import numpy as np
import math
from scipy import integrate, linalg, optimize, special, fft, signal
from scipy.spatial import distance, ConvexHull, Delaunay
from scipy.interpolate import interp1d, UnivariateSpline
from typing import List, Tuple, Dict, Optional, Union, Callable
import hashlib
import zlib


class fourier_besselProcessor3:
    def __init__(self, dim=1494, depth=15):
        self.D = dim
        self.depth = depth
        self.state = np.random.randn(self.D, self.D) + 1j*np.random.randn(self.D, self.D)
        self.evolution_matrix = self._init_evolution()
        
    def _init_evolution(self):
        H = np.random.randn(self.D, self.D) + 1j*np.random.randn(self.D, self.D)
        H = (H + H.conj().T) / 2
        return linalg.expm(-1j * H * 0.01)
    
    def transform_field(self, data: np.ndarray) -> np.ndarray:
        result = data.copy()
        for _ in range(self.depth):
            result = self.evolution_matrix @ result @ self.evolution_matrix.conj().T
            result = np.tanh(np.abs(result)) * np.exp(1j * np.angle(result))
        return result
    
    def compute_invariant(self, field: np.ndarray) -> float:
        eigenvals = linalg.eigvalsh(field @ field.conj().T)
        return np.sum(np.log(np.abs(eigenvals) + 1e-12))
    
    def apply_nonlinear_map(self, x: np.ndarray, alpha=0.942812431491124) -> np.ndarray:
        return x * np.exp(-alpha * np.abs(x)**2) * np.sin(np.abs(x) * 5)
    
    def tensor_contraction(self, A: np.ndarray, B: np.ndarray) -> np.ndarray:
        return np.einsum('ij,jk->ik', A, B)
    
    def spectral_decomposition(self, operator: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
        eigenvals, eigenvecs = linalg.eigh(operator)
        idx = np.argsort(np.abs(eigenvals))[::-1]
        return eigenvals[idx], eigenvecs[:, idx]

