Using Vector Functions

Data type suffixes

The vector functions present a 32-byte floating-point integer data type by default. The data type for vector functions can be changed by using type suffixes:

• _I8 - 8-byte signed integer

• _I16 - 16-byte signed integer

• _I32 - 32-byte signed integer

• _I64 - 64-byte signed integer

• _F32 - 32-byte floating-point number (this is the default)

• _F64 - 64-byte floating-point number

Inserting Vectors as Blobs from an External Application

As a best practice when inserting binary data into a table from an external application, first convert a vector blob to its hexadecimal representation. Then in SingleStore, execute the INSERT statement using the UNHEX() built-in function to convert the hex representation back to its original binary format.

Consider the following example written in Python (3.8), which uses a few modules to generate vectors and convert them to hex:

import numpy
import struct

vector = numpy.random.random(1024)
vectorStr = "".join([str(struct.pack('f', elem)) for elem in vector])
vectorStrEncoded = vectorStr.encode("utf-8").hex()

When this code is executed, a random floating point vector is generated:

[0.09361789  0.22198475  0.36929942 ...,  0.97525847  0.98422799  0.26693578]

The vector is then converted to a binary string representation. Finally, the resulting vector is hex encoded:

bdbabf3df84f633ed014bd3ef6ca183ffc759b ... 48ca303e8aaa793f5ef67b3fcfab883e

Using the hex-encoded vector, you can connect to the database and execute a query that calls the UNHEX() built-in function to convert the vector to its original binary format during insertion:

memsqlConnection.query('INSERT INTO TABLE vectors VALUES (UNHEX("%s"))' % (vectorStrEncoded))

You can also do:

memsqlConnection.query('SELECT EUCLIDEAN_DISTANCE(UNHEX("%s"), UNHEX("%s"))' % (vectorStrEncoded, vectorStrEncoded))

Performance Note

DOT_PRODUCT(), EUCLIDEAN_DISTANCE(), and VECTOR_SUB() are high-performance functions implemented for fast vector operations, using single-instruction multiple-data (SIMD) processor instructions.

Once the vectors have been stored in a table in the binary format, you do not need to use the UNHEX built-in to use the blob with the vector builtins.

-DOT_PRODUCT takes in two vector blob arguments and returns the scalar dot product of those two vectors

-VECTOR_SUB takes in two vector blob arguments and returns a vector blob which is a result of the second argument vector being subtracted from the first argument vector

-EUCLIDEAN_DISTANCE takes in two vector blob arguments and returns the scalar euclidean distance between the two vectors. EUCLIDEAN_DISTANCE(v1, v2) is equal to sqrt(DOT_PRODUCT(VECTOR_SUB(v1, v2), VECTOR_SUB(v1, v2))). However, because EUCLIDEAN_DISTANCE is more efficient with memory bandwidth, we expect the former to be faster than the latter.

For each of the three builtins, the input blob arguments must be the same length, and their binary length must be a multiple of 4 or 8.

If the result for either DOT_PRODUCT or EUCLIDEAN_DISTANCE is infinity, negative infinity, or NaN, null will be returned instead.

SELECT DOT_PRODUCT(JSON_ARRAY_PACK('[1.0, 0.5, 2.0]'), JSON_ARRAY_PACK('[1.0, 0.5, 2.0]')) "Result";

+--------+
| Result |
+--------+
|   5.25 |
+--------+

SET @v1 = JSON_ARRAY_PACK('[1,2,3,4]');

SET @v2 = JSON_ARRAY_PACK('[1,1,0,0]');

SET @v3 = JSON_ARRAY_PACK('[0,1]');

SET @v4 = JSON_ARRAY_PACK_I8('[0,0,0,0,1]');

SELECT DOT_PRODUCT(@v1,@v2);

+----------------------+
| DOT_PRODUCT(@v1,@v2) |
+----------------------+
|                    3 |
+----------------------+

SELECT LENGTH(@v1), LENGTH(@v4);

+-------------+-------------+
| LENGTH(@v1) | LENGTH(@v4) |
+-------------+-------------+
|          16 |           5 |
+-------------+-------------+
/* Note: the length is in bytes, not elements */

SELECT DOT_PRODUCT(@v1,@v3);

ERROR 1940 (HY000): Error with a vector function: argument sizes do not match

SELECT DOT_PRODUCT(@v1, @v4);

ERROR 1940 (HY000): Error with a vector function: argument sizes do not match

Use Cases

A common use case for these functions is to work with floating-point vectors that describe images, such as images of faces or products. These vectors can be created using a neural network trained to categorize the images. Objects are inserted into a table. One field of the object is the vector that describes the image, obtained by feeding the image into the neural network. Queries using DOT_PRODUCT() or EUCLIDEAN_DISTANCE() can then be run to find the closest matches. For example, the following query retrieves the 10 closest matches to the constant vector in the query, based on a cosine similarity match implemented using DOT_PRODUCT().

SELECT t.*, DOT_PRODUCT(t.vector, UNHEX("...constant vector...")) AS score
FROM t
ORDER BY score DESC
LIMIT 10;