Merge pull request #287 from fslaborg/update-interval

docs/Interpolation.fsx

@@ -444,7 +444,7 @@ To reduce this overfitting you can use x axis nodes that are spaced according to
 // new x values are determined in the x axis range of the data. These should reduce overshooting behaviour.
 // since the original data consisted of 16 points, 16 nodes are initialized
 let xs_cheby = 
-    Interpolation.Approximation.chebyshevNodes (Intervals.Interval<float>.Create(0.,3.)) 16
+    Interpolation.Approximation.chebyshevNodes (Interval.CreateClosed(0.,3.)) 16
 
 // to get the corresponding y values to the xs_cheby a linear spline is generated that approximates the new y values
 let ys_cheby =

docs/Intervals.fsx

@@ -38,7 +38,8 @@ The interval module enables working with closed intervals. A closed interval inc
 
   - $[1,2], \left\{ x | 1 \le x \le 2 \right\}$ - closed interval; 1 and 2 are _included_
   - $(1,2), \left\{ x | 1 < x < 2 \right\}$ - open interval; 1 and 2 are _excluded_
-  - $[1,2), \left\{ x | 1 \le x < 2 \right\}$ - half open interval; 1 is _included_ but 2 is _excluded_
+  - $[1,2), \left\{ x | 1 \le x < 2 \right\}$ - right open interval; 1 is _included_ but 2 is _excluded_
+  - $(1,2], \left\{ x | 1 < x \le 2 \right\}$ - left open interval; 1 is _excluded_ but 2 is _included_
 
 
 **Interval creation**
@@ -47,8 +48,17 @@ The interval module enables working with closed intervals. A closed interval inc
 open FSharp.Stats
 open Plotly.NET
 
+let myInterval = Interval.CreateLeftOpen (-3.,2.)
+
+let loi = sprintf "myInterval is: %s" (myInterval.ToString())
+
+(*** include-value:loi***)
+
+(**
+When intervals are created from sequences, always closed intervals are generated!
+*)
 let collection = [3.0; -2.0; 5.0; 1.0; -6.0; 100.0]
-let interval = Intervals.ofSeq collection
+let interval = Interval.ofSeq collection
 
 (*** include-value:interval***)
 
@@ -64,7 +74,7 @@ open Plotly.NET.StyleParam
 
 let interval01 = 
     Chart.Point([])
-    |> Chart.withShape (Shape.init(ShapeType=ShapeType.Rectangle,X0=Intervals.getStart interval,X1=Intervals.getEnd interval,Y0=1,Y1=2,FillColor=Color.fromHex "#1f77b4"))
+    |> Chart.withShape (Shape.init(ShapeType=ShapeType.Rectangle,X0=Interval.getStart interval,X1=Interval.getEnd interval,Y0=1,Y1=2,FillColor=Color.fromHex "#1f77b4"))
     |> Chart.withTemplate ChartTemplates.lightMirrored
     |> Chart.withXAxisStyle ("",MinMax=(-10.,120.))
     |> Chart.withYAxisStyle ("",MinMax=(0.,5.))
@@ -83,8 +93,8 @@ interval01 |> GenericChart.toChartHTML
 *)
 
 let collectionBy = [("a",3.0); ("b",-2.0); ("c",5.0); ("d",1.0); ("e",-6.0); ("f",100.0)]
-let intervalByFst = Intervals.ofSeqBy fst collectionBy
-let intervalBySnd = Intervals.ofSeqBy snd collectionBy
+let intervalByFst = Interval.ofSeqBy fst collectionBy
+let intervalBySnd = Interval.ofSeqBy snd collectionBy
 
 (*** include-value:intervalByFst***)
 (*** include-value:intervalBySnd***)
@@ -104,15 +114,15 @@ i + j = [a+b,c+d]
 
 *)
 
-let i02 = Intervals.create 6.  8.
-let i03 = Intervals.create 5. 10.
-let addedInterval = Intervals.add i02 i03
+let i02 = Interval.CreateClosed<float> (6.,8.)
+let i03 = Interval.CreateClosed<float> (5.,10.)
+let addedInterval = Interval.add i02 i03
 
