Calculate Distance

This section provides examples of how to calculate the distance between vectors and rows in a table. The examples use the books table with the book_embedding column, which contains the embeddings of books.

Overview

Currently we support the following distance functions and distance operators for calculating the distance between vectors.

Distance metric

Distance function

Distance operator

Supported data types

Euclidean

l2sq_dist

<->

REAL[], VECTOR

Cosine

cos_dist

<=>

REAL[], VECTOR

Hamming

hamming_dist

<+>

INTEGER[]

Distance functions

You can use the provided distance functions to calculate the distance between vectors

sql

SELECT l2sq_dist(ARRAY[0,0.1,0], ARRAY[0.5,0.0,0.2]); -- Euclidean
SELECT cos_dist(ARRAY[0,1,0], ARRAY[1,1,1]);          -- Cosine
SELECT hamming_dist(ARRAY[0,1,0], ARRAY[1,1,1]);      -- Hamming

You can also use the provided distance functions to fetch records based on embedding distance without an index. This will run an exact search over all rows.

sql

SELECT title FROM books ORDER BY l2sq_dist(book_embedding, '{0,0,0}') LIMIT 2;

Distance operators

You can use the provided distance operators to calculate the distance between vectors

sql

SELECT ARRAY[0,0.1,0] <-> ARRAY[0.5,0.0,0.2]; -- Euclidean
SELECT ARRAY[0,1,0] <=> ARRAY[1,1,1];         -- Cosine
SELECT ARRAY[0,1,0] <+> ARRAY[1,1,1];         -- Hamming

You can also use the provided distance operators to fetch records based on embedding distance. If there is an index created for the embedding column, this query will use the index. Otherwise, it will run an exact search over all rows.

sql

SELECT title FROM books ORDER BY book_embedding <-> '{0,0,0}' LIMIT 2;

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