Added StreamingStatistics.Entropy function

src/Numerics/Statistics/StreamingStatistics.cs

@@ -309,5 +309,44 @@ namespace MathNet.Numerics.Statistics
             }
             return comoment/n;
         }
+
+        /// <summary>
+        /// Calculates the entropy of a stream of double values. 
+        /// Returns NaN if any of the values in the stream are NaN.
+        /// </summary>
+        /// <param name="stream">The input stream to evaluate.</param>
+        /// <returns></returns>
+        public static double Entropy(IEnumerable<double> stream)
+        {
+            // http://en.wikipedia.org/wiki/Shannon_entropy
+
+            var index = new Dictionary<double, double>();
+
+            // count the number of occurrences of each item in the stream
+            int totalCount = 0;
+            foreach (double value in stream)
+            {
+                if (double.IsNaN(value)) return double.NaN;
+
+                double currentValueCount = 0;
+                
+                if (index.TryGetValue(value, out currentValueCount))
+                    index[value] = ++currentValueCount;
+                else
+                    index.Add(value, 1);
+                
+                ++totalCount;
+            }
+
+            // calculate the entropy of the stream
+            double entropy = 0;            
+            foreach (var item in index)
+            {
+                double p = item.Value / totalCount;
+                entropy += p * Math.Log(p, 2);
+            }
+
+            return -entropy;
+        }
     }
 }

src/UnitTests/StatisticsTests/StatisticsTests.cs

@@ -115,6 +115,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
             Assert.That(() => StreamingStatistics.PopulationStandardDeviation(data), Throws.Exception.TypeOf<NullReferenceException>());
             Assert.That(() => StreamingStatistics.Covariance(data, data), Throws.Exception.TypeOf<NullReferenceException>());
             Assert.That(() => StreamingStatistics.PopulationCovariance(data, data), Throws.Exception.TypeOf<NullReferenceException>());
+            Assert.That(() => StreamingStatistics.Entropy(data), Throws.Exception.TypeOf<NullReferenceException>());
 
             Assert.That(() => new RunningStatistics(data), Throws.Exception);
             Assert.That(() => new RunningStatistics().PushRange(data), Throws.Exception);
@@ -173,6 +174,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
             Assert.DoesNotThrow(() => StreamingStatistics.PopulationStandardDeviation(data));
             Assert.DoesNotThrow(() => StreamingStatistics.Covariance(data, data));
             Assert.DoesNotThrow(() => StreamingStatistics.PopulationCovariance(data, data));
+            Assert.DoesNotThrow(() => StreamingStatistics.Entropy(data));
 
             Assert.That(() => new RunningStatistics(data), Throws.Nothing);
             Assert.That(() => new RunningStatistics().PushRange(data), Throws.Nothing);
@@ -1013,6 +1015,33 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
             Assert.That(new DescriptiveStatistics(shorter).Kurtosis, Is.EqualTo(-1.36).Within(1e-4), "DescriptiveStatistics.Kurtosis: shorter");
             Assert.That(new DescriptiveStatistics(longer).Kurtosis, Is.EqualTo(-1.36).Within(1e-4), "DescriptiveStatistics.Kurtosis: longer");
         }
+
+        [Test]
+        public void EntropyIsMinimum()
+        {
+            var data1 = new double[] { 1, 1, 1, 1, 1 };
+            Assert.That(StreamingStatistics.Entropy(data1) == 0);
+
+            var data2 = new double[] { 0, 0 };
+            Assert.That(StreamingStatistics.Entropy(data2) == 0);
+        }
+
+        [Test]
+        public void EntropyIsMaximum()
+        {
+            var data1 = new double[] { 1, 2  };
+            Assert.That(StreamingStatistics.Entropy(data1) == 1.0);
+
+            var data2 = new double[] { 1, 2, 3, 4 };
+            Assert.That(StreamingStatistics.Entropy(data2) == 2.0);
+        }
+
+        [Test]
+        public void EntropyOfNaNIsNaN()
+        {
+            var data = new double[] { 1, 2, double.NaN };
+            Assert.That(double.IsNaN(StreamingStatistics.Entropy(data)));
+        }
     }
 }