Vector Functionals

Functions to compute various vector norms and distances.

Usage

l0_pseudo_norm(x)

hamming_distance(x, y)

l1_norm(x)

l1_distance(x, y)

l2_norm(x)

l2_distance(x, y)

sup_norm(x)

sup_distance(x, y)

lp_norm(x, p)

lp_distance(x, y, p)

total_variation(x)

Arguments

x

A numeric vector.

y

A numeric vector of the same length as x (for distance functions).

p

A positive integer indicating the order of the norm or distance (for Lp functions).

Value

A single numeric value with the computed norm or distance.

See also

Boost Documentation for more details on the mathematical background.

Examples

# L0 Pseudo Norm
l0_pseudo_norm(c(1, 0, 2, 0, 3))
#> [1] 3
# Hamming Distance
hamming_distance(c(1, 0, 1), c(0, 1, 1))
#> [1] 2
# L1 Norm
l1_norm(c(1, -2, 3))
#> [1] 6
# L1 Distance
l1_distance(c(1, -2, 3), c(4, -5, 6))
#> [1] 9
# L2 Norm
l2_norm(c(3, 4))
#> [1] 5
# L2 Distance
l2_distance(c(3, 4), c(0, 0))
#> [1] 5
# Supremum Norm
sup_norm(c(1, -2, 3))
#> [1] 3
# Supremum Distance
sup_distance(c(1, -2, 3), c(4, -5, 6))
#> [1] 3
# Lp Norm
lp_norm(c(1, -2, 3), 3)
#> [1] 3.301927
# Lp Distance
lp_distance(c(1, -2, 3), c(4, -5, 6), 3)
#> [1] 4.326749
# Total Variation
total_variation(c(1, 2, 1, 3))
#> [1] 4