"""
Advanced 4D Geometry Module - Ultra Precision
Developer:  MERO (mero@ps.com)
Version: 2.0.0
Trillion-Scale Calculations Support
© 2025 MERO.  All rights reserved. 

This module contains ultra-precise 4D geometric calculations
supporting billions of computation iterations with advanced
tensor operations and quaternion mathematics.
"""

import numpy as np
from typing import Tuple, List, Union, Optional, Dict, Any
from dataclasses import dataclass
from scipy.linalg import eig, qr, svd
from scipy.interpolate import interp1d
import quaternion as quat_lib
import warnings

warnings.filterwarnings('ignore')

@dataclass
class Point4D:
    """Ultra-precise 4D point with extended precision arithmetic"""
    x: np.float64
    y: np.float64
    z: np.float64
    w: np.float64
    precision: str = "ultra"  # ultra, high, standard
    
    def __post_init__(self):
        self.coords = np.array([self.x, self.y, self.z, self.w], dtype=np.float128 if self.precision == "ultra" else np.float64)
    
    @property
    def magnitude_4d(self) -> np.float64:
        """Calculate true 4D magnitude"""
        return np.sqrt(np.sum(self.coords ** 2))
    
    @property
    def magnitude_euclidean(self) -> np.float64:
        """Euclidean distance in 4D space"""
        return np.linalg.norm(self.coords)
    
    @property
    def minkowski_norm(self) -> np.float64:
        """Minkowski metric for spacetime (w as time)"""
        spatial = np.sqrt(self.x**2 + self.y**2 + self.z**2)
        return np.sqrt(spatial**2 - self.w**2) if spatial > abs(self.w) else np.sqrt(self.w**2 - spatial**2)
    
    def distance_to(self, other: 'Point4D', metric: str = 'euclidean') -> np.float64:
        """
        Multiple distance metrics in 4D
        - euclidean: standard 4D distance
        - minkowski: spacetime interval
        - taxicab: Manhattan distance
        - chebyshev:  Chebyshev distance
        """
        diff = self.coords - other.coords
        
        if metric == 'euclidean':
            return np.float64(np.sqrt(np. sum(diff ** 2)))
        elif metric == 'minkowski':
            spatial = np.sqrt(diff[0]**2 + diff[1]**2 + diff[2]**2)
            return np.sqrt(spatial**2 - diff[3]**2)
        elif metric == 'taxicab':
            return np. float64(np.sum(np.abs(diff)))
        elif metric == 'chebyshev':
            return np.float64(np.max(np.abs(diff)))
        else:
            return np.float64(np.sqrt(np.sum(diff ** 2)))
    
    def projection_to_3d(self, method: str = 'perspective', distance:  float = 5.0) -> 'Point3D':
        """
        Project 4D point to 3D with multiple methods
        - orthogonal: ignore W dimension
        - perspective: 4D perspective projection
        - stereographic: stereographic projection from north pole
        - conformal: conformal mapping
        """
        if method == 'orthogonal':
            return Point3D(self.x, self. y, self.z)
        
        elif method == 'perspective':
            scale = distance / (distance + self.w) if self.w > -distance else 1.0
            return Point3D(self.x * scale, self.y * scale, self.z * scale)
        
        elif method == 'stereographic':
            if abs(self.w - 1.0) < 1e-10:
                return Point3D(float('inf'), float('inf'), float('inf'))
            scale = 1.0 / (1.0 - self.w)
            return Point3D(self.x * scale, self.y * scale, self.z * scale)
        
        elif method == 'conformal':
            r_sq = self.x**2 + self.y**2 + self.z**2 + self.w**2
            factor = 2.0 / (r_sq + 1.0)
            return Point3D(self.x * factor, self.y * factor, self.z * factor)
        
        else:
            return Point3D(self.x, self.y, self.z)
    
    def rotate_4d(self, rotation_matrix: np.ndarray) -> 'Point4D': 
        """Apply 4D rotation matrix"""
        rotated = rotation_matrix @ self.coords
        return Point4D(*rotated, precision=self.precision)
    
    def apply_lorentz_transformation(self, velocity: np.ndarray, c: float = 299792458.0) -> 'Point4D':
        """Apply Lorentz transformation for