"""F5-conf-04: VFI vs closed form for optimal growth with log utility.
Run from workspace root: ~/wp29/venv/bin/python out/analysis.py"""
import json, os
import numpy as np
import 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"])
evals = [float(p["eval_y_1"]), float(p["eval_y_2"]), float(p["eval_y_3"])]
assert str(p["grid_spacing"]).strip().lower() == "log"

# ---- 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 on log-spaced grid, choice = next-period output y' on the same grid ----
y = np.exp(np.linspace(np.log(y_min), np.log(y_max), n))
k_needed = y ** (1.0 / alpha)                # capital needed to reach y' : k = y'^(1/alpha)
C = y[:, None] - k_needed[None, :]           # consumption for (y, y')
feasible = C > 0
U = np.full_like(C, -np.inf)
U[feasible] = np.log(C[feasible])

V = np.zeros(n)
it = 0; sup = np.inf
while sup >= tol:
    V_new = np.max(U + beta * V[None, :], axis=1)
    sup = float(np.max(np.abs(V_new - V)))
    V = V_new; it += 1
    if it > 100000:
        raise RuntimeError("VFI did not converge")
idx = np.argmax(U + beta * V[None, :], axis=1)
c_grid = y - k_needed[idx]
at_upper = int(np.sum(idx == n - 1)); at_lower = int(np.sum(idx == 0))

# interpolate (linear in ln y) to evaluation points
ly = np.log(y)
c_num = [float(np.interp(np.log(e), ly, c_grid)) for e in evals]
c_cf = [float(c_closed(e)) for e in evals]
V_num_1 = float(np.interp(0.0, ly, V))
on_grid = [bool(np.any(np.isclose(y, e, rtol=1e-12))) for e in evals]

# diagnostics over the whole grid
max_err_grid = float(np.max(np.abs(c_grid - c_closed(y))))
max_V_err_grid = float(np.max(np.abs(V - V_closed(y))))

issues = []
if not all(on_grid):
    issues.append({"issue": "Evaluation points " + ", ".join(str(e) for e, g in zip(evals, on_grid) if not g)
                   + " are not grid nodes of the prescribed log grid.",
                   "handling": "VFI policy and value linearly interpolated in ln y between adjacent grid nodes, as TASK.md allows."})
issues.append({"issue": "TASK does not prescribe the choice set for VFI.",
               "handling": "Discrete choice of next-period output y' on the same 400-point grid (c = y - y'^(1/alpha)); no off-grid optimisation. Initial guess V0 = 0."})

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": float(max(abs(a - b) for a, b in zip(c_num, c_cf))),
    "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": issues,
    "n_input_rows": {"model.csv": int(len(df))},
    "n_analysed": n,
    "random_seed": None,
    "diagnostics": {
        "max_abs_policy_error_on_grid": max_err_grid,
        "max_abs_value_error_on_grid": max_V_err_grid,
        "value_error_y1": V_num_1 - float(V_closed(1.0)),
        "error_bound_from_stopping_rule": beta * sup / (1 - beta),
        "grid_log_step": float(ly[1] - ly[0]),
        "n_grid_points_choosing_upper_bound": at_upper,
        "n_grid_points_choosing_lower_bound": at_lower,
        "closed_form_A": float(A), "closed_form_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))