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# Euclidean Distance¶

## Functional Interface¶

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

Calculate pairwise euclidean distances.

$d_{euc}(x,y) = ||x - y||_2 = \sqrt{\sum_{d=1}^D (x_d - y_d)^2}$

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_euclidean_distance
>>> x = torch.tensor([[2, 3], [3, 5], [5, 8]], dtype=torch.float32)
>>> y = torch.tensor([[1, 0], [2, 1]], dtype=torch.float32)
>>> pairwise_euclidean_distance(x, y)
tensor([[3.1623, 2.0000],
[5.3852, 4.1231],
[8.9443, 7.6158]])
>>> pairwise_euclidean_distance(x)
tensor([[0.0000, 2.2361, 5.8310],
[2.2361, 0.0000, 3.6056],
[5.8310, 3.6056, 0.0000]])


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