"""F5-conf-04: VFI vs closed form, optimal growth with log utility.
Run from workspace root: ~/wp29/venv/bin/python out/analysis.py
Reads only data/model.csv; deterministic (no randomness)."""
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, beta = float(p["alpha"]), float(p["beta"])
y_min, y_max, N = float(p["y_min"]), float(p["y_max"]), 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"])]
data_issues = []

# ---------- Closed form (guess-and-verify: V = A0 + B ln y) ----------
ab = alpha * beta
B = 1.0 / (1.0 - ab)
A0 = (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: A0 + B * np.log(np.asarray(y))
savings_rate = ab  # (y - c)/y

# ---------- VFI on the prescribed grid (discrete choice of next-period output on the grid) ----------
grid = np.exp(np.linspace(np.log(y_min), np.log(y_max), N))
k_needed = grid ** (1.0 / alpha)              # capital required to reach each y' on the grid
C = grid[:, None] - k_needed[None, :]          # consumption for (y today, y' tomorrow)
feas = C > 0
U = np.full(C.shape, -np.inf)
U[feas] = np.log(C[feas])
V = np.zeros(N)
n_iter, sup_change = 0, np.inf
while sup_change >= tol:
    RHS = U + beta * V[None, :]
    V_new = RHS.max(axis=1)
    sup_change = float(np.max(np.abs(V_new - V)))
    V = V_new
    n_iter += 1
    if n_iter > 100000:
        raise RuntimeError("VFI did not converge")
pol_idx = (U + beta * V[None, :]).argmax(axis=1)
c_pol = grid - k_needed[pol_idx]

# Diagnostics: is the grid bound binding? (policy at the edge of the y' grid)
edge_hits = int(np.sum((pol_idx == 0) | (pol_idx == N - 1)))
yprime_closed = (ab * grid) ** alpha
if yprime_closed.min() < y_min or yprime_closed.max() > y_max:
    data_issues.append({"issue": "closed-form next-period output leaves the prescribed grid",
                        "handling": "reported; truncation may bias VFI near bounds"})

# Interpolation at evaluation points: c linear in y; V linear in ln y
c_num = [float(np.interp(y, grid, c_pol)) for y in evals]
cc = [float(c_closed(y)) for y in evals]
on_node = [bool(np.any(np.isclose(grid, y, rtol=0, atol=1e-12))) for y in evals]
V_num_1 = float(np.interp(np.log(1.0), np.log(grid), V))

# Theoretical bound on the remaining VFI error from the stopping rule
vfi_err_bound = beta / (1 - beta) * sup_change

results = {
    "task_id": "F5-conf-04",
    "c_closed_y05": cc[0], "c_closed_y1": cc[1], "c_closed_y2": cc[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, cc))),
    "value_closed_y1": float(V_closed(1.0)),
    "value_num_y1": V_num_1,
    "savings_rate_closed_form": float(savings_rate),
    "contraction_modulus": float(beta),
    "grid_points_used": int(N),
    "n_iterations": int(n_iter),
    "final_sup_change": float(sup_change),
    "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
    "baseline_closed_form_B_coefficient": float(B),
    "diag_eval_points_on_grid_node": on_node,
    "diag_policy_edge_hits": edge_hits,
    "diag_closed_yprime_min": float(yprime_closed.min()),
    "diag_closed_yprime_max": float(yprime_closed.max()),
    "diag_grid_log_step": float(np.log(grid[1] / grid[0])),
    "diag_vfi_tolerance_error_bound": float(vfi_err_bound),
    "diag_value_abs_error_y1": float(abs(V_num_1 - float(V_closed(1.0)))),
    "diag_value_sup_error_grid": float(np.max(np.abs(V - V_closed(grid)))),
    "diag_policy_sup_error_grid": float(np.max(np.abs(c_pol - c_closed(grid)))),
    "diag_policy_max_rel_error_eval": float(max(abs(a - b) / b for a, b in zip(c_num, cc))),
}
os.makedirs(os.path.join(ROOT, "out"), exist_ok=True)
with open(os.path.join(ROOT, "out", "results.json"), "w") as f:
    json.dump(results, f, indent=2)
for k, v in results.items():
    print(f"{k}: {v}")