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VECTOR_NORM (Transact-SQL) (Preview)

  • Article

Applies to: Azure SQL Database

Note

This data type is in preview and is subject to change. Make sure to read preview usage terms in the Service Level Agreements (SLA) for Online Services document.

The function VECTOR_NORM takes a vector as an input and returns the norm of the vector (which is a measure of its length or magnitude) in a given norm type

For example, if you want to calculate the Euclidean norm (which is the most common norm type), you can use:

SELECT VECTOR_NORM ( vector_column, 'norm2' )
FROM ...

Syntax

Transact-SQL syntax conventions

VECTOR_NORM ( vector_column, norm_type )

Arguments

vector_column

An expression that evaluates to a vector. This column must be of the new vector data type

norm_type

A string with the name of the norm type to use to calculate the norm of the given vector. The following norm types are supported:

  • norm1 - The 1-norm, which is the sum of the absolute values of the vector components.
  • norm2 - The 2-norm, also known as the Euclidean Norm which is the square root of the sum of the squares of the vector components.
  • norminf - The infinity norm, which is the maximum of the absolute values of the vector components.

Return value

The function returns a float value that represents the norm of the vector using the specified norm type.

An error is returned if norm_type isn't a valid norm type and if the vector_column is not of the vector type.

Examples

Example 1

The following example creates a vector with three dimensions from a string with a JSON array.

DECLARE @v VECTOR(3) = '[1, 2, 3]';

SELECT 
    vector_norm(@v, 'norm2') AS norm2,
    vector_norm(@v, 'norm1') AS norm1,
    vector_norm(@v, 'norminf') AS norminf;

The expected return values would be:

norm2 norm1 norminf
3.7416573867739413 6.0 3.0

Example 2

The following example calculates the norm of each vector in a table.

CREATE TABLE dbo.vectors
(
  ID INT PRIMARY KEY,
  v VECTOR(3) NOT NULL
);

INSERT INTO dbo.vectors (ID, v) VALUES 
(1, '[0.1, -2, 42]'),
(2, '[2, 0.1, -42]');

SELECT 
  ID, 
  VECTOR_NORM(v, 'norm2') AS norm 
FROM 
  dbo.vectors;

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