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5 changes: 3 additions & 2 deletions
5
src/FSharp.Stats/Algebra/INumeric.fs → src/FSharp.Stats/INumeric.fs
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| Original file line number | Diff line number | Diff line change |
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| namespace FSharp.Stats | ||
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| module Intervals = | ||
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| /// Closed interval [Start,End] | ||
| type Interval<'a> = | ||
| | ClosedInterval of 'a * 'a | ||
| | Empty | ||
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| /// Creates closed interval [min,max] by given min and max | ||
| let create min max = | ||
| ClosedInterval (min, max) | ||
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| /// Creates closed interval [min,max] by given start and size | ||
| let ofSize min size = | ||
| ClosedInterval (min, min + size) | ||
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| /// Returns the size of an closed interval | ||
| let inline trySize interval = | ||
| match interval with | ||
| | ClosedInterval (min,max) -> Some (max - min) | ||
| | Empty -> None | ||
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| /// Returns the interval as a string | ||
| let toString interval = | ||
| match interval with | ||
| | ClosedInterval (min,max) -> sprintf "[%A,%A]" min max | ||
| | Empty -> "[empty]" | ||
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| /// Add two given intervals. | ||
| let add a b = | ||
| match a,b with | ||
| | ClosedInterval (minA,maxA), ClosedInterval (minB,maxB) | ||
| -> ClosedInterval (minA + minB, maxA + maxB) | ||
| | ClosedInterval (min,max), Empty -> a | ||
| | Empty, ClosedInterval (min,max) -> b | ||
| | Empty,Empty -> Empty | ||
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| /// Subtract a given interval from the other interval. | ||
| let subtract a b = | ||
| match a,b with | ||
| | ClosedInterval (minA,maxA), ClosedInterval (minB,maxB) | ||
| -> ClosedInterval (minA - maxB, maxA - minB) | ||
| | ClosedInterval (min,max), Empty -> a | ||
| | Empty, ClosedInterval (min,max) -> b | ||
| | Empty,Empty -> Empty | ||
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| // a0----a1 | ||
| // b0-----b1 | ||
| /// Checking for intersection of both intervals | ||
| let isIntersection a b = | ||
| match a,b with | ||
| | ClosedInterval (minA,maxA), ClosedInterval (minB,maxB) | ||
| -> minA <= maxB && minB <= maxA | ||
| | ClosedInterval (min,max), Empty -> false | ||
| | Empty, ClosedInterval (min,max) -> false | ||
| | Empty,Empty -> true | ||
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| /// Returns the intersection of this interval with another. | ||
| let intersect a b = | ||
| if not (isIntersection a b) then | ||
| None | ||
| else | ||
| match a,b with | ||
| | ClosedInterval (minA,maxA), ClosedInterval (minB,maxB) | ||
| -> if not (minA <= maxB && minB <= maxA) then | ||
| None | ||
| else | ||
| let min' = max minA minB | ||
| let max' = min maxA maxB | ||
| ClosedInterval (min',max') |> Some | ||
| | ClosedInterval (min,max), Empty -> None | ||
| | Empty, ClosedInterval (min,max) -> None | ||
| | Empty,Empty -> Some (Empty) | ||
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| /// Get the value at a given percentage within (0.0 - 1.0) or outside (< 0.0, > 1.0) of the interval. Rounding to nearest neighbour occurs when needed. | ||
| let inline getValueAt percentage interval = | ||
| match trySize interval with | ||
| | Some size -> percentage * (float size) | ||
| | None -> nan | ||
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| /// Does the given value lie in the interval or not. | ||
| let liesInInterval value interval = | ||
| match interval with | ||
| | ClosedInterval (min,max) -> value >= min && value <= max | ||
| | Empty -> false | ||
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| // #################################################### | ||
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| // interval tree | ||
| //http://www.geeksforgeeks.org/interval-tree/ | ||
| // https://fgiesen.wordpress.com/2011/10/16/checking-for-interval-overlap/ | ||
