Add Spearman Rank Correlation Coefficient

More more info see
https://en.wikipedia.org/wiki/Spearman_rank_correlation

src/Examples/Statistics.cs

@@ -77,7 +77,7 @@ namespace Examples
             Console.WriteLine(@"{0} - Standard deviation", chiSquare.StdDev.ToString(" #0.00000;-#0.00000"));
             Console.WriteLine(@"{0} - Skewness", chiSquare.Skewness.ToString(" #0.00000;-#0.00000"));
             Console.WriteLine();
-            
+
             // 2. Generate 1000 samples of the ChiSquare(5) distribution
             Console.WriteLine(@"2. Generate 1000 samples of the ChiSquare(5) distribution");
             var data = new double[1000];
@@ -120,12 +120,14 @@ namespace Examples
 
             // 5. Correlation coefficient between 1000 samples of ChiSquare(5) and ChiSquare(2.5)
             Console.WriteLine(@"5. Correlation coefficient between 1000 samples of ChiSquare(5) and ChiSquare(2.5) is {0}", Correlation.Pearson(data, dataB).ToString("N04"));
+            Console.WriteLine(@"6. Ranked correlation coefficient between 1000 samples of ChiSquare(5) and ChiSquare(2.5) is {0}", Correlation.Spearman(data, dataB).ToString("N04"));
             Console.WriteLine();
 
             // 6. Correlation coefficient between 1000 samples of f(x) = x * 2 and f(x) = x * x
             data = SignalGenerator.EquidistantInterval(x => x * 2, 0, 100, 1000);
             dataB = SignalGenerator.EquidistantInterval(x => x * x, 0, 100, 1000);
-            Console.WriteLine(@"6. Correlation coefficient between 1000 samples of f(x) = x * 2 and f(x) = x * x is {0}", Correlation.Pearson(data, dataB).ToString("N04"));
+            Console.WriteLine(@"7. Correlation coefficient between 1000 samples of f(x) = x * 2 and f(x) = x * x is {0}", Correlation.Pearson(data, dataB).ToString("N04"));
+            Console.WriteLine(@"8. Ranked correlation coefficient between 1000 samples of f(x) = x * 2 and f(x) = x * x is {0}", Correlation.Spearman(data, dataB).ToString("N04"));
             Console.WriteLine();
         }
     }

src/Numerics/Statistics/Correlation.cs

@@ -32,7 +32,7 @@ namespace MathNet.Numerics.Statistics
 {
     using System;
     using System.Collections.Generic;
-    using Properties;
+    using System.Linq;
 
     /// <summary>
     /// A class with correlation measures between two datasets.
@@ -88,5 +88,47 @@ namespace MathNet.Numerics.Statistics
 
             return r / Math.Sqrt(varA * varB);
         }
+
+        /// <summary>
+        /// Computes the Spearman Ranked Correlation Coefficient.
+        /// </summary>
+        /// <param name="dataA">Sample data series A.</param>
+        /// <param name="dataB">Sample data series B.</param>
+        /// <returns>The Spearman Ranked Correlation Coefficient.</returns>
+        public static double Spearman(IEnumerable<double> dataA, IEnumerable<double> dataB)
+        {
+            return Pearson(RankedSeries(dataA.ToList()), RankedSeries(dataB.ToList()));
+        }
+
+        private static IEnumerable<double> RankedSeries(ICollection<double> series)
+        {
+            if (series == null || series.Count == 0)
+                return Enumerable.Empty<double>();
+
+            var rankedSamples = series.Select((sample, index) => new { Sample = sample, RankIndex = index }).OrderBy(s => s.Sample).ToList();
+
+            var rankedArray = new double[series.Count];
+
+            var previousSample = rankedSamples.Select((sampleIndex, index) => new { SampleIndex = sampleIndex, LoopIndex = index }).First();
+            foreach (var rankedSampleIndex in rankedSamples.Select((sampleIndex, index) => new { SampleIndex = sampleIndex, LoopIndex = index }))
+            {
+                var currentSample = rankedSampleIndex;
+
+                if (Math.Abs(currentSample.SampleIndex.Sample - previousSample.SampleIndex.Sample) <= 0)
+                    continue;
+
+                var rankedValue = (currentSample.LoopIndex + previousSample.LoopIndex - 1) / 2d + 1;
+                foreach (var index in Enumerable.Range(previousSample.LoopIndex, currentSample.LoopIndex - previousSample.LoopIndex))
+                    rankedArray[rankedSamples[index].RankIndex] = rankedValue;
+
+                previousSample = currentSample;
+            }
+
+            var finalValue = (rankedSamples.Count + previousSample.LoopIndex - 1) / 2d + 1;
+            foreach (var index in Enumerable.Range(previousSample.LoopIndex, rankedSamples.Count - previousSample.LoopIndex))
+                rankedArray[rankedSamples[index].RankIndex] = finalValue;
+
+            return rankedArray;
+        }
     }
 }

src/UnitTests/StatisticsTests/CorrelationTests.cs

@@ -71,7 +71,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
             var dataB = _data["lew"].Data.Take(200);
 
             var corr = Correlation.Pearson(dataA, dataB);
-            AssertHelpers.AlmostEqual(corr, -0.029470861580726, 13);
+            AssertHelpers.AlmostEqual(-0.029470861580726, corr, 13);
         }
 
         /// <summary>
@@ -84,6 +84,30 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
             var dataB = _data["lew"].Data;
             Assert.Throws<ArgumentOutOfRangeException>(() => Correlation.Pearson(dataA, dataB));
         }
+
+        /// <summary>
+        /// Spearman correlation test.
+        /// </summary>
+        [Test]
+        public void SpearmanCorrelationTest()
+        {
+            var dataA = _data["lottery"].Data.Take(200);
+            var dataB = _data["lew"].Data.Take(200);
+
+            var corr = Correlation.Spearman(dataA, dataB);
+            AssertHelpers.AlmostEqual(-0.0382856977898528, corr, 13);
+        }
+
+        /// <summary>
+        /// Spearman correlation test fail.
+        /// </summary>
+        [Test]
+        public void SpearmanCorrelationTestFail()
+        {
+            var dataA = _data["lottery"].Data;
+            var dataB = _data["lew"].Data;
+            Assert.Throws<ArgumentOutOfRangeException>(() => Correlation.Spearman(dataA, dataB));
+        }
     }
 #endif
 }