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

HERE = os.path.dirname(os.path.abspath(__file__))
ROOT = os.path.dirname(HERE)
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"])
evals = [float(p["eval_y_1"]), float(p["eval_y_2"]), float(p["eval_y_3"])]
data_issues = [{"issue": "Evaluation points y=0.5, 1.0, 2.0 (and y=1 for V) are not nodes of the prescribed 400-point log grid.",
                "handling": "VFI policy and value are linearly interpolated in ln y between adjacent grid nodes (as allowed by TASK.md); grid itself unchanged."},
               {"issue": "VFI implemented as discrete choice of next-period output y' restricted to the same grid (consumption c = y - y'^(1/alpha)); infeasible choices (c<=0) excluded.",
                "handling": "Design choice, not a deviation from prescribed parameters; it introduces a discretisation error in the policy reported as max_abs_error_policy."}]
assert spacing == "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 - 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(np.asarray(y))

# ---- VFI: discrete choice of next-period output y' on the same 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')
feasible = C > 0
U = np.where(feasible, np.log(np.where(feasible, C, 1.0)), -np.inf)

V = np.zeros(N)
n_iter = 0
while True:
    RHS = U + beta * V[None, :]
    V_new = RHS.max(axis=1)
    n_iter += 1
    diff = np.max(np.abs(V_new - V))
    V = V_new
    if diff < tol:
        break
    if n_iter > 100000:
        raise RuntimeError("VFI did not converge")
pol_idx = (U + beta * V[None, :]).argmax(axis=1)
c_grid = grid - k_needed[pol_idx]

# check that the optimal choice is not at a grid boundary (truncation)
n_at_lower = int(np.sum(pol_idx == 0)); n_at_upper = int(np.sum(pol_idx == N - 1))

lg = np.log(grid)
interp = lambda f, y: float(np.interp(np.log(y), lg, f))   # linear in ln y
on_node = [bool(np.any(np.isclose(grid, y, rtol=1e-12, atol=0))) for y in evals]

c_num = [interp(c_grid, y) for y in evals]
c_cf = [float(c_closed(y)) for y in evals]
max_err = float(max(abs(x - z) for x, z in zip(c_num, c_cf)))
v_num_1 = interp(V, 1.0)
v_cf_1 = float(V_closed(1.0))

# diagnostics (not required keys)
diag = {
    "eval_points_are_grid_nodes": on_node,
    "policy_at_lower_bound_count": n_at_lower,
    "policy_at_upper_bound_count": n_at_upper,
    "max_abs_policy_error_over_grid": float(np.max(np.abs(c_grid - c_closed(grid)))),
    "max_abs_value_error_over_grid": float(np.max(np.abs(V - V_closed(grid)))),
    "grid_log_step": float(lg[1] - lg[0]),
    "closed_form_a": float(a), "closed_form_b": float(b),
}

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": v_cf_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_iter),
    "final_sup_change": float(diff),
    "feasibility": "complete", "feasibility_reason": None,
    "data_issues": data_issues,
    "n_input_rows": {"model.csv": int(len(df))},
    "n_analysed": int(N),
    "random_seed": None,
    "diagnostics": diag,
}
with open(os.path.join(HERE, "results.json"), "w") as f:
    json.dump(res, f, indent=2)
print(json.dumps(res, indent=2))