"""F2-conf-03: Monte Carlo coverage of OLS CIs under heteroskedasticity.
Run from workspace root: ~/wp29/venv/bin/python out/analysis.py"""
import json, os
import numpy as np, 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 = []
if d.isna().any().any():
    issues.append({"issue": "missing values", "handling": "none expected; would abort"})
x, sig = d["x"].to_numpy(float), d["sigma"].to_numpy(float)
n = len(x)
assert n == 30 and (sig > 0).all()

X = np.column_stack([np.ones(n), x])
XtX_inv = np.linalg.inv(X.T @ X)
xc = x - x.mean(); Sxx = xc @ xc
w = xc / Sxx                                   # beta_hat = beta + sum w_i sigma_i eps_i
sd_exact = float(np.sqrt(np.sum(w**2 * sig**2)))
tcrit = stats.t.ppf(0.5 + LEVEL / 2, n - 2)

rng = np.random.default_rng(SEED)
eps = rng.standard_normal((R, n))
Y = ALPHA + BETA * x + sig * eps               # R x n
B = Y @ X @ XtX_inv                            # (XtX)^-1 X'y for each row (XtX_inv symmetric)
E = Y - B @ X.T                                # residuals
s2 = (E**2).sum(1) / (n - 2)
se_conv = np.sqrt(s2 * XtX_inv[1, 1])
# HC0 sandwich slope variance: sum (row-2 of (XtX)^-1 X')_i^2 e_i^2 ; HC1 = HC0 * n/(n-2)
a = (XtX_inv @ X.T)[1]                         # equals w
se_hc1 = np.sqrt((a**2 * E**2).sum(1) * n / (n - 2))
bh = B[:, 1]
cov_conv = float(np.mean(np.abs(bh - BETA) <= tcrit * se_conv))
cov_hc1 = float(np.mean(np.abs(bh - BETA) <= tcrit * se_hc1))
mcse_nom = float(np.sqrt(LEVEL * (1 - LEVEL) / R))
undercovers = bool(cov_conv < LEVEL - 3 * mcse_nom)

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(bh, ddof=1)),
    "mean_se_conventional": float(se_conv.mean()),
    "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(len(d))},
    "random_seed": SEED,
    # supplementary keys
    "t_crit_28": float(tcrit),
    "mcse_binomial_at_nominal": mcse_nom,
    "mcse_coverage_conventional": float(np.sqrt(cov_conv * (1 - cov_conv) / R)),
    "mcse_coverage_hc1": float(np.sqrt(cov_hc1 * (1 - cov_hc1) / R)),
    "undercover_threshold": float(LEVEL - 3 * mcse_nom),
    "mean_se_hc1": float(se_hc1.mean()),
    "sd_beta_conventional_formula_homoskedastic": float(np.sqrt(np.mean(sig**2) * XtX_inv[1, 1])),
    "mean_beta_hat_mc": float(bh.mean()),
}
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))