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Merge pull request #325 from kevmal/interval-intersect
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Support intersect of mixed interval types
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@bvenn
bvenn authored Apr 23, 2024
2 parents 3533493 + 4e15a05 commit d3bfb58
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214 changes: 139 additions & 75 deletions src/FSharp.Stats/Interval.fs
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Original file line number Diff line number Diff line change
Expand Up @@ -288,92 +288,156 @@ module Interval =
| Interval.Empty,Interval.Empty -> Interval.Empty
| _ -> failwithf "Subtraction of (half) open intervals is not supported!"

// a0----a1
// b0-----b1
/// <summary>Checking for intersection of both intervals</summary>
/// <remarks></remarks>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
/// <example>
/// <code>
/// </code>
/// </example>
let inline isIntersection (a: Interval<'a>) b =

/// <summary>Checks if two intervals intersect</summary>
/// <param name="a">The first interval</param>
/// <param name="b">The second interval</param>
/// <returns>True if the intervals intersect, false otherwise</returns>
let inline isIntersection a b =
match a,b with
| Interval.Empty, Interval.Empty -> true
| Interval.Empty, _ | _, Interval.Empty -> false
| Interval.Closed (minA,maxA), Interval.Closed (minB,maxB) -> minA <= maxB && minB <= maxA
| Interval.Closed (minA,maxA), Interval.Open (minB,maxB) -> minA < maxB && minB < maxA
| Interval.Closed (minA,maxA), Interval.RightOpen (minB,maxB) -> minA < maxB && minB <= maxA
| Interval.Closed (minA,maxA), Interval.LeftOpen (minB,maxB) -> minA <= maxB && minB < maxA
| Interval.Closed (_,_), Interval.Empty -> false
| Interval.Open (minA,maxA), Interval.Closed (minB,maxB) -> minA < maxB && minB < maxA
| Interval.Open (minA,maxA), Interval.Open (minB,maxB) -> minA < maxB && minB < maxA
| Interval.Open (minA,maxA), Interval.RightOpen (minB,maxB) -> minA < maxB && minB < maxA
| Interval.Open (minA,maxA), Interval.LeftOpen (minB,maxB) -> minA < maxB && minB < maxA
| Interval.Open (_,_), Interval.Empty -> false
| Interval.LeftOpen (minA,maxA), Interval.Closed (minB,maxB) -> minA < maxB && minB <= maxA
| Interval.LeftOpen (minA,maxA), Interval.Open (minB,maxB) -> minA < maxB && minB < maxA
| Interval.LeftOpen (minA,maxA), Interval.RightOpen (minB,maxB) -> minA <= maxB && minB <= maxA
| Interval.LeftOpen (minA,maxA), Interval.LeftOpen (minB,maxB) -> minA < maxB && minB < maxA
| Interval.LeftOpen (_,_), Interval.Empty -> false
| Interval.RightOpen (minA,maxA), Interval.Closed (minB,maxB) -> minA <= maxB && minB < maxA
| Interval.RightOpen (minA,maxA), Interval.Open (minB,maxB) -> minA < maxB && minB < maxA
| Interval.RightOpen (minA,maxA), Interval.RightOpen (minB,maxB) -> minA < maxB && minB < maxA
| Interval.RightOpen (minA,maxA), Interval.LeftOpen (minB,maxB) -> minA <= maxB && minB <= maxA
| Interval.RightOpen (_,_), Interval.Empty -> false
| Interval.Empty, Interval.Closed (_,_) -> false
| Interval.Empty, Interval.Open (_,_) -> false
| Interval.Empty, Interval.LeftOpen (_,_) -> false
| Interval.Empty, Interval.RightOpen (_,_) -> false
