import numpy as np
from typing import List, Tuple, Optional, Callable, Dict, Any
import torch
from scipy.optimize import minimize, differential_evolution
from scipy.interpolate import RBFInterpolator

class MEROGeometricAlgorithms:
    
    @staticmethod
    def hypersphere_sampling_4d(num_points: int, radius: float = 1.0) -> np.ndarray:
        angles = np.random.randn(num_points, 3)
        angles = angles / np.linalg.norm(angles, axis=1, keepdims=True)
        
        u = np.random.uniform(0, 1, num_points)
        
        points = np.zeros((num_points, 4))
        points[:, 0] = radius * np.cbrt(u) * np.cos(angles[:, 0])
        points[:, 1] = radius * np.cbrt(u) * np.sin(angles[:, 0]) * np.cos(angles[:, 1])
        points[:, 2] = radius * np. cbrt(u) * np.sin(angles[:, 0]) * np.sin(angles[:, 1]) * np.cos(angles[:, 2])
        points[:, 3] = radius * np.cbrt(u) * np.sin(angles[:, 0]) * np.sin(angles[:, 1]) * np.sin(angles[:, 2])
        
        return points
    
    @staticmethod
    def delaunay_4d(points:  np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
        from scipy.spatial import SphericalVoronoi, geometric_slerp
        from scipy.spatial import Delaunay
        
        try:
            delaunay = Delaunay(points)
            return delaunay.points, delaunay.simplices
        except:
            return points, np.array([])
    
    @staticmethod
    def voronoi_4d(points: np.ndarray) -> Dict[str, Any]:
        from scipy.spatial import Voronoi
        
        vor = Voronoi(points)
        
        return {
            'points': vor.points,
            'vertices': vor.vertices,
            'regions': vor.regions,
            'point_region':  vor.point_region
        }
    
    @staticmethod
    def convex_hull_4d(points: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
        from scipy.spatial import ConvexHull
        
        hull = ConvexHull(points)
        return hull.points, hull.simplices
    
    @staticmethod
    def minkowski_sum_4d(shape1: np.ndarray, shape2: np.ndarray) -> np.ndarray:
        result = []
        for p1 in shape1:
            for p2 in shape2:
                result.append(p1 + p2)
        return np.array(result)
    
    @staticmethod
    def grassmannian_interpolation(p1: np.ndarray, p2: np.ndarray, t: float) -> np.ndarray:
        u, s, vt = np.linalg.svd(np.outer(p1, p2))
        
        angle = np.arccos(np. clip(np.dot(p1 / np.linalg.norm(p1), 
                                         p2 / np.linalg.norm(p2)), -1, 1))
        
        if np.abs(angle) < 1e-10:
            return p1
        
        interpolated = (np.sin((1 - t) * angle) / np.sin(angle)) * p1 + \
                      (np.sin(t * angle) / np.sin(angle)) * p2
        
        return interpolated
    
    @staticmethod
    def ricci_tensor_approximation_4d(metric_tensor: np.ndarray) -> np.ndarray:
        dim = 4
        ricci = np.zeros((dim, dim))
        
        for i in range(dim):
            for j in range(dim):
                epsilon = 1e-6
                
                metric_plus = metric_tensor. copy()
                metric_minus = metric_tensor.copy()
                
                metric_plus[i, j] += epsilon
                metric_minus[i, j] -= epsilon
                
                det_plus = np.linalg.det(metric_plus)
                det_minus = np.linalg.det(metric_minus)
                
                ricci[i, j] = (det_plus - det_minus) / (2 * epsilon)
        
        return ricci
    
    @staticmethod
    def geodesic_equation_solver(start: np.ndarray, initial_velocity: np.ndarray,
                                metric_tensor: np.ndarray,
                                time_steps: int = 100,
                                dt: float = 0.01) -> List[np.ndarray]:
        
        positions = [start. copy()]
        velocity = initial_velocity.copy()
        position = start.copy()
        
        for _ in range(time_steps):
            metric_inv = np.linalg.inv(metric_tensor)
            
            acceleration = np.zeros(4)
            for i in range(4):
                for j in range(4):
                    for k in range(4):
                        christoffel_ijk = (metric_tensor[i, j] + metric_tensor[i, k]) / 4
                        acceleration[i] -= christoffel_ijk * velocity[j] * velocity[k]
            
            velocity += acceleration * dt
            position += velocity * dt
            
            positions.append(position.copy())
        
        return positions


class MEROOptimizationEngine:
    
    @staticmethod
    def shape_optimization(target_shape: np.ndarray,
                          initial_shape: np.ndarray,
                          num_iterations: int = 1000) -> Tuple[np.ndarray, float]:
        
        def objective(params):
            transformed = MEROOptimizationEngine._apply_transformation(initial_shape, params)
            return np.linalg.norm(transformed - target_shape)
        
        initial_guess = np.zeros(10)
        
        result = minimize(objective, initial_guess, method='L-BFGS-B')
        
        return MEROOptimizationEngine._apply_transformation(initial_shape, result.x), float(result.fun)
    
    @staticmethod
    def _apply_transformation(shape: np.ndarray, params: np.ndarray) -> np.ndarray:
        angles = params[:4]
        translation = params[4:8]
        scale = params[8:10]
        
        transformed = shape.copy()
        
        for i, angle in enumerate(angles):
            matrix = MEROOptimizationEngine._rotation_matrix_plane(angle, i)
            transformed = transformed @ matrix. T
        
        transformed = transformed * scale[0] + translation[: 3]
        
        return transformed
    
    @staticmethod
    def _rotation_matrix_plane(angle: float, plane_index: int) -> np.ndarray:
        cos_a = np.cos(angle)
        sin_a = np.sin(angle)
        matrix = np.eye(4)
        
        planes = [(0, 1), (0, 2), (0, 3), (1, 2)]
        if plane_index < len(planes):
            i, j = planes[plane_index]
            matrix[i, i] = cos_a
            matrix[i, j] = -sin_a
            matrix[j, i] = sin_a
            matrix[j, j] = cos_a
        
        return matrix
    
    @staticmethod
    def symmetry_breaking_optimization(shape: np.ndarray,
                                      symmetry_constraints: List[Callable],
                                      num_points: int = 50) -> np.ndarray:
        
        def constraint_penalty(params):
            penalty = 0
            for constraint in symmetry_constraints:
                penalty += constraint(params) ** 2
            return penalty
        
        bounds = [(-10, 10) for _ in range(shape.size)]
        
        result = differential_evolution(constraint_penalty, bounds, seed=42, maxiter=1000)
        
        optimized = shape.copy()
        for i, val in enumerate(result.x):
            if i < shape.size:
                optimized. flat[i] = val
        
        return optimized


class MEROFluidDynamics4D:
    
    def __init__(self, grid_size: int = 32):
        self.grid_size = grid_size
        self.velocity_field = np.zeros((grid_size, grid_size, grid_size, 4))
        self.pressure_field = np.zeros((grid_size, grid_size, grid_size))
        self.density_field = np.ones((grid_size, grid_size, grid_size)) * 0.1
    
    def advect_field(self, field: np.ndarray, velocity: np.ndarray, dt: float = 0.01) -> np.ndarray:
        indices = np.indices(field.shape)
        
        coordinates = np.array([indices[i] for i in range(len(field.shape))])
        
        new_coords = coordinates - velocity * dt
        
        advected = np.zeros_like(field)
        for idx in np.ndindex(field.shape):
            try:
                value = field[tuple(np.maximum(0, np.minimum(np.array(idx) - 1, self.grid_size - 1)))]
                advected[idx] = value
            except: 
                pass
        
        return advected
    
    def apply_forces(self, external_force: np.ndarray, dt: float = 0.01):
        self.velocity_field += external_force * dt
    
    def project_incompressible(self):
        divergence = np.zeros((self.grid_size, self. grid_size, self.grid_size))
        
        for i in range(self.grid_size):
            for j in range(self.grid_size):
                for k in range(self.grid_size):
                    div = 0
                    if i > 0:
                        div -= self.velocity_field[i-1, j, k, 0]
                    if i < self.grid_size - 1:
                        div += self.velocity_field[i+1, j, k, 0]
                    if j > 0:
                        div -= self.velocity_field[i, j-1, k, 1]
                    if j < self. grid_size - 1:
                        div += self.velocity_field[i, j+1, k, 1]
                    if k > 0:
                        div -= self.velocity_field[i, j, k-1, 2]
                    if k < self.grid_size - 1:
                        div += self.velocity_field[i, j, k+1, 2]
                    
                    divergence[i, j, k] = div / (2 * self.grid_size)
        
        self.pressure_field = divergence
    
    def step(self, external_force: np.ndarray, dt: float = 0.01):
        self.apply_forces(external_force, dt)
        self.project_incompressible()


class MERONeuralField:
    
    def __init__(self, hidden_dim: int = 128):
        self.mlp = self._build_mlp(4, hidden_dim, 1)
    
    def _build_mlp(self, input_dim: int, hidden_dim: int, output_dim: int) -> torch.nn.Module:
        return torch.nn.Sequential(
            torch.nn.Linear(input_dim, hidden_dim),
            torch.nn.ReLU(),
            torch.nn.Linear(hidden_dim, hidden_dim),
            torch.nn.ReLU(),
            torch.nn.Linear(hidden_dim, output_dim),
            torch.nn.Sigmoid()
        )
    
    def sample_field(self, coordinates: torch.Tensor) -> torch.Tensor:
        with torch.no_grad():
            return self.mlp(coordinates)
    
    def fit_field(self, sample_points: torch.Tensor, values: torch.Tensor, 
                 epochs: int = 100, lr: float = 0.001):
        
        optimizer = torch.optim.Adam(self.mlp.parameters(), lr=lr)
        criterion = torch.nn.MSELoss()
        
        for epoch in range(epochs):
            optimizer.zero_grad()
            
            predictions = self.mlp(sample_points)
            loss = criterion(predictions, values)
            
            loss.backward()
            optimizer.step()
            
            if epoch % 20 == 0:
                pass