"""F2-conf-03: Monte Carlo coverage of OLS CIs under heteroskedasticity (fixed design)."""
import json, os
import numpy as np, pandas as pd
from scipy import stats

ROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
df = pd.read_csv(os.path.join(ROOT, "data", "design.csv"))
issues = []
n_rows = len(df)
if df[["x", "sigma"]].isna().any().any(): issues.append({"issue": "missing values", "handling": "none expected; would abort"})
if (df["sigma"] <= 0).any(): issues.append({"issue": "non-positive sigma", "handling": "flagged"})
if not np.array_equal(df["i"].values, np.arange(1, 31)): issues.append({"issue": "index not 1..30", "handling": "used rows as given"})

ALPHA, BETA, R, SEED = 1.0, 0.5, 2000, 20261030
x = df["x"].to_numpy(float); sig = df["sigma"].to_numpy(float); n = len(x)
X = np.column_stack([np.ones(n), x])
XtXi = np.linalg.inv(X.T @ X)
A = XtXi @ X.T                       # 2 x n, beta_hat = A y
tcrit = stats.t.ppf(0.975, n - 2)

# (c) exact SD: Var(b1) = sum_i a_i^2 sigma_i^2
a1 = A[1]
sd_exact = float(np.sqrt(np.sum(a1**2 * sig**2)))

rng = np.random.default_rng(SEED)
eps = rng.standard_normal((R, n))
Y = ALPHA + BETA * x + sig * eps                 # R x n
B = Y @ A.T                                      # R x 2
E = Y - B @ X.T                                  # residuals
s2 = (E**2).sum(1) / (n - 2)
se_conv = np.sqrt(s2 * XtXi[1, 1])
hc0 = (E**2) @ (a1**2)                           # sandwich var for slope
se_hc1 = np.sqrt(hc0 * n / (n - 2))
b1 = B[:, 1]
cov_conv = float(np.mean(np.abs(b1 - BETA) <= tcrit * se_conv))
cov_hc1 = float(np.mean(np.abs(b1 - BETA) <= tcrit * se_hc1))
mcse_conv = float(np.sqrt(0.95 * 0.05 / R))      # binomial SE at nominal p
under = bool(cov_conv < 0.95 - 3 * mcse_conv)

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(b1, ddof=1)),
    "mean_se_conventional": float(se_conv.mean()),
    "conventional_ci_undercovers": under,
    "n_replications": R,
    "n_obs_per_replication": n,
    "feasibility": "complete",
    "feasibility_reason": None,
    "data_issues": issues,
    "n_input_rows": {"design.csv": n_rows},
    "random_seed": SEED,
    # supplementary
    "mcse_binomial_at_0.95": mcse_conv,
    "mcse_coverage_conventional_at_estimate": float(np.sqrt(cov_conv * (1 - cov_conv) / R)),
    "mcse_coverage_hc1_at_estimate": float(np.sqrt(cov_hc1 * (1 - cov_hc1) / R)),
    "mean_se_hc1": float(se_hc1.mean()),
    "expected_se_conv_sq_exact": float(XtXi[1, 1] * np.sum(sig**2 * (1 - np.diag(X @ A))) / (n - 2)),
    "t_crit": float(tcrit),
}
with open(os.path.join(ROOT, "out", "results.json"), "w") as f:
    json.dump(res, f, indent=2)
print(json.dumps(res, indent=2))