 (*** hide ***)
 let interval02 = 
-    let i1 = Shape.init(ShapeType=ShapeType.Rectangle,X0=Intervals.getStart i02,X1=Intervals.getEnd i02,Y0=1,Y1=2,FillColor=Color.fromHex "#1f77b4")
-    let i2 = Shape.init(ShapeType=ShapeType.Rectangle,X0=Intervals.getStart i03,X1=Intervals.getEnd i03,Y0=3,Y1=4,FillColor=Color.fromHex "#ff7f0e")
-    let re = Shape.init(ShapeType=ShapeType.Rectangle,X0=Intervals.getStart addedInterval,X1=Intervals.getEnd addedInterval,Y0=5,Y1=6,FillColor=Color.fromHex "#2ca02c")
+    let i1 = Shape.init(ShapeType=ShapeType.Rectangle,X0=Interval.getStart i02,X1=Interval.getEnd i02,Y0=1,Y1=2,FillColor=Color.fromHex "#1f77b4")
+    let i2 = Shape.init(ShapeType=ShapeType.Rectangle,X0=Interval.getStart i03,X1=Interval.getEnd i03,Y0=3,Y1=4,FillColor=Color.fromHex "#ff7f0e")
+    let re = Shape.init(ShapeType=ShapeType.Rectangle,X0=Interval.getStart addedInterval,X1=Interval.getEnd addedInterval,Y0=5,Y1=6,FillColor=Color.fromHex "#2ca02c")
     Chart.Point([])
     |> Chart.withShapes [i1;i2;re]
     |> Chart.withTemplate ChartTemplates.lightMirrored
@@ -137,13 +147,13 @@ i - j = [a-d,b-c]
 
 *)
 
-let subInterval = Intervals.subtract i02 i03
+let subInterval = Interval.subtract i02 i03
 
 (*** hide ***)
 let interval03 = 
-    let i1 = Shape.init(ShapeType=ShapeType.Rectangle,X0=Intervals.getStart i02,X1=Intervals.getEnd i02,Y0=1,Y1=2,FillColor=Color.fromHex "#1f77b4")
-    let i2 = Shape.init(ShapeType=ShapeType.Rectangle,X0=Intervals.getStart i03,X1=Intervals.getEnd i03,Y0=3,Y1=4,FillColor=Color.fromHex "#ff7f0e")
-    let re = Shape.init(ShapeType=ShapeType.Rectangle,X0=Intervals.getStart subInterval,X1=Intervals.getEnd subInterval,Y0=5,Y1=6,FillColor=Color.fromHex "#2ca02c")
+    let i1 = Shape.init(ShapeType=ShapeType.Rectangle,X0=Interval.getStart i02,X1=Interval.getEnd i02,Y0=1,Y1=2,FillColor=Color.fromHex "#1f77b4")
+    let i2 = Shape.init(ShapeType=ShapeType.Rectangle,X0=Interval.getStart i03,X1=Interval.getEnd i03,Y0=3,Y1=4,FillColor=Color.fromHex "#ff7f0e")
+    let re = Shape.init(ShapeType=ShapeType.Rectangle,X0=Interval.getStart subInterval,X1=Interval.getEnd subInterval,Y0=5,Y1=6,FillColor=Color.fromHex "#2ca02c")
     Chart.Point([])
     |> Chart.withShapes [i1;i2;re]
     |> Chart.withTemplate ChartTemplates.lightMirrored
@@ -162,15 +172,15 @@ Closed intervals include their margins. If a margin is shared between two interv
 
 *)
 
-let i04 = Intervals.create 2.  8.
-let i05 = Intervals.create 5. 10.
-let intInterval = Intervals.intersect i04 i05
+let i04 = Interval.CreateClosed<float> (2.,8.)
+let i05 = Interval.CreateClosed<float> (5.,10.)
+let intInterval = Interval.intersect i04 i05
 
 (*** hide ***)
 let interval04 = 
-    let i1 = Shape.init(ShapeType=ShapeType.Rectangle,X0=Intervals.getStart i04,X1=Intervals.getEnd i04,Y0=1,Y1=2,FillColor=Color.fromHex "#1f77b4")
-    let i2 = Shape.init(ShapeType=ShapeType.Rectangle,X0=Intervals.getStart i05,X1=Intervals.getEnd i05,Y0=3,Y1=4,FillColor=Color.fromHex "#ff7f0e")
-    let re = Shape.init(ShapeType=ShapeType.Rectangle,X0=Intervals.getStart intInterval.Value,X1=Intervals.getEnd intInterval.Value,Y0=5,Y1=6,FillColor=Color.fromHex "#2ca02c")
+    let i1 = Shape.init(ShapeType=ShapeType.Rectangle,X0=Interval.getStart i04,X1=Interval.getEnd i04,Y0=1,Y1=2,FillColor=Color.fromHex "#1f77b4")
+    let i2 = Shape.init(ShapeType=ShapeType.Rectangle,X0=Interval.getStart i05,X1=Interval.getEnd i05,Y0=3,Y1=4,FillColor=Color.fromHex "#ff7f0e")
+    let re = Shape.init(ShapeType=ShapeType.Rectangle,X0=Interval.getStart intInterval,X1=Interval.getEnd intInterval,Y0=5,Y1=6,FillColor=Color.fromHex "#2ca02c")
     Chart.Point([])
     |> Chart.withShapes [i1;i2;re]
     |> Chart.withTemplate ChartTemplates.lightMirrored

docs/Signal.fsx

@@ -73,15 +73,15 @@ let sampleO1 = [|45.;42.;45.5;43.;47.;51.;34.;45.;44.;46.;48.;37.;46.;|]
 
 let outlierBordersO1 = Signal.Outliers.tukey 1.5 sampleO1
 
-let lowerBorderO1 = Intervals.getStart outlierBordersO1
+let lowerBorderO1 = Interval.getStart outlierBordersO1
 // result: 37.16667
 
