"""F5-conf-04: VFI vs closed form for Brock-Mirman growth with log utility.
Run from workspace root: ~/wp29/venv/bin/python out/analysis.py"""
import json, os
import numpy as np, pandas as pd

df = pd.read_csv("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"]); spacing = str(p["grid_spacing"]).strip()
ev = [float(p["eval_y_1"]), float(p["eval_y_2"]), float(p["eval_y_3"])]
assert spacing == "log"

# ---- closed form (guess V = A + B ln y, verify) ----
ab = alpha * beta
B = 1.0 / (1.0 - ab)
A = (np.log(1 - ab) + (ab / (1 - ab)) * np.log(ab)) / (1 - beta)
c_closed = lambda y: (1 - ab) * np.asarray(y)
V_closed = lambda y: A + B * np.log(y)

# ---- VFI: discrete choice of next-period output y' on the grid ----
grid = np.exp(np.linspace(np.log(y_min), np.log(y_max), N))
k_needed = grid ** (1.0 / alpha)            # savings needed to reach y'
C = grid[:, None] - k_needed[None, :]       # consumption for (y, y')
U = np.where(C > 0, np.log(np.where(C > 0, C, 1.0)), -np.inf)
V = np.zeros(N)
it = 0; sup = np.inf
while sup >= tol:
    RHS = U + beta * V[None, :]
    Vn = RHS.max(axis=1)
    sup = float(np.max(np.abs(Vn - V)))
    V = Vn; it += 1
    if it > 100000:
        raise RuntimeError("VFI did not converge")
pol_idx = (U + beta * V[None, :]).argmax(axis=1)
c_grid = grid - k_needed[pol_idx]

c_num = np.interp(ev, grid, c_grid)        # linear interpolation in y
v_num_1 = float(np.interp(1.0, grid, V))
c_cl = c_closed(ev)
err = np.abs(c_num - c_cl)

# diagnostics (not required keys)
sup_V_err = float(np.max(np.abs(V - V_closed(grid))))
sup_c_err_grid = float(np.max(np.abs(c_grid - c_closed(grid))))

res = {
    "task_id": "F5-conf-04",
    "c_closed_y05": float(c_cl[0]), "c_closed_y1": float(c_cl[1]), "c_closed_y2": float(c_cl[2]),
    "c_num_y05": float(c_num[0]), "c_num_y1": float(c_num[1]), "c_num_y2": float(c_num[2]),
    "max_abs_error_policy": float(err.max()),
    "value_closed_y1": float(V_closed(1.0)),
    "value_num_y1": v_num_1,
    "savings_rate_closed_form": float(ab),
    "contraction_modulus": beta,
    "grid_points_used": N,
    "n_iterations": it,
    "final_sup_change": sup,
    "feasibility": "complete",
    "feasibility_reason": None,
    "data_issues": [
        {"issue": "Evaluation points 0.5, 1.0, 2.0 are not nodes of the 400-point log grid.",
         "handling": "VFI policy c(y) and value V(y) linearly interpolated in y between adjacent grid nodes, as allowed by the task."},
        {"issue": "Choice variable discretised: next-period output y' restricted to the same grid (discrete-choice VFI); log utility unbounded so -inf assigned to infeasible c<=0.",
         "handling": "Standard grid-search VFI; every grid y has feasible choices (y'=y_min always feasible), so no node is dropped. Discretisation error is reported."},
    ],
    "n_input_rows": {"model.csv": int(len(df))},
    "n_analysed": N,
    "random_seed": None,
    "diagnostics": {
        "sup_abs_error_value_on_grid": sup_V_err,
        "sup_abs_error_policy_on_grid": sup_c_err_grid,
        "abs_error_policy_each_eval": [float(x) for x in err],
        "iteration_error_bound_beta_tol_over_1mbeta": beta * tol / (1 - beta),
        "grid_log_step": float(np.log(grid[1] / grid[0])),
        "steady_state_y": float(ab ** (alpha / (1 - alpha))),
        "A": float(A), "B": float(B),
    },
}
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))