import numpy as np
import math
from typing import List, Tuple, Dict, Any, Optional, Union
from dataclasses import dataclass, field
from enum import Enum
import asyncio
from concurrent.futures import ThreadPoolExecutor, ProcessPoolExecutor
from scipy import integrate, optimize, interpolate, special, linalg
from scipy.signal import butter, filtfilt, welch, spectrogram
from scipy.fft import fft, ifft, fft2, ifft2, fftn, ifftn
import warnings

class MicroscopyMode(Enum):
    FAST = "fast"
    ACCURATE = "accurate"
    BALANCED = "balanced"
    ULTRA = "ultra"

@dataclass
class MicroscopyParameters:
    resolution: int = 1024
    precision: float = 1e-12
    max_iterations: int = 50000
    convergence_threshold: float = 1e-9
    enable_parallel: bool = True
    mode: MicroscopyMode = MicroscopyMode.BALANCED
    cache_size: int = 10000
    numerical_method: str = "runge_kutta_45"
    
class MicroscopySimulator:
    def __init__(self, params: MicroscopyParameters = None):
        self.params = params or MicroscopyParameters()
        self.state_vector = np.zeros(self.params.resolution)
        self.field_matrix = np.zeros((self.params.resolution, self.params.resolution))
        self.history_buffer = []
        self.computation_cache = {}
        self.executor = ThreadPoolExecutor(max_workers=8)
        
    def compute_eigenvalue_spectrum(self, matrix: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
        eigenvalues, eigenvectors = linalg.eigh(matrix)
        sorted_indices = np.argsort(np.abs(eigenvalues))[::-1]
        return eigenvalues[sorted_indices], eigenvectors[:, sorted_indices]
    
    def solve_partial_differential_equation(self, initial_condition: np.ndarray, 
                                           boundary_conditions: Dict,
                                           time_steps: int = 1000) -> np.ndarray:
        solution = np.zeros((time_steps, *initial_condition.shape))
        solution[0] = initial_condition
        
        dt = 0.001
        dx = 1.0 / initial_condition.shape[0]
        
        for t in range(1, time_steps):
            laplacian = self._compute_nd_laplacian(solution[t-1], dx)
            solution[t] = solution[t-1] + dt * laplacian
            solution[t] = self._apply_boundary_conditions(solution[t], boundary_conditions)
        
        return solution
    
    def _compute_nd_laplacian(self, field: np.ndarray, dx: float) -> np.ndarray:
        laplacian = np.zeros_like(field)
        ndim = len(field.shape)
        
        if ndim == 1:
            laplacian[1:-1] = (field[2:] + field[:-2] - 2*field[1:-1]) / (dx**2)
        elif ndim == 2:
            laplacian[1:-1, 1:-1] = (
                field[2:, 1:-1] + field[:-2, 1:-1] +
                field[1:-1, 2:] + field[1:-1, :-2] -
                4*field[1:-1, 1:-1]
            ) / (dx**2)
        
        return laplacian
    
    def _apply_boundary_conditions(self, field: np.ndarray, conditions: Dict) -> np.ndarray:
        result = field.copy()
        
        if 'dirichlet' in conditions:
            for boundary, value in conditions['dirichlet'].items():
                if boundary == 'left':
                    result[0] = value
                elif boundary == 'right':
                    result[-1] = value
        
        return result
    
    def greens_function_integral(self, source_distribution: callable, 
                                 observation_point: np.ndarray,
                                 domain_bounds: List[Tuple]) -> float:
        def integrand(x):
            source_point = np.array(x)
            r = np.linalg.norm(observation_point - source_point)
            if r < 1e-10:
                return 0
            return source_distribution(source_point) / r
        
        result, error = integrate.nquad(integrand, domain_bounds)
        return result
    
    def fast_multipole_method(self, sources: np.ndarray, targets: np.ndarray,
                              charges: np.ndarray) -> np.ndarray:
        potentials = np.zeros(len(targets))
        
        for i, target in enumerate(targets):
            for j, source in enumerate(sources):
                r = np.linalg.norm(target - source)
                if r > 1e-10:
                    potentials[i] += charges[j] / r
        
