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 ElasticYoungsModulusConfig:
    resolution: int = 4096
    precision: float = 1e-18
    max_iter: int = 100000
    adaptive: bool = True
    parallel: bool = True

class ElasticYoungsModulusProcessor:
    def __init__(self, cfg: ElasticYoungsModulusConfig = None):
        self.cfg = cfg or ElasticYoungsModulusConfig()
        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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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_YoungsModulus_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)
