This library provides some set theory operations on sets represented by arrays
containing integer intervals.
If this sounds weird, here's an example: the set { 1, 2, 3, 7, 8, 9 } contains
the two contiguous integer intervals 1..3 and 7..9.
This library represents these values using half-closed intervals (end is not
included in the interval), so [1, 4) and [7, 10).
The corresponding python data structure is suspiciously similar:
[ (1, 4), (7, 10) ].
On this kind of set, the library now provides the following operations:
from interval_sets import *
setB = coalesce(setA)
# Sorts (potentially ill-formed) setA, removes overlaps and merges adjacent
# ranges. This function is useful to bring a set of random intervals into the
# correct format.
setC = union(setA, setB)
# Computes the union of setA and setB, or A ∪ B
setC = intersect(setA, setB)
# Computes the intersection of setA and setB , or A ∩ B
setC = difference(setA, setB)
# Computes the relative complement of setA in setB, or A \ B
vol = volume(setA)
# Computes the number of elements contained in setA, or | A |This library treats sets as immutable, so none of these operations modify any of the arrays passed to them.
Attention: Within each set, intervals are required to be sorted and non-overlapping. Behavior is undefined if these criteria are not met. You can bring any array of unsorted, overlapping intervals into the correct form using the coalesce function.
This is a library I needed for analysis @ unihd-ceg.
Copyright (c) 2018 Alexander Matz, Heidelberg University
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