Vector Functions and Operators

This document lists the functions and operators available for Vector data types.

Warning

This feature is experimental. It is not recommended that you use it in the production environment. This feature might be changed without prior notice. If you find a bug, you can report an issue on GitHub.

Note

Vector data types and these vector functions are available on TiDB Self-Managed, TiDB Cloud Starter, TiDB Cloud Essential, and TiDB Cloud Dedicated. For TiDB Self-Managed and TiDB Cloud Dedicated, the TiDB version must be v8.4.0 or later (v8.5.0 or later is recommended).

Vector functions

The following functions are designed specifically for Vector data types.

Vector distance functions:

Function name	Description	Supported by vector index
`VEC_L2_DISTANCE`	Calculates L2 distance (Euclidean distance) between two vectors	Yes
`VEC_COSINE_DISTANCE`	Calculates the cosine distance between two vectors	Yes
`VEC_NEGATIVE_INNER_PRODUCT`	Calculates the negative of the inner product between two vectors	No
`VEC_L1_DISTANCE`	Calculates L1 distance (Manhattan distance) between two vectors	No

Other vector functions:

Function name	Description
`VEC_DIMS`	Returns the dimension of a vector
`VEC_L2_NORM`	Calculates the L2 norm (Euclidean norm) of a vector
`VEC_FROM_TEXT`	Converts a string into a vector
`VEC_AS_TEXT`	Converts a vector into a string

Extended built-in functions and operators

The following built-in functions and operators are extended to support operations on Vector data types.

Arithmetic operators:

Name	Description
`+`	Vector element-wise addition operator
`-`	Vector element-wise subtraction operator

For more information about how vector arithmetic works, see Vector Data Type | Arithmetic.

Aggregate (GROUP BY) functions:

Name	Description
`COUNT()`	Return a count of the number of rows returned
`COUNT(DISTINCT)`	Return the count of a number of different values
`MAX()`	Return the maximum value
`MIN()`	Return the minimum value

Comparison functions and operators:

Name	Description
`BETWEEN ... AND ...`	Check whether a value is within a range of values
`COALESCE()`	Return the first non-NULL argument
`=`	Equal operator
`<=>`	NULL-safe equal to operator
`>`	Greater than operator
`>=`	Greater than or equal operator
`GREATEST()`	Return the largest argument
`IN()`	Check whether a value is within a set of values
`IS NULL`	Test whether a value is `NULL`
`ISNULL()`	Test whether the argument is `NULL`
`LEAST()`	Return the smallest argument
`<`	Less than operator
`<=`	Less than or equal operator
`NOT BETWEEN ... AND ...`	Check whether a value is not within a range of values
`!=`, `<>`	Not equal operator
`NOT IN()`	Check whether a value is not within a set of values

For more information about how vectors are compared, see Vector Data Type | Comparison.

Control flow functions:

Name	Description
`CASE`	Case operator
`IF()`	If/else construct
`IFNULL()`	Null if/else construct
`NULLIF()`	Return `NULL` if expr1 = expr2

Cast functions:

Name	Description
`CAST()`	Cast a value as a string or vector
`CONVERT()`	Cast a value as a string

For more information about how to use CAST(), see Vector Data Type | Cast.

Full references

VEC_L2_DISTANCE

VEC_L2_DISTANCE(vector1, vector2)

Calculates the L2 distance (Euclidean distance) between two vectors using the following formula:

$DISTANCE(p,q)=\sqrt {\sum \limits _{i=1}^{n}{(p_{i}-q_{i})^{2}}}$

The two vectors must have the same number of dimensions. Otherwise, an error is returned.

Example:

SELECT VEC_L2_DISTANCE('[0, 3]', '[4, 0]');

+-------------------------------------+
| VEC_L2_DISTANCE('[0, 3]', '[4, 0]') |
+-------------------------------------+
|                                   5 |
+-------------------------------------+

VEC_COSINE_DISTANCE

VEC_COSINE_DISTANCE(vector1, vector2)

Calculates the cosine distance between two vectors using the following formula:

$DISTANCE(p,q)=1.0 - {\frac {\sum \limits _{i=1}^{n}{p_{i}q_{i}}}{{\sqrt {\sum \limits _{i=1}^{n}{p_{i}^{2}}}}\cdot {\sqrt {\sum \limits _{i=1}^{n}{q_{i}^{2}}}}}}$

The two vectors must have the same number of dimensions. Otherwise, an error is returned.

