from __future__ import annotations

from codeop import PyCF_ALLOW_INCOMPLETE_INPUT
from typing import List, Optional, Tuple
import numpy as np
from ellipsoide import EllipsoidTriaxial
from GHA_triaxial.gha1_ana import gha1_ana
from GHA_triaxial.gha1_approx import gha1_approx
from Hansen_ES_CMA import escma
from utils_angle import wrap_to_pi
from numpy.typing import NDArray
import winkelumrechnungen as wu


def ellipsoid_formparameter(ell: EllipsoidTriaxial):
    """
    Berechnet die Formparameter des dreiachsigen Ellipsoiden nach Karney (2025), Gl. (2)
    :param ell: Ellipsoid
    :return: e, k und k'
    """
    nenner = np.sqrt(max(ell.ax * ell.ax - ell.b * ell.b, 0.0))
    k = np.sqrt(max(ell.ay * ell.ay - ell.b * ell.b, 0.0)) / nenner
    k_ = np.sqrt(max(ell.ax * ell.ax - ell.ay * ell.ay, 0.0)) / nenner
    e = np.sqrt(max(ell.ax * ell.ax - ell.b * ell.b, 0.0)) / ell.ay

    return e, k, k_


def ENU_beta_omega(beta: float, omega: float, ell: EllipsoidTriaxial) \
        -> Tuple[NDArray, NDArray, NDArray, float, float, NDArray]:
    """
    Analytische ENU-Basis in ellipsoidische Koordinaten (β, ω) nach Karney (2025), S. 2
    :param beta: Beta Koordinate
    :param omega: Omega Koordinate
    :param ell: Ellipsoid
    :return:    E_hat = Einheitsrichtung entlang wachsendem ω (East)
                N_hat = Einheitsrichtung entlang wachsendem β (North)
                U_hat = Einheitsnormale (Up)
                En & Nn = Längen der unnormierten Ableitungen
                R (XYZ) = Punkt in XYZ
    """
    # Berechnungshilfen
    omega = wrap_to_pi(omega)
    cb = np.cos(beta)
    sb = np.sin(beta)
    co = np.cos(omega)
    so = np.sin(omega)
    # D = sqrt(a^2 - c^2)
    D = np.sqrt(ell.ax*ell.ax - ell.b*ell.b)
    # Sx = sqrt(a^2 - b^2 sin^2β - c^2 cos^2β)
    Sx = np.sqrt(ell.ax*ell.ax - ell.ay*ell.ay*(sb*sb) - ell.b*ell.b*(cb*cb))
    # Sz = sqrt(a^2 sin^2ω + b^2 cos^2ω - c^2)
    Sz = np.sqrt(ell.ax*ell.ax*(so*so) + ell.ay*ell.ay*(co*co) - ell.b*ell.b)

    # Karney Gl. (4)
    X = ell.ax * co * Sx / D
    Y = ell.ay * cb * so
    Z = ell.b * sb * Sz / D
    R = np.array([X, Y, Z], dtype=float)

    # --- Ableitungen - Karney Gl. (5a,b,c)---
    # E = ∂R/∂ω
    dX_dw = -ell.ax * so * Sx / D
    dY_dw =  ell.ay * cb * co
    dZ_dw = ell.b * sb * (so * co * (ell.ax*ell.ax - ell.ay*ell.ay) / Sz) / D
    E = np.array([dX_dw, dY_dw, dZ_dw], dtype=float)

    # N = ∂R/∂β
    dX_db = ell.ax * co * (sb * cb * (ell.b*ell.b - ell.ay*ell.ay) / Sx) / D
    dY_db = -ell.ay * sb * so
    dZ_db =  ell.b * cb * Sz / D
    N = np.array([dX_db, dY_db, dZ_db], dtype=float)

    # U = Grad(x^2/a^2 + y^2/b^2 + z^2/c^2 - 1)
    U = np.array([X/(ell.ax*ell.ax), Y/(ell.ay*ell.ay), Z/(ell.b*ell.b)], dtype=float)

    En = np.linalg.norm(E)
    Nn = np.linalg.norm(N)
    Un = np.linalg.norm(U)

