The ML.LP_NORM function

This document describes theML.LP_NORM scalar function, which lets youcompute theL^p norm fora vector, where^p is the degree.

Syntax

ML.LP_NORM(vector, degree)

Arguments

ML.LP_NORM has the following arguments:

• vector: anARRAY<Numerical type> value that represents a vector,whereNumerical type can beBIGNUMERIC,FLOAT64,INT64 orNUMERIC. For exampleARRAY<BIGNUMERIC>.

  Each element of the array denotes one dimension of the vector. An exampleof a four-dimensional vector is[0.0, 1.0, 1.0, 0.0].

  The function calculates the^p degree norm of the numerical typevalues in all the values in the array.

• degree: aFLOAT64 value that specifies the degree. This can be0.0,any value >=1.0, orCAST('INF' AS FLOAT64) to return the L_infinitynorm of the vector, which is the largest magnitude of the values inthe vector.

  Commonly used values are1.0 to calculate theManhattannormof the vector and2.0 to calculate theEuclideannorm ofthe vector.

Output

ML.LP_NORM returns aFLOAT64 value that represents the L^p normfor the vector. ReturnsNULL ifvector isNULL.

Example

The following example gets the Euclidean norm for vectors consisting ofARRAY<FLOAT64> values:

1. Create the tablet1:

   CREATETABLEmydataset.t1(v1ARRAY<FLOAT64>,v2ARRAY<FLOAT64>)

2. Populatet1:

   INSERTmydataset.t1(v1,v2)VALUES([4.1,0.5,1.0],[3.0,0.0,2.5])

3. Calculate the Euclidean norm forv1 andv2:

   SELECTv1,ML.LP_NORM(v1,2.0)ASv1_norm,v2,ML.LP_NORM(v2,2.0)ASv2_normFROMmydataset.t1;

   This query produces the following output:

   +---------------------------+-----+-------------------+|v1|v1_norm|v2|v2_norm|+---------------------------+-----+-------------------+|4.1|4.2497058721751557|3.0|3.905124837953327|+-----||-----|||0.5||0.0||+-----||-----+||1.0||2.5||+---------------------------+-----+-------------------+

What's next

• For information about the supported SQL statements and functions for eachmodel type, seeEnd-to-end user journey for each model.