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


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

    def __init__(
        self,
        aggr: str = "add",
        normalize: bool = True,
        root_weight: float = 1.0,
    ):
        super().__init__(aggr=aggr)

        self.normalize = normalize
        assert (
            aggr == "add"
        ), "Per somme pesate, l'aggregazione deve essere 'add'."
        self.root_weight = float(root_weight)

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

    def message(self, x_j, edge_weight):
        """
        TODO: add docstring.
        """
        return edge_weight.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.
        """
        return self.root_weight * aggr_out + (1 - self.root_weight) * x


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

    def __init__(self, max_iters: int = 1000, threshold: float = 1e-4):
        """
        TODO: add docstring.
        """
        super().__init__()
        self.max_iters = max_iters
        self.threshold = threshold
        self.fd_step = FiniteDifferenceStep(
            aggr="add", normalize=True, root_weight=1.0
        )

    @staticmethod
    def _compute_deg(edge_index, edge_weight, num_nodes):
        """
        TODO: add docstring.
        """
        deg = torch.zeros(num_nodes, device=edge_index.device)
        deg = deg.scatter_add(0, edge_index[1], edge_weight)
        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_weight, c, boundary_mask, boundary_values
    ):
        """
        TODO: add docstring.
        """
        c_ij = self._compute_c_ij(c, edge_index)
        edge_weight = edge_weight * c_ij
        deg = self._compute_deg(edge_index, edge_weight, x.size(0))
        conv_thres = self.threshold * torch.norm(x)
        for _i in tqdm(range(self.max_iters)):
            out = self.fd_step(x, edge_index, edge_weight, deg)
            out[boundary_mask] = boundary_values.unsqueeze(-1)
            if torch.norm(out - x) < conv_thres:
                break
            x = out
        return out