For embeddings from OpenAI, it is recommended that you use this function.

Example:

SELECT VEC_COSINE_DISTANCE('[1, 1]', '[-1, -1]');

+-------------------------------------------+
| VEC_COSINE_DISTANCE('[1, 1]', '[-1, -1]') |
+-------------------------------------------+
|                                         2 |
+-------------------------------------------+

VEC_NEGATIVE_INNER_PRODUCT

VEC_NEGATIVE_INNER_PRODUCT(vector1, vector2)

Calculates the distance by using the negative of the inner product between two vectors, using the following formula:

$DISTANCE(p,q)=- INNER\_PROD(p,q)=-\sum \limits _{i=1}^{n}{p_{i}q_{i}}$

The two vectors must have the same number of dimensions. Otherwise, an error is returned.

Example:

SELECT VEC_NEGATIVE_INNER_PRODUCT('[1, 2]', '[3, 4]');

+------------------------------------------------+
| VEC_NEGATIVE_INNER_PRODUCT('[1, 2]', '[3, 4]') |
+------------------------------------------------+
|                                            -11 |
+------------------------------------------------+

VEC_L1_DISTANCE

VEC_L1_DISTANCE(vector1, vector2)

Calculates the L1 distance (Manhattan distance) between two vectors using the following formula:

$DISTANCE(p,q)=\sum \limits _{i=1}^{n}{|p_{i}-q_{i}|}$

The two vectors must have the same number of dimensions. Otherwise, an error is returned.

Example:

SELECT VEC_L1_DISTANCE('[0, 0]', '[3, 4]');

+-------------------------------------+
| VEC_L1_DISTANCE('[0, 0]', '[3, 4]') |
+-------------------------------------+
|                                   7 |
+-------------------------------------+

VEC_DIMS

VEC_DIMS(vector)

Returns the dimension of a vector.

Examples:

SELECT VEC_DIMS('[1, 2, 3]');

+-----------------------+
| VEC_DIMS('[1, 2, 3]') |
+-----------------------+
|                     3 |
+-----------------------+

SELECT VEC_DIMS('[]');

+----------------+
| VEC_DIMS('[]') |
+----------------+
|              0 |
+----------------+

VEC_L2_NORM

VEC_L2_NORM(vector)

Calculates the L2 norm (Euclidean norm) of a vector using the following formula:

$NORM(p)=\sqrt {\sum \limits _{i=1}^{n}{p_{i}^{2}}}$

Example:

SELECT VEC_L2_NORM('[3, 4]');

+-----------------------+
| VEC_L2_NORM('[3, 4]') |
+-----------------------+
|                     5 |
+-----------------------+

VEC_FROM_TEXT

VEC_FROM_TEXT(string)

Converts a string into a vector. In many cases, this conversion is done implicitly, for example when inserting data into a column of the VECTOR data type. However, in expressions where implicit conversion is not supported (such as arithmetic operations on vectors), you need to explicitly call this function.

Example:

SELECT VEC_FROM_TEXT('[1, 2]') + VEC_FROM_TEXT('[3, 4]');

+-------------------------------------------------+
| VEC_FROM_TEXT('[1,2]') + VEC_FROM_TEXT('[3,4]') |
+-------------------------------------------------+
| [4,6]                                           |
+-------------------------------------------------+

VEC_AS_TEXT

VEC_AS_TEXT(vector)

Converts a vector into a string.

Example:

SELECT VEC_AS_TEXT('[1.000, 2.5]');

+-----------------------------+
| VEC_AS_TEXT('[1.000, 2.5]') |
+-----------------------------+
| [1,2.5]                     |
+-----------------------------+

MySQL compatibility

The vector functions and the extended usage of built-in functions and operators over vector data types are TiDB specific, and are not supported in MySQL.

Vector Functions and Operators

Vector functions

Extended built-in functions and operators

Full references

VEC_L2_DISTANCE

VEC_COSINE_DISTANCE

VEC_NEGATIVE_INNER_PRODUCT

VEC_L1_DISTANCE

VEC_DIMS

VEC_L2_NORM

VEC_FROM_TEXT

VEC_AS_TEXT

MySQL compatibility

See also

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