
# Copyright (c) 2024 WeatherFlow
# Implementation inspired by Meta's flow matching approach

import torch
from torch import Tensor
from typing import Callable, Optional, Tuple
from torchdiffeq import odeint

class WeatherODESolver:
    """ODE solver for weather flow matching with physics constraints."""
    
    def __init__(
        self,
        rtol: float = 1e-5,
        atol: float = 1e-5,
        method: str = 'dopri5',
        physics_constraints: bool = True
    ):
        self.rtol = rtol
        self.atol = atol
        self.method = method
        self.physics_constraints = physics_constraints
    
    def solve(
        self,
        velocity_fn: Callable,
        x0: Tensor,
        t_span: Tensor,
        **kwargs
    ) -> Tuple[Tensor, dict]:
        """Solve the ODE system with weather-specific handling.
        
        Args:
            velocity_fn: Function computing velocity field
            x0: Initial conditions
            t_span: Time points to solve for
            **kwargs: Additional args for velocity function
            
        Returns:
            Tuple of (solution trajectory, solver stats)
        """
        def ode_func(t: Tensor, x: Tensor) -> Tensor:
            # Compute velocity field
            v = velocity_fn(x, t, **kwargs)
            
            if self.physics_constraints:
                # Apply physics constraints (conservation laws)
                v = self._apply_physics_constraints(v, x)
            
            return v
        
        solution = odeint(
            ode_func,
            x0,
            t_span,
            rtol=self.rtol,
            atol=self.atol,
            method=self.method
        )
        
        return solution, {"success": True}  # Add more stats as needed
    
    def _apply_physics_constraints(self, v: Tensor, x: Tensor) -> Tensor:
        """Apply physics-based constraints to velocity field.
        
        Currently implements:
        - Mass conservation
        - Energy conservation (approximate)
        """
        # Mass conservation: ensure velocity field is divergence-free
        # This is a simplified version - would need proper spherical operators
        if v.dim() > 2:
            div = torch.zeros_like(v)
            div[..., :-1] = torch.diff(v, dim=-1)
            v = v - div
        
        # Energy conservation: soft constraint via normalization
        v_norm = torch.norm(v, dim=-1, keepdim=True)
        v = torch.where(v_norm > 1.0, v / v_norm, v)
        
        return v

    def solve_heun(
        self,
        velocity_fn: Callable,
        x0: Tensor,
        t_span: Tensor,
        **kwargs
    ) -> Tensor:
        """Solve ODE using Heun's method (p.8).
        
        Args:
            velocity_fn: Function computing velocity field
            x0: Initial conditions
            t_span: Time points to solve for
            
        Returns:
            ODE solution trajectory
        """
        device = x0.device
        dtype = x0.dtype
        n_steps = len(t_span)
        solution = torch.zeros((n_steps, *x0.shape), device=device, dtype=dtype)
        solution[0] = x0
        
        for i in range(1, n_steps):
            dt = t_span[i] - t_span[i-1]
            x = solution[i-1]
            t = t_span[i-1]
            
            # Initial guess
            x_prime = x + dt * velocity_fn(x, t, **kwargs)
            
            # Correction step
            solution[i] = x + 0.5 * dt * (velocity_fn(x, t, **kwargs) + 
                                        velocity_fn(x_prime, t + dt, **kwargs))
        
        return solution
    
    def ode_to_sde(
        self,
        ode_fn: Callable, 
        score_fn: Callable, 
        sigma_t: Callable[[Tensor], Tensor]
    ) -> Callable:
        """Convert an ODE to its equivalent SDE with the same marginal distribution.
        
        Implements Theorem 13 from p.19.
        
        Args:
            ode_fn: Function computing ODE vector field
            score_fn: Function computing score ∇log p_t
            sigma_t: Function mapping time to diffusion coefficient
            
        Returns:
            SDE drift function
        """
        def sde_drift_fn(x: Tensor, t: Tensor) -> Tensor:
            """Compute the SDE drift term.
            
            Args:
                x: Current state
                t: Current time
                
            Returns:
                SDE drift term
            """
            sigma_val = sigma_t(t)
            ode_term = ode_fn(x, t)
            score_term = score_fn(x, t)
            
            # Formula from Theorem 13, Eq. 25
            return ode_term + (sigma_val**2 / 2) * score_term
        
        return sde_drift_fn
