import torch
import torch.nn as nn
import torch.nn.functional as F
from typing import Callable, Dict, Optional, Tuple
from ..path import ProbPath, GaussianProbPath

class ScoreMatchingModel(nn.Module):
    """Score matching model as described in p.28-30, Theorem 20.
    
    This model learns to predict the score function ∇log p_t(x).
    """
    
    def __init__(
        self,
        encoder: nn.Module,
        path: ProbPath,
        parameterization: str = "score", # "score" or "noise"
        input_channels: int = 4,
        hidden_dim: int = 256
    ):
        super().__init__()
        self.encoder = encoder
        self.path = path
        self.parameterization = parameterization
        # Initialize network layers would be here
        
    def forward(self, x: torch.Tensor, t: torch.Tensor) -> torch.Tensor:
        """Compute score estimate.
        
        Args:
            x: Input state
            t: Time values in [0, 1]
            
        Returns:
            Score estimate ∇log p_t(x) or noise prediction depending on parameterization
        """
        # Pass through network to compute score or noise
        return self.encoder(x, t)
    
    def compute_score_matching_loss(self, x: torch.Tensor, z: torch.Tensor, t: torch.Tensor, 
                                   noise: Optional[torch.Tensor] = None) -> torch.Tensor:
        """Compute conditional score matching loss as in p.29, Algorithm 4.
        
        Args:
            x: Sampled point from p_t(·|z)
            z: Data point
            t: Time value
            noise: Optional noise sample used to create x
            
        Returns:
            Conditional score matching loss
        """
        if isinstance(self.path, GaussianProbPath):
            # For Gaussian paths, we can compute the score analytically
            if self.parameterization == "score":
                # Get target score
                score_target = self.path.get_conditional_score(x, z, t)
                score_pred = self(x, t)
                return F.mse_loss(score_pred, score_target)
            else:  # noise prediction parameterization
                # If noise wasn't provided, compute it
                if noise is None:
                    alpha_t = self.path.alpha_schedule(t)
                    beta_t = self.path.beta_schedule(t)
                    noise = (x - alpha_t * z) / beta_t
                
                # Predict noise directly as in p.29
                noise_pred = self(x, t)
                return F.mse_loss(noise_pred, noise)
        else:
            # For general probability paths
            score_target = self.path.get_conditional_score(x, z, t)
            score_pred = self(x, t)
            return F.mse_loss(score_pred, score_target)
    
    def get_vector_field(self, x: torch.Tensor, t: torch.Tensor, sigma_t: float = 0.0) -> torch.Tensor:
        """Convert score to vector field using Eq. 54 (for Gaussian paths).
        
        This implements the conversion formula from p.30, Proposition 1.
        
        Args:
            x: Input state
            t: Time value
            sigma_t: Diffusion coefficient
            
        Returns:
            Vector field
        """
        if not isinstance(self.path, GaussianProbPath):
            raise ValueError("Conversion only implemented for Gaussian paths")
            
        alpha_t = self.path.alpha_schedule(t)
        beta_t = self.path.beta_schedule(t)
        
        # Compute derivatives
        with torch.enable_grad():
            t_param = t.detach().requires_grad_(True)
            alpha_t_param = self.path.alpha_schedule(t_param)
            beta_t_param = self.path.beta_schedule(t_param)
            
            alpha_dot = torch.autograd.grad(alpha_t_param, t_param, 
                                           torch.ones_like(alpha_t_param))[0]
            beta_dot = torch.autograd.grad(beta_t_param, t_param,
                                          torch.ones_like(beta_t_param))[0]
                
        # Get score
        if self.parameterization == "noise":
            # Convert noise prediction to score
            noise_pred = self(x, t)
            score = -noise_pred / beta_t
        else:
            score = self(x, t)
            
        # Apply conversion formula from p.30, Eq. 54
        coef = (beta_t**2 * alpha_dot/alpha_t - beta_dot*beta_t)
        drift = coef * score + (alpha_dot/alpha_t) * x
        
        # Add diffusion term if needed
        if sigma_t > 0:
            drift = drift + (sigma_t**2 / 2) * score
            
        return drift
