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# Linear Similarity¶

## Functional Interface¶

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

Calculate pairwise linear similarity.

If both and are passed in, the calculation will be performed pairwise between the rows of and . If only is passed in, the calculation will be performed between the rows of .

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_linear_similarity
>>> x = torch.tensor([[2, 3], [3, 5], [5, 8]], dtype=torch.float32)
>>> y = torch.tensor([[1, 0], [2, 1]], dtype=torch.float32)
>>> pairwise_linear_similarity(x, y)
tensor([[ 2.,  7.],
[ 3., 11.],
[ 5., 18.]])
>>> pairwise_linear_similarity(x)
tensor([[ 0., 21., 34.],
[21.,  0., 55.],
[34., 55.,  0.]])

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