
# 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
