import torch
import torch.nn as nn


class FrequencyPositionalEmbedding(nn.Module):
    """The sin/cosine positional embedding. Given an input tensor `x` of shape [n_batch, ..., c_dim], it converts
    each feature dimension of `x[..., i]` into:
        [
            sin(x[..., i]),
            sin(f_1*x[..., i]),
            sin(f_2*x[..., i]),
            ...
            sin(f_N * x[..., i]),
            cos(x[..., i]),
            cos(f_1*x[..., i]),
            cos(f_2*x[..., i]),
            ...
            cos(f_N * x[..., i]),
            x[..., i]     # only present if include_input is True.
        ], here f_i is the frequency.

    Denote the space is [0 / num_freqs, 1 / num_freqs, 2 / num_freqs, 3 / num_freqs, ..., (num_freqs - 1) / num_freqs].
    If logspace is True, then the frequency f_i is [2^(0 / num_freqs), ..., 2^(i / num_freqs), ...];
    Otherwise, the frequencies are linearly spaced between [1.0, 2^(num_freqs - 1)].

    Args:
        num_freqs (int): the number of frequencies, default is 6;
        logspace (bool): If logspace is True, then the frequency f_i is [..., 2^(i / num_freqs), ...],
            otherwise, the frequencies are linearly spaced between [1.0, 2^(num_freqs - 1)];
        input_dim (int): the input dimension, default is 3;
        include_input (bool): include the input tensor or not, default is True.

    Attributes:
        frequencies (torch.Tensor): If logspace is True, then the frequency f_i is [..., 2^(i / num_freqs), ...],
                otherwise, the frequencies are linearly spaced between [1.0, 2^(num_freqs - 1);

        out_dim (int): the embedding size, if include_input is True, it is input_dim * (num_freqs * 2 + 1),
            otherwise, it is input_dim * num_freqs * 2.

    """

    def __init__(
        self,
        num_freqs: int = 6,
        logspace: bool = True,
        input_dim: int = 3,
        include_input: bool = True,
        include_pi: bool = True,
    ) -> None:
        """The initialization"""

        super().__init__()

        if logspace:
            frequencies = 2.0 ** torch.arange(num_freqs, dtype=torch.float32)
        else:
            frequencies = torch.linspace(
                1.0, 2.0 ** (num_freqs - 1), num_freqs, dtype=torch.float32
            )

        if include_pi:
            frequencies *= torch.pi

        self.register_buffer("frequencies", frequencies, persistent=False)
        self.include_input = include_input
        self.num_freqs = num_freqs

        self.out_dim = self.get_dims(input_dim)

    def get_dims(self, input_dim):
        temp = 1 if self.include_input or self.num_freqs == 0 else 0
        out_dim = input_dim * (self.num_freqs * 2 + temp)

        return out_dim

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        """Forward process.

        Args:
            x: tensor of shape [..., dim]

        Returns:
            embedding: an embedding of `x` of shape [..., dim * (num_freqs * 2 + temp)]
                where temp is 1 if include_input is True and 0 otherwise.
        """

        if self.num_freqs > 0:
            embed = (x[..., None].contiguous() * self.frequencies).view(
                *x.shape[:-1], -1
            )
            if self.include_input:
                return torch.cat((x, embed.sin(), embed.cos()), dim=-1)
            else:
                return torch.cat((embed.sin(), embed.cos()), dim=-1)
        else:
            return x
