"""Is the flat regime DETECTABLE from evaluations already paid for?

Established by diag_model_order.py and its checks: two thirds of the wide-bracket gap sit
on the flat families (fun3-fun6), where Chandrupatla bisects 93-100% of his steps and our
step removes 0.41-0.81 halvings of the bracket per evaluation - less than bisection's 1.

On an approach |f| ~ K e^m the tangent step lands at e(1 - 1/m): it beats bisection's
halving only while 1 - 1/m < 1/2, i.e. m < 2.  The 2 is bisection's 1/2 rewritten, not a
chosen number.  m is what _local_order reads from the three latest evaluations.

Question measured here, BEFORE anything is built: does "m >= 2" separate the states of
the flat families from the states of the canonical set?  _local_order is known to fire
falsely (derived3_m: m > 1 on 27.9% of APS steps, excursions to 34.8), so the separation
is the whole question.  If APS states cross m >= 2 about as often as flat ones, the regime
is NOT detectable this way and no gate may be built on it.

    python -u diag_flat_detectable.py
"""
from __future__ import annotations

from collections import defaultdict

from scipy.optimize._tstutils import _APS_TESTS_DICTS, _CHANDRUPATLA_TESTS_DICTS

from diag_model_order import ACC, MAXFEV, OURS, XTOL
from simroot.pure import _local_order, pure_root

FLAT = ("fun3", "fun4", "fun5", "fun6")


def states(f, a, b, r):
    st = {"trace": []}
    x, _n, conv = pure_root(f, a, b, XTOL, MAXFEV, stats=st, **OURS)
    if not (conv and abs(float(x) - r) <= ACC):
        return []
    out = []
    for s in st["trace"]:
        if s["xp2"] is None:
            continue
        out.append(_local_order(s["x"], s["fx"], s["xp"], s["fp"], s["xp2"], s["fp2"]))
    return out


def main():
    groups = defaultdict(list)
    for d in _APS_TESTS_DICTS:
        a, b = (float(v) for v in d["bracket"])
        f = (lambda ff, aa: lambda t: ff(t, *aa))(d["f"], d.get("args", ()))
        groups["APS (canonical)"] += states(f, a, b, float(d["root"]))
    for d in _CHANDRUPATLA_TESTS_DICTS:
        a, b = (float(v) for v in d["bracket"])
        fam = str(d["ID"]).split(".")[0]
        key = "CHA flat fun3-6" if fam in FLAT else "CHA other"
        groups[key] += states(d["f"], a, b, float(d["root"]))

    print(f"{'group':<18} {'states':>7} {'m > 1':>8} {'m >= 2':>8}")
    shares = {}
    for k in ("APS (canonical)", "CHA other", "CHA flat fun3-6"):
        ms = groups[k]
        n = max(len(ms), 1)
        gt1 = 100.0 * sum(m > 1.0 for m in ms) / n
        ge2 = 100.0 * sum(m >= 2.0 for m in ms) / n
        shares[k] = (len(ms), gt1, ge2)
        print(f"{k:<18} {len(ms):7d} {gt1:7.1f}% {ge2:7.1f}%")
    return shares       # for verify_article.py


if __name__ == "__main__":
    main()