import torch
from torch.optim.optimizer import Optimizer
from typing import Optional, Tuple, Union, Callable, List, Dict, Any
from ..projective import ProjectiveUHG

class ProjectiveOptimizer(Optimizer):
    """Base class for optimizers using projective geometry.
    
    All optimization steps are performed using pure projective geometry,
    following UHG principles without any manifold concepts.
    
    Args:
        params: Iterable of parameters to optimize
        defaults: Default optimizer settings
    """
    def __init__(
        self,
        params: List[torch.Tensor],
        defaults: Dict[str, Any]
    ):
        super().__init__(params, defaults)
        self.uhg = ProjectiveUHG()
        
    def project_gradients(self, p: torch.Tensor) -> torch.Tensor:
        """Project gradients using projective geometry.
        
        Args:
            p: Parameter tensor
            
        Returns:
            Projected gradients
        """
        if p.grad is None:
            return p.grad
            
        # Project using projective transformation
        matrix = self.uhg.get_projective_matrix(p.size(-1))
        return self.uhg.transform(p.grad, matrix)
        
    def update_parameter(
        self,
        p: torch.Tensor,
        d_p: torch.Tensor,
        lr: float
    ) -> torch.Tensor:
        """Update parameter using projective geometry.
        
        Args:
            p: Current parameter value
            d_p: Update direction
            lr: Learning rate
            
        Returns:
            Updated parameter value
        """
        # Create projective transformation for update
        matrix = torch.eye(p.size(-1) + 1, device=p.device)
        matrix[:-1] -= lr * d_p
        
        # Apply projective transformation
        return self.uhg.transform(p, matrix)
        
    def preserve_cross_ratio(
        self,
        group: Dict[str, Any],
        state: Dict[str, Any],
        p: torch.Tensor
    ) -> None:
        """Preserve cross-ratios between optimization steps.
        
        Args:
            group: Optimizer parameter group
            state: Optimizer state
            p: Parameter tensor
        """
        # Initialize state if needed
        if len(state) == 0:
            state['step'] = 0
            state['prev_p'] = p.clone()
            return
            
        # Compute cross-ratio between steps
        prev_p = state['prev_p']
        cr = self.uhg.cross_ratio(prev_p, p, prev_p, p)
        
        # Create projective transformation to preserve cross-ratio
        matrix = self.uhg.get_projective_matrix(p.size(-1))
        matrix = matrix * cr.view(-1, 1, 1)
        
        # Apply transformation
        p_adj = self.uhg.transform(p, matrix)
        
        # Update state
        state['prev_p'] = p_adj.clone()
        state['step'] += 1
        
    @torch.no_grad()
    def step(self, closure: Optional[Callable] = None) -> Optional[float]:
        """Perform a single optimization step.
        
        Args:
            closure: Closure that reevaluates the model and returns loss
            
        Returns:
            Optional loss value from closure
        """
        loss = None
        if closure is not None:
            with torch.enable_grad():
                loss = closure()
                
        for group in self.param_groups:
            for p in group['params']:
                if p.grad is None:
                    continue
                    
                # Get state for current parameter
                state = self.state[p]
                
                # Project gradients using projective geometry
                d_p = self.project_gradients(p)
                
                # Update parameter
                p_new = self.update_parameter(p, d_p, group['lr'])
                
                # Preserve cross-ratio
                self.preserve_cross_ratio(group, state, p_new)
                
                # Update parameter in-place
                p.data.copy_(p_new)
                
        return loss 