import torch
from torch_scatter import scatter_add
from torch_geometric.utils import add_self_loops, remove_self_loops

from .num_nodes import maybe_num_nodes


def get_laplacian(edge_index, edge_weight=None, normalization=None, dtype=None,
                  num_nodes=None):
    r""" Computes the graph Laplacian of the graph given by :obj:`edge_index`
    and optional :obj:`edge_weight`.

    Args:
        edge_index (LongTensor): The edge indices.
        edge_weight (Tensor, optional): One-dimensional edge weights.
            (default: :obj:`None`)
        normalization (str, optional): The normalization scheme for the graph
            Laplacian (default: :obj:`None`):

            1. :obj:`None`: No normalization
            :math:`\mathbf{L} = \mathbf{D} - \mathbf{A}`

            2. :obj:`"sym"`: Symmetric normalization
            :math:`\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1/2} \mathbf{A}
            \mathbf{D}^{-1/2}`

            3. :obj:`"rw"`: Random-walk normalization
            :math:`\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1} \mathbf{A}`
        dtype (torch.dtype, optional): The desired data type of returned tensor
            in case :obj:`edge_weight=None`. (default: :obj:`None`)
        num_nodes (int, optional): The number of nodes, *i.e.*
            :obj:`max_val + 1` of :attr:`edge_index`. (default: :obj:`None`)
    """

    assert normalization in [None, 'sym', 'rw'], 'Invalid normalization'

    edge_index, edge_weight = remove_self_loops(edge_index, edge_weight)

    if edge_weight is None:
        edge_weight = torch.ones(edge_index.size(1), dtype=dtype,
                                 device=edge_index.device)

    num_nodes = maybe_num_nodes(edge_index, num_nodes)

    row, col = edge_index
    deg = scatter_add(edge_weight, row, dim=0, dim_size=num_nodes)

    if normalization is None:
        # L = D - A.
        edge_index, _ = add_self_loops(edge_index, num_nodes=num_nodes)
        edge_weight = torch.cat([-edge_weight, deg], dim=0)
    elif normalization == 'sym':
        # Compute A_norm = -D^{-1/2} A D^{-1/2}.
        deg_inv_sqrt = deg.pow(-0.5)
        deg_inv_sqrt[deg_inv_sqrt == float('inf')] = 0
        edge_weight = deg_inv_sqrt[row] * edge_weight * deg_inv_sqrt[col]

        # L = I - A_norm.
        edge_index, edge_weight = add_self_loops(edge_index, -edge_weight,
                                                 fill_value=1,
                                                 num_nodes=num_nodes)
    else:
        # Compute A_norm = -D^{-1} A.
        deg_inv = 1.0 / deg
        deg_inv[deg_inv == float('inf')] = 0
        edge_weight = deg_inv[row] * edge_weight

        # L = I - A_norm.
        edge_index, edge_weight = add_self_loops(edge_index, -edge_weight,
                                                 fill_value=1,
                                                 num_nodes=num_nodes)

    return edge_index, edge_weight
