"""Why the contraction-ratio similarity came out inverted: the rho sequence itself.

diag_contraction_similarity.py falsified "successive contraction ratios are similar on
the flat families": they are LESS similar there than on the canonical set.  The picture
behind the hypothesis - rho constant at about (1 - 1/m)^m - holds for pure Newton steps on
x^m.  The explanation to check is that our safeguarded run is not pure: the projection
interleaves forced moves, so rho alternates.  Printed per step for one flat problem and
one canonical problem: rho_n, and whether the step was the similarity step as proposed or
was changed by the safeguard (x_new != x + raw).

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

from scipy.optimize._tstutils import _APS_TESTS_DICTS, _CHANDRUPATLA_TESTS_DICTS

from simroot.pure import pure_root

CFG = dict(similarity="ratio", scale="derived3", guard="project")


def show(name, f, a, b):
    evals = []

    def g(t):
        v = f(t)
        evals.append((t, v))
        return v
    st = {"trace": []}
    pure_root(g, a, b, 1e-12, 200, stats=st, **CFG)
    # map each traced state to the evaluation that followed it
    order = [e[0] for e in evals]
    print(f"\n== {name}: {len(evals)} evaluations")
    print(f"   {'k':>3} {'rho_n=|f_n/f_(n-1)|':>22} {'step as proposed?':>18}")
    for k, s in enumerate(st["trace"][:40]):
        proposed = s["x"] + s["raw"]
        try:
            i = order.index(s["x"])
        except ValueError:
            continue
        if i + 1 >= len(evals):
            break
        x_next, f_next = evals[i + 1]
        rho = abs(f_next / s["fx"]) if s["fx"] != 0.0 else float("nan")
        kept = "yes" if x_next == proposed else "CHANGED"
        print(f"   {k:3d} {rho:22.3e} {kept:>18}")


def main():
    cha = {str(d["ID"]): d for d in _CHANDRUPATLA_TESTS_DICTS}
    d = cha["fun5.1"]
    show("fun5.1 = x^9 (flat)", d["f"], *(float(v) for v in d["bracket"]))
    d = cha["fun4.3"]
    show("fun4.3 = 6(x-2)^5 on a wide bracket (flat)", d["f"],
         *(float(v) for v in d["bracket"]))
    d = _APS_TESTS_DICTS[10]
    f = (lambda ff, aa: lambda t: ff(t, *aa))(d["f"], d.get("args", ()))
    show(f"{d['ID']} (canonical)", f, *(float(v) for v in d["bracket"]))


if __name__ == "__main__":
    main()