Vector Functions

This section provides reference information for vector functions in Databend. These functions enable comprehensive vector operations including distance calculations, similarity measurements, and vector analysis for machine learning applications, vector search, and AI-powered analytics.

Distance Functions

Function	Description	Example
COSINE_DISTANCE	Calculates Cosine distance between vectors (range: 0-1)	COSINE_DISTANCE([1,2,3]::VECTOR(3), [4,5,6]::VECTOR(3))
L1_DISTANCE	Calculates Manhattan (L1) distance between vectors	L1_DISTANCE([1,2,3]::VECTOR(3), [4,5,6]::VECTOR(3))
L2_DISTANCE	Calculates Euclidean (straight-line) distance	L2_DISTANCE([1,2,3]::VECTOR(3), [4,5,6]::VECTOR(3))
INNER_PRODUCT	Calculates the inner product (dot product) of two vectors	INNER_PRODUCT([1,2,3]::VECTOR(3), [4,5,6]::VECTOR(3))

Vector Analysis Functions

Function	Description	Example
VECTOR_NORM	Calculates the L2 norm (magnitude) of a vector	VECTOR_NORM([1,2,3]::VECTOR(3))
VECTOR_DIMS	Returns the dimensionality of a vector	VECTOR_DIMS([1,2,3]::VECTOR(3))

Distance Functions Comparison

Function	Description	Range	Best For	Use Cases
COSINE_DISTANCE	Cosine distance between vectors	[0, 1]	When direction matters more than magnitude	• Document similarity • Semantic search • Recommendation systems • Text analysis
L1_DISTANCE	Manhattan (L1) distance between vectors	[0, ∞)	Robust to outliers	• Feature comparison • Outlier detection • Grid-based pathfinding • Clustering algorithms
L2_DISTANCE	Euclidean (straight-line) distance	[0, ∞)	When magnitude and absolute differences are important	• Image similarity • Geographical data • Anomaly detection • Feature-based clustering
INNER_PRODUCT	Dot product of two vectors	(-∞, ∞)	When both magnitude and direction are important	• Neural networks • Machine learning • Physics calculations • Vector projections

Vector Analysis Functions Comparison

Function	Description	Range	Best For	Use Cases
VECTOR_NORM	L2 norm (magnitude) of a vector	[0, ∞)	Vector normalization and magnitude	• Vector normalization • Feature scaling • Magnitude calculations • Physics applications
VECTOR_DIMS	Number of vector dimensions	[1, 4096]	Vector validation and processing	• Data validation • Dynamic processing • Debugging • Compatibility checks