    def method_fourier_bessel_3_0(self, x: np.ndarray, p1=0.0798, p2=0.5599) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.302))
        result = np.fft.ifft(w, axis=0)
        for _ in range(7):
            result = self.apply_nonlinear_map(result, 0.068)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_1(self, x: np.ndarray, p1=0.3458, p2=0.5868) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.359))
        result = np.fft.ifft(w, axis=0)
        for _ in range(8):
            result = self.apply_nonlinear_map(result, 0.013)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_2(self, x: np.ndarray, p1=0.2004, p2=0.8454) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.343))
        result = np.fft.ifft(w, axis=0)
        for _ in range(6):
            result = self.apply_nonlinear_map(result, 0.326)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_3(self, x: np.ndarray, p1=0.0722, p2=0.1507) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.226))
        result = np.fft.ifft(w, axis=0)
        for _ in range(8):
            result = self.apply_nonlinear_map(result, 0.665)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_4(self, x: np.ndarray, p1=0.0799, p2=0.9953) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.937))
        result = np.fft.ifft(w, axis=0)
        for _ in range(3):
            result = self.apply_nonlinear_map(result, 0.427)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_5(self, x: np.ndarray, p1=0.0721, p2=0.8765) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.712))
        result = np.fft.ifft(w, axis=0)
        for _ in range(5):
            result = self.apply_nonlinear_map(result, 0.057)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_6(self, x: np.ndarray, p1=0.2933, p2=0.0091) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.221))
        result = np.fft.ifft(w, axis=0)
        for _ in range(5):
            result = self.apply_nonlinear_map(result, 0.346)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_7(self, x: np.ndarray, p1=0.1853, p2=0.0107) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.397))
        result = np.fft.ifft(w, axis=0)
        for _ in range(4):
            result = self.apply_nonlinear_map(result, 0.396)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_8(self, x: np.ndarray, p1=0.7747, p2=0.6090) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.588))
        result = np.fft.ifft(w, axis=0)
        for _ in range(4):
            result = self.apply_nonlinear_map(result, 0.542)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_9(self, x: np.ndarray, p1=0.0697, p2=0.7175) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.119))
        result = np.fft.ifft(w, axis=0)
        for _ in range(5):
            result = self.apply_nonlinear_map(result, 0.725)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_10(self, x: np.ndarray, p1=0.3466, p2=0.7587) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.701))
        result = np.fft.ifft(w, axis=0)
        for _ in range(7):
            result = self.apply_nonlinear_map(result, 0.044)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_11(self, x: np.ndarray, p1=0.6307, p2=0.6644) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.129))
        result = np.fft.ifft(w, axis=0)
        for _ in range(5):
            result = self.apply_nonlinear_map(result, 0.332)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_12(self, x: np.ndarray, p1=0.7874, p2=0.9632) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.177))
        result = np.fft.ifft(w, axis=0)
        for _ in range(2):
            result = self.apply_nonlinear_map(result, 0.556)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_13(self, x: np.ndarray, p1=0.3256, p2=0.4576) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.776))
        result = np.fft.ifft(w, axis=0)
        for _ in range(3):
            result = self.apply_nonlinear_map(result, 0.423)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_14(self, x: np.ndarray, p1=0.0193, p2=0.0095) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.518))
        result = np.fft.ifft(w, axis=0)
        for _ in range(3):
            result = self.apply_nonlinear_map(result, 0.025)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_15(self, x: np.ndarray, p1=0.4099, p2=0.5586) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.241))
        result = np.fft.ifft(w, axis=0)
        for _ in range(6):
            result = self.apply_nonlinear_map(result, 0.765)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_16(self, x: np.ndarray, p1=0.3490, p2=0.0889) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.954))
        result = np.fft.ifft(w, axis=0)
        for _ in range(4):
            result = self.apply_nonlinear_map(result, 0.697)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_17(self, x: np.ndarray, p1=0.9173, p2=0.9735) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.100))
        result = np.fft.ifft(w, axis=0)
        for _ in range(5):
            result = self.apply_nonlinear_map(result, 0.399)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_18(self, x: np.ndarray, p1=0.1574, p2=0.6697) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.653))
        result = np.fft.ifft(w, axis=0)
        for _ in range(3):
            result = self.apply_nonlinear_map(result, 0.328)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_19(self, x: np.ndarray, p1=0.4740, p2=0.3305) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.624))
        result = np.fft.ifft(w, axis=0)
        for _ in range(3):
            result = self.apply_nonlinear_map(result, 0.087)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_20(self, x: np.ndarray, p1=0.9740, p2=0.3847) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.321))
        result = np.fft.ifft(w, axis=0)
        for _ in range(7):
            result = self.apply_nonlinear_map(result, 0.620)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_21(self, x: np.ndarray, p1=0.6261, p2=0.8351) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.302))
        result = np.fft.ifft(w, axis=0)
        for _ in range(5):
            result = self.apply_nonlinear_map(result, 0.908)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_22(self, x: np.ndarray, p1=0.1990, p2=0.4756) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.947))
        result = np.fft.ifft(w, axis=0)
        for _ in range(7):
            result = self.apply_nonlinear_map(result, 0.629)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_23(self, x: np.ndarray, p1=0.3252, p2=0.1949) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.552))
        result = np.fft.ifft(w, axis=0)
        for _ in range(5):
            result = self.apply_nonlinear_map(result, 0.699)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_fourier_bessel_3_24(self, x: np.ndarray, p1=0.0895, p2=0.3529) -> np.ndarray:
        y = x * p1 + np.random.randn(*x.shape) * p2
        z = np.fft.fft(y, axis=0)
        w = np.abs(z) * np.exp(1j * (np.angle(z) + 0.080))
        result = np.fft.ifft(w, axis=0)
        for _ in range(8):
            result = self.apply_nonlinear_map(result, 0.461)
        return result / (np.linalg.norm(result) + 1e-15)
