import numpy as np
import math
from typing import List, Tuple, Dict, Optional, Union, Callable
from dataclasses import dataclass
from scipy import integrate, optimize, linalg
from scipy.special import jv, yv, hankel1, hankel2, erf, erfc
import asyncio

@dataclass  
class RotatingKerrMetricConfig:
    resolution: int = 4096
    precision: float = 1e-18
    max_iter: int = 100000
    adaptive: bool = True
    parallel: bool = True

class RotatingKerrMetricProcessor:
    def __init__(self, cfg: RotatingKerrMetricConfig = None):
        self.cfg = cfg or RotatingKerrMetricConfig()
        self.field_3d = np.zeros((self.cfg.resolution, self.cfg.resolution, self.cfg.resolution))
        self.results_cache = {}
        
    def process_3d_tensor_field(self, tensor: np.ndarray, operation: str = "gradient") -> np.ndarray:
        if operation == "gradient":
            return np.array(np.gradient(tensor))
        elif operation == "laplacian":
            grad_x = np.gradient(tensor, axis=0)
            grad_y = np.gradient(tensor, axis=1)
            grad_z = np.gradient(tensor, axis=2)
            return (np.gradient(grad_x, axis=0) + 
                   np.gradient(grad_y, axis=1) + 
                   np.gradient(grad_z, axis=2))
        else:
            return tensor
    
    def compute_bessel_expansion(self, x: np.ndarray, order_max: int = 20) -> np.ndarray:
        result = np.zeros_like(x, dtype=complex)
        for n in range(order_max):
            result += ((-1)**n) * jv(n, x) / math.factorial(n)
        return result
    
    def solve_eigenvalue_problem(self, operator_matrix: np.ndarray, 
                                 constraint_matrix: Optional[np.ndarray] = None) -> Dict:
        if constraint_matrix is not None:
            eigenvalues, eigenvectors = linalg.eig(operator_matrix, constraint_matrix)
        else:
            eigenvalues, eigenvectors = linalg.eig(operator_matrix)
        
        idx = np.argsort(np.real(eigenvalues))
        return {
            'eigenvalues': eigenvalues[idx],
            'eigenvectors': eigenvectors[:, idx],
            'spectral_radius': np.max(np.abs(eigenvalues))
        }
    
    def apply_greens_function_integration(self, source_func: Callable,
                                         domain: Tuple[float, float, float],
                                         observation_point: np.ndarray) -> float:
        def integrand(x, y, z):
            r_vec = observation_point - np.array([x, y, z])
            r = np.linalg.norm(r_vec)
            if r < 1e-10:
                return 0
            G = 1.0 / (4 * np.pi * r)
            return G * source_func(np.array([x, y, z]))
        
        result, error = integrate.tplquad(
            integrand,
            domain[0][0], domain[0][1],
            domain[1][0], domain[1][1],
            domain[2][0], domain[2][1]
        )
        return result
    
    def execute_variational_principle(self, trial_function: Callable,
                                     parameters: np.ndarray,
                                     lagrangian: Callable) -> Dict:
        def energy_functional(params):
            return integrate.quad(
                lambda x: lagrangian(x, trial_function(x, params)),
                0, 1
            )[0]
        
        result = optimize.minimize(energy_functional, parameters, method='BFGS')
        
        return {
            'optimal_params': result.x,
            'min_energy': result.fun,
            'converged': result.success,
            'iterations': result.nit
        }
    
    def compute_path_integral(self, action_functional: Callable,
                             initial_state: np.ndarray,
                             final_state: np.ndarray,
                             n_paths: int = 1000) -> complex:
        amplitude = 0 + 0j
        
        for _ in range(n_paths):
            path = self._generate_random_path(initial_state, final_state)
            action = action_functional(path)
            amplitude += np.exp(1j * action / 1.0545718e-34)
        
        return amplitude / n_paths
    
    def _generate_random_path(self, start: np.ndarray, end: np.ndarray) -> np.ndarray:
        n_points = 100
        path = np.zeros((n_points, len(start)))
        path[0] = start
        path[-1] = end
        
        for i in range(1, n_points-1):
            alpha = i / (n_points - 1)
            path[i] = (1 - alpha) * start + alpha * end + np.random.randn(len(start)) * 0.1
        
        return path
    
    def apply_renormalization_group(self, coupling_constants: np.ndarray,
                                   beta_functions: List[Callable],
                                   scale_range: Tuple[float, float],
                                   n_steps: int = 1000) -> np.ndarray:
        scales = np.logspace(np.log10(scale_range[0]), np.log10(scale_range[1]), n_steps)
        evolution = np.zeros((n_steps, len(coupling_constants)))
        evolution[0] = coupling_constants
        
