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# Linear Similarity¶

## Functional Interface¶

torchmetrics.functional.pairwise_linear_similarity(x, y=None, reduction=None, zero_diagonal=None)[source]

Calculate pairwise linear similarity.

$s_{lin}(x,y) = <x,y> = \sum_{d=1}^D x_d \cdot y_d$

If both $$x$$ and $$y$$ are passed in, the calculation will be performed pairwise between the rows of $$x$$ and $$y$$. If only $$x$$ is passed in, the calculation will be performed between the rows of $$x$$.

Parameters:
Return type:

Tensor

Returns:

A [N,N] matrix of distances if only x is given, else a [N,M] matrix

Example

>>> import torch
>>> from torchmetrics.functional.pairwise import pairwise_linear_similarity
>>> x = torch.tensor([[2, 3], [3, 5], [5, 8]], dtype=torch.float32)
>>> y = torch.tensor([[1, 0], [2, 1]], dtype=torch.float32)
>>> pairwise_linear_similarity(x, y)
tensor([[ 2.,  7.],
[ 3., 11.],
[ 5., 18.]])
>>> pairwise_linear_similarity(x)
tensor([[ 0., 21., 34.],
[21.,  0., 55.],
[34., 55.,  0.]])


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