vvsandClaude Opus 5
f5d036c9d8
The flat regime is not detectable by the three-point order estimate: m >= 2 (the exact condition for a tangent step to lose to a halving) fires on 0.2% of APS states and on only 5.8% of states of pure powers of order 3-19. Paper corrected where it said the whole gap is model order (widelimit, decision, abstract, future work - the refuted log transform removed). WARNING recorded in FINDINGS_model_order.md: article/sim_numerics.tex has carried a STALE header since the first commit (current text = sim_numerics.md, unchanged since 08-24); every paper edit of 09-20/21 went into the .tex, the .md has none of them. Which file is canonical is Valeri's call. The new text numbers trace to results_diag_*.txt but are not yet machine-checked by verify_article.py. Trace hook in pure_root is behaviour-neutral and pinned; 762 pass on the server twice. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
67 lines
2.6 KiB
Python
67 lines
2.6 KiB
Python
"""Is the flat regime DETECTABLE from evaluations already paid for?
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Established by diag_model_order.py and its checks: two thirds of the wide-bracket gap sit
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on the flat families (fun3-fun6), where Chandrupatla bisects 93-100% of his steps and our
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step removes 0.41-0.81 halvings of the bracket per evaluation - less than bisection's 1.
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On an approach |f| ~ K e^m the tangent step lands at e(1 - 1/m): it beats bisection's
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halving only while 1 - 1/m < 1/2, i.e. m < 2. The 2 is bisection's 1/2 rewritten, not a
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chosen number. m is what _local_order reads from the three latest evaluations.
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Question measured here, BEFORE anything is built: does "m >= 2" separate the states of
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the flat families from the states of the canonical set? _local_order is known to fire
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falsely (derived3_m: m > 1 on 27.9% of APS steps, excursions to 34.8), so the separation
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is the whole question. If APS states cross m >= 2 about as often as flat ones, the regime
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is NOT detectable this way and no gate may be built on it.
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python -u diag_flat_detectable.py
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"""
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from __future__ import annotations
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from collections import defaultdict
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from scipy.optimize._tstutils import _APS_TESTS_DICTS, _CHANDRUPATLA_TESTS_DICTS
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from diag_model_order import ACC, MAXFEV, OURS, XTOL
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from simroot.pure import _local_order, pure_root
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FLAT = ("fun3", "fun4", "fun5", "fun6")
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def states(f, a, b, r):
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st = {"trace": []}
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x, _n, conv = pure_root(f, a, b, XTOL, MAXFEV, stats=st, **OURS)
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if not (conv and abs(float(x) - r) <= ACC):
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return []
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out = []
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for s in st["trace"]:
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if s["xp2"] is None:
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continue
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out.append(_local_order(s["x"], s["fx"], s["xp"], s["fp"], s["xp2"], s["fp2"]))
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return out
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def main():
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groups = defaultdict(list)
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for d in _APS_TESTS_DICTS:
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a, b = (float(v) for v in d["bracket"])
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f = (lambda ff, aa: lambda t: ff(t, *aa))(d["f"], d.get("args", ()))
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groups["APS (canonical)"] += states(f, a, b, float(d["root"]))
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for d in _CHANDRUPATLA_TESTS_DICTS:
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a, b = (float(v) for v in d["bracket"])
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fam = str(d["ID"]).split(".")[0]
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key = "CHA flat fun3-6" if fam in FLAT else "CHA other"
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groups[key] += states(d["f"], a, b, float(d["root"]))
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print(f"{'group':<18} {'states':>7} {'m > 1':>8} {'m >= 2':>8}")
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for k in ("APS (canonical)", "CHA other", "CHA flat fun3-6"):
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ms = groups[k]
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n = max(len(ms), 1)
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gt1 = 100.0 * sum(m > 1.0 for m in ms) / n
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ge2 = 100.0 * sum(m >= 2.0 for m in ms) / n
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print(f"{k:<18} {len(ms):7d} {gt1:7.1f}% {ge2:7.1f}%")
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if __name__ == "__main__":
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main()
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