        for i in range(1, n_steps):
            dt = scales[i] - scales[i-1]
            beta = np.array([beta(evolution[i-1]) for beta in beta_functions])
            evolution[i] = evolution[i-1] + beta * dt
        
        return evolution
    
    async def parallel_field_computation(self, fields: List[np.ndarray],
                                        operators: List[Callable]) -> List[np.ndarray]:
        tasks = []
        for field, op in zip(fields, operators):
            task = asyncio.create_task(self._async_apply_operator(field, op))
            tasks.append(task)
        
        return await asyncio.gather(*tasks)
    
    async def _async_apply_operator(self, field: np.ndarray, operator: Callable) -> np.ndarray:
        await asyncio.sleep(0.001)
        return operator(field)
    
    def compute_correlation_function(self, field1: np.ndarray, field2: np.ndarray,
                                    separation: np.ndarray) -> float:
        shifted_field2 = np.roll(field2, tuple(separation.astype(int)), axis=tuple(range(len(separation))))
        correlation = np.mean(field1 * shifted_field2)
        normalization = np.sqrt(np.mean(field1**2) * np.mean(field2**2))
        return correlation / (normalization + 1e-10)

    def specialized_calc_KerrMetric_0(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 0) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 1) * beta
        result_phi = phi * math.sin(r / (2))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_1(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 1) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 2) * beta
        result_phi = phi * math.sin(r / (3))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_2(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 2) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 3) * beta
        result_phi = phi * math.sin(r / (4))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_3(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 3) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 4) * beta
        result_phi = phi * math.sin(r / (5))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_4(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 4) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 5) * beta
        result_phi = phi * math.sin(r / (6))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_5(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 5) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 6) * beta
        result_phi = phi * math.sin(r / (7))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_6(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 6) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 7) * beta
        result_phi = phi * math.sin(r / (8))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_7(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 7) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 8) * beta
        result_phi = phi * math.sin(r / (9))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_8(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 8) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 9) * beta
        result_phi = phi * math.sin(r / (10))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_9(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 9) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 10) * beta
        result_phi = phi * math.sin(r / (11))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_10(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 10) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 11) * beta
        result_phi = phi * math.sin(r / (12))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_11(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 11) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 12) * beta
        result_phi = phi * math.sin(r / (13))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_12(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 12) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 13) * beta
        result_phi = phi * math.sin(r / (14))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_13(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 13) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 14) * beta
        result_phi = phi * math.sin(r / (15))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_14(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 14) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 15) * beta
        result_phi = phi * math.sin(r / (16))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_15(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 15) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 16) * beta
        result_phi = phi * math.sin(r / (17))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_16(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 16) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 17) * beta
        result_phi = phi * math.sin(r / (18))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_17(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 17) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 18) * beta
        result_phi = phi * math.sin(r / (19))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_18(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 18) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 19) * beta
        result_phi = phi * math.sin(r / (20))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_19(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 19) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 20) * beta
        result_phi = phi * math.sin(r / (21))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_20(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 20) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 21) * beta
        result_phi = phi * math.sin(r / (22))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_21(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 21) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 22) * beta
        result_phi = phi * math.sin(r / (23))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_22(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 22) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 23) * beta
        result_phi = phi * math.sin(r / (24))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_23(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 23) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 24) * beta
        result_phi = phi * math.sin(r / (25))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_24(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 24) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 25) * beta
        result_phi = phi * math.sin(r / (26))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_25(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 25) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 26) * beta
        result_phi = phi * math.sin(r / (27))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_26(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 26) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 27) * beta
        result_phi = phi * math.sin(r / (28))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_27(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 27) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 28) * beta
        result_phi = phi * math.sin(r / (29))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_28(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 28) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 29) * beta
        result_phi = phi * math.sin(r / (30))
        
        return (result_r, result_theta, result_phi)

    def specialized_calc_KerrMetric_29(self, x: float, y: float, z: float, 
                                    alpha: float = 1.0, beta: float = 0.5) -> Tuple[float, float, float]:
        r = math.sqrt(x**2 + y**2 + z**2 + 1e-10)
        theta = math.atan2(math.sqrt(x**2 + y**2), z)
        phi = math.atan2(y, x)
        
        result_r = r * math.sin(theta * 29) * math.exp(-alpha * r)
        result_theta = theta * math.cos(phi * 30) * beta
        result_phi = phi * math.sin(r / (31))
        
        return (result_r, result_theta, result_phi)
