A quick review of intervals
The open interval from a to b, denoted (a, b), consists of all numbers between a and b excluding the endpoints a and b.
Open circles in the graph indicate that the endpoints are excluded:
The closed interval from a to b, denoted [a, b], consists of all numbers between a and b including the endpoints a and b.
Solid circles in the graph indicate that the endpoints are included:
The symbol -∞ indicates that the interval extends indefinitely to the left:
And ∞ indicates that the interval extends indefinitely to the right:
Create intervals in R
We will use the intervals package in R to create intervals.
The function Intervals() takes as input a matrix and creates a collection of intervals with common endpoints closure.
Here’s an example:
library("intervals")
# x is a collection of intervals
# that are all left-closed and right-open
x = Intervals(
matrix(c(3, 9,
-1, 4,
2, Inf), nrow = 3, byrow = TRUE),
closed = c(TRUE, FALSE), # intervals are of the form [a, b)
type = "Z" # inputs are integers
)
# name the intervals
rownames(x) = c("a","b","c")
print(x)
Output:
Object of class Intervals 3 intervals over R: a [3, 9) b [-1, 4) c [2, Inf)
If you want a collection of intervals with different endpoints closure, use the function: Intervals_full().
Alternatively you can transform an “Intervals” object to an “Intervals_full” object using the following code:
y = as( x, "Intervals_full" ) print(y)
Output:
Object of class Intervals_full 3 intervals over R: a [3, 9) b [-1, 4) c [2, Inf)
Open all intervals in y
open_intervals(y) print(y)
Output:
Object of class Intervals_full 3 intervals over Z: (2, 9) (-2, 4) (1, Inf)
Now we need to close some endpoints in y.
y has 3 intervals, so it has 6 endpoints, numbered from 1 to 6 and counted vertically as follows:
1 4
2 5
3 6
# closing some endpoints in y closed(y)[1] = TRUE closed(y)[3] = TRUE closed(y)[4] = TRUE print(y)
Output:
Object of class Intervals_full 3 intervals over Z: [3, 9] [-1, 4) [2, Inf)
Graph intervals in R
plot(x, xlim = c(-2, 10))
Output:
plot(y, xlim = c(-2, 10))
Output:
References
For more information, refer to the “intervals” package documentation on CRAN.