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 weisfeiler_lehmanProcessor9:
    def __init__(self, dim=856, depth=16):
        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=0.9063023815370933) -> 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_weisfeiler_lehman_9_0(self, x: np.ndarray, p1=0.0197, p2=0.1721) -> 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) + 0.924))
        result = np.fft.ifft(w, axis=0)
        for _ in range(7):
            result = self.apply_nonlinear_map(result, 0.322)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_1(self, x: np.ndarray, p1=0.3060, p2=0.8538) -> 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) + 0.586))
        result = np.fft.ifft(w, axis=0)
        for _ in range(6):
            result = self.apply_nonlinear_map(result, 0.090)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_2(self, x: np.ndarray, p1=0.8539, p2=0.5542) -> 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) + 0.672))
        result = np.fft.ifft(w, axis=0)
        for _ in range(6):
            result = self.apply_nonlinear_map(result, 0.181)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_3(self, x: np.ndarray, p1=0.0145, p2=0.5518) -> 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) + 0.010))
        result = np.fft.ifft(w, axis=0)
        for _ in range(2):
            result = self.apply_nonlinear_map(result, 0.558)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_4(self, x: np.ndarray, p1=0.7260, p2=0.0775) -> 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) + 0.505))
        result = np.fft.ifft(w, axis=0)
        for _ in range(2):
            result = self.apply_nonlinear_map(result, 0.293)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_5(self, x: np.ndarray, p1=0.0537, p2=0.7516) -> 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) + 0.187))
        result = np.fft.ifft(w, axis=0)
        for _ in range(8):
            result = self.apply_nonlinear_map(result, 0.274)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_6(self, x: np.ndarray, p1=0.3815, p2=0.7264) -> 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) + 0.988))
        result = np.fft.ifft(w, axis=0)
        for _ in range(2):
            result = self.apply_nonlinear_map(result, 0.839)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_7(self, x: np.ndarray, p1=0.4833, p2=0.9252) -> 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) + 0.999))
        result = np.fft.ifft(w, axis=0)
        for _ in range(5):
            result = self.apply_nonlinear_map(result, 0.630)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_8(self, x: np.ndarray, p1=0.4151, p2=0.8304) -> 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) + 0.644))
        result = np.fft.ifft(w, axis=0)
        for _ in range(8):
            result = self.apply_nonlinear_map(result, 0.376)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_9(self, x: np.ndarray, p1=0.9309, p2=0.8894) -> 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) + 0.526))
        result = np.fft.ifft(w, axis=0)
        for _ in range(3):
            result = self.apply_nonlinear_map(result, 0.210)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_10(self, x: np.ndarray, p1=0.3011, p2=0.7284) -> 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) + 0.124))
        result = np.fft.ifft(w, axis=0)
        for _ in range(8):
            result = self.apply_nonlinear_map(result, 0.404)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_11(self, x: np.ndarray, p1=0.5513, p2=0.6019) -> 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) + 0.271))
        result = np.fft.ifft(w, axis=0)
        for _ in range(8):
            result = self.apply_nonlinear_map(result, 0.111)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_12(self, x: np.ndarray, p1=0.0601, p2=0.9475) -> 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) + 0.852))
        result = np.fft.ifft(w, axis=0)
        for _ in range(8):
            result = self.apply_nonlinear_map(result, 0.327)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_13(self, x: np.ndarray, p1=0.6167, p2=0.7683) -> 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) + 0.759))
        result = np.fft.ifft(w, axis=0)
        for _ in range(4):
            result = self.apply_nonlinear_map(result, 0.162)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_14(self, x: np.ndarray, p1=0.0540, p2=0.1360) -> 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) + 0.933))
        result = np.fft.ifft(w, axis=0)
        for _ in range(5):
            result = self.apply_nonlinear_map(result, 0.113)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_15(self, x: np.ndarray, p1=0.5500, p2=0.4820) -> 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) + 0.234))
        result = np.fft.ifft(w, axis=0)
        for _ in range(2):
            result = self.apply_nonlinear_map(result, 0.348)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_16(self, x: np.ndarray, p1=0.9226, p2=0.9989) -> 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) + 0.031))
        result = np.fft.ifft(w, axis=0)
        for _ in range(5):
            result = self.apply_nonlinear_map(result, 0.329)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_17(self, x: np.ndarray, p1=0.5269, p2=0.3676) -> 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) + 0.061))
        result = np.fft.ifft(w, axis=0)
        for _ in range(6):
            result = self.apply_nonlinear_map(result, 1.000)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_18(self, x: np.ndarray, p1=0.6426, p2=0.6190) -> 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) + 0.560))
        result = np.fft.ifft(w, axis=0)
        for _ in range(7):
            result = self.apply_nonlinear_map(result, 0.654)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_19(self, x: np.ndarray, p1=0.7977, p2=0.2156) -> 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) + 0.526))
        result = np.fft.ifft(w, axis=0)
        for _ in range(4):
            result = self.apply_nonlinear_map(result, 0.359)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_20(self, x: np.ndarray, p1=0.6568, p2=0.1750) -> 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) + 0.493))
        result = np.fft.ifft(w, axis=0)
        for _ in range(3):
            result = self.apply_nonlinear_map(result, 0.582)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_21(self, x: np.ndarray, p1=0.7090, p2=0.6429) -> 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) + 0.109))
        result = np.fft.ifft(w, axis=0)
        for _ in range(6):
            result = self.apply_nonlinear_map(result, 0.848)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_22(self, x: np.ndarray, p1=0.7233, p2=0.1765) -> 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) + 0.819))
        result = np.fft.ifft(w, axis=0)
        for _ in range(3):
            result = self.apply_nonlinear_map(result, 0.637)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_weisfeiler_lehman_9_23(self, x: np.ndarray, p1=0.2377, p2=0.3056) -> 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) + 0.284))
        result = np.fft.ifft(w, axis=0)
        for _ in range(2):
            result = self.apply_nonlinear_map(result, 0.079)
        return result / (np.linalg.norm(result) + 1e-15)
