from typing import Optional

from torch import Tensor
from torch_sparse import SparseTensor, matmul

from torch_geometric.nn.conv import MessagePassing
from torch_geometric.nn.conv.gcn_conv import gcn_norm
from torch_geometric.nn.dense.linear import Linear
from torch_geometric.typing import Adj, OptTensor


class SGConv(MessagePassing):
    r"""The simple graph convolutional operator from the `"Simplifying Graph
    Convolutional Networks" <https://arxiv.org/abs/1902.07153>`_ paper

    .. math::
        \mathbf{X}^{\prime} = {\left(\mathbf{\hat{D}}^{-1/2} \mathbf{\hat{A}}
        \mathbf{\hat{D}}^{-1/2} \right)}^K \mathbf{X} \mathbf{\Theta},

    where :math:`\mathbf{\hat{A}} = \mathbf{A} + \mathbf{I}` denotes the
    adjacency matrix with inserted self-loops and
    :math:`\hat{D}_{ii} = \sum_{j=0} \hat{A}_{ij}` its diagonal degree matrix.
    The adjacency matrix can include other values than :obj:`1` representing
    edge weights via the optional :obj:`edge_weight` tensor.

    Args:
        in_channels (int): Size of each input sample, or :obj:`-1` to derive
            the size from the first input(s) to the forward method.
        out_channels (int): Size of each output sample.
        K (int, optional): Number of hops :math:`K`. (default: :obj:`1`)
        cached (bool, optional): If set to :obj:`True`, the layer will cache
            the computation of :math:`{\left(\mathbf{\hat{D}}^{-1/2}
            \mathbf{\hat{A}} \mathbf{\hat{D}}^{-1/2} \right)}^K \mathbf{X}` on
            first execution, and will use the cached version for further
            executions.
            This parameter should only be set to :obj:`True` in transductive
            learning scenarios. (default: :obj:`False`)
        add_self_loops (bool, optional): If set to :obj:`False`, will not add
            self-loops to the input graph. (default: :obj:`True`)
        bias (bool, optional): If set to :obj:`False`, the layer will not learn
            an additive bias. (default: :obj:`True`)
        **kwargs (optional): Additional arguments of
            :class:`torch_geometric.nn.conv.MessagePassing`.

    Shapes:
        - **input:**
          node features :math:`(|\mathcal{V}|, F_{in})`,
          edge indices :math:`(2, |\mathcal{E}|)`,
          edge weights :math:`(|\mathcal{E}|)` *(optional)*
        - **output:**
          node features :math:`(|\mathcal{V}|, F_{out})`
    """

    _cached_x: Optional[Tensor]

    def __init__(self, in_channels: int, out_channels: int, K: int = 1,
                 cached: bool = False, add_self_loops: bool = True,
                 bias: bool = True, **kwargs):
        kwargs.setdefault('aggr', 'add')
        super().__init__(**kwargs)

        self.in_channels = in_channels
        self.out_channels = out_channels
        self.K = K
        self.cached = cached
        self.add_self_loops = add_self_loops

        self._cached_x = None

        self.lin = Linear(in_channels, out_channels, bias=bias)

        self.reset_parameters()

    def reset_parameters(self):
        self.lin.reset_parameters()
        self._cached_x = None

    def forward(self, x: Tensor, edge_index: Adj,
                edge_weight: OptTensor = None) -> Tensor:
        """"""
        cache = self._cached_x
        if cache is None:
            if isinstance(edge_index, Tensor):
                edge_index, edge_weight = gcn_norm(  # yapf: disable
                    edge_index, edge_weight, x.size(self.node_dim), False,
                    self.add_self_loops, self.flow, dtype=x.dtype)
            elif isinstance(edge_index, SparseTensor):
                edge_index = gcn_norm(  # yapf: disable
                    edge_index, edge_weight, x.size(self.node_dim), False,
                    self.add_self_loops, self.flow, dtype=x.dtype)

            for k in range(self.K):
                # propagate_type: (x: Tensor, edge_weight: OptTensor)
                x = self.propagate(edge_index, x=x, edge_weight=edge_weight,
                                   size=None)
                if self.cached:
                    self._cached_x = x
        else:
            x = cache.detach()

        return self.lin(x)

    def message(self, x_j: Tensor, edge_weight: Tensor) -> Tensor:
        return edge_weight.view(-1, 1) * x_j

    def message_and_aggregate(self, adj_t: SparseTensor, x: Tensor) -> Tensor:
        return matmul(adj_t, x, reduce=self.aggr)

    def __repr__(self) -> str:
        return (f'{self.__class__.__name__}({self.in_channels}, '
                f'{self.out_channels}, K={self.K})')
