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Euclidean Distance

Functional Interface

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

Calculates 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
  • 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 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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