-let upperBorderO1 = Intervals.getEnd outlierBordersO1
+let upperBorderO1 = Interval.getEnd outlierBordersO1
 // result: 51.83333
 
 let (inside,outside) =
     sampleO1 
-    |> Array.partition (fun x -> Intervals.liesInInterval x outlierBordersO1)
+    |> Array.partition (fun x -> outlierBordersO1.liesInInterval x)
 
 let tukeyOutlierChart =
     [

src/FSharp.Stats/Array.fs

@@ -12,12 +12,12 @@ module Array =
                 let current = a.[index]
                 loop (index+1) (min current minimum) (max current maximum)
             else
-                Intervals.create minimum maximum          
+                Interval.CreateClosed<'a> (minimum,maximum)
         //Init by fist value
         if a.Length > 1 then
             loop 1 a.[0] a.[0] 
         else
-            Intervals.Interval.Empty
+            Interval.Empty
 
 
     // Swaps items of left and right index

src/FSharp.Stats/ConfidenceInterval.fs

@@ -16,4 +16,4 @@ module ConfidenceInterval =
     let ci ciLevel (sample : seq<float>)=
         let mean  = Seq.mean  sample
         let delta = ciDeviation ciLevel sample
-        Intervals.create (mean - delta) (mean + delta)
+        Interval.CreateClosed<float> ((mean - delta),(mean + delta))

src/FSharp.Stats/Distributions/Bandwidth.fs

@@ -46,7 +46,7 @@ module Bandwidth =
             |> Seq.filter (fun v -> not (isInf v))
 
         let interval = Seq.range data' 
-        let dmin,dmax = Intervals.values interval
+        let dmin,dmax = Interval.values interval
 
         fromBinNumber dmin dmax (float(Seq.length(data)))
 

src/FSharp.Stats/Distributions/Continuous/ChiSquared.fs

@@ -84,7 +84,7 @@ type ChiSquared =
     /// Returns the support of the exponential distribution: [0, Positive Infinity).
     static member Support dof =
         ChiSquared.CheckParam dof
-        Intervals.create 0. System.Double.PositiveInfinity
+        Interval.CreateClosed<float> (0.,System.Double.PositiveInfinity)
 
 
     /// A string representation of the distribution.

src/FSharp.Stats/Distributions/Continuous/Exponential.fs

@@ -90,7 +90,7 @@ type Exponential =
     /// Returns the support of the exponential distribution: [0, Positive Infinity).
     static member Support lambda =
         Exponential.CheckParam lambda
-        Intervals.create 0.0 System.Double.PositiveInfinity
+        Interval.CreateClosed<float> (0.0,System.Double.PositiveInfinity)
 
 
     /// A string representation of the distribution.

src/FSharp.Stats/Distributions/Continuous/Uniform.fs

@@ -78,7 +78,7 @@ type Uniform =
     /// Returns the support of the exponential distribution: [0, Positive Infinity).
     static member Support min max =
         Uniform.CheckParam min max
-        Intervals.create min max
+        Interval.CreateClosed<float> (min,max)
 
     /// A string representation of the distribution.
     static member ToString min max =

src/FSharp.Stats/Distributions/Discrete/Bernoulli.fs

@@ -94,7 +94,7 @@ type Bernoulli =
     /// Returns the support of the bernoulli distribution: {0, 1}.
     static member Support p =
         Bernoulli.CheckParam p
-        Intervals.create 0 1 
+        Interval.CreateClosed<int> (0,1) 
 
     /// A string representation of the distribution.
     static member ToString p =

src/FSharp.Stats/Distributions/Discrete/Binomial.fs

@@ -119,7 +119,7 @@ type Binomial =
     /// Returns the support of the Binomial distribution: (0., n).
     static member Support p n =
         Binomial.CheckParam p n
-        Intervals.create 0 n
+        Interval.CreateClosed<int> (0,n)
 
 
     /// A string representation of the distribution.

src/FSharp.Stats/Distributions/Discrete/Hypergeometric.fs

@@ -150,7 +150,7 @@ type Hypergeometric =
     /// Returns the support of the hypergeometric distribution: (0., Positive Infinity).
     static member Support N K n =
         Hypergeometric.CheckParam N K n
-        Intervals.create (max 0 (n + K - N) ) (min K n)
+        Interval.CreateClosed<int> ((max 0 (n + K - N) ),(min K n))
 
