# Cosine Similarity¶

## Functional Interface¶

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

Calculate pairwise cosine similarity.

$s_{cos}(x,y) = \frac{<x,y>}{||x|| \cdot ||y||} = \frac{\sum_{d=1}^D x_d \cdot y_d }{\sqrt{\sum_{d=1}^D x_i^2} \cdot \sqrt{\sum_{d=1}^D y_i^2}}$

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:
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_cosine_similarity
>>> x = torch.tensor([[2, 3], [3, 5], [5, 8]], dtype=torch.float32)
>>> y = torch.tensor([[1, 0], [2, 1]], dtype=torch.float32)
>>> pairwise_cosine_similarity(x, y)
tensor([[0.5547, 0.8682],
[0.5145, 0.8437],
[0.5300, 0.8533]])
>>> pairwise_cosine_similarity(x)
tensor([[0.0000, 0.9989, 0.9996],
[0.9989, 0.0000, 0.9998],
[0.9996, 0.9998, 0.0000]])