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# Source code for torch.nn.modules.distance

from .module import Module
from .. import functional as F

from torch import Tensor

__all__ = ['PairwiseDistance', 'CosineSimilarity']

[docs]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)

[docs]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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