One-Dimensional Wasserstein Distance Using North-West Corner Algorithm

Applies the north-west corner algorithm to obtain the p-Wasserstein distance between two one-dimensional empirical distributions.

Usage

nw_corner_distance(
  x,
  y,
  presorted = FALSE,
  p = 2,
  eps = sqrt(.Machine$double.eps)
)

Arguments

x, y

Vectors representing one-dimensional empirical distributions.

presorted

Set to TRUE if both x and y are sorted to obtain a speed-up.

p

Order of the Wasserstein distance.

eps

Numerical precision for floating point comparisons.

Value

The p-Wasserstein distance between x and y.

Examples

x <- rnorm(10)
y <- rnorm(40)
nw_corner_distance(x, y)
#> [1] 0.4523439
nw_corner_distance(sort(x), sort(y), presorted = TRUE)
#> [1] 0.4523439