"""Macro F0.5 exactly as `ps.pdf` defines it.

Per S1 entity:
    F0.5 = (1.25 * P * R) / (0.25 * P + R)
macro-averaged over ALL S1 entities. A singleton (no true match) scores 1.0 for a correct
empty prediction and 0.0 for any prediction.

Substituting P = TP/k and R = TP/T collapses this to the identity the whole project relies on:

    F0.5 = 1.25 * TP / (0.25 * T + k)

because FP = k - TP and FN = T - TP cancel the TP contributions in the denominator. This is
exact, not an approximation.

THE BREAK-EVEN EXCHANGE RATE, derived from that identity. With D = 0.25T + k, adding one
prediction
  * gains  1.25 (D - TP) / (D (D+1))   if it is a true positive
  * loses  1.25 TP      / (D (D+1))    if it is a false positive
so an extra pair is worth taking only when its TP:FP ratio beats

    TP / (D - TP)

This is an OPERATING-POINT-DEPENDENT number, not a universal constant. In the idealised limit
TP -> T and k -> T (so D = 1.25T) it tends to T / 0.25T = 4. At the shipped operating point it
is lower: measured mean T = 3.449, mean k = 3.316, mean TP = 3.300 over 20,000 validation
entities gives D = 4.178 and a break-even of 3.300 / 0.878 = ~3.8:1.

    Any batch of pairs added to the prediction set must be better than roughly 3.8-4 true
    for every 1 false - about 80% precision - or macro F0.5 falls.

(An earlier version of this analysis asserted "exactly 4:1". That is only the limiting value;
the self-test below checks the formula itself rather than the round number.)

Measured on validation, the best band below our threshold offered 1.90:1 (386 TP / 203 FP),
and the next best 1.54:1. Both are far under the break-even either way, which is why lowering
the threshold could not buy recall, and why any new candidate source has to clear ~80%
precision to be worth including at all.
"""
from __future__ import annotations

import numpy as np


def entity_f05(pred: set, truth: set) -> float:
    """F0.5 for one S1 entity. `pred` and `truth` are sets of S2/S3 identifiers."""
    k, t = len(pred), len(truth)
    if t == 0:
        return 1.0 if k == 0 else 0.0           # singleton: empty is perfect, anything is 0
    if k == 0:
        return 0.0
    tp = len(pred & truth)
    if tp == 0:
        return 0.0
    return 1.25 * tp / (0.25 * t + k)


def macro_f05(preds: dict, truths: dict, ids):
    """Macro F0.5 over `ids`.

    preds  : {entity -> iterable of predicted targets}  (missing == predicted empty)
    truths : {entity -> iterable of true targets}       (missing == true singleton)
    ids    : the entity list to average over - MUST be every S1 entity being scored, not
             just the ones with predictions, or singletons silently vanish from the average.

    Returns (summary_dict, per_entity_array).
    """
    per = np.empty(len(ids), np.float64)
    tp_sum = k_sum = t_sum = 0
    for i, q in enumerate(ids):
        p = preds.get(q) or ()
        t = truths.get(q) or ()
        p = p if isinstance(p, set) else set(p)
        t = t if isinstance(t, set) else set(t)
        per[i] = entity_f05(p, t)
        tp_sum += len(p & t)
        k_sum += len(p)
        t_sum += len(t)
    return {
        "f05": float(per.mean()) if len(per) else 0.0,
        "precision": (tp_sum / k_sum) if k_sum else 0.0,   # pooled, for diagnosis only
        "recall": (tp_sum / t_sum) if t_sum else 0.0,
        "n": len(ids),
        "tp": tp_sum, "k": k_sum, "t": t_sum,
        "pred_per_entity": (k_sum / len(ids)) if len(ids) else 0.0,
    }, per


def entity_scores(preds: dict, truths: dict, ids):
    return macro_f05(preds, truths, ids)[1]


def slice_report(preds: dict, truths: dict, ids, by: dict, label="slice"):
    """Macro F0.5 broken out by an arbitrary per-entity key (country, singleton flag, ...).

