Description
The VECTOR_DOT_PRODUCT function finds the dot product of two input vectors. These vectors must be of a numeric type, either integer, double, or decimal. The result is the value of the dot product, represented as a double, and can be useful when trying to determine the similarity between two vectors.
The dot product of two vectors is the sum of the products of each pair of elements in the same position of the two input vectors. The formula for this calculation is presented below:
If the input vectors are unit vectors, the dot product is the same value as the cosine of the angle between the two vectors. The larger the dot product, the more similar the vectors are. InterSystems recommends using this function when operating on unit vectors, as the calculation takes advantage of the efficiency of the VECTOR type.
To find the similarity between two vectors that are not unit vectors, use the VECTOR_COSINE function.
Examples
The following example uses the VECTOR_DOT_PRODUCT function on two integer vectors.
SELECT VECTOR_DOT_PRODUCT(TO_VECTOR('6,4,5',integer), TO_VECTOR('1,4,3',integer))
The following example uses the VECTOR_DOT_PRODUCT function to return the text descriptions that are most similar to the results based on the similarity between the vector stored in each row and an input vector. In reality, an embedding vector has many more than three elements; however, for the sake of keeping this example brief, the embedding vector is represented as having three elements.
SELECT TOP 5 Description FROM Sample.DescAndEmbedding emb
ORDER BY VECTOR_COSINE(Embedding,TO_VECTOR('1,1,1',double)) DESC
