Distance functions

L1Distance

Introduced in: v21.11

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

Syntax

Arguments

• vector1 — First vector. Tuple(T) or Array(T)
• vector2 — Second vector. Tuple(T) or Array(T)

Returned value

Returns the 1-norm distance. UInt32 or Float64

Examples

Basic usage

L1Norm

Introduced in: v21.11

Calculates the sum of absolute values of a vector.

Syntax

Arguments

• vector — Vector or tuple of numeric values. Array(T) or Tuple(T)

Returned value

Returns the L1-norm or taxicab geometry distance. UInt* or Float* or Decimal

Examples

Basic usage

L1Normalize

Introduced in: v21.11

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

Syntax

Arguments

• tuple — A tuple of numeric values. Tuple(T)

Returned value

Returns the unit vector. Tuple(Float64)

Examples

Basic usage

L2Distance

Introduced in: v21.11

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

Syntax

Arguments

• vector1 — First vector. Tuple(T) or Array(T)
• vector2 — Second vector. Tuple(T) or Array(T)

Returned value

Returns the 2-norm distance. Float64

Examples

Basic usage

L2Norm

Introduced in: v21.11

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

Syntax

Arguments

• vector — Vector or tuple of numeric values. Tuple(T) or Array(T)

Returned value

Returns the L2-norm or Euclidean distance. UInt* or Float*

Examples

Basic usage

L2Normalize

Introduced in: v21.11

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

Syntax

Arguments

• tuple — A tuple of numeric values. Tuple(T)

Returned value

Returns the unit vector. Tuple(Float64)

Examples

Basic usage

L2SquaredDistance

Introduced in: v22.7

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

Syntax

Arguments

• vector1 — First vector. Tuple(T) or Array(T)
• vector2 — Second vector. Tuple(T) or Array(T)

Returned value

Returns the sum of the squares of the difference between the corresponding elements of two vectors. Float64

Examples

Basic usage

L2SquaredNorm

Introduced in: v22.7

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

Syntax

Arguments

• vector — Vector or tuple of numeric values. Array(T) or Tuple(T)

Returned value

Returns the L2-norm squared. UInt* or Float* or Decimal

Examples

Basic usage

LinfDistance

Introduced in: v21.11

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

Syntax

Arguments

• vector1 — First vector. Tuple(T) or Array(T)
• vector2 — Second vector. Tuple(T) or Array(T)

Returned value

Returns the Infinity-norm distance. Float64

Examples

Basic usage

LinfNorm

Introduced in: v21.11

Calculates the maximum of absolute values of a vector.

Syntax

Arguments

• vector — Vector or tuple of numeric values. Array(T) or Tuple(T)

Returned value

Returns the Linf-norm or the maximum absolute value. Float64

Examples

Basic usage

LinfNormalize

Introduced in: v21.11

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

Syntax

Arguments

• tuple — A tuple of numeric values. Tuple(T)

Returned value

Returns the unit vector. Tuple(Float64)

Examples

Basic usage

LpDistance

Introduced in: v21.11

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

Syntax

Arguments

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

Returned value

Returns the p-norm distance. Float64

Examples

Basic usage

LpNorm

Introduced in: v21.11

Calculates the p-norm of a vector, which is the p-th root of the sum of the p-th powers of the absolute values of its elements.

Special cases:

• When p=1, it's equivalent to L1Norm (Manhattan distance).
• When p=2, it's equivalent to L2Norm (Euclidean distance).
• When p=∞, it's equivalent to LinfNorm (maximum norm).

Syntax

Arguments

• vector — Vector or tuple of numeric values. Tuple(T) or Array(T)
• p — The power. Possible values are real numbers in the range [1; inf). UInt* or Float*

Returned value

Returns the Lp-norm. Float64

Examples

Basic usage

LpNormalize

Introduced in: v21.11

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

Syntax

Arguments

• tuple — A tuple of numeric values. Tuple(T)
• p — The power. Possible values are any number in the range range from [1; inf). UInt* or Float*

Returned value

Returns the unit vector. Tuple(Float64)

Examples

Basic usage

cosineDistance

Introduced in: v1.1

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(T) or Array(T)
• vector2 — Second tuple. Tuple(T) or Array(T)

Returned value

Returns the cosine of the angle between two vectors subtracted from one. Float64

Examples

Basic usage