math.interval-utils
v0.3.0
Published
operations with intervals of real numbers
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math.interval-utils
This library provides a data structure and functions to do operations with intervals.
Version
0.3.0
Install
npm install math.inteval-utils --save
Index
Interval
Data structure and valid values
Real interval can be represented with an pair of real numbers and two flags to indicate if these numbers are included or not in interval. This library defines the Interval
type as the set of arrays of two objects with value
and limit
number properties:
[
{
value: (Number)
limit: (0|1)
},
{
value: (Number)
limit: (-1|0)
}
]
value
properties correspond to the values of interval and limit
properties correspond to if values of interval are included or not.
- If limit is
0
, it indicates that value is included. - If the
limit
of first item is1
, it indicates that firstvalue
is not included in interval. - If the
limit
of second item is-1
, it indicates that secondvalue
is not included in interval.
For example:
(1, 5]
is represented with:
[
{
value: 1
limit: 1
},
{
value: 5
limit: 0
}
]
[-1, 3]
is represented with:
[
{
value: -1
limit: 0
},
{
value: 3
limit: 0
}
]
(10, 12)
is represented with:
[
{
value: 10
limit: 1
},
{
value: 12
limit: -1
}
]
Empty interval
An interval is empty in these cases:
value
of first element is greater thanvalue
of second element.value
of first and second elements are equal butlimit
of first element is greater thanlimit
of second element.
Functions
areDisjoint :: (Interval, Interval) -> Boolean
Given two interval inputs, it returns true
or false
depending on intervals are disjoint or not, respectively.
Example:
const { areDisjoint } = require('math.interval-utils')
// [1, 3)
const interval1 = [
{value: 1, limit: 0},
{value: 3, limit: -1}
]
// (1, 2)
const interval2 = [
{value: 1, limit: 1},
{value: 2, limit: -1}
]
// {1}
const interval3 = [
{value: 1, limit: 0},
{value: 1, limit: 0}
]
areDisjoint(interval1, interval2) // false
areDisjoint(interval2, interval3) // true
areEqual :: (Interval, Interval) -> Boolean
Given two interval inputs, it returns true
or false
depending on intervals are equal or not, respectively.
Example:
const { areEqual } = require('math.interval-utils')
// [1, 3)
const interval1 = [
{value: 1, limit: 0},
{value: 3, limit: -1}
]
// [1, 3)
const interval2 = [
{value: 1, limit: 0},
{value: 3, limit: -1}
]
// [1, 3]
const interval3 = [
{value: 1, limit: 0},
{value: 3, limit: 0}
]
areEqual(interval1, interval2) // true
areEqual(interval2, interval3) // false
contains :: (Interval, Interval) -> Boolean
Given two interval inputs, it returns true
or false
if first interval contains the second interval or not, respectively.
Example:
const { contains } = require('math.interval-utils')
// [1, 3)
const interval1 = [
{value: 1, limit: 0},
{value: 3, limit: -1}
]
// (1, 2)
const interval2 = [
{value: 1, limit: 1},
{value: 2, limit: -1}
]
contains(interval1, interval2) // true
contains(interval2, interval1) // false
intersection :: (Interval, Interval) -> Interval
Given two interval inputs, it returns the intersection of these intervals.
Example:
const { intersection } = require('math.interval-utils')
const I = {}
// [1, 3)
I['[1, 3)'] = [
{value: 1, limit: 0},
{value: 3, limit: -1}
]
// (1, 2)
I['(1, 2)'] = [
{value: 1, limit: 1},
{value: 2, limit: -1}
]
// (3, 4)
I['(3, 4)'] = [
{value: 3, limit: 1},
{value: 4, limit: -1}
]
intersection(I['[1, 3)'], I['(1, 2)']) // (1, 2)
intersection(I['(1, 2)'], I['(3, 4)']) // (3, 4)
intersection(I['[1, 3)'], I['(3, 4)']) // empty
isEmpty :: Interval -> Boolean
Given an interval
, it returns true
or false
if interval
is empty or not, respectively.
Example:
const { isEmpty } = require('math.interval-utils')
// [2, -2]
const interval1 = [
{value: 2, limit: 0},
{value: -2, limit: 0}
]
// (1, 1]
const interval2 = [
{value: 1, limit: 1},
{value: 1, limit: 0}
]
// [1, 1]
const interval3 = [
{value: 1, limit: 0},
{value: 1, limit: 0}
]
isEmpty(interval1) // true
isEmpty(interval2) // true
isEmpty(interval3) // false
isInterval :: Interval -> Boolean
It returns true
or false
if interval
is an Interval.
