from scipy.interpolate import LinearNDInterpolator
import numpy as np
from scipy.stats import levy_stable
from .quantiles import compute_quantile_ratios

def mock_lookup_alpha_beta(v_alpha, v_beta):
    """
    Placeholder lookup for alpha and beta based on v_alpha and v_beta.

    In real implementation, interpolate over McCulloch's tables.
    """
    # Simulate mapping logic
    alpha = np.clip(3.5 - 1.5 * (v_alpha - 2), 0.6, 2.0)
    beta = np.clip(v_beta, -1.0, 1.0)
    return alpha, beta

def mcculloch_quantile_init(X):
    """
    Estimate initial (α, β, γ, δ) using McCulloch quantile method.

    Returns:
        dict with keys: alpha, beta, gamma, delta
    """
    ratios = compute_quantile_ratios(X)
    alpha, beta = mock_lookup_alpha_beta(ratios["v_alpha"], ratios["v_beta"])
    gamma = ratios["v_gamma"]
    delta = -ratios["v_delta"]

    return {
        "alpha": alpha,
        "beta": beta,
        "gamma": gamma,
        "delta": delta
    }

def generate_mcculloch_table(alpha_grid, beta_grid, size=100_000, seed=42):
    """
    Generate McCulloch quantile table for (v_alpha, v_beta) values across (α, β).

    Returns:
        dict of {(α, β): (v_alpha, v_beta)} with standardized parameters
    """
    np.random.seed(seed)
    lookup = {}

    for alpha in alpha_grid:
        for beta in beta_grid:
            X = levy_stable.rvs(alpha, beta, loc=0, scale=1, size=size)
            q = compute_quantile_ratios(X)
            lookup[(round(alpha, 2), round(beta, 2))] = (q["v_alpha"], q["v_beta"])

    return lookup

def build_mcculloch_interpolators(table):
    """
    Build interpolators to get alpha, beta from (v_alpha, v_beta)

    Returns:
        interpolate_alpha, interpolate_beta functions
    """
    points = []
    alphas, betas = [], []

    for (a, b), (va, vb) in table.items():
        points.append((va, vb))
        alphas.append(a)
        betas.append(b)

    interp_alpha = LinearNDInterpolator(points, alphas)
    interp_beta = LinearNDInterpolator(points, betas)

    return interp_alpha, interp_beta

def mcculloch_lookup_estimate(X, interp_alpha, interp_beta):
    q = compute_quantile_ratios(X)
    alpha = float(interp_alpha(q["v_alpha"], q["v_beta"]))
    beta = float(interp_beta(q["v_alpha"], q["v_beta"]))
    gamma = q["v_gamma"]
    delta = -q["v_delta"]

    return {
        "alpha": alpha,
        "beta": beta,
        "gamma": gamma,
        "delta": delta
    }
