Euclidean Distance

Functional Interface

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

Calculate pairwise euclidean distances.

d_{e u c} (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:

x (Tensor) – Tensor with shape [N, d]
y (Optional[Tensor]) – Tensor with shape [M, d], optional
reduction (Optional[Literal['mean', 'sum', 'none', None]]) – reduction to apply along the last dimension. Choose between ‘mean’, ‘sum’ (applied along column dimension) or ‘none’, None for no reduction
zero_diagonal (Optional[bool]) – if the diagonal of the distance matrix should be set to 0. If only x is given this defaults to True else if y is also given it defaults to False

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]])