    N_hat = N / Nn
    E_hat = E / En
    U_hat = U / Un
    E_hat = E_hat - float(np.dot(E_hat, N_hat)) * N_hat
    E_hat = E_hat / max(np.linalg.norm(E_hat), 1e-18)

    return E_hat, N_hat, U_hat, En, Nn, R


def jacobi_konstante(beta: float, omega: float, alpha: float, ell: EllipsoidTriaxial) -> float:
    """
    Jacobi-Konstante nach Karney (2025), Gl. (14)
    :param beta: Beta Koordinate
    :param omega: Omega Koordinate
    :param alpha: Azimut alpha
    :param ell: Ellipsoid
    :return: Jacobi-Konstante
    """
    e, k, k_ = ellipsoid_formparameter(ell)
    gamma_jacobi = float((k ** 2) * (np.cos(beta) ** 2) * (np.sin(alpha) ** 2) - (k_ ** 2) * (np.sin(omega) ** 2) * (np.cos(alpha) ** 2))

    return gamma_jacobi


def azimuth_at_ESpoint(P_prev: NDArray, P_curr: NDArray, E_hat_curr: NDArray, N_hat_curr: NDArray, U_hat_curr: NDArray) -> float:
    """
    Berechnet das Azimut in der lokalen Tangentialebene am aktuellen Punkt P_curr, gemessen
    an der Bewegungsrichtung vom vorherigen Punkt P_prev nach P_curr.
    :param P_prev: vorheriger Punkt
    :param P_curr: aktueller Punkt
    :param E_hat_curr: Einheitsvektor der lokalen Tangentialrichtung am Punkt P_curr
    :param N_hat_curr: Einheitsvektor der lokalen Tangentialrichtung am Punkt P_curr
    :param U_hat_curr: Einheitsnormalenvektor am Punkt P_curr
    :return: Azimut in Radiant
    """
    v = (P_curr - P_prev).astype(float)
    vT = v - float(np.dot(v, U_hat_curr)) * U_hat_curr
    vTn = max(np.linalg.norm(vT), 1e-18)
    vT_hat = vT / vTn
    #vT_hat = vT / np.linalg.norm(vT)
    sE = float(np.dot(vT_hat, E_hat_curr))
    sN = float(np.dot(vT_hat, N_hat_curr))

    return wrap_to_pi(float(np.arctan2(sE, sN)))


def optimize_next_point(beta_i: float, omega_i: float, alpha_i: float, ds: float, gamma0: float,
                        ell: EllipsoidTriaxial, maxSegLen: float = 1000.0, sigma0: float = None) -> Tuple[float, float, NDArray, float]:
    """
    Berechnung der 1. GHA mithilfe der CMA-ES.
    Die CMA-ES optimiert sukzessive einen Punkt, der maxSegLen vom vorherigen Punkt entfernt und zusätzlich auf der
    geodätischen Linien liegt. Somit entsteht ein Geodäten ähnlicher Polygonzug auf der Oberfläche des dreiachsigen Ellipsoids.
    :param beta_i: Beta Koordinate am Punkt i
    :param omega_i: Omega Koordinate am Punkt i
    :param alpha_i: Azimut am Punkt i
    :param ds: Gesamtlänge
    :param gamma0: Jacobi-Konstante am Startpunkt
    :param ell: Ellipsoid
    :param maxSegLen: maximale Segmentlänge
    :param sigma0:
    :return:
    """
    # Startbasis
    E_i, N_i, U_i, En_i, Nn_i, P_i = ENU_beta_omega(beta_i, omega_i, ell)
    # Prediktor: dβ ≈ ds cosα / |N|, dω ≈ ds sinα / |E|

    En_eff = max(En_i, 1e-9)
    Nn_eff = max(Nn_i, 1e-9)

    d_beta = ds * np.cos(alpha_i) / Nn_eff
    d_omega = ds * np.sin(alpha_i) / En_eff

    # optional: harte Schritt-Clamps (verhindert wrap-chaos)
    d_beta = float(np.clip(d_beta, -0.2, 0.2))  # rad
    d_omega = float(np.clip(d_omega, -0.2, 0.2))  # rad


    #d_beta = ds * float(np.cos(alpha_i)) / Nn_i
    #d_omega = ds * float(np.sin(alpha_i)) / En_i
    beta_pred = beta_i + d_beta
    omega_pred = wrap_to_pi(omega_i + d_omega)

    xmean = np.array([beta_pred, omega_pred], dtype=float)

    if sigma0 is None:
        R0 = (ell.ax + ell.ay + ell.b) / 3
        sigma0 = 1e-5 * (ds / R0)

    def fitness(x: NDArray) -> float:
        """
        Fitnessfunktion: Fitnesscheck erfolgt anhand der Segmentlänge und der Jacobi-Konstante.
        Die Segmentlänge muss möglichst gut zum Sollwert passen. Die Jacobi-Konstante am Punkt x muss zur
        Jacobi-Konstanten am Startpunkt passen, damit der Polygonzug auf derselben geodätischen Linie bleibt.
        :param x: Koordinate in beta, lambda aus der CMA-ES
        :return: Fitnesswert (f)
        """
        beta = x[0]
        omega = wrap_to_pi(x[1])

