VECTOR_KTH_ELEMENT

`VECTOR_KTH_ELEMENT` is a function that returns the k-th element in a vector expression.

Syntax

`VECTOR_KTH_ELEMENT(vector_expression, k)`

Arguments

• `vector_expression`: An expression that evaluates to a vector. Vectors can be stored in SingleStore using the native `VECTOR` type (Vector Type) or the `BLOB` type (BLOB Types). SingleStore recommends using the `VECTOR` type when possible.

• `k`: A 0-indexed number to determine which element in the vector to be returned. A positive index counts from the beginning of the vector. A negative index counts from the end of the vector.

Return Type

When the vector_expression is a `VECTOR`, the return type is the element type of that `VECTOR`.

When the vector_expression is a `BLOB`, then the return type will be by default a `BLOB` that contains a vector encoded as 32-bit floating point numbers (`F32`). Alternatively if a suffix is used, the return type will be a `BLOB` that contains a vector encoded using the type of the suffix.

See Using Suffixes for Other Element Types with BLOBs for more information on using suffixes with vectors encoded as `BLOB`s.

Using VECTOR_KTH_ELEMENT with the VECTOR Data Type

The examples below show three uses of `VECTOR_KTH_ELEMENT` with different types of `VECTOR` arguments.

Example 1 - Vector with F32 Element Type

First create a table of vectors of length 4 using the `VECTOR` data type and insert data into that table.

```CREATE TABLE vectors (id int, vec VECTOR(4) not null);
INSERT INTO vectors VALUES (1, '[0.45, 0.55, 0.495, 0.5]');INSERT INTO vectors VALUES (2, '[0.1, 0.8, 0.2, 0.555]');INSERT INTO vectors VALUES (3, '[-0.5, -0.03, -0.1, 0.86]');INSERT INTO vectors VALUES (4, '[0.5, 0.3, 0.807, 0.1]');```

The following SQL extracts the 2nd element of each of those vectors. k is 0-indexed, so we use the value '1' to extract the 2nd element.

Click the Playground icon to the right of the SQL listing to try this query. Also, try experimenting and writing your own query.

`SELECT id, VECTOR_KTH_ELEMENT(vec, 1)FROM vectorsORDER BY id;`
``````+------+----------------------------+
| id   | VECTOR_KTH_ELEMENT(vec, 1) |
+------+----------------------------+
|    1 |          0.550000011920929 |
|    2 |          0.800000011920929 |
|    3 |      -0.029999999329447746 |
|    4 |        0.30000001192092896 |
+------+----------------------------+``````

Notice that the results do not exactly match the values in the `INSERT`. This is because elements in the `VECTOR` data type are stored as floating-point numbers and the values in the `INSERT` statement are not perfectly representable in floating-point.

Example 2 - Vector with I16 Element Type

This example shows how to use `VECTOR_KTH_ELEMENT` with a `VECTOR` with an elementType of 16-bit integer (`I16`).

```CREATE TABLE vectors_i16(id INT, vec VECTOR(3, I16));
INSERT INTO vectors_i16 VALUES(1, '[1, 2, 3]');INSERT INTO vectors_i16 VALUES(2, '[4, 5, 6]');INSERT INTO vectors_i16 VALUES(3, '[1, 4, 8]');```

The following SQL extracts the 2nd element of each of those vectors.

`SELECT id, VECTOR_KTH_ELEMENT(vec, 1)FROM vectors_i16ORDER BY id;`
``````+------+----------------------------+
| id   | VECTOR_KTH_ELEMENT(vec, 1) |
+------+----------------------------+
|    1 |                          2 |
|    2 |                          5 |
|    3 |                          4 |
+------+----------------------------+``````

Example 3 - Using a Negative Value for k

Negative numbers can be used for k to count from the end of the vectors. As shown below, using k = -1 will extract the last element of the vectors.

