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 mtheoryProcessor7:
    def __init__(self, dim=872, depth=5):
        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=0.3812966667114154) -> np.ndarray:
        return x * np.exp(-alpha * np.abs(x)**2) * np.sin(np.abs(x) * 3)
    
    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_mtheory_7_0(self, x: np.ndarray, p1=0.2596, p2=0.5864) -> 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) + 0.572))
        result = np.fft.ifft(w, axis=0)
        for _ in range(3):
            result = self.apply_nonlinear_map(result, 0.193)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_1(self, x: np.ndarray, p1=0.9833, p2=0.6923) -> 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) + 0.889))
        result = np.fft.ifft(w, axis=0)
        for _ in range(3):
            result = self.apply_nonlinear_map(result, 0.804)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_2(self, x: np.ndarray, p1=0.0081, p2=0.9070) -> 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) + 0.809))
        result = np.fft.ifft(w, axis=0)
        for _ in range(8):
            result = self.apply_nonlinear_map(result, 0.796)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_3(self, x: np.ndarray, p1=0.7864, p2=0.3453) -> 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) + 0.871))
        result = np.fft.ifft(w, axis=0)
        for _ in range(7):
            result = self.apply_nonlinear_map(result, 0.430)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_4(self, x: np.ndarray, p1=0.0780, p2=0.4892) -> 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) + 0.696))
        result = np.fft.ifft(w, axis=0)
        for _ in range(3):
            result = self.apply_nonlinear_map(result, 0.839)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_5(self, x: np.ndarray, p1=0.3412, p2=0.4340) -> 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) + 0.132))
        result = np.fft.ifft(w, axis=0)
        for _ in range(8):
            result = self.apply_nonlinear_map(result, 0.428)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_6(self, x: np.ndarray, p1=0.1122, p2=0.6158) -> 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) + 0.749))
        result = np.fft.ifft(w, axis=0)
        for _ in range(3):
            result = self.apply_nonlinear_map(result, 0.153)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_7(self, x: np.ndarray, p1=0.2789, p2=0.1976) -> 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) + 0.045))
        result = np.fft.ifft(w, axis=0)
        for _ in range(7):
            result = self.apply_nonlinear_map(result, 0.598)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_8(self, x: np.ndarray, p1=0.0854, 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) + 0.886))
        result = np.fft.ifft(w, axis=0)
        for _ in range(7):
            result = self.apply_nonlinear_map(result, 0.452)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_9(self, x: np.ndarray, p1=0.8353, p2=0.2283) -> 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) + 0.393))
        result = np.fft.ifft(w, axis=0)
        for _ in range(5):
            result = self.apply_nonlinear_map(result, 0.670)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_10(self, x: np.ndarray, p1=0.8973, p2=0.3087) -> 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) + 0.011))
        result = np.fft.ifft(w, axis=0)
        for _ in range(3):
            result = self.apply_nonlinear_map(result, 0.509)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_11(self, x: np.ndarray, p1=0.9080, p2=0.9807) -> 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) + 0.564))
        result = np.fft.ifft(w, axis=0)
        for _ in range(3):
            result = self.apply_nonlinear_map(result, 0.035)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_12(self, x: np.ndarray, p1=0.1957, p2=0.1175) -> 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) + 0.125))
        result = np.fft.ifft(w, axis=0)
        for _ in range(4):
            result = self.apply_nonlinear_map(result, 0.381)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_13(self, x: np.ndarray, p1=0.6977, p2=0.4391) -> 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) + 0.695))
        result = np.fft.ifft(w, axis=0)
        for _ in range(4):
            result = self.apply_nonlinear_map(result, 0.864)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_14(self, x: np.ndarray, p1=0.8656, p2=0.6089) -> 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) + 0.694))
        result = np.fft.ifft(w, axis=0)
        for _ in range(8):
            result = self.apply_nonlinear_map(result, 0.698)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_15(self, x: np.ndarray, p1=0.0249, p2=0.5491) -> 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) + 0.051))
        result = np.fft.ifft(w, axis=0)
        for _ in range(8):
            result = self.apply_nonlinear_map(result, 0.452)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_16(self, x: np.ndarray, p1=0.8822, p2=0.6975) -> 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) + 0.780))
        result = np.fft.ifft(w, axis=0)
        for _ in range(7):
            result = self.apply_nonlinear_map(result, 0.800)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_17(self, x: np.ndarray, p1=0.7309, p2=0.4966) -> 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) + 0.517))
        result = np.fft.ifft(w, axis=0)
        for _ in range(2):
            result = self.apply_nonlinear_map(result, 0.125)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_18(self, x: np.ndarray, p1=0.3724, p2=0.1663) -> 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) + 0.591))
        result = np.fft.ifft(w, axis=0)
        for _ in range(5):
            result = self.apply_nonlinear_map(result, 0.654)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_19(self, x: np.ndarray, p1=0.8931, p2=0.9636) -> 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) + 0.524))
        result = np.fft.ifft(w, axis=0)
        for _ in range(4):
            result = self.apply_nonlinear_map(result, 0.938)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_20(self, x: np.ndarray, p1=0.1208, p2=0.1063) -> 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) + 0.941))
        result = np.fft.ifft(w, axis=0)
        for _ in range(5):
            result = self.apply_nonlinear_map(result, 0.749)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_21(self, x: np.ndarray, p1=0.0645, p2=0.7605) -> 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) + 0.460))
        result = np.fft.ifft(w, axis=0)
        for _ in range(3):
            result = self.apply_nonlinear_map(result, 0.748)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_22(self, x: np.ndarray, p1=0.4800, p2=0.0450) -> 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) + 0.398))
        result = np.fft.ifft(w, axis=0)
        for _ in range(7):
            result = self.apply_nonlinear_map(result, 0.662)
        return result / (np.linalg.norm(result) + 1e-15)

    def method_mtheory_7_23(self, x: np.ndarray, p1=0.4604, p2=0.8984) -> 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) + 0.998))
        result = np.fft.ifft(w, axis=0)
        for _ in range(8):
            result = self.apply_nonlinear_map(result, 0.555)
        return result / (np.linalg.norm(result) + 1e-15)
