"""F5-conf-04: VFI vs closed-form policy, optimal growth with log utility.
Run from workspace root: ~/wp29/venv/bin/python out/analysis.py
Deterministic; no randomness used (random_seed = null)."""
import json, os
import numpy as np
import pandas as pd

ROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
df = pd.read_csv(os.path.join(ROOT, "data", "model.csv"))
p = dict(zip(df["parameter"], df["value"]))
alpha = float(p["alpha"]); beta = float(p["beta"])
y_min = float(p["y_min"]); y_max = float(p["y_max"]); N = int(float(p["grid_points"]))
spacing = str(p["grid_spacing"]).strip(); tol = float(p["vfi_tolerance"])
eval_y = [float(p["eval_y_1"]), float(p["eval_y_2"]), float(p["eval_y_3"])]
assert spacing == "log" and 0 < alpha < 1 and 0 < beta < 1 and 0 < y_min < y_max and N > 1
data_issues = []

# ---- Closed form (guess-and-verify V = A + B ln y): B = 1/(1-ab), c = (1-ab) y
ab = alpha * beta
B = 1.0 / (1.0 - ab)
A = (np.log(1.0 - ab) + ab / (1.0 - ab) * np.log(ab)) / (1.0 - beta)
c_closed = lambda y: (1.0 - ab) * y
V_closed = lambda y: A + B * np.log(y)
savings_rate = ab  # baseline quantity

# ---- VFI on prescribed grid: state y_i, choice y'_j on the same grid,
# consumption c_ij = y_i - (y'_j)^(1/alpha) (capital needed to produce y'_j); infeasible if c<=0.
grid = np.exp(np.linspace(np.log(y_min), np.log(y_max), N))
k_needed = grid ** (1.0 / alpha)
C = grid[:, None] - k_needed[None, :]
U = np.where(C > 0, np.log(np.where(C > 0, C, 1.0)), -np.inf)
V = np.zeros(N)
n_it, sup = 0, np.inf
while sup >= tol:
    Vn = np.max(U + beta * V[None, :], axis=1)
    sup = float(np.max(np.abs(Vn - V)))
    V = Vn; n_it += 1
    if n_it > 100000:
        raise RuntimeError("VFI did not converge")
jstar = np.argmax(U + beta * V[None, :], axis=1)
c_pol = grid - k_needed[jstar]

# check policy is interior w.r.t. grid bounds (no corner at the top/bottom of the choice grid)
n_low = int(np.sum(jstar == 0)); n_high = int(np.sum(jstar == N - 1))
if n_low or n_high:
    data_issues.append({"issue": f"VFI choice hits grid bound at {n_low} (low) / {n_high} (high) states",
                        "handling": "reported; policy near those states is truncated by the grid"})

lg = np.log(grid)
interp = lambda f, y: float(np.interp(np.log(y), lg, f))  # linear in ln y between nodes
for y in eval_y:
    if not np.any(np.isclose(grid, y, rtol=0, atol=1e-12)):
        pass  # off-node: linear interpolation in ln y (allowed by the task)
c_num = [interp(c_pol, y) for y in eval_y]
c_cf = [float(c_closed(y)) for y in eval_y]
max_err = float(max(abs(a - b) for a, b in zip(c_num, c_cf)))

res = {
    "task_id": "F5-conf-04",
    "c_closed_y05": c_cf[0], "c_closed_y1": c_cf[1], "c_closed_y2": c_cf[2],
    "c_num_y05": c_num[0], "c_num_y1": c_num[1], "c_num_y2": c_num[2],
    "max_abs_error_policy": max_err,
    "value_closed_y1": float(V_closed(1.0)),
    "value_num_y1": interp(V, 1.0),
    "savings_rate_closed_form": float(savings_rate),
    "contraction_modulus": float(beta),
    "grid_points_used": int(N),
    "n_iterations": int(n_it),
    "final_sup_change": float(sup),
    "feasibility": "complete",
    "feasibility_reason": None,
    "data_issues": data_issues,
    "n_input_rows": {"model.csv": int(len(df))},
    "n_analysed": int(N),
    "random_seed": None,
    # supplementary diagnostics (not required keys)
    "diag_eval_points_on_grid": [bool(np.any(np.isclose(grid, y, rtol=0, atol=1e-12))) for y in eval_y],
    "diag_grid_log_step": float(lg[1] - lg[0]),
    "diag_policy_max_abs_error_on_grid": float(np.max(np.abs(c_pol - c_closed(grid)))),
    "diag_value_max_abs_error_on_grid": float(np.max(np.abs(V - V_closed(grid)))),
    "diag_value_tolerance_bound": float(beta * tol / (1 - beta)),
    "diag_value_abs_error_y1": abs(interp(V, 1.0) - float(V_closed(1.0))),
    "diag_closed_form_A": float(A), "diag_closed_form_B": float(B),
    "diag_choice_at_lower_bound": n_low, "diag_choice_at_upper_bound": n_high,
}
os.makedirs(os.path.join(ROOT, "out"), exist_ok=True)
with open(os.path.join(ROOT, "out", "results.json"), "w") as f:
    json.dump(res, f, indent=2)
print(json.dumps(res, indent=2))