`SELECT id, VECTOR_KTH_ELEMENT(vec, -1)FROM vectors_i16ORDER BY id;`
``````+------+-----------------------------+
| id   | VECTOR_KTH_ELEMENT(vec, -1) |
+------+-----------------------------+
|    1 |                           3 |
|    2 |                           6 |
|    3 |                           8 |
+------+-----------------------------+``````

Using VECTOR_KTH_ELEMENT with Vectors as BLOBs

The following examples and descriptions show the use of `VECTOR_KTH_ELEMENT` to multiply the elements of vector stored as a `BLOB`.

Example 1 - BLOB Argument

Create a table with a column of type `BLOB` to store the vectors. The second column in this table, with column name `vec` and type `BLOB`, will store the vectors. This example demonstrates storing vector data using `BLOB`s, hence the column of type `BLOB` named `vec`.

Then use the `JSON_ARRAY_PACK` built-in function to easily insert properly formatted vectors.

```CREATE TABLE vectors_b (id int, vec BLOB not null);
INSERT INTO vectors_b VALUES (1, JSON_ARRAY_PACK('[0.1, 0.8, 0.2, 0.555]')); INSERT INTO vectors_b VALUES (2, JSON_ARRAY_PACK('[0.45, 0.55, 0.495, 0.5]'));```

The following SQL extracts the 2nd element of each of those vectors.

`SELECT id, VECTOR_KTH_ELEMENT(vec, 1)FROM vectors_bORDER BY id;`
``````+------+----------------------------+
| id   | VECTOR_KTH_ELEMENT(vec, 1) |
+------+----------------------------+
|    1 |          0.800000011920929 |
|    2 |          0.550000011920929 |
+------+----------------------------+``````

The return type in this case will be a 32-bit floating-point number as that is the default type for vector element storage.

Using Suffixes for Other Element Types with BLOBs

The default element type for vector storage and processing is 32-bit floating point (`F32`). However, other element types are supported.

You can specify the datatype of the vector elements to be used in the operation by adding a suffix to the function. All operations are done using the specified datatype. Omitting the suffix from the function is equivalent to suffixing it with `_F32`.

When using a suffix, the return type will be the type of the suffix.

Note

The functions with suffixes do not work with the `VECTOR` type.

The following table lists the suffixes and their data type.

Suffix

Data Type

`_I8`

8-bit signed integer

`_I16`

16-bit signed integer

`_I32`

32-bit signed integer

`_I64`

64-bit signed integer

`_F32`

32-bit floating-point number (IEEE standard format)

`_F64`

64-bit floating-point number (IEEE standard format)

Example 2 - BLOBs with 16-bit Integers

Below is an example of using `JSON_ARRAY_PACK` and `VECTOR_KTH_ELEMENT` with 16-bit signed integers.

First create a table of vectors stored as 16-bit integers. Note the use of the `_I16` suffix on `JSON_ARRAY_PACK`.

```CREATE TABLE vectors_b_i (id int, vec BLOB not null);
INSERT INTO vectors_b_i VALUES (1, JSON_ARRAY_PACK_I16('[1, 3, 2, 5]')); INSERT INTO vectors_b_i VALUES(2, JSON_ARRAY_PACK_I16('[23, 4, 1, 8]'));```

The following SQL extracts the 2nd element of each of those vectors.

`SELECT id, VECTOR_KTH_ELEMENT_I16(vec, 1)FROM vectors_b_iORDER BY id;`
``````+------+--------------------------------+
| id   | VECTOR_KTH_ELEMENT_I16(vec, 1) |
+------+--------------------------------+
|    1 |                              3 |
|    2 |                              4 |
+------+--------------------------------+``````

Note

Be sure that the suffixes you use to pack the vector data match the suffixes you use to unpack the data and the suffixes you use on functions to process that data.

Formatting Binary Vector Data for BLOBs

When using the `BLOB` type for vector operations, vector data can be formatted using `JSON_ARRAY_PACK`. If your vector data is already in a packed binary format, you can load that data into the `BLOB`s. The data must be encoded as a `BLOB` containing packed numbers in little-endian byte order. Vectors stored as `BLOB`s can be of any length; however, the input blob length must be divisible by the size of the packed vector elements (1, 2, 4 , or 8 bytes, depending on the vector element).