
"""
Coupling Flow Integrator ("The Perfect Integrator").
Based on Normalizing Flows (NICE/RealNVP).
Uses separate coupling layers for Position and Velocity to guarantee exactly geometric volume preservation.
Jacobian Determinant is strictly 1.0.

Structure:
    v' = v + F(x)  (Shear transformation on v)
    x' = x + G(v') (Shear transformation on x)
    
This requires F(x) to be INDEPENDENT of v.
Standard Christoffel symbols \Gamma(v, x) are quadratic in v.
To enforce "Perfect" symplectic behavior (separable Hamiltonian logic),
we approximate the force F(x) by evaluating \Gamma at v=0 (or a learned proxy).
"""
import torch
import torch.nn as nn

try:
    from gfn.geometry.boundaries import apply_boundary_python
except ImportError:
    def apply_boundary_python(x, tid): return x

class CouplingFlowIntegrator(nn.Module):
    def __init__(self, christoffel, dt=0.01):
        super().__init__()
        self.christoffel = christoffel
        self.dt = dt
        
        # "Drift" Network (The Warper)
        # In standard physics, x' = x + v*dt. This is linear drift.
        # In a coupling flow, we can use x' = x + G(v).
        # We learn a small residual MLP to warp space-time based on velocity.
        # This makes the "mass" effective dynamic (Special Relativity vibe).
        # Automatic dimension discovery
        if hasattr(christoffel, 'dim'):
            self.dim = christoffel.dim
        elif hasattr(christoffel, 'W') and christoffel.W is not None:
             self.dim = christoffel.W.shape[0]
        else:
            self.dim = 16 # Fallback
             
        self.drift_net = nn.Sequential(
            nn.Linear(self.dim, self.dim),
            nn.Tanh(),
            nn.Linear(self.dim, self.dim)
        )
        # Init as near-zero to start with standard kinematics
        nn.init.zeros_(self.drift_net[2].weight)
        nn.init.zeros_(self.drift_net[2].bias)

    def forward(self, x, v, force=None, dt_scale=1.0, steps=1, collect_christ=False, **kwargs):
        # Determine Topology
        topo_id = getattr(self.christoffel, 'topology_id', 0)
        if topo_id == 0 and hasattr(self.christoffel, 'is_torus') and self.christoffel.is_torus:
                topo_id = 1

        # We can approximate coupling flow with Verlet fused if needed, but it's logically different
        # For now, standard Python loop for stability
        for _ in range(steps):
            dt = self.dt * dt_scale
            
            if force is None:
                f_in = torch.zeros_like(x)
            else:
                f_in = force
                
            # Symmetric Splitting (Verification)
            v_dummy = torch.zeros_like(x)
            acc_1 = -self.christoffel(v_dummy, x, force=f_in, **kwargs) + f_in
            v_half = v + 0.5 * dt * acc_1
            
            warp = self.drift_net(v_half)
            x = x + dt * (v_half + warp)
            
            # Apply Boundary (Torus)
            x = apply_boundary_python(x, topo_id)
            
            acc_2 = -self.christoffel(v_dummy, x, force=f_in, **kwargs) + f_in
            v = v_half + 0.5 * dt * acc_2
            
        return x, v
