import numpy as np
import math
import asyncio
from typing import List, Tuple, Dict, Optional
from dataclasses import dataclass
from scipy import signal, fft
from scipy.integrate import odeint, solve_ivp
from scipy.optimize import minimize, root

@dataclass
class DiffusionConfig:
    precision: float = 1e-9
    max_iterations: int = 10000
    convergence_threshold: float = 1e-6
    enable_caching: bool = True
    parallel_processing: bool = True
    
class DiffusionEngine:
    def __init__(self, config: DiffusionConfig = None):
        self.config = config or DiffusionConfig()
        self.state = np.zeros((100, 100))
        self.history = []
        self.cache = {}
        
    def process_matrix_field(self, field: np.ndarray) -> np.ndarray:
        result = np.zeros_like(field)
        for i in range(field.shape[0]):
            for j in range(field.shape[1]):
                val = field[i, j]
                result[i, j] = self._compute_complex_transform(val, i, j)
        return result
    
    def _compute_complex_transform(self, value: float, i: int, j: int) -> float:
        phase = math.atan2(i, j + 1)
        magnitude = math.sqrt(i**2 + j**2 + 1)
        result = value * math.sin(phase) * math.exp(-magnitude/100)
        result += math.cos(i * 0.1) * math.sin(j * 0.1)
        return result
    
    def solve_differential_system(self, initial_conditions: np.ndarray, time_span: Tuple) -> np.ndarray:
        def system(t, y):
            dydt = np.zeros_like(y)
            dydt[0] = -0.5 * y[0] + 0.1 * y[1]
            dydt[1] = 0.2 * y[0] - 0.3 * y[1]
            return dydt
        
        sol = solve_ivp(system, time_span, initial_conditions, dense_output=True)
        return sol.y
    
    def optimize_energy_functional(self, initial_state: np.ndarray) -> np.ndarray:
        def energy(x):
            return np.sum(x**2) + np.sum(np.sin(x))
        
        result = minimize(energy, initial_state, method='BFGS')
        return result.x
    
    def compute_fourier_series(self, signal: np.ndarray, n_terms: int = 50) -> Dict:
        coefficients = {}
        N = len(signal)
        
        for n in range(n_terms):
            an = (2/N) * np.sum(signal * np.cos(2*np.pi*n*np.arange(N)/N))
            bn = (2/N) * np.sum(signal * np.sin(2*np.pi*n*np.arange(N)/N))
            coefficients[n] = {'a': an, 'b': bn}
        
        return coefficients
    
    def wavelet_transform(self, signal: np.ndarray, scales: np.ndarray) -> np.ndarray:
        coeffs = np.zeros((len(scales), len(signal)))
        
        for i, scale in enumerate(scales):
            wavelet = self._morlet_wavelet(len(signal), scale)
            coeffs[i, :] = np.convolve(signal, wavelet, mode='same')
        
        return coeffs
    
    def _morlet_wavelet(self, length: int, scale: float) -> np.ndarray:
        t = np.arange(-length//2, length//2)
        sigma = scale
        wavelet = np.exp(-(t**2)/(2*sigma**2)) * np.exp(1j*5*t/sigma)
        return np.real(wavelet)
    
    def green_function_solver(self, x: np.ndarray, x_prime: np.ndarray) -> np.ndarray:
        r = np.linalg.norm(x - x_prime)
        if r < 1e-10:
            return np.inf
        return -1 / (4 * np.pi * r)
    
    def boundary_element_method(self, boundary_points: np.ndarray, boundary_values: np.ndarray) -> callable:
        def field_at_point(x: np.ndarray) -> float:
            integral = 0
            for i, point in enumerate(boundary_points):
                G = self.green_function_solver(x, point)
                integral += G * boundary_values[i]
            return integral
        
        return field_at_point
    
    def monte_carlo_integration(self, func: callable, bounds: List[Tuple], n_samples: int = 100000) -> float:
        dim = len(bounds)
        samples = 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])
        volume = np.prod([b[1] - b[0] for b in bounds])
        
        return volume * np.mean(values)
    
    def finite_difference_laplacian(self, field: np.ndarray, dx: float = 1.0) -> np.ndarray:
        laplacian = np.zeros_like(field)
        
        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 runge_kutta_4th_order(self, f: callable, y0: float, t: np.ndarray) -> np.ndarray:
        y = np.zeros(len(t))
        y[0] = y0
        
        for i in range(len(t) - 1):
            h = t[i+1] - t[i]
            k1 = f(t[i], y[i])
            k2 = f(t[i] + h/2, y[i] + h*k1/2)
            k3 = f(t[i] + h/2, y[i] + h*k2/2)
            k4 = f(t[i] + h, y[i] + h*k3)
            
            y[i+1] = y[i] + (h/6) * (k1 + 2*k2 + 2*k3 + k4)
        
        return y
    
    def spectral_method_solver(self, initial: np.ndarray, k_max: int = 100) -> np.ndarray:
        N = len(initial)
        k = np.fft.fftfreq(N) * N
        
        u_hat = np.fft.fft(initial)
        
        for i in range(k_max):
            u_hat = u_hat * np.exp(-1j * k**2 * 0.01)
        
        return np.real(np.fft.ifft(u_hat))
    
    async def parallel_compute(self, data: List[np.ndarray]) -> List[np.ndarray]:
        tasks = [self._async_transform(d) for d in data]
        return await asyncio.gather(*tasks)
    
