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# Manhattan Distance¶

## Functional Interface¶

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

Calculate pairwise manhattan distance.

$d_{man}(x,y) = ||x-y||_1 = \sum_{d=1}^D |x_d - y_d|$

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_manhattan_distance
>>> x = torch.tensor([[2, 3], [3, 5], [5, 8]], dtype=torch.float32)
>>> y = torch.tensor([[1, 0], [2, 1]], dtype=torch.float32)
>>> pairwise_manhattan_distance(x, y)
tensor([[ 4.,  2.],
[ 7.,  5.],
[12., 10.]])
>>> pairwise_manhattan_distance(x)
tensor([[0., 3., 8.],
[3., 0., 5.],
[8., 5., 0.]])


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