Distance Functions

L1Norm

Calculates the sum of absolute values of a vector.

Syntax

Alias: normL1.

Arguments

• vector — Tuple or Array.

Returned value

• L1-norm or taxicab geometry distance. UInt, Float or Decimal.

Examples

Query:

Result:

L2Norm

Calculates the square root of the sum of the squares of the vector values.

Syntax

Alias: normL2.

Arguments

• vector — Tuple or Array.

Returned value

• L2-norm or Euclidean distance. Float.

Example

Query:

Result:

L2SquaredNorm

Calculates the square root of the sum of the squares of the vector values (the L2Norm) squared.

Syntax

Alias: normL2Squared.

*Arguments

• vector — Tuple or Array.

Returned value

• L2-norm squared. Float.

Example

Query:

Result:

LinfNorm

Calculates the maximum of absolute values of a vector.

Syntax

Alias: normLinf.

Arguments

• vector — Tuple or Array.

Returned value

• Linf-norm or the maximum absolute value. Float.

Example

Query:

Result:

LpNorm

Calculates the root of p-th power of the sum of the absolute values of a vector in the power of p.

Syntax

Alias: normLp.

Arguments

• vector — Tuple or Array.
• p — The power. Possible values: real number in [1; inf). UInt or Float.

Returned value

• Lp-norm. Float.

Example

Query:

Result:

L1Distance

Calculates the distance between two points (the values of the vectors are the coordinates) in L1 space (1-norm (taxicab geometry distance)).

Syntax

Alias: distanceL1.

Arguments

• vector1 — First vector. Tuple or Array.
• vector2 — Second vector. Tuple or Array.

Returned value

• 1-norm distance. Float.

Example

Query:

Result:

L2Distance

Calculates the distance between two points (the values of the vectors are the coordinates) in Euclidean space (Euclidean distance).

Syntax

Alias: distanceL2.

Arguments

• vector1 — First vector. Tuple or Array.
• vector2 — Second vector. Tuple or Array.

Returned value

• 2-norm distance. Float.

Example

Query:

Result:

L2SquaredDistance

Calculates the sum of the squares of the difference between the corresponding elements of two vectors.

Syntax

Alias: distanceL2Squared.

Arguments

• vector1 — First vector. Tuple or Array.
• vector2 — Second vector. Tuple or Array.

Returned value

• Sum of the squares of the difference between the corresponding elements of two vectors. Float.

Example

Query:

Result:

LinfDistance

Calculates the distance between two points (the values of the vectors are the coordinates) in L_{inf} space (maximum norm).

Syntax

Alias: distanceLinf.

Arguments

• vector1 — First vector. Tuple or Array.
• vector1 — Second vector. Tuple or Array.

Returned value

• Infinity-norm distance. Float.

Example

Query:

Result:

LpDistance

Calculates the distance between two points (the values of the vectors are the coordinates) in Lp space (p-norm distance).

Syntax

Alias: distanceLp.

Arguments

• vector1 — First vector. Tuple or Array.
• vector2 — Second vector. Tuple or Array.
• p — The power. Possible values: real number from [1; inf). UInt or Float.

Returned value

• p-norm distance. Float.

Example

Query:

Result:

L1Normalize

Calculates the unit vector of a given vector (the values of the tuple are the coordinates) in L1 space (taxicab geometry).

Syntax

Alias: normalizeL1.

Arguments

• tuple — Tuple.

Returned value

• Unit vector. Tuple of Float.

Example

Query:

Result:

L2Normalize

Calculates the unit vector of a given vector (the values of the tuple are the coordinates) in Euclidean space (using Euclidean distance).

Syntax

Alias: normalizeL1.

Arguments

• tuple — Tuple.

Returned value

• Unit vector. Tuple of Float.

Example

Query:

Result:

LinfNormalize

Calculates the unit vector of a given vector (the values of the tuple are the coordinates) in L_{inf} space (using maximum norm).

Syntax

Alias: normalizeLinf .

Arguments

• tuple — Tuple.

Returned value

• Unit vector. Tuple of Float.

Example

Query:

Result:

LpNormalize

Calculates the unit vector of a given vector (the values of the tuple are the coordinates) in Lp space (using p-norm).

Syntax

Alias: normalizeLp .

Arguments

• tuple — Tuple.
• p — The power. Possible values: any number from [1;inf). UInt or Float.

Returned value

• Unit vector. Tuple of Float.

Example

Query:

Result:

cosineDistance

Calculates the cosine distance between two vectors (the values of the tuples are the coordinates). The smaller the returned value is, the more similar are the vectors.

Syntax

Arguments

• vector1 — First tuple. Tuple or Array.
• vector2 — Second tuple. Tuple or Array.

Returned value

• Cosine of the angle between two vectors subtracted from one. Float.

Examples

Query:

Result: