Merge pull request #2 from bellacapilla/master

Addition of Pearson, Spearman and Kendall correlations.

src/FSharp.Stats/Correlation.fs

@@ -1,10 +1,79 @@
 namespace FSharp.Stats
 
-
-
 module Correlation =
 
     /// Pearson correlation 
-    let pearsonCorrelation dataA dataB = raise (System.NotImplementedException())
+    let inline pearson (seq1:seq<'T>) (seq2:seq<'T>) : float =
+        use e = seq1.GetEnumerator()
+        use e2 = seq2.GetEnumerator()
+        let zero = LanguagePrimitives.GenericZero< 'T > 
+        let one = LanguagePrimitives.GenericOne<'T> 
+        let rec loop n (sumX: 'T) (sumY: 'T) (sumXY: 'T) (sumXX: 'T) (sumYY: 'T) = 
+            match (e.MoveNext() && e2.MoveNext()) with
+                | true  -> 
+                    loop (n + one) (sumX + e.Current) (sumY + e2.Current) (sumXY + (e.Current * e2.Current)) (sumXX + (e.Current * e.Current)) (sumYY + (e2.Current * e2.Current))
+                | false -> 
+                    if n > zero then  
+
+                        // Covariance
+                        let cov = float ((sumXY * n) - (sumX * sumY))
+
+                        // Standard Deviation
+                        let stndDev1 = sqrt (float ((n * sumXX) - (sumX * sumX)))
+                        let stndDev2 = sqrt (float ((n * sumYY) - (sumY * sumY)))
+
+                        // Correlation
+                        cov / (stndDev1 * stndDev2)
+
+                    else nan
+        loop zero zero zero zero zero zero
+
+    /// Spearman Correlation (with ranks)
+    let spearman array1 array2 =
+
+        let spearRank1 = FSharp.Stats.Rank.rankFirst array1 
+        let spearRank2 = FSharp.Stats.Rank.rankFirst array2
+
+        pearson spearRank1 spearRank2
+
+    /// Kendall Correlation Coefficient 
+    let kendall (setA:_[]) (setB:_[]) =
+        let lengthArray = Array.length setA
+        let inline kendallCorrFun (setA:_[]) (setB:_[]) =
+            let rec loop i j cCon cDisc cTieA cTieB cPairs =      
+                if i < lengthArray - 1 then
+                    if j <= lengthArray - 1 then
+                        if j > i then
+                            if (setA.[i] > setA.[j] && setB.[i] > setB.[j]) || (setA.[i] < setA.[j] && setB.[i] < setB.[j]) then
+                                loop i (j+1) (cCon + 1.0) cDisc cTieA cTieB (cPairs + 1.0)
+
+                            elif (setA.[i] > setA.[j] && setB.[i] < setB.[j]) || (setA.[i] < setA.[j] && setB.[i] > setB.[j]) then
+                                loop i (j+1) cCon (cDisc + 1.0) cTieA cTieB (cPairs + 1.0)
+
+                            else
+                                if (setA.[i] = setA.[j]) then
+                                    loop i (j+1) cCon cDisc (cTieA + 1.0) cTieB (cPairs + 1.0)
+
+                                else
+                                    loop i (j+1) cCon cDisc cTieA (cTieB + 1.0) (cPairs + 1.0)
+                        else
+                            loop i (j+1) cCon cDisc cTieA cTieB cPairs
+
+                    else 
+                        loop (i+1) 1 cCon cDisc cTieA cTieB cPairs
+
+                else
+                    let floatLength = lengthArray |> float
 
+                    if (cTieA <> 0.0) || (cTieB <> 0.0) then
+                        let n = (floatLength * (floatLength - 1.0)) / 2.0
+                        let n1 = (cTieA * (cTieA - 1.0)) / 2.0
+                        let n2 = (cTieB * (cTieB - 1.0)) / 2.0
+                        (cCon - cDisc) / (sqrt ((n - n1) * (n - n2)))
+
+                    else
+                        (cCon - cDisc) / ((floatLength * (floatLength - 1.0)) / 2.0)
+
+            loop 0 1 0.0 0.0 0.0 0.0 0.0
 
+        kendallCorrFun (FSharp.Stats.Rank.rankFirst setA ) (FSharp.Stats.Rank.rankFirst setB )