import numpy as np
import torch
from torch import Tensor
import torch.nn as nn

@torch.jit.script
def positional_encoding(
        v: Tensor,
        sigma: float,
        m: int) -> Tensor:
    r"""Computes :math:`\gamma(\mathbf{v}) = (\dots, \cos{2 \pi \sigma^{(j/m)} \mathbf{v}} , \sin{2 \pi \sigma^{(j/m)} \mathbf{v}}, \dots)`
        where :math:`j \in \{0, \dots, m-1\}`

    Args:
        v (Tensor): input tensor of shape :math:`(N, *, \text{input_size})`
        sigma (float): constant chosen based upon the domain of :attr:`v`
        m (int): [description]

    Returns:
        Tensor: mapped tensor of shape :math:`(N, *, 2 \cdot m \cdot \text{input_size})`

    See :class:`~rff.layers.PositionalEncoding` for more details.
    """
    j = torch.arange(m, device=v.device)
    coeffs = 2 * np.pi * sigma ** (j / m)
    vp = coeffs * torch.unsqueeze(v, -1)
    vp_cat = torch.cat((torch.cos(vp), torch.sin(vp)), dim=-1)
    return vp_cat.flatten(-2, -1)


class PositionalEncoding(nn.Module):
    """Layer for mapping coordinates using the positional encoding"""

    def __init__(self, sigma: float, m: int):
        r"""
        Args:
            sigma (float): frequency constant
            m (int): number of frequencies to map to
        """
        super().__init__()
        self.sigma = sigma
        self.m = m

    def forward(self, v: Tensor) -> Tensor:
        r"""Computes :math:`\gamma(\mathbf{v}) = (\dots, \cos{2 \pi \sigma^{(j/m)} \mathbf{v}} , \sin{2 \pi \sigma^{(j/m)} \mathbf{v}}, \dots)`

        Args:
            v (Tensor): input tensor of shape :math:`(N, *, \text{input_size})`

        Returns:
            Tensor: mapped tensor of shape :math:`(N, *, 2 \cdot m \cdot \text{input_size})`
        """
        return positional_encoding(v, self.sigma, self.m)