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vector_norm function

Applies to: check marked yes Databricks Runtime 18.1 and above

Computes the Lp norm of a vector using the specified degree.

Syntax

vector_norm(vector [, degree ])

Arguments

  • vector: An ARRAY<FLOAT> expression representing the vector.
  • degree: Optional. A FLOAT value specifying the norm type; defaults to 2.0 (Euclidean norm). Supported values:
    • 1.0 — L1 norm (Manhattan): sum of absolute values
    • 2.0 — L2 norm (Euclidean): square root of sum of squares
    • float('inf') — L∞ (infinity norm): maximum absolute value

Returns

A FLOAT value representing the norm of the vector. The result is non-negative.

Returns 0.0 for empty vectors. Returns NULL if the input is NULL or contains NULL.

Notes

  • Only ARRAY<FLOAT> is supported; other types such as ARRAY<DOUBLE> or ARRAY<DECIMAL> raise an error. An unsupported degree value raises INVALID_VECTOR_NORM_DEGREE.
  • L2 norm is the most common in dense embedding workloads; L1 is used in sparse and probabilistic applications; L∞ is used in worst-case analysis.

Error conditions

Examples

-- L2 norm (Euclidean) - classic 3-4-5 triangle
> SELECT vector_norm(array(3.0f, 4.0f), 2.0f);
  5.0

-- L1 norm (Manhattan)
> SELECT vector_norm(array(3.0f, 4.0f), 1.0f);
  7.0

-- L∞ norm (infinity)
> SELECT vector_norm(array(3.0f, 4.0f), float('inf'));
  4.0

-- Empty vector returns 0.0
> SELECT vector_norm(array(), 2.0);
  0.0
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