| Interval.Empty,Interval.Empty -> true
| Interval.Open (minA,maxA), Interval.Open (minB,maxB)
| Interval.LeftOpen (minA,maxA), Interval.LeftOpen (minB,maxB)
| Interval.RightOpen (minA,maxA), Interval.RightOpen (minB,maxB) -> minA < maxB && minB < maxA && max minA minB < min maxA maxB
| Interval.Open (minB,maxB), Interval.Closed (minA,maxA)
| Interval.Closed (minA,maxA), Interval.Open (minB,maxB) -> (minB < minA && maxB > minA) || (minB >= minA && ((maxB <= maxA && minB <> maxB) || (minB < maxA && maxB > maxA)))
| Interval.RightOpen (minB,maxB), Interval.Closed (minA,maxA)
| Interval.Closed (minA,maxA), Interval.RightOpen (minB,maxB) -> minA < maxB && minB <= maxA && not (maxB <= maxA && max minA minB = maxB)
| Interval.LeftOpen (minB,maxB), Interval.Closed (minA,maxA)
| Interval.Closed (minA,maxA), Interval.LeftOpen (minB,maxB) -> minA <= maxB && minB < maxA && not (minB >= minA && min maxA maxB = minB)
| Interval.RightOpen (minB,maxB), Interval.Open (minA,maxA)
| Interval.Open (minA,maxA), Interval.RightOpen (minB,maxB) -> minA < maxB && minB < maxA && not ((minB > minA && min maxA maxB = minB) || min maxA maxB = minA)
| Interval.LeftOpen (minB,maxB), Interval.Open (minA,maxA)
| Interval.Open (minA,maxA), Interval.LeftOpen (minB,maxB) -> minA < maxB && minB < maxA && not((maxB < maxA && max minA minB = maxB) || max minA minB = maxA)
| Interval.RightOpen (minB,maxB), Interval.LeftOpen (minA,maxA)
| Interval.LeftOpen (minA,maxA), Interval.RightOpen (minB,maxB) -> minA <= maxB && minB <= maxA && not((maxB <= maxA && (minA = maxB || (minA < minB && minB = maxB)) || minA = maxA))


/// <summary>Returns the intersection of this interval with another.</summary>
/// <remarks></remarks>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
/// <example>
/// <code>
/// </code>
/// </example>
let inline intersect (a: Interval<'a>) b =
if not (isIntersection a b) then
Interval.Empty
else
match a,b with
| Interval.Closed (minA,maxA), Interval.Closed (minB,maxB) ->
if not (minA <= maxB && minB <= maxA) then
/// <summary>Returns the intersection of two intervals</summary>
/// <param name="a">The first interval</param>
/// <param name="b">The second interval</param>
/// <returns>The intersection of the two intervals</returns>
/// <exception cref="System.Exception">Thrown when trying to intersect mixed interval types</exception>
let inline intersect a b =
match a,b with
| Interval.Empty, _ | _, Interval.Empty -> Interval.Empty
| Interval.Closed (minA,maxA), Interval.Closed (minB,maxB) ->
if minA <= maxB && minB <= maxA then
Interval.Closed(max minA minB, min maxA maxB)
else
Interval.Empty
| Interval.Open (minA,maxA), Interval.Open (minB,maxB) ->
let min' = max minA minB
let max' = min maxA maxB
if min' < max' then
Interval.Open(min',max')
else
Interval.Empty
| Interval.LeftOpen (minA,maxA), Interval.LeftOpen (minB,maxB) ->
let min' = max minA minB
let max' = min maxA maxB
if min' < max' then
Interval.LeftOpen(min',max')
else
Interval.Empty
| Interval.RightOpen (minA,maxA), Interval.RightOpen (minB,maxB) ->
let min' = max minA minB
let max' = min maxA maxB
if min' < max' then
Interval.RightOpen(min',max')
else
Interval.Empty
| Interval.Open (minB,maxB), Interval.Closed (minA,maxA)
