"""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, csv
import numpy as np

ROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
DATA = os.path.join(ROOT, "data", "model.csv")
OUT = os.path.join(ROOT, "out")

with open(DATA, newline="") as f:
    rows = list(csv.DictReader(f))
p = {r["parameter"]: r["value"] for r in rows}
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"]))
assert p["grid_spacing"].strip() == "log"
tol = float(p["vfi_tolerance"])
eval_y = [float(p["eval_y_1"]), float(p["eval_y_2"]), float(p["eval_y_3"])]

# ---------------- closed form (guess-and-verify V = A + B ln y) ----------------
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)
savings_rate = ab

# ---------------- VFI on prescribed grid (discrete choice of y' on grid) --------
grid = np.exp(np.linspace(np.log(y_min), np.log(y_max), N))
k_needed = grid ** (1.0 / alpha)                 # capital needed to reach y' = grid[j]
C = grid[:, None] - k_needed[None, :]            # c(i, j) = y_i - y'_j^(1/alpha)
feasible = C > 0
U = np.full_like(C, -np.inf)
U[feasible] = np.log(C[feasible])
assert feasible.any(axis=1).all(), "some grid point has no feasible choice"

V = np.zeros(N)
n_iter = 0
sup_change = np.inf
max_iter = 100000
while sup_change >= tol and n_iter < max_iter:
    W = U + beta * V[None, :]
    V_new = W.max(axis=1)
    sup_change = float(np.max(np.abs(V_new - V)))
    V = V_new
    n_iter += 1
converged = sup_change < tol
pol_j = (U + beta * V[None, :]).argmax(axis=1)
c_pol = grid - k_needed[pol_j]

# boundary diagnostics: does the optimal choice ever hit grid edges?
hits_lower = int(np.sum(pol_j == 0)); hits_upper = int(np.sum(pol_j == N - 1))

# interpolation at evaluation points: linear in ln y (grid is uniform in ln y)
lg = np.log(grid)
interp = lambda f, y: float(np.interp(np.log(y), lg, f))
c_num = [interp(c_pol, y) for y in eval_y]
c_cl = [float(c_closed(y)) for y in eval_y]
on_grid = [bool(np.any(np.isclose(grid, y, rtol=1e-12, atol=0))) for y in eval_y]
max_err = float(max(abs(a - b) for a, b in zip(c_num, c_cl)))

# whole-grid diagnostics (for report only)
grid_policy_err = float(np.max(np.abs(c_pol - c_closed(grid))))
grid_value_err = float(np.max(np.abs(V - V_closed(grid))))

data_issues = []
if not all(on_grid):
    data_issues.append({"issue": "Evaluation points %s are not grid nodes of the log-spaced grid" %
                        [y for y, o in zip(eval_y, on_grid) if not o],
                        "handling": "VFI policy and value interpolated linearly in ln(y) between adjacent grid nodes"})
data_issues.append({"issue": "Design choice: the choice variable is next-period output y' restricted to the same grid (discrete-choice VFI); consumption c = y - y'^(1/alpha)",
                    "handling": "No deviation from prescribed grid/parameters; discretisation error of order of the grid spacing is reported, not corrected"})

feas = "complete" if converged else "partial"
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": float(V_closed(1.0)),
    "value_num_y1": interp(V, 1.0),
    "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": feas,
    "feasibility_reason": None if converged else "VFI did not reach tolerance within max_iter",
    "data_issues": data_issues,
    "n_input_rows": {"model.csv": len(rows)},
    "n_analysed": int(N),
    "random_seed": None,
    # supplementary diagnostics
    "diag_grid_log_step": float(lg[1] - lg[0]),
    "diag_max_abs_policy_error_on_grid": grid_policy_err,
    "diag_max_abs_value_error_on_grid": grid_value_err,
    "diag_policy_hits_lower_bound": hits_lower,
    "diag_policy_hits_upper_bound": hits_upper,
    "diag_value_error_y1": interp(V, 1.0) - float(V_closed(1.0)),
    "diag_closed_form_A": float(A), "diag_closed_form_B": float(B),
    "diag_vfi_error_bound_beta_over_1mbeta_times_final_change": float(beta / (1 - beta) * sup_change),
}
os.makedirs(OUT, exist_ok=True)
with open(os.path.join(OUT, "results.json"), "w") as f:
    json.dump(res, f, indent=2)
with open(os.path.join(OUT, "exclusions.csv"), "w") as f:
    f.write("step,rule,n_before,n_after,n_removed,rationale\n")
    f.write("1,none (all parameter rows used),%d,%d,0,model.csv contains only parameters; nothing excluded\n" % (len(rows), len(rows)))
print(json.dumps({k: v for k, v in res.items() if k != "data_issues"}, indent=1))