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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 abc
import torch.nn as nn
from torch import Tensor
class Manifold(nn.Module, metaclass=abc.ABCMeta):
"""A manifold class that contains projection operations and logarithm and exponential maps."""
@abc.abstractmethod
def expmap(self, x: Tensor, u: Tensor) -> Tensor:
r"""Computes exponential map :math:`\exp_x(u)`.
Args:
x (Tensor): point on the manifold
u (Tensor): tangent vector at point :math:`x`
Raises:
NotImplementedError: if not implemented
Returns:
Tensor: transported point
"""
raise NotImplementedError
@abc.abstractmethod
def logmap(self, x: Tensor, y: Tensor) -> Tensor:
r"""Computes logarithmic map :math:`\log_x(y)`.
Args:
x (Tensor): point on the manifold
y (Tensor): point on the manifold
Raises:
NotImplementedError: if not implemented
Returns:
Tensor: tangent vector at point :math:`x`
"""
raise NotImplementedError
@abc.abstractmethod
def projx(self, x: Tensor) -> Tensor:
"""Project point :math:`x` on the manifold.
Args:
x (Tensor): point to be projected
Raises:
NotImplementedError: if not implemented
Returns:
Tensor: projected point on the manifold
"""
raise NotImplementedError
@abc.abstractmethod
def proju(self, x: Tensor, u: Tensor) -> Tensor:
"""Project vector :math:`u` on a tangent space for :math:`x`.
Args:
x (Tensor): point on the manifold
u (Tensor): vector to be projected
Raises:
NotImplementedError: if not implemented
Returns:
Tensor: projected tangent vector
"""
raise NotImplementedError
class Euclidean(Manifold):
"""The Euclidean manifold."""
def expmap(self, x: Tensor, u: Tensor) -> Tensor:
return x + u
def logmap(self, x: Tensor, y: Tensor) -> Tensor:
return y - x
def projx(self, x: Tensor) -> Tensor:
return x
def proju(self, x: Tensor, u: Tensor) -> Tensor:
return u
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