Interval Arithmetic

Functions for computing relationships between numeric intervals. All functions accept intervals as numeric vectors of length 2 or matrices with 2 columns (one interval per row). Unordered bounds are silently sorted; rows are recycled to equal length.

Usage

overlap(x, y)

overlaps(x, y)

distance(x, y)

x %overlaps% y

Arguments

x

a numeric vector of length 2 c(lower, upper), or a numeric matrix with 2 columns where each row defines one interval.

y

a numeric vector of length 2 c(lower, upper), or a numeric matrix with 2 columns where each row defines one interval.

Value

overlap

numeric vector of overlap lengths (0 if no overlap).

overlaps

logical vector; TRUE if intervals share at least one point.

distance

numeric vector of gap lengths between non-overlapping intervals (0 if overlapping or touching).

%overlaps%

logical vector; operator wrapper for overlaps().

Details

Intervals are treated as closed, i.e., \([a, b]\). Consequently:

• Two intervals sharing only a boundary point have overlap 0 but overlaps returns TRUE.

• distance returns 0 whenever intervals touch or overlap.

• The returned vector is always unnamed, whatever dimnames the inputs carry.

See also

Other data.interval: between-operators, range-operators

Examples

# overlap length
overlap(c(1, 5), c(3, 7))   # 2
#> [1] 2
overlap(c(1, 3), c(3, 5))   # 0 (boundary only)
#> [1] 0

# overlap check
overlaps(c(1, 5), c(3, 7))  # TRUE
#> [1] TRUE
overlaps(c(1, 3), c(3, 5))  # TRUE  (boundary counts)
#> [1] TRUE
overlaps(c(1, 2), c(3, 4))  # FALSE
#> [1] FALSE

# gap distance
distance(c(1, 2), c(4, 5))  # 2
#> [1] 2
distance(c(1, 5), c(3, 7))  # 0
#> [1] 0

# operator
c(1, 5) %overlaps% c(3, 7)  # TRUE
#> [1] TRUE

# vectorised (matrix input)
m <- matrix(c(1,3, 2,6, 5,8), ncol = 2, byrow = TRUE)
overlap(m, c(4, 7))
#> [1] 0 2 2