import torch
import torch.nn as nn
from torch_geometric.nn import MessagePassing


class FiniteDifferenceStep(MessagePassing):
    """
    TODO: add docstring.
    """

    def __init__(self, aggr: str = "add", root_weight: float = 1.0):
        super().__init__(aggr=aggr)
        assert (
            aggr == "add"
        ), "Per somme pesate, l'aggregazione deve essere 'add'."
        # self.root_weight = float(root_weight)
        self.p = torch.nn.Parameter(torch.tensor(0.8))
        self.a = root_weight

    def forward(self, x, edge_index, edge_attr, deg):
        """
        TODO: add docstring.
        """
        out = self.propagate(edge_index, x=x, edge_attr=edge_attr, deg=deg)
        return out

    def message(self, x_j, edge_attr):
        """
        TODO: add docstring.
        """
        p = torch.clamp(self.p, 0.0, 1.0)
        return p * edge_attr.view(-1, 1) * x_j

    def aggregate(self, inputs, index, deg):
        """
        TODO: add docstring.
        """
        out = super().aggregate(inputs, index)
        deg = deg + 1e-7
        return out / deg.view(-1, 1)

    def update(self, aggr_out, x):
        """
        TODO: add docstring.
        """
        a = torch.clamp(self.a, 0.0, 1.0)
        return a * aggr_out + (1 - a) * x
        # return self.a * aggr_out + (1 - self.a) * x


class GraphFiniteDifference(nn.Module):
    """
    TODO: add docstring.
    """

    def __init__(self, max_iters: int = 5000, threshold: float = 1e-4):
        """
        TODO: add docstring.
        """
        super().__init__()
        self.max_iters = max_iters
        self.threshold = threshold
        self.fd_step = FiniteDifferenceStep(aggr="add", root_weight=1.0)

    @staticmethod
    def _compute_deg(edge_index, edge_attr, num_nodes):
        """
        TODO: add docstring.
        """
        deg = torch.zeros(num_nodes, device=edge_index.device)
        deg = deg.scatter_add(0, edge_index[1], edge_attr)
        return deg + 1e-7

    @staticmethod
    def _compute_c_ij(c, edge_index):
        """
        TODO: add docstring.
        """
        return (0.5 * (c[edge_index[0]] + c[edge_index[1]])).squeeze()

    def forward(
        self,
        x,
        edge_index,
        edge_attr,
        c,
        boundary_mask,
        boundary_values,
        **kwargs,
    ):
        """
        TODO: add docstring.
        """
        edge_attr = 1 / edge_attr[:, -1]
        c_ij = self._compute_c_ij(c, edge_index)
        edge_attr = edge_attr * c_ij
        deg = self._compute_deg(edge_index, edge_attr, x.size(0))

        # Calcola la soglia staccando x dal grafo
        conv_thres = self.threshold * torch.norm(x.detach())

        for _i in range(self.max_iters):
            out = self.fd_step(x, edge_index, edge_attr, deg)
            out[boundary_mask] = boundary_values.unsqueeze(-1)

            # Controllo convergenza senza tracciamento gradienti
            with torch.no_grad():
                residual_norm = torch.norm(out - x)

            if residual_norm < conv_thres:
                break

            # --- OTTIMIZZAZIONE CHIAVE ---
            # Stacca 'out' dal grafo prima della prossima iterazione
            # per evitare BPTT e risparmiare memoria.
            x = out.detach()

        # Il 'out' finale restituito mantiene i gradienti
        # dell'ULTIMA chiamata a fd_step, permettendo al modello
        # di apprendere correttamente.
        return out, _i + 1