import torch


def build_relative_position(query_size, key_size, device):
    """
    Build relative position according to the query and key

    We assume the absolute position of query \\(P_q\\) is range from (0, query_size) and the absolute position of key
    \\(P_k\\) is range from (0, key_size), The relative positions from query to key is \\(R_{q \\rightarrow k} =
    P_q - P_k\\)

    Args:
        query_size (int): the length of query
        key_size (int): the length of key

    Return:
        `torch.LongTensor`: A tensor with shape [1, query_size, key_size]

    """

    q_ids = torch.arange(query_size, dtype=torch.long, device=device)
    k_ids = torch.arange(key_size, dtype=torch.long, device=device)
    rel_pos_ids = q_ids[:, None] - k_ids.view(1, -1).repeat(query_size, 1)
    rel_pos_ids = rel_pos_ids[:query_size, :]
    rel_pos_ids = rel_pos_ids.unsqueeze(0)
    return rel_pos_ids