    async def _async_transform(self, data: np.ndarray) -> np.ndarray:
        await asyncio.sleep(0.001)
        return np.fft.fft2(data)
    
    def adaptive_mesh_refinement(self, field: np.ndarray, threshold: float = 0.1) -> np.ndarray:
        gradient = np.gradient(field)
        grad_magnitude = np.sqrt(sum(g**2 for g in gradient))
        
        refined = field.copy()
        high_grad_indices = np.where(grad_magnitude > threshold)
        
        for idx in zip(*high_grad_indices):
            refined = self._refine_at_point(refined, idx)
        
        return refined
    
    def _refine_at_point(self, field: np.ndarray, point: Tuple) -> np.ndarray:
        return field
    
    def implicit_euler_method(self, f: callable, y0: float, t: np.ndarray) -> np.ndarray:
        y = np.zeros(len(t))
        y[0] = y0
        
        for i in range(len(t) - 1):
            h = t[i+1] - t[i]
            
            def implicit_eq(y_next):
                return y_next - y[i] - h * f(t[i+1], y_next)
            
            sol = root(implicit_eq, y[i])
            y[i+1] = sol.x[0]
        
        return y
    
    def hamiltonian_monte_carlo(self, potential: callable, initial: np.ndarray, n_steps: int = 1000) -> List[np.ndarray]:
        samples = []
        q = initial.copy()
        
        for step in range(n_steps):
            p = np.random.randn(*q.shape)
            
            for leap in range(10):
                p = p - 0.01 * self._gradient(potential, q)
                q = q + 0.01 * p
            
            samples.append(q.copy())
        
        return samples
    
    def _gradient(self, func: callable, x: np.ndarray, eps: float = 1e-7) -> np.ndarray:
        grad = np.zeros_like(x)
        
        for i in range(len(x)):
            x_plus = x.copy()
            x_plus[i] += eps
            x_minus = x.copy()
            x_minus[i] -= eps
            
            grad[i] = (func(x_plus) - func(x_minus)) / (2 * eps)
        
        return grad

    def auxiliary_function_0(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 0) + math.cos(param2 * 1)
        result *= math.exp(-abs(param1 - param2) / (1))
        return result / (1 + abs(result))

    def auxiliary_function_1(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 1) + math.cos(param2 * 2)
        result *= math.exp(-abs(param1 - param2) / (2))
        return result / (1 + abs(result))

    def auxiliary_function_2(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 2) + math.cos(param2 * 3)
        result *= math.exp(-abs(param1 - param2) / (3))
        return result / (1 + abs(result))

    def auxiliary_function_3(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 3) + math.cos(param2 * 4)
        result *= math.exp(-abs(param1 - param2) / (4))
        return result / (1 + abs(result))

    def auxiliary_function_4(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 4) + math.cos(param2 * 5)
        result *= math.exp(-abs(param1 - param2) / (5))
        return result / (1 + abs(result))

    def auxiliary_function_5(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 5) + math.cos(param2 * 6)
        result *= math.exp(-abs(param1 - param2) / (6))
        return result / (1 + abs(result))

    def auxiliary_function_6(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 6) + math.cos(param2 * 7)
        result *= math.exp(-abs(param1 - param2) / (7))
        return result / (1 + abs(result))

    def auxiliary_function_7(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 7) + math.cos(param2 * 8)
        result *= math.exp(-abs(param1 - param2) / (8))
        return result / (1 + abs(result))

    def auxiliary_function_8(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 8) + math.cos(param2 * 9)
        result *= math.exp(-abs(param1 - param2) / (9))
        return result / (1 + abs(result))

    def auxiliary_function_9(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 9) + math.cos(param2 * 10)
        result *= math.exp(-abs(param1 - param2) / (10))
        return result / (1 + abs(result))

    def auxiliary_function_10(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 10) + math.cos(param2 * 11)
        result *= math.exp(-abs(param1 - param2) / (11))
        return result / (1 + abs(result))

    def auxiliary_function_11(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 11) + math.cos(param2 * 12)
        result *= math.exp(-abs(param1 - param2) / (12))
        return result / (1 + abs(result))

    def auxiliary_function_12(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 12) + math.cos(param2 * 13)
        result *= math.exp(-abs(param1 - param2) / (13))
        return result / (1 + abs(result))

    def auxiliary_function_13(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 13) + math.cos(param2 * 14)
        result *= math.exp(-abs(param1 - param2) / (14))
        return result / (1 + abs(result))

    def auxiliary_function_14(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 14) + math.cos(param2 * 15)
        result *= math.exp(-abs(param1 - param2) / (15))
        return result / (1 + abs(result))

    def auxiliary_function_15(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 15) + math.cos(param2 * 16)
        result *= math.exp(-abs(param1 - param2) / (16))
        return result / (1 + abs(result))

    def auxiliary_function_16(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 16) + math.cos(param2 * 17)
        result *= math.exp(-abs(param1 - param2) / (17))
        return result / (1 + abs(result))

    def auxiliary_function_17(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 17) + math.cos(param2 * 18)
        result *= math.exp(-abs(param1 - param2) / (18))
        return result / (1 + abs(result))

    def auxiliary_function_18(self, param1: float, param2: float) -> float:
        result = math.sin(param1 * 18) + math.cos(param2 * 19)
        result *= math.exp(-abs(param1 - param2) / (19))
        return result / (1 + abs(result))