Example:
const { isInterval } = require('math.interval-utils')
const interval1 = [
{value: 2, limit: 0},
{value: -2, limit: 0}
]
const interval2 = [
{value: -2, limit: 0}
]
const interval3 = [
{value: 2, limit: 0},
{value: Infinity, limit: -1}
]
isInterval(interval1) // true
isInterval(interval2) // false
isInterval(interval3) // true
multiIntersection :: ([Interval], [Interval]) -> [Interval]
Given two lists of disjoint sorted intervals, it returns a new list of disjoint sorted intervals that represent the intersection of these sets.
Example:
// (1, 3) U {4} U [5, 6)
const listIntervals1 = [[
{value: 1, limit: 1},
{value: 3, limit: -1}
], [
{value: 4, limit: 0},
{value: 4, limit: 0}
], [
{value: 5, limit: 0},
{value: 6, limit: -1}
]]
// {0} U [1, 2] U (3, 4] U (5, 7)
const listIntervals2 = [[
{value: 0, limit: 0},
{value: 0, limit: 0}
], [
{value: 3, limit: 1},
{value: 4, limit: 0}
], [
{value: 5, limit: 1},
{value: 7, limit: -1}
]]
// returns (1, 2] U {4} U (5, 6)
multiIntersection(listIntervals1, listIntervals2) // [[
{value: 1, limit: 1},
{value: 2, limit: 0}
], [
{value: 4, limit: 0},
{value: 4, limit: 0}
], [
{value: 5, limit: 1},
{value: 6, limit: -1}
]]
This method has better perfomance than recolecting the intersections of each interval of each lists and intersecting one by one.
numToInterval :: Number -> Interval
Given a number input, it returns an singleton interval that contains this number.
Example:
const { numToInterval } = require('math.interval-utils')
// returns {5} or [5, 5]
numToInterval(5) /* returns [
{value: 5, limit: 0},
{value: 5, limit: 0}
]*/
parser :: string -> Either Interval String
Given a string that represents an interval, it returns an Either.Right value that saves an interval. If the string does not represent an interval it returns and Either.Left value that saves an error.
Example:
const { Right, Left } = require('data.either')
const { parser } = require('math.interval-utils')
parser('(2, 3]') /* Right [
{value: 2, limit: 1},
{value: 3, limit: 0}
] */
parser('{5}') /* Right([
{value: 5, limit: 0},
{value: 5, limit: 0}
]) */
parser('(2, 5(') // Left('"(2, 5(" does not match to interval expression')
relativeComplement :: (Interval, Interval) -> [Interval]
Given two interval inputs, it returns a list of intevals that represents the relative complement. It means, the set of numbers that belongs to the first interval but not the second.
Example:
const { relativeComplement } = require('math.interval-utils')
const I = {}
// [1, 5)
I['[1, 5)'] = [
{value: 1, limit: 0},
{value: 5, limit: -1}
]
// (2, 3)
I['(2, 3)'] = [
{value: 2, limit: 1},
{value: 3, limit: -1}
]
// [4, 6]
I['[4, 6]'] = [
{value: 4, limit: 0},
{value: 6, limit: 0}
]
// returns [1, 2] U [3, 5)
relativeComplement(I['[1, 5)'], I['(2, 3)']) /* [[
{value: 1, limit: 0},
{value: 2, limit: 0}
], [
{value: 3, limit: 0},
{value: 5, limit: -1}
]] */
// returns [1, 4)
relativeComplement(I['[1, 5)'], I['[4, 6]']) /* [[
{value: 1, limit: 0},
{value: 4, limit: -1}
]] */
// returns (2, 3)
relativeComplement(I['(2, 3)'], I['[4, 6]']) /* [[
{value: 2, limit: 1},
{value: 3, limit: -1}
]] */
// returns empty array relativeComplement(I['(2, 3)'], I['[1, 5)']) // []
union :: [Interval] -> [Interval]
Given an array of intervals, it returns an array of sorted disjoint intervals that represents the union of these intervals.
Example:
const { union } = require('math.interval-utils').union
const I = {}
// [1, 3)
I['[1, 3)'] = [
{value: 1, limit: 0},
{value: 3, limit: -1}
]
// (2, 4)
I['(2, 4)'] = [
{value: 2, limit: 1},
{value: 4, limit: -1}
]
// [5, 5]
I['[5, 5]'] = [
{value: 5, limit: 0},
{value: 5, limit: 0}
]
// (5, 6)
I['(5, 6)'] = [
{value: 5, limit: 1},
{value: 6, limit: -1}
]
// returns [1, 4) U [5, 6)
union([interval1, interval2 interval3, interval4]) /* [[
{value: 1, limit: 0},
{value: 4, limit: -1}
], [
{value: 5, limit: 0},
{value: 6, limit: -1}
]] */
LICENSE
MIT