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from .module import Module
from .. import functional as F
from torch import Tensor
__all__ = ['PairwiseDistance', 'CosineSimilarity']
class PairwiseDistance(Module):
r"""
Computes the pairwise distance between input vectors, or between columns of input matrices.
Distances are computed using ``p``-norm, with constant ``eps`` added to avoid division by zero
if ``p`` is negative, i.e.:
.. math ::
\mathrm{dist}\left(x, y\right) = \left\Vert x-y + \epsilon e \right\Vert_p,
where :math:`e` is the vector of ones and the ``p``-norm is given by.
.. math ::
\Vert x \Vert _p = \left( \sum_{i=1}^n \vert x_i \vert ^ p \right) ^ {1/p}.
Args:
p (real, optional): the norm degree. Can be negative. Default: 2
eps (float, optional): Small value to avoid division by zero.
Default: 1e-6
keepdim (bool, optional): Determines whether or not to keep the vector dimension.
Default: False
Shape:
- Input1: :math:`(N, D)` or :math:`(D)` where `N = batch dimension` and `D = vector dimension`
- Input2: :math:`(N, D)` or :math:`(D)`, same shape as the Input1
- Output: :math:`(N)` or :math:`()` based on input dimension.
If :attr:`keepdim` is ``True``, then :math:`(N, 1)` or :math:`(1)` based on input dimension.
Examples::
>>> pdist = nn.PairwiseDistance(p=2)
>>> input1 = torch.randn(100, 128)
>>> input2 = torch.randn(100, 128)
>>> output = pdist(input1, input2)
"""
__constants__ = ['norm', 'eps', 'keepdim']
norm: float
eps: float
keepdim: bool
def __init__(self, p: float = 2., eps: float = 1e-6, keepdim: bool = False) -> None:
super().__init__()
self.norm = p
self.eps = eps
self.keepdim = keepdim
def forward(self, x1: Tensor, x2: Tensor) -> Tensor:
return F.pairwise_distance(x1, x2, self.norm, self.eps, self.keepdim)
class CosineSimilarity(Module):
r"""Returns cosine similarity between :math:`x_1` and :math:`x_2`, computed along `dim`.
.. math ::
\text{similarity} = \dfrac{x_1 \cdot x_2}{\max(\Vert x_1 \Vert _2 \cdot \Vert x_2 \Vert _2, \epsilon)}.
Args:
dim (int, optional): Dimension where cosine similarity is computed. Default: 1
eps (float, optional): Small value to avoid division by zero.
Default: 1e-8
Shape:
- Input1: :math:`(\ast_1, D, \ast_2)` where D is at position `dim`
- Input2: :math:`(\ast_1, D, \ast_2)`, same number of dimensions as x1, matching x1 size at dimension `dim`,
and broadcastable with x1 at other dimensions.
- Output: :math:`(\ast_1, \ast_2)`
Examples::
>>> input1 = torch.randn(100, 128)
>>> input2 = torch.randn(100, 128)
>>> cos = nn.CosineSimilarity(dim=1, eps=1e-6)
>>> output = cos(input1, input2)
"""
__constants__ = ['dim', 'eps']
dim: int
eps: float
def __init__(self, dim: int = 1, eps: float = 1e-8) -> None:
super().__init__()
self.dim = dim
self.eps = eps
def forward(self, x1: Tensor, x2: Tensor) -> Tensor:
return F.cosine_similarity(x1, x2, self.dim, self.eps)
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