    Model-1's contribution to the project was that slice-level reporting is where the real
    failures show up: the shipped run scored us 0.9832 / india 0.9806 on validation while
    France - which has no labels at all - came out at an implied 0.946.
    """
    groups: dict = {}
    for q in ids:
        groups.setdefault(by.get(q, "?"), []).append(q)
    rows = []
    for key in sorted(groups, key=str):
        g = groups[key]
        m, _ = macro_f05(preds, truths, g)
        rows.append({label: key, "n": len(g), "f05": m["f05"],
                     "precision": m["precision"], "recall": m["recall"],
                     "pred_per_entity": m["pred_per_entity"]})
    return rows


def oracle_f05(candidates: dict, truths: dict, ids):
    """Best macro F0.5 reachable from a candidate set: predict truth AND candidates, and
    predict empty for genuine singletons.

    THE CEILING THAT MATTERS. Measured on the shipped candidates this was 0.9942 against a
    shipped 0.9821 - so the scorer lost 0.0121 and blocking lost 0.0058. Model-5 s25 is right
    that you must never optimise the decision layer while this number is the bottleneck.

    Note the distinction Model-5 s33 rule 9 insists on: this is NOT pair recall. Pair recall
    on the same candidates was 0.9824, which is a different and much less useful number.
    """
    preds = {}
    for q in ids:
        hit = set(candidates.get(q) or ()) & set(truths.get(q) or ())
        if hit:
            preds[q] = hit
    return macro_f05(preds, truths, ids)


def pair_recall(candidates: dict, truths: dict, ids):
    """Fraction of true pairs present in the candidate set, plus per-entity coverage rates."""
    got = tot = 0
    all_present = 0
    n_nonsing = 0
    for q in ids:
        t = set(truths.get(q) or ())
        if not t:
            continue
        n_nonsing += 1
        c = set(candidates.get(q) or ())
        h = len(t & c)
        got += h
        tot += len(t)
        if h == len(t):
            all_present += 1
    return {
        "pair_recall": got / tot if tot else 0.0,
        "true_pairs": tot,
        "retrieved": got,
        "all_match_rate": all_present / n_nonsing if n_nonsing else 0.0,
    }


# --------------------------------------------------------------------------- self-test
def _selftest():
    """ps.pdf's worked example: one true positive, three true matches, one prediction."""
    got = entity_f05({"a"}, {"a", "b", "c"})
    assert abs(got - 0.7142857) < 1e-6, got                      # 1.25*1/(0.75+1)
    assert entity_f05(set(), set()) == 1.0                       # singleton, empty
    assert entity_f05({"a"}, set()) == 0.0                       # singleton, predicted
    assert entity_f05(set(), {"a"}) == 0.0                       # missed everything
    assert entity_f05({"a"}, {"a"}) == 1.0                       # perfect
    assert abs(entity_f05({"a", "x"}, {"a"}) - 1.25 / 2.25) < 1e-9

    # Break-even exchange rate: verify TP/(D-TP) against brute-force deltas, and confirm it
    # tends to 4 only in the limit TP -> T, k -> T.
    def brute_ratio(T, TP, k):
        D = 0.25 * T + k
        base = 1.25 * TP / D
        gain = 1.25 * (TP + 1) / (0.25 * T + k + 1) - base       # one more, correct
        loss = base - 1.25 * TP / (0.25 * T + k + 1)             # one more, wrong
        return gain, loss, loss / gain, TP / (D - TP)

    for T, TP, k in [(4, 3, 3), (10, 9, 9), (100, 99, 99), (4, 2, 2), (8, 7, 8)]:
        gain, loss, emp, formula = brute_ratio(T, TP, k)
        assert gain > 0 and loss > 0
        assert abs(emp - formula) < 1e-9, (T, TP, k, emp, formula)

    # the limit: as TP=k=T grows, TP/(D-TP) -> 4
    lim = [brute_ratio(T, T - 1, T - 1)[3] for T in (4, 40, 400, 4000)]
    assert lim[-1] > 3.9 and lim[0] < lim[-1] < 4.0, lim

    # the shipped operating point (20,000 val entities): T=68,983 k=66,324 TP=66,009
    n = 20000
    T, k, TP = 68983 / n, 66324 / n, 66009 / n
    D = 0.25 * T + k
    shipped = TP / (D - TP)
    assert 3.6 < shipped < 3.9, shipped
    print(f"evaluate.py self-test OK (ps.pdf example = 0.714286; "
          f"break-even formula verified; shipped operating point = {shipped:.2f}:1, "
          f"limit -> 4:1)")


if __name__ == "__main__":
    _selftest()