| // https://github.com/Whathecode/Framework-Class-Library-Extension/blob/master/Whathecode.System/Arithmetic/Range/Interval.cs | ||
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| ///// <summary> | ||
| ///// Get a percentage how far inside (0.0 - 1.0) or outside (< 0.0, > 1.0) the interval a certain value lies. | ||
| ///// For single intervals, '1.0' is returned when inside the interval, '-1.0' otherwise. | ||
| ///// </summary> | ||
| ///// <param name = "position">The position value to get the percentage for.</param> | ||
| ///// <returns>The percentage indicating how far inside (or outside) the interval the given value lies.</returns> | ||
| //let getPercentageFor position r = | ||
| // let inside = liesInInterval position r | ||
| // let sizeR = size r | ||
| // if (sizeR = 0.0) then | ||
| // if inside then 1.0 else -1.0 | ||
| // else | ||
| // let rangeP = create r.Start position | ||
| // size rangeP / sizeR | ||
| // | ||
| ///// Map a value from the source range, to a value in another range (target) linearly. | ||
| //let map source target value = | ||
| // let tmp = getPercentageFor value source | ||
| // getValueAt tmp target | ||
| // | ||
| ///// Limit a given value to the range of the intertval. When the value is smaller/bigger than the range, snap it to the range border. | ||
| //let clampSingelton value r = | ||
| // if value < r.Start then r.Start | ||
| // elif value > r.End then r.End | ||
| // else value | ||
| // | ||
| // | ||
| // | ||
| ///// Limit the target range to the source range. | ||
| ///// When part of the given range lies outside of this range, it isn't included in the resulting range. | ||
| //let clamp source target = | ||
| // failwith "not implemented" | ||
| // | ||
| // | ||
| ///// Split the interval into two intervals at the given point, or nearest valid point. | ||
| //let split atPoint interval = | ||
| // failwith "not implemented" | ||
| // | ||
| // | ||
| // | ||
| // | ||
| // | ||
| ///// Get values for each step within the interval. | ||
| //let getValues stepSize interval = | ||
| // let rec gen c = | ||
| // seq { | ||
| // if c <= interval.End then | ||
| // let uc = c + stepSize | ||
| // yield uc | ||
| // yield! gen uc | ||
| // } | ||
| // gen interval.Start | ||
| // | ||
| // | ||
| ///// Returns a reversed version of the current interval, swapping the start position with the end position. | ||
| //let reverse interval = | ||
| // create interval.End interval.Start | ||
| // | ||
| ///// Checks if interval is reversed | ||
| //let isReversed interval = | ||
| // interval.End < interval.Start | ||
| // | ||
| ///// Returns an interval offsetted from the current interval by a specified amount. | ||
| //let move amount interval = | ||
| // create (interval.Start + amount) (interval.End + amount) | ||
| // | ||
| ///// <summary> | ||
| ///// Returns a scaled version of the current interval, but prevents the interval from exceeding the values specified in a passed limit. | ||
| ///// This is useful to prevent <see cref="ArgumentOutOfRangeException" /> during calculations for certain types. | ||
| ///// </summary> | ||
| ///// <param name="scale"> | ||
| ///// Percentage to scale the interval up or down. | ||
| ///// Smaller than 1.0 to scale down, larger to scale up. | ||
| ///// </param> | ||
| ///// <param name="limit">The limit which the interval snaps to when scaling exceeds it.</param> | ||
| ///// <param name="aroundPercentage">The percentage inside the interval around which to scale.</param> | ||
| //let scale a = | ||
| // failwith "not implemented" | ||
| // | ||
| /////<summary> | ||
| ///// Returns an expanded interval of the current interval up to the given value. | ||
| ///// When the value lies within the interval the returned interval is the same. | ||
| ///// </summary> | ||
| ///// <param name = "value">The value up to which to expand the interval.</param> | ||
| ///// <param name = "include">Include the value to which is expanded in the interval.</param> | ||
| //let expandTo a = | ||
| // failwith "not implemented" | ||
| // | ||
| //let r1 = create 1.5 2.5 | ||
| //let r2 = create 2.0 4.5 | ||
| // | ||
| //let r3 = create 5.0 6.0 | ||
| // | ||
| // | ||
| //getPercentageFor 2.6 r1 | ||
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