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# Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the CC-by-NC license found in the
# LICENSE file in the root directory of this source tree.
import math
import torch
from torch import Tensor
from flow_matching.utils.manifolds import Manifold
class FlatTorus(Manifold):
r"""Represents a flat torus on the :math:`[0, 2\pi]^D` subspace. Isometric to the product of 1-D spheres."""
def expmap(self, x: Tensor, u: Tensor) -> Tensor:
return (x + u) % (2 * math.pi)
def logmap(self, x: Tensor, y: Tensor) -> Tensor:
return torch.atan2(torch.sin(y - x), torch.cos(y - x))
def projx(self, x: Tensor) -> Tensor:
return x % (2 * math.pi)
def proju(self, x: Tensor, u: Tensor) -> Tensor:
return u
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