| Interval.Closed (minA,maxA), Interval.Open (minB,maxB) ->
if minB >= minA then
if maxB <= maxA then
if minB = maxB then
Interval.Empty
else
Interval.Open(minB,maxB)
elif minB >= maxA then
Interval.Empty
else
let min' = max minA minB
let max' = min maxA maxB
Interval.Closed (min',max')
| Interval.Closed (min,max), Interval.Empty -> Interval.Empty
| Interval.Empty, Interval.Closed (min,max) -> Interval.Empty
| Interval.Empty,Interval.Empty -> Interval.Empty
| Interval.LeftOpen (minA,maxA), Interval.LeftOpen (minB,maxB) ->
if not (minA < maxB && minB < maxA) then
Interval.LeftOpen(minB,maxA)
else
if maxB <= maxA then
if maxB <= minA then
Interval.Empty
else
Interval.RightOpen(minA,maxB)
else Interval.Closed(minA,maxA)
| Interval.RightOpen (minB,maxB), Interval.Closed (minA,maxA)
| Interval.Closed (minA,maxA), Interval.RightOpen (minB,maxB) ->
let min' = max minA minB
if maxB <= maxA then
if min' >= maxB then
Interval.Empty
else
let min' = max minA minB
let max' = min maxA maxB
Interval.LeftOpen (min',max')
| Interval.RightOpen (minA,maxA), Interval.RightOpen (minB,maxB) ->
if not (minA < maxB && minB < maxA) then
Interval.Empty
Interval.RightOpen(min',maxB)
elif min' <= maxA then
Interval.Closed(min',maxA)
else
Interval.Empty
| Interval.LeftOpen (minB,maxB), Interval.Closed (minA,maxA)
| Interval.Closed (minA,maxA), Interval.LeftOpen (minB,maxB) ->
let max' = min maxA maxB
if minB >= minA then
if max' <= minB then
Interval.Empty
else
Interval.LeftOpen(minB,max')
elif minA <= max' then
Interval.Closed(minA,max')
else
Interval.Empty
| Interval.RightOpen (minB,maxB), Interval.Open (minA,maxA)
| Interval.Open (minA,maxA), Interval.RightOpen (minB,maxB) ->
let max' = min maxA maxB
if minB > minA then
if max' <= minB then
Interval.Empty
else
Interval.RightOpen(minB,max')
elif minA >= max' then
Interval.Empty
else
Interval.Open(minA,max')
| Interval.LeftOpen (minB,maxB), Interval.Open (minA,maxA)
| Interval.Open (minA,maxA), Interval.LeftOpen (minB,maxB) ->
let min' = max minA minB
if maxB < maxA then
if min' >= maxB then
Interval.Empty
else
let min' = max minA minB
let max' = min maxA maxB
Interval.RightOpen (min',max')
| Interval.Open (minA,maxA), Interval.Open (minB,maxB) ->
if not (minA < maxB && minB < maxA) then
Interval.LeftOpen(min',maxB)
elif min' >= maxA then
Interval.Empty
else
Interval.Open(min',maxA)
| Interval.RightOpen (minB,maxB), Interval.LeftOpen (minA,maxA)
| Interval.LeftOpen (minA,maxA), Interval.RightOpen (minB,maxB) ->
if maxB <= maxA then
if minA >= minB then
if minA >= maxB then
Interval.Empty
else
Interval.Open(minA,maxB)
elif minB >= maxB then
Interval.Empty
else
let min' = max minA minB
let max' = min maxA maxB
Interval.Open (min',max')
| _ -> failwithf "Intersection of mixed interval types is not supported!"
Interval.RightOpen(minB,maxB)
else
if minA >= minB then
if minA >= maxA then
Interval.Empty
else
Interval.LeftOpen(minA,maxA)
elif minB <= maxA then
Interval.Closed(minB,maxA)
else
Interval.Empty

/// <summary>Get the value at a given percentage within (0.0 - 1.0) or outside (&lt; 0.0, &gt; 1.0) of the interval. Rounding to nearest neighbour occurs when needed.</summary>
/// <remarks></remarks>
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