        P = ell.ell2cart_karney(beta, omega) # in kartesischer Koordinaten
        d = float(np.linalg.norm(P - P_i)) # Distanz zwischen

        # maxSegLen einhalten
        J_len = ((d - ds) / ds) ** 2
        w_len = 1.0

        # Azimut für Jacobi-Konstante
        E_j, N_j, U_j, _, _, _ = ENU_beta_omega(beta, omega, ell)
        alpha_end = azimuth_at_ESpoint(P_i, P, E_j, N_j, U_j)

        # Jacobi-Konstante
        g_end = jacobi_konstante(beta, omega, alpha_end, ell)
        J_gamma = (g_end - gamma0) ** 2
        w_gamma = 10

        f = float(w_len * J_len + w_gamma * J_gamma)

        return f


    xb = escma(fitness, N=2, xmean=xmean, sigma=sigma0) # Aufruf CMA-ES

    beta_best = xb[0]
    omega_best = wrap_to_pi(xb[1])
    P_best = ell.ell2cart_karney(beta_best, omega_best)
    E_j, N_j, U_j, _, _, _ = ENU_beta_omega(beta_best, omega_best, ell)
    alpha_end = azimuth_at_ESpoint(P_i, P_best, E_j, N_j, U_j)

    return beta_best, omega_best, P_best, alpha_end


def gha1_ES(ell: EllipsoidTriaxial, beta0: float, omega0: float, alpha0: float, s_total: float, maxSegLen: float = 1000, all_points: boolean = False)\
        -> Tuple[NDArray, float, NDArray] | Tuple[NDArray, float]:
    """
    Aufruf der 1. GHA mittels CMA-ES
    :param ell: Ellipsoid
    :param beta0: Beta Startkoordinate
    :param omega0: Omega Startkoordinate
    :param alpha0: Azimut Startkoordinate
    :param s_total: Gesamtstrecke
    :param maxSegLen: maximale Segmentlänge
    :param all_points: Alle Punkte ausgeben?
    :return: Zielpunkt Pk, Azimut am Zielpunkt und Punktliste
    """
    beta = float(beta0)
    omega = wrap_to_pi(float(omega0))
    alpha = wrap_to_pi(float(alpha0))

    gamma0 = jacobi_konstante(beta, omega, alpha, ell) # Referenz-γ0

    P_all: List[NDArray] = [ell.ell2cart_karney(beta, omega)]
    alpha_end: List[float] = [alpha]

    s_acc = 0.0
    step = 0
    nsteps_est = int(np.ceil(s_total / maxSegLen))
    while s_acc < s_total - 1e-9:
        step += 1
        ds = min(maxSegLen, s_total - s_acc)
        # print(f"[GHA1-ES] Step {step}/{nsteps_est}  ds={ds:.3f} m  s_acc={s_acc:.3f} m  beta={beta:.6f}  omega={omega:.6f}  alpha={alpha:.6f}")

        beta, omega, P, alpha = optimize_next_point(beta_i=beta, omega_i=omega, alpha_i=alpha, ds=ds, gamma0=gamma0,
                                                    ell=ell, maxSegLen=maxSegLen)
        s_acc += ds
        P_all.append(P)
        alpha_end.append(alpha)
        if step > nsteps_est + 50:
            raise RuntimeError("Zu viele Schritte – vermutlich Konvergenzproblem / falsche Azimut-Konvention.")
    Pk = P_all[-1]
    alpha1 = float(alpha_end[-1])

    if all_points:
        return Pk, alpha1, np.array(P_all)
    else:
        return Pk, alpha1


if __name__ == "__main__":
    ell = EllipsoidTriaxial.init_name("BursaSima1980round")
    s = 180000
    #alpha0 = 3
    alpha0 = wu.gms2rad([5 ,0 ,0])
    beta = 0
    omega = 0
    P0 = ell.ell2cart(beta, omega)
    point1, alpha1 = gha1_ana(ell, P0, alpha0=alpha0, s=s, maxM=100, maxPartCircum=32)
    point1app, alpha1app = gha1_approx(ell, P0, alpha0=alpha0, s=s, ds=1000)

    res, alpha, points = gha1_ES(ell, beta0=beta, omega0=-omega, alpha0=alpha0, s_total=s, maxSegLen=1000)

    print(point1)
    print(res)
    print(alpha)
    print(points)
    #print("alpha1 (am Endpunkt):", res.alpha1)
    print(res - point1)
    print(point1app - point1, "approx")