Statistics: introduce unsorted ArrayStatistics

src/Numerics/Numerics.csproj

@@ -111,6 +111,7 @@
     <Compile Include="SpecialFunctions\ModifiedStruve.cs" />
     <Compile Include="SpecialFunctions\ModifiedBessel.cs" />
     <Compile Include="SpecialFunctions\Logistic.cs" />
+    <Compile Include="Statistics\ArrayStatistics.cs" />
     <Compile Include="Statistics\SortedArrayStatistics.cs" />
     <Compile Include="TargetedPatchingOptOutAttribute.cs" />
     <Compile Include="Distributions\Continuous\Cauchy.cs" />

src/Numerics/Statistics/ArrayStatistics.cs

@@ -0,0 +1,96 @@
+// <copyright file="ArrayStatistics.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+//
+// Copyright (c) 2009-2013 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace MathNet.Numerics.Statistics
+{
+    public static class ArrayStatistics
+    {
+        // TODO: Benchmark various options to find out the best approach (-> branch prediction)
+        // TODO: consider leveraging MKL 
+
+        /// <summary>
+        /// Returns the smallest value from the unsorted data array.
+        /// Returns NaN if data is empty or any entry is NaN.
+        /// </summary>
+        /// <param name="data">Sample array, no sorting is assumed.</param>
+        public static double Minimum(double[] data)
+        {
+            if (data == null || data.Length == 0) return double.NaN;
+
+            var min = double.PositiveInfinity;
+            for (int i = 0; i < data.Length; i++)
+            {
+                if (data[i] < min || double.IsNaN(data[i]))
+                {
+                    min = data[i];
+                }
+            }
+            return min;
+        }
+
+        /// <summary>
+        /// Returns the smallest value from the unsorted data array.
+        /// Returns NaN if data is empty or any entry is NaN.
+        /// </summary>
+        /// <param name="data">Sample array, no sorting is assumed.</param>
+        public static double Maximum(double[] data)
+        {
+            if (data == null || data.Length == 0) return double.NaN;
+
+            var max = double.NegativeInfinity;
+            for (int i = 0; i < data.Length; i++)
+            {
+                if (data[i] > max || double.IsNaN(data[i]))
+                {
+                    max = data[i];
+                }
+            }
+            return max;
+        }
+
+        /// <summary>
+        /// Returns the sample mean from the unsorted data array.
+        /// Returns NaN if data is empty or any entry is NaN.
+        /// </summary>
+        /// <param name="data">Sample array, no sorting is assumed.</param>
+        public static double Mean(double[] data)
+        {
+            if (data == null || data.Length == 0) return double.NaN;
+
+            double mean = 0;
+            ulong m = 0;
+            for (int i = 0; i < data.Length; i++)
+            {
+                mean += (data[i] - mean) / ++m;
+            }
+            return mean;
+        }
+    }
+}

src/Portable/Portable.csproj

@@ -1020,6 +1020,9 @@
     <Compile Include="..\numerics\specialfunctions\Stability.cs">
       <Link>SpecialFunctions\Stability.cs</Link>
     </Compile>
+    <Compile Include="..\Numerics\Statistics\ArrayStatistics.cs">
+      <Link>Statistics\ArrayStatistics.cs</Link>
+    </Compile>
     <Compile Include="..\Numerics\Statistics\Correlation.cs">
       <Link>Statistics\Correlation.cs</Link>
     </Compile>

src/UnitTests/StatisticsTests/StatisticsTests.cs

@@ -89,7 +89,8 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
         public void Mean(string dataSet)
         {
             var data = _data[dataSet];
-            AssertHelpers.AlmostEqual(data.Mean, data.Data.Mean(), 15);
+            AssertHelpers.AlmostEqual(data.Mean, Statistics.Mean(data.Data), 15);
+            AssertHelpers.AlmostEqual(data.Mean, ArrayStatistics.Mean(data.Data), 15);
         }
 
         /// <summary>
@@ -107,7 +108,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
         public void NullableMean(string dataSet)
         {
             var data = _data[dataSet];
-            AssertHelpers.AlmostEqual(data.Mean, data.DataWithNulls.Mean(), 15);
+            AssertHelpers.AlmostEqual(data.Mean, Statistics.Mean(data.DataWithNulls), 15);
         }
 
         /// <summary>
@@ -117,7 +118,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
         public void MeanThrowsArgumentNullException()
         {
