"""F5-conf-04: VFI vs closed form for log-utility Cobb-Douglas growth (full depreciation).
Run from workspace root: ~/wp29/venv/bin/python out/analysis.py
"""
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"]))
tol = float(p["vfi_tolerance"])
assert str(p["grid_spacing"]).strip() == "log"
evals = [float(p["eval_y_1"]), float(p["eval_y_2"]), float(p["eval_y_3"])]

# ---------- closed form (guess V = A + B ln y, verified in report) ----------
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) * np.asarray(y)
V_closed = lambda y: A + B * np.log(y)

# ---------- VFI: discrete choice of next-period output y' on the grid ----------
lny = np.linspace(np.log(y_min), np.log(y_max), N)
y = np.exp(lny)
k_needed = y ** (1.0 / alpha)                # savings needed to reach y' = grid[j]
C = y[:, None] - k_needed[None, :]           # consumption for (state i, choice j)
feasible = C > 0
U = np.full_like(C, -np.inf)
U[feasible] = np.log(C[feasible])

V = np.zeros(N)
n_it = 0
while True:
    RHS = U + beta * V[None, :]
    Vn = RHS.max(axis=1)
    sup = float(np.max(np.abs(Vn - V)))
    V = Vn
    n_it += 1
    if sup < tol:
        break
pol_j = (U + beta * V[None, :]).argmax(axis=1)
c_grid = C[np.arange(N), pol_j]

# check whether the choice ever hits grid bounds
hits_lower = bool(np.any(pol_j == 0)); hits_upper = bool(np.any(pol_j == N - 1))

# interpolate (linear in ln y) at evaluation points
interp = lambda f, x: float(np.interp(np.log(x), lny, f))
c_num = [interp(c_grid, e) for e in evals]
c_cl = [float(c_closed(e)) for e in evals]
max_err = float(max(abs(a - b) for a, b in zip(c_num, c_cl)))
v_num_1 = interp(V, 1.0)
v_cl_1 = float(V_closed(1.0))

# whole-grid diagnostics (not required keys)
sup_policy_err_grid = float(np.max(np.abs(c_grid - c_closed(y))))
sup_value_err_grid = float(np.max(np.abs(V - V_closed(y))))

issues = []
for e in evals:
    if not np.any(np.isclose(y, e, rtol=0, atol=1e-12)):
        issues.append({"issue": f"evaluation point y={e} is not a grid node",
                       "handling": "VFI policy/value linearly interpolated in ln y between adjacent grid nodes"})
issues.append({"issue": "VFI choice variable not specified in model.csv",
               "handling": "next-period output y' chosen from the same 400-point log grid (discrete choice, no off-grid interpolation of V); V initialised at 0"})

res = {
    "task_id": "F5-conf-04",
    "c_closed_y05": c_cl[0], "c_closed_y1": c_cl[1], "c_closed_y2": c_cl[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": v_cl_1, "value_num_y1": v_num_1,
    "savings_rate_closed_form": float(ab),
    "contraction_modulus": float(beta),
    "grid_points_used": int(N),
    "n_iterations": int(n_it),
    "final_sup_change": sup,
    "feasibility": "complete", "feasibility_reason": None,
    "data_issues": issues,
    "n_input_rows": {"model.csv": int(len(df))},
    "n_analysed": int(N),
    "random_seed": None,
    "diagnostics": {
        "grid_log_step": float(lny[1] - lny[0]),
        "sup_abs_policy_error_on_grid": sup_policy_err_grid,
        "sup_abs_value_error_on_grid": sup_value_err_grid,
        "value_error_bound_from_tolerance": float(beta * tol / (1 - beta)),
        "policy_hits_lower_grid_bound": hits_lower,
        "policy_hits_upper_grid_bound": hits_upper,
        "closed_form_A": float(A), "closed_form_B": float(B),
        "steady_state_y": float(ab ** (alpha / (1 - alpha))),
    },
}
with open(os.path.join(ROOT, "out", "results.json"), "w") as f:
    json.dump(res, f, indent=2)
print(json.dumps(res, indent=2))