Manhattan Distance

Functional Interface

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

Calculate pairwise manhattan distance.

d_{m a n} (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:

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_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.]])