"""
Various positional encodings for the transformer.
"""
import math
import torch
from torch import nn

def PE1d_sincos(seq_length, dim):
    """
    :param d_model: dimension of the model
    :param length: length of positions
    :return: length*d_model position matrix
    """
    if dim % 2 != 0:
        raise ValueError("Cannot use sin/cos positional encoding with "
                         "odd dim (got dim={:d})".format(dim))
    pe = torch.zeros(seq_length, dim)
    position = torch.arange(0, seq_length).unsqueeze(1)
    div_term = torch.exp((torch.arange(0, dim, 2, dtype=torch.float) *
                         -(math.log(10000.0) / dim)))
    pe[:, 0::2] = torch.sin(position.float() * div_term)
    pe[:, 1::2] = torch.cos(position.float() * div_term)

    return pe.unsqueeze(1)


class PositionEmbedding(nn.Module):
    """
    Absolute pos embedding (standard), learned.
    """
    def __init__(self, seq_length, dim, dropout, grad=False):
        super().__init__()
        self.embed = nn.Parameter(data=PE1d_sincos(seq_length, dim), requires_grad=grad)
        self.dropout = nn.Dropout(p=dropout)
        
    def forward(self, x):
        # x.shape: bs, seq_len, feat_dim
        l = x.shape[1]
        x = x.permute(1, 0, 2) + self.embed[:l].expand(x.permute(1, 0, 2).shape)
        x = self.dropout(x.permute(1, 0, 2))
        return x