# Copyright (c) Facebook, Inc. and its affiliates.
# All rights reserved.
#
# This source code is licensed under the BSD-style license found in the
# LICENSE file in the root directory of this source tree.

import torch


class HarmonicEmbedding(torch.nn.Module):
    def __init__(
        self,
        n_harmonic_functions: int = 6,
        omega_0: float = 1.0,
        logspace: bool = True,
        append_input: bool = True,
    ) -> None:
        """
        Given an input tensor `x` of shape [minibatch, ... , dim],
        the harmonic embedding layer converts each feature
        (i.e. vector along the last dimension) in `x`
        into a series of harmonic features `embedding`,
        where for each i in range(dim) the following are present
        in embedding[...]:
            ```
            [
                sin(f_1*x[..., i]),
                sin(f_2*x[..., i]),
                ...
                sin(f_N * x[..., i]),
                cos(f_1*x[..., i]),
                cos(f_2*x[..., i]),
                ...
                cos(f_N * x[..., i]),
                x[..., i],              # only present if append_input is True.
            ]
            ```
        where N corresponds to `n_harmonic_functions-1`, and f_i is a scalar
        denoting the i-th frequency of the harmonic embedding.

        If `logspace==True`, the frequencies `[f_1, ..., f_N]` are
        powers of 2:
            `f_1, ..., f_N = 2**torch.arange(n_harmonic_functions)`

        If `logspace==False`, frequencies are linearly spaced between
        `1.0` and `2**(n_harmonic_functions-1)`:
            `f_1, ..., f_N = torch.linspace(
                1.0, 2**(n_harmonic_functions-1), n_harmonic_functions
            )`

        Note that `x` is also premultiplied by the base frequency `omega_0`
        before evaluating the harmonic functions.

        Args:
            n_harmonic_functions: int, number of harmonic
                features
            omega_0: float, base frequency
            logspace: bool, Whether to space the frequencies in
                logspace or linear space
            append_input: bool, whether to concat the original
                input to the harmonic embedding. If true the
                output is of the form (x, embed.sin(), embed.cos()

        """
        super().__init__()

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

        self.register_buffer("_frequencies", frequencies * omega_0, persistent=False)
        self.append_input = append_input

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        """
        Args:
            x: tensor of shape [..., dim]
        Returns:
            embedding: a harmonic embedding of `x`
                of shape [..., (n_harmonic_functions * 2 + int(append_input)) * dim]
        """
        embed = (x[..., None] * self._frequencies).view(*x.shape[:-1], -1)
        embed = torch.cat(
            (embed.sin(), embed.cos(), x)
            if self.append_input
            else (embed.sin(), embed.cos()),
            dim=-1,
        )
        return embed

    @staticmethod
    def get_output_dim_static(
        input_dims: int,
        n_harmonic_functions: int,
        append_input: bool,
    ) -> int:
        """
        Utility to help predict the shape of the output of `forward`.

        Args:
            input_dims: length of the last dimension of the input tensor
            n_harmonic_functions: number of embedding frequencies
            append_input: whether or not to concat the original
                input to the harmonic embedding
        Returns:
            int: the length of the last dimension of the output tensor
        """
        return input_dims * (2 * n_harmonic_functions + int(append_input))

    def get_output_dim(self, input_dims: int = 3) -> int:
        """
        Same as above. The default for input_dims is 3 for 3D applications
        which use harmonic embedding for positional encoding,
        so the input might be xyz.
        """
        return self.get_output_dim_static(
            input_dims, len(self._frequencies), self.append_input
        )