 
 

src/FSharp.Stats/Distributions/Discrete/Poisson.fs

@@ -141,7 +141,7 @@ type Poisson =
     /// Returns the support interval for this distribution.
     static member Support lambda =
         Poisson.CheckParam lambda
-        Intervals.create 0 System.Int32.MaxValue
+        Interval.CreateClosed<int> (0,System.Int32.MaxValue)
 
     /// A string representation of the distribution.
     static member ToString lambda =

src/FSharp.Stats/Distributions/KernelDensity.fs

@@ -133,7 +133,7 @@ module KernelDensity =
 
 
     let estimateWithWeight weights kernel bandwidth data =
-        let _from,_to = Array.range data |> Intervals.values
+        let _from,_to = Array.range data |> Interval.values
         estimateWith 3 _from _to 512 weights kernel bandwidth data
 
 
@@ -143,7 +143,7 @@ module KernelDensity =
 
 
     let estimate kernel bandwidth data =
-        let _from,_to = Array.range data |> Intervals.values
+        let _from,_to = Array.range data |> Interval.values
         let weights = Array.create data.Length (1./float data.Length)
         estimateWith 3 _from _to 512 weights kernel bandwidth data
 

src/FSharp.Stats/FSharp.Stats.fsproj

@@ -35,7 +35,7 @@
     <Compile Include="Ops.fs" />
     <Compile Include="Random.fs" />
     <Compile Include="ServiceLocator.fs" />
-    <Compile Include="Intervals.fs" />
+    <Compile Include="Interval.fs" />
     <Compile Include="Permutation.fs" />
     <Compile Include="BigRational.fs" />
     <Compile Include="INumeric.fs" />

src/FSharp.Stats/Interpolation.fs

@@ -1482,7 +1482,7 @@ module Interpolation =
         /// <param name="n">number of points that should be placed within the interval (incl. start and end)</param>
         /// <returns>Collection of chebyshev spaced x values.</returns>
         /// <remarks>www.mscroggs.co.uk/blog/57</remarks>
-        let chebyshevNodes (interval: Intervals.Interval<float>) n = 
+        let chebyshevNodes (interval: Interval<float>) n = 
             let center = 0.5 * (interval.TryStart.Value + interval.TryEnd.Value)
             let halfrange = 0.5 * (interval.TryEnd.Value - interval.TryStart.Value) 
             Array.init n (fun i -> 
@@ -1497,8 +1497,8 @@ module Interpolation =
         /// <param name="interval">start and end value of interpolation range</param>
         /// <param name="n">number of points that should be placed within the interval (incl. start and end)</param>
         /// <returns>Collection of equally spaced x values.</returns>
-        let equalNodes (interval: Intervals.Interval<float>) n = 
-            let range = Intervals.getSize interval
+        let equalNodes (interval: Interval<float>) n = 
+            let range = Interval.getSize interval
             Vector.init n (fun k -> interval.TryStart.Value + float k * range / (float n - 1.))
 
 
@@ -1513,7 +1513,7 @@ module Interpolation =
         /// <param name="n">number of points that should be placed within the interval (incl. start and end)</param>
         /// <param name="spacing">X values can be spaced equally or according to chebyshev.</param>
         /// <returns>Coefficients for polynomial interpolation. Use Polynomial.fit to predict function values.</returns>
-        static member approxWithPolynomial (f: float -> float,i: Intervals.Interval<float>,n: int,spacing: Approximation.Spacing) = 
+        static member approxWithPolynomial (f: float -> float,i: Interval<float>,n: int,spacing: Approximation.Spacing) = 
             match spacing with
             | Approximation.Equally -> 
                 let xVal = Approximation.equalNodes i n 
@@ -1536,14 +1536,14 @@ module Interpolation =
         static member approxWithPolynomialFromValues (xData: seq<float>,yData: seq<float>,n: int,spacing: Approximation.Spacing) = 
             match spacing with
             | Approximation.Equally -> 
-                let i = Intervals.ofSeq xData
+                let i = Interval.ofSeq xData
                 let linearSplineCoeff = LinearSpline.interpolate (Array.ofSeq xData) (Array.ofSeq yData)
                 let f = LinearSpline.predict linearSplineCoeff
                 let xVal = Approximation.equalNodes i n 
                 let yVal = Vector.map f xVal
                 Polynomial.interpolate xVal yVal
             | Approximation.Chebyshev ->    
-                let i = Intervals.ofSeq xData
+                let i = Interval.ofSeq xData
                 let linearSplineCoeff = LinearSpline.interpolate (Array.ofSeq xData) (Array.ofSeq yData)
                 let f = LinearSpline.predict linearSplineCoeff
                 let xVal = Approximation.chebyshevNodes i n