"""F2-conf-03: Monte Carlo coverage of OLS slope CIs under heteroskedasticity.
Run from workspace root: ~/wp29/venv/bin/python out/analysis.py
Reads only data/design.csv; writes out/results.json deterministically."""
import json, os
import numpy as np
import pandas as pd
from scipy import stats

SEED = 20261030
ALPHA, BETA, R, LEVEL = 1.0, 0.5, 2000, 0.95

d = pd.read_csv("data/design.csv")
issues = []
assert d.shape[0] == 30 and d[["x", "sigma"]].notna().all().all() and (d.sigma > 0).all()
x = d["x"].to_numpy(float); s = d["sigma"].to_numpy(float); n = len(x); df = n - 2
tcrit = stats.t.ppf(0.5 + LEVEL / 2, df)

xc = x - x.mean(); Sxx = np.sum(xc ** 2); w = xc / Sxx
sd_exact = float(np.sqrt(np.sum(w ** 2 * s ** 2)))          # (c) analytic

rng = np.random.default_rng(SEED)
eps = rng.standard_normal((R, n))
Y = ALPHA + BETA * x + s * eps                               # R x n
bhat = (Y - Y.mean(axis=1, keepdims=True)) @ xc / Sxx
ahat = Y.mean(axis=1) - bhat * x.mean()
e = Y - ahat[:, None] - bhat[:, None] * x
se_conv = np.sqrt(np.sum(e ** 2, axis=1) / df / Sxx)
hc0 = np.sum((xc ** 2) * e ** 2, axis=1) / Sxx ** 2
se_hc1 = np.sqrt(hc0 * n / df)

cov_conv = float(np.mean(np.abs(bhat - BETA) <= tcrit * se_conv))
cov_hc1 = float(np.mean(np.abs(bhat - BETA) <= tcrit * se_hc1))
mcse_nominal = float(np.sqrt(LEVEL * (1 - LEVEL) / R))
undercovers = bool((LEVEL - cov_conv) > 3 * mcse_nominal)

res = {
    "task_id": "F2-conf-03",
    "coverage_conventional": cov_conv,
    "coverage_hc1": cov_hc1,
    "sd_beta_exact": sd_exact,
    "sd_beta_mc": float(np.std(bhat, ddof=1)),
    "mean_se_conventional": float(np.mean(se_conv)),
    "conventional_ci_undercovers": undercovers,
    "n_replications": R,
    "n_obs_per_replication": n,
    "feasibility": "complete",
    "feasibility_reason": None,
    "data_issues": issues,
    "n_input_rows": {"design.csv": int(d.shape[0])},
    "random_seed": SEED,
    # supplementary diagnostics
    "t_crit_28": float(tcrit),
    "mcse_at_nominal": mcse_nominal,
    "undercoverage_threshold": float(LEVEL - 3 * mcse_nominal),
    "mcse_coverage_conventional": float(np.sqrt(cov_conv * (1 - cov_conv) / R)),
    "mcse_coverage_hc1": float(np.sqrt(cov_hc1 * (1 - cov_hc1) / R)),
    "mean_se_hc1": float(np.mean(se_hc1)),
    "mean_bhat_mc": float(np.mean(bhat)),
    "sd_beta_homoskedastic_formula": float(np.sqrt(np.mean(s ** 2) / Sxx)),
}
os.makedirs("out", exist_ok=True)
with open("out/results.json", "w") as f:
    json.dump(res, f, indent=2)
print(json.dumps(res, indent=2))