import torch
from typing import Optional, Callable
from .base import ProjectiveSampler

class ProjectiveHMC(ProjectiveSampler):
    """Hamiltonian Monte Carlo sampler in projective space.
    
    Implements HMC using pure projective geometry operations,
    following UHG principles.
    
    Args:
        log_prob_fn: Function computing log probability of points
        step_size: Size of integration steps
        n_steps: Number of integration steps per sample
        temperature: Temperature parameter for sampling
    """
    def __init__(
        self,
        log_prob_fn: Callable[[torch.Tensor], torch.Tensor],
        step_size: float = 0.1,
        n_steps: int = 10,
        temperature: float = 1.0
    ):
        super().__init__(log_prob_fn, temperature)
        self.step_size = step_size
        self.n_steps = n_steps
        
    def sample(
        self,
        n_samples: int,
        initial_point: Optional[torch.Tensor] = None,
        **kwargs
    ) -> torch.Tensor:
        """Generate samples using projective HMC.
        
        Args:
            n_samples: Number of samples to generate
            initial_point: Starting point for sampling
            **kwargs: Additional sampling parameters
            
        Returns:
            Tensor of sampled points
        """
        if initial_point is None:
            # Create random projective transformation
            matrix = self.uhg.get_projective_matrix(3)
            # Apply to standard basis to get initial point
            initial_point = self.uhg.transform(torch.eye(3), matrix)[0]
            
        samples = []
        current_x = initial_point
        
        for _ in range(n_samples):
            # Sample momentum using projective transformation
            matrix = self.uhg.get_projective_matrix(3)
            p = self.uhg.transform(torch.randn_like(current_x), matrix)
            
            # Store initial state
            current_p = p
            proposed_x = current_x
            proposed_p = current_p
            
            # Integrate using projective operations
            for _ in range(self.n_steps):
                # Half step in momentum
                force = self._compute_force(proposed_x)
                proposed_p = self.uhg.transform(
                    proposed_p,
                    torch.eye(3) + self.step_size/2 * force.unsqueeze(-1)
                )
                
                # Full step in position
                proposed_x = self.uhg.transform(
                    proposed_x,
                    torch.eye(3) + self.step_size * proposed_p.unsqueeze(-1)
                )
                
                # Half step in momentum
                force = self._compute_force(proposed_x)
                proposed_p = self.uhg.transform(
                    proposed_p,
                    torch.eye(3) + self.step_size/2 * force.unsqueeze(-1)
                )
                
            # Compute acceptance probability using cross-ratio
            current_energy = (
                self._compute_energy(current_x) +
                self.uhg.cross_ratio(current_x, current_p, current_x, current_p) / 2
            )
            proposed_energy = (
                self._compute_energy(proposed_x) +
                self.uhg.cross_ratio(proposed_x, proposed_p, proposed_x, proposed_p) / 2
            )
            
            # Accept or reject
            if torch.rand(1) < torch.exp(current_energy - proposed_energy):
                current_x = proposed_x
                
            samples.append(current_x)
            
        return torch.stack(samples) 