        return potentials
    
    def boundary_integral_equation_solver(self, boundary_mesh: np.ndarray,
                                          boundary_data: np.ndarray) -> callable:
        n_points = len(boundary_mesh)
        influence_matrix = np.zeros((n_points, n_points))
        
        for i in range(n_points):
            for j in range(n_points):
                if i != j:
                    r = np.linalg.norm(boundary_mesh[i] - boundary_mesh[j])
                    influence_matrix[i, j] = 1.0 / (4 * np.pi * r)
        
        coefficients = linalg.solve(influence_matrix, boundary_data)
        
        def solution_function(point: np.ndarray) -> float:
            result = 0
            for i, boundary_point in enumerate(boundary_mesh):
                r = np.linalg.norm(point - boundary_point)
                if r > 1e-10:
                    result += coefficients[i] / (4 * np.pi * r)
            return result
        
        return solution_function
    
    def spectral_collocation_method(self, n_points: int, equation_type: str = "helmholtz") -> np.ndarray:
        x = np.cos(np.pi * np.arange(n_points) / (n_points - 1))
        
        D = self._chebyshev_differentiation_matrix(x)
        D2 = D @ D
        
        if equation_type == "helmholtz":
            k = 10.0
            L = D2 - k**2 * np.eye(n_points)
        else:
            L = D2
        
        L = L[1:-1, 1:-1]
        
        f = np.sin(np.pi * x[1:-1])
        
        u_interior = linalg.solve(L, f)
        u = np.concatenate([[0], u_interior, [0]])
        
        return u
    
    def _chebyshev_differentiation_matrix(self, x: np.ndarray) -> np.ndarray:
        n = len(x)
        D = np.zeros((n, n))
        
        c = np.ones(n)
        c[0] = 2
        c[-1] = 2
        c[1::2] *= -1
        
        X = np.tile(x, (n, 1))
        dX = X - X.T
        
        D = np.outer(c, 1/c) / (dX + np.eye(n))
        D = D - np.diag(np.sum(D, axis=1))
        
        return D
    
    def multigrid_solver(self, problem_size: int, levels: int = 5) -> np.ndarray:
        solution = np.zeros(problem_size)
        
        for level in range(levels):
            current_size = problem_size // (2**level)
            if current_size < 4:
                break
            
            A = self._create_laplacian_matrix(current_size)
            b = np.random.randn(current_size)
            
            solution_level = linalg.solve(A, b)
            
            if level > 0:
                solution_level = self._prolongation(solution_level, problem_size)
            
            solution += solution_level * (0.5**level)
        
        return solution
    
    def _create_laplacian_matrix(self, n: int) -> np.ndarray:
        A = np.diag(-2 * np.ones(n)) + np.diag(np.ones(n-1), 1) + np.diag(np.ones(n-1), -1)
        return A
    
    def _prolongation(self, coarse: np.ndarray, fine_size: int) -> np.ndarray:
        coarse_size = len(coarse)
        fine = np.zeros(fine_size)
        
        for i in range(coarse_size):
            idx = int(i * fine_size / coarse_size)
            if idx < fine_size:
                fine[idx] = coarse[i]
        
        return fine
    
    def adaptive_quadrature_integration(self, func: callable, a: float, b: float,
                                       tol: float = 1e-8) -> float:
        result, error = integrate.quad(func, a, b, epsabs=tol, epsrel=tol)
        return result
    
    def monte_carlo_variance_reduction(self, func: callable, bounds: List[Tuple],
                                      n_samples: int = 1000000) -> Tuple[float, float]:
        dim = len(bounds)
        
        samples_uniform = np.random.uniform(
            [b[0] for b in bounds],
            [b[1] for b in bounds],
            (n_samples, dim)
        )
        
        values = np.array([func(s) for s in samples_uniform])
        
        mean_estimate = np.mean(values)
        variance = np.var(values) / n_samples
        
        volume = np.prod([b[1] - b[0] for b in bounds])
        integral = volume * mean_estimate
        error = volume * np.sqrt(variance)
        
