        h = float(h)
        if scheme == "ulmc":
            fl, conv = X.ulmc_floor(X.f, X.df, X.ddf, X.BETA, h)
        else:
            fl, conv = X.od_floor(scheme, X.f, X.df, X.BETA, X.ALPHA, h)
        floors[scheme].append({"h": h, "stiff_floor": fl, "rel_change": conv})
        a = np.array([X.ALPHA]); mult = np.array([float(X.D - X.M_RIDGE)])
        S0, m0 = C.init_cold(a, X.BETA)
        mp = (U.ulmc_maps(a, h, C.gamma_of(X.BETA)) if scheme == "ulmc"
              else U.lmc_maps(a, h) if scheme == "lmc"
              else U.composite_lmc_maps(a, h, X.ALPHA))
        tab[scheme].append((h, U.kl_curve(mp, S0, m0, a, mult, NGRID) + X.M_RIDGE * fl))
    print("built", scheme, flush=True)

rows = []
for eps in (0.048, 0.035, 0.026, 0.019, 0.014, 0.0105, 0.008):
    row = {"eps": float(eps)}
    for scheme in ("ulmc", "lmc", "composite"):
        best = None
        for h, curve in tab[scheme]:
            n = U.first_below(NGRID, curve, eps * eps)
            if n and (best is None or n < best[0]):
                best = (n, h)
        row[scheme] = {"N_eps": best[0] if best else None,
                       "h_star": best[1] if best else None,
                       "bias_limited": bool(best and best[1] < HS[scheme][-1] * 0.999)}
    if row["ulmc"]["N_eps"] and row["composite"]["N_eps"]:
        row["speedup_ulmc_over_composite"] = row["composite"]["N_eps"] / row["ulmc"]["N_eps"]
        row["speedup_ulmc_over_lmc"] = row["lmc"]["N_eps"] / row["ulmc"]["N_eps"]
    rows.append(row)
    print("eps %.4f" % eps, {k: (row[k]["N_eps"], row[k]["bias_limited"])
                             for k in ("ulmc", "lmc", "composite")},
          "speedup %.3f" % row.get("speedup_ulmc_over_composite", 0), flush=True)

sat = [r for r in rows if r["ulmc"]["bias_limited"] and r["composite"]["bias_limited"]]
res["extended"] = {
    "rows": rows, "floors": floors,
    "saturated_rows": [(r["eps"], r["speedup_ulmc_over_composite"]) for r in sat],
    "asymptotic_speedup": float(np.mean([r["speedup_ulmc_over_composite"] for r in sat[-3:]])) if len(sat) >= 3 else None,
    "ulmc_ever_beats_composite": bool(any(r.get("speedup_ulmc_over_composite", 0) > 1 for r in rows)),
}
for sch in ("ulmc", "lmc", "composite"):
    ok = [r for r in rows if r[sch]["N_eps"] and r[sch]["bias_limited"]]
    s, r2 = C.fit_exponent([r["eps"] for r in ok], [r[sch]["N_eps"] for r in ok])
    res["extended"][f"{sch}_eps_exponent_bias_limited_only"] = s
    res["extended"][f"{sch}_r2"] = r2
    res["extended"][f"{sch}_n_bias_limited_points"] = len(ok)
C.dump("c6_extended", res)
print("asymptotic speedup:", res["extended"]["asymptotic_speedup"],
      "ever beats:", res["extended"]["ulmc_ever_beats_composite"])