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

class SoundAcousticWaveguideProcessor:
    def __init__(self, cfg: SoundAcousticWaveguideConfig = None):
        self.cfg = cfg or SoundAcousticWaveguideConfig()
        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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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_AcousticWaveguide_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)
