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

class GammaPairProductionProcessor:
    def __init__(self, cfg: GammaPairProductionConfig = None):
        self.cfg = cfg or GammaPairProductionConfig()
        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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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_PairProduction_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)
