# Minkowski Distance¶

## Functional Interface¶

torchmetrics.functional.pairwise_minkowski_distance(x, y=None, exponent=2, reduction=None, zero_diagonal=None)[source]

Calculate pairwise minkowski distances.

$d_{minkowski}(x,y,p) = ||x - y||_p = \sqrt[p]{\sum_{d=1}^D (x_d - y_d)^p}$

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_minkowski_distance
>>> x = torch.tensor([[2, 3], [3, 5], [5, 8]], dtype=torch.float32)
>>> y = torch.tensor([[1, 0], [2, 1]], dtype=torch.float32)
>>> pairwise_minkowski_distance(x, y, exponent=4)
tensor([[3.0092, 2.0000],
[5.0317, 4.0039],
[8.1222, 7.0583]])
>>> pairwise_minkowski_distance(x, exponent=4)
tensor([[0.0000, 2.0305, 5.1547],
[2.0305, 0.0000, 3.1383],
[5.1547, 3.1383, 0.0000]])