import torch
from typing import Optional, Callable, Dict, Any, Tuple
from ..manifolds.base import Manifold

class HyperbolicSampler:
    """Base class for sampling in hyperbolic space.
    
    All sampling operations are performed directly in hyperbolic space
    using UHG principles, without tangent space mappings.
    
    Args:
        manifold: The hyperbolic manifold to sample on
        log_prob_fn: Function computing log probability of points
        temperature: Temperature parameter for sampling
    """
    def __init__(
        self,
        manifold: Manifold,
        log_prob_fn: Callable[[torch.Tensor], torch.Tensor],
        temperature: float = 1.0
    ):
        self.manifold = manifold
        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 from the distribution.
        
        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 conservative force field in hyperbolic space.
        
        Uses cross-ratio derivatives instead of gradients.
        
        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 self.manifold.project(x, force)
        
    def _reflect(
        self,
        x: torch.Tensor,
        v: torch.Tensor,
        force: torch.Tensor
    ) -> Tuple[torch.Tensor, torch.Tensor]:
        """Reflect velocity through force field.
        
        All operations performed in hyperbolic space.
        
        Args:
            x: Current position
            v: Current velocity
            force: Force at current position
            
        Returns:
            Updated position and velocity
        """
        # Compute reflection line using force
        line = self.manifold.join(x, force)
        
        # Reflect position and velocity
        x_new = self.manifold.reflect(x, line)
        v_new = self.manifold.reflect(v, line)
        
        return x_new, v_new
        
    def _check_constraints(self, x: torch.Tensor) -> torch.Tensor:
        """Ensure points satisfy hyperbolic constraints.
        
        Args:
            x: Points to check
            
        Returns:
            Normalized points
        """
        return self.manifold.normalize(x)


class HyperbolicHMC(HyperbolicSampler):
    """Hamiltonian Monte Carlo sampler in hyperbolic space.
    
    Implements HMC directly in hyperbolic space using UHG operations,
    without tangent space mappings.
    
    Args:
        manifold: The hyperbolic manifold to sample on
        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,
        manifold: Manifold,
        log_prob_fn: Callable[[torch.Tensor], torch.Tensor],
        step_size: float = 0.1,
        n_steps: int = 10,
        temperature: float = 1.0
    ):
        super().__init__(manifold, 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 hyperbolic 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:
            # Sample initial point uniformly from hyperbolic space
            initial_point = self.manifold.random_uniform(n_samples)
            
        samples = []
        current_x = initial_point
        
        for _ in range(n_samples):
            # Sample momentum from hyperbolic space
            p = self.manifold.random_normal_like(current_x)
            
            # Store initial state
            current_p = p
            proposed_x = current_x
            proposed_p = current_p
            
            # Integrate Hamiltonian dynamics
            for _ in range(self.n_steps):
                # Half step in momentum
                force = self._compute_force(proposed_x)
                proposed_p = self.manifold.mobius_add(
                    proposed_p,
                    self.manifold.mobius_scalar_mul(
                        self.step_size / 2,
                        force
                    )
                )
                
                # Full step in position
                proposed_x = self.manifold.mobius_add(
                    proposed_x,
                    self.manifold.mobius_scalar_mul(
                        self.step_size,
                        proposed_p
                    )
                )
                
                # Half step in momentum
                force = self._compute_force(proposed_x)
                proposed_p = self.manifold.mobius_add(
                    proposed_p,
                    self.manifold.mobius_scalar_mul(
                        self.step_size / 2,
                        force
                    )
                )
                
                # Ensure constraints are satisfied
                proposed_x = self._check_constraints(proposed_x)
                proposed_p = self.manifold.project(proposed_x, proposed_p)
                
            # Compute acceptance probability
            current_energy = (
                self._compute_energy(current_x) +
                self.manifold.inner(current_x, current_p).sum() / 2
            )
            proposed_energy = (
                self._compute_energy(proposed_x) +
                self.manifold.inner(proposed_x, proposed_p).sum() / 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) 