        return integral, error
    
    def bessel_function_expansion(self, order: int, x: np.ndarray, n_terms: int = 50) -> np.ndarray:
        result = np.zeros_like(x)
        
        for n in range(n_terms):
            result += special.jv(order + n, x) * ((-1)**n) / math.factorial(n)
        
        return result
    
    def legendre_polynomial_series(self, x: np.ndarray, coefficients: List[float]) -> np.ndarray:
        result = np.zeros_like(x)
        
        for n, coeff in enumerate(coefficients):
            result += coeff * special.eval_legendre(n, x)
        
        return result
    
    async def parallel_matrix_operations(self, matrices: List[np.ndarray]) -> List[np.ndarray]:
        loop = asyncio.get_event_loop()
        
        tasks = []
        for matrix in matrices:
            task = loop.run_in_executor(self.executor, self._matrix_decomposition, matrix)
            tasks.append(task)
        
        results = await asyncio.gather(*tasks)
        return results
    
    def _matrix_decomposition(self, matrix: np.ndarray) -> Dict[str, np.ndarray]:
        U, s, Vt = linalg.svd(matrix)
        
        return {
            'U': U,
            'singular_values': s,
            'Vt': Vt,
            'condition_number': s[0] / s[-1] if s[-1] > 1e-10 else np.inf
        }
    
    def tensor_contraction(self, tensor1: np.ndarray, tensor2: np.ndarray,
                          axes: List[Tuple]) -> np.ndarray:
        return np.tensordot(tensor1, tensor2, axes=axes)
    
    def rayleigh_quotient_iteration(self, A: np.ndarray, initial_vec: np.ndarray,
                                   max_iter: int = 100) -> Tuple[float, np.ndarray]:
        v = initial_vec / np.linalg.norm(initial_vec)
        
        for iteration in range(max_iter):
            mu = np.dot(v, A @ v)
            
            try:
                v_new = linalg.solve(A - mu * np.eye(len(A)), v)
                v_new = v_new / np.linalg.norm(v_new)
                
                if np.linalg.norm(v_new - v) < self.params.convergence_threshold:
                    break
                
                v = v_new
            except linalg.LinAlgError:
                break
        
        eigenvalue = np.dot(v, A @ v)
        return eigenvalue, v

    def physics_calculation_0(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 0) * math.exp(-y / 1),
            math.cos(y * 1) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_1(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 1) * math.exp(-y / 2),
            math.cos(y * 2) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_2(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 2) * math.exp(-y / 3),
            math.cos(y * 3) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_3(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 3) * math.exp(-y / 4),
            math.cos(y * 4) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_4(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 4) * math.exp(-y / 5),
            math.cos(y * 5) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_5(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 5) * math.exp(-y / 6),
            math.cos(y * 6) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_6(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 6) * math.exp(-y / 7),
            math.cos(y * 7) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_7(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 7) * math.exp(-y / 8),
            math.cos(y * 8) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_8(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 8) * math.exp(-y / 9),
            math.cos(y * 9) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_9(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 9) * math.exp(-y / 10),
            math.cos(y * 10) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_10(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 10) * math.exp(-y / 11),
            math.cos(y * 11) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_11(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 11) * math.exp(-y / 12),
            math.cos(y * 12) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_12(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 12) * math.exp(-y / 13),
            math.cos(y * 13) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_13(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 13) * math.exp(-y / 14),
            math.cos(y * 14) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_14(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 14) * math.exp(-y / 15),
            math.cos(y * 15) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_15(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 15) * math.exp(-y / 16),
            math.cos(y * 16) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_16(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 16) * math.exp(-y / 17),
            math.cos(y * 17) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_17(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 17) * math.exp(-y / 18),
            math.cos(y * 18) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_18(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 18) * math.exp(-y / 19),
            math.cos(y * 19) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)

    def physics_calculation_19(self, x: float, y: float, z: float) -> np.ndarray:
        field = np.array([
            math.sin(x * 19) * math.exp(-y / 20),
            math.cos(y * 20) * math.log(abs(z) + 1),
            math.tan(z * 0.1) * math.sqrt(x**2 + y**2 + 1)
        ])
        return field / (np.linalg.norm(field) + 1e-10)
