"""F5-conf-02: Finite-sample bias of OLS AR(1) coefficient (with intercept).
Run from workspace root: ~/wp29/venv/bin/python out/analysis.py
Reads only data/design.csv; writes out/results.json and out/exclusions.csv.
"""
import json, math, csv
from pathlib import Path
import numpy as np
import pandas as pd

ROOT = Path(__file__).resolve().parent.parent
d = pd.read_csv(ROOT / "data" / "design.csv")
p = dict(zip(d["parameter"], d["value"]))
n = int(p["n"]); rho = float(p["rho"]); sigma = float(p["sigma"])
R = int(p["n_replications"]); seed = int(p["seed"])
assert str(p["intercept"]).strip().lower() == "yes"
assert str(p["initial_condition"]).strip().lower() == "stationary"
assert abs(rho) < 1

# --- Baseline / analytical quantities ---
bias_analytical = -(1 + 3 * rho) / n
se_asymptotic = math.sqrt((1 - rho ** 2) / n)

# --- Monte Carlo (vectorised over replications), c = 0 ---
rng = np.random.default_rng(seed)
# Draw order: first y_1 for all R replications, then the (R, n-1) innovation matrix.
y = np.empty((R, n))
y[:, 0] = rng.normal(0.0, sigma / math.sqrt(1 - rho ** 2), size=R)
eps = rng.normal(0.0, sigma, size=(R, n - 1))
for t in range(1, n):
    y[:, t] = rho * y[:, t - 1] + eps[:, t - 1]

# OLS of y_t on (1, y_{t-1}), t = 2..n: slope = cov(x,z)/var(x) with demeaning
x = y[:, :-1]; z = y[:, 1:]
xc = x - x.mean(axis=1, keepdims=True)
zc = z - z.mean(axis=1, keepdims=True)
rho_hat = (xc * zc).sum(axis=1) / (xc ** 2).sum(axis=1)

# Spot check against explicit least squares for the first replication
X0 = np.column_stack([np.ones(n - 1), x[0]])
b0 = np.linalg.lstsq(X0, z[0], rcond=None)[0]
assert abs(b0[1] - rho_hat[0]) < 1e-10

# Exclusion ledger: non-finite estimates (none expected)
finite = np.isfinite(rho_hat)
rh = rho_hat[finite]
with open(ROOT / "out" / "exclusions.csv", "w", newline="") as f:
    w = csv.writer(f)
    w.writerow(["step", "rule", "n_before", "n_after", "n_removed", "rationale"])
    w.writerow([1, "drop replications with non-finite rho_hat", R, int(finite.sum()),
                int(R - finite.sum()), "OLS slope undefined if regressor has zero variance (probability zero)"])

rho_hat_mean = float(rh.mean())
rho_hat_sd = float(rh.std(ddof=1))
bias_mc = rho_hat_mean - rho
bias_mc_se = rho_hat_sd / math.sqrt(rh.size)
disc = (bias_mc - bias_analytical) / bias_mc_se

res = {
    "task_id": "F5-conf-02",
    "bias_analytical": bias_analytical,
    "bias_mc": bias_mc,
    "bias_mc_se": bias_mc_se,
    "rho_hat_mean": rho_hat_mean,
    "rho_hat_sd_mc": rho_hat_sd,
    "discrepancy_se_units": disc,
    "se_asymptotic": se_asymptotic,
    "n_replications": R,
    "feasibility": "complete",
    "feasibility_reason": None,
    "data_issues": [],
    "n_input_rows": {"design.csv": int(len(d))},
    "n_analysed": int(rh.size),
    "random_seed": seed,
    # supplementary (not required) descriptive quantities
    "supp_bias_analytical_n_minus_1": -(1 + 3 * rho) / (n - 1),
    "supp_rho_hat_median": float(np.median(rh)),
    "supp_ratio_bias_mc_to_analytical": bias_mc / bias_analytical,
    "supp_ratio_sd_mc_to_se_asymptotic": rho_hat_sd / se_asymptotic,
}
with open(ROOT / "out" / "results.json", "w") as f:
    json.dump(res, f, indent=2)
for k, v in res.items():
    print(f"{k}: {v}")