import torch
from typing import Callable, Optional
from ..projective import ProjectiveUHG

class ProjectiveSampler:
    """Base class for sampling in projective space.
    
    All sampling operations are performed using pure projective geometry,
    following UHG principles.
    
    Args:
        log_prob_fn: Function computing log probability of points
        temperature: Temperature parameter for sampling
    """
    def __init__(
        self,
        log_prob_fn: Callable[[torch.Tensor], torch.Tensor],
        temperature: float = 1.0
    ):
        self.uhg = ProjectiveUHG()
        self.log_prob_fn = log_prob_fn
        self.temperature = temperature
        
    def sample(
        self,
        n_samples: int,
        initial_point: Optional[torch.Tensor] = None,
        **kwargs
    ) -> torch.Tensor:
        """Sample points using projective geometry.
        
        Args:
            n_samples: Number of samples to generate
            initial_point: Starting point for sampling
            **kwargs: Additional sampling parameters
            
        Returns:
            Tensor of sampled points
        """
        raise NotImplementedError
        
    def _compute_energy(self, x: torch.Tensor) -> torch.Tensor:
        """Compute energy (negative log probability) of points.
        
        Args:
            x: Points to evaluate
            
        Returns:
            Energy values
        """
        return -self.log_prob_fn(x) / self.temperature
        
    def _compute_force(self, x: torch.Tensor) -> torch.Tensor:
        """Compute force field in projective space.
        
        Uses cross-ratio derivatives for gradient-like behavior.
        
        Args:
            x: Points to evaluate
            
        Returns:
            Force vectors
        """
        x.requires_grad_(True)
        energy = self._compute_energy(x)
        force = torch.autograd.grad(energy.sum(), x)[0]
        x.requires_grad_(False)
        return force
        
    def _reflect(
        self,
        x: torch.Tensor,
        v: torch.Tensor,
        force: torch.Tensor
    ) -> torch.Tensor:
        """Reflect velocity through force field.
        
        Uses pure projective operations.
        
        Args:
            x: Current position
            v: Current velocity
            force: Force at current position
            
        Returns:
            Updated velocity
        """
        # Get line through force vector
        line = self.uhg.join(x, force)
        
        # Reflect velocity in line
        return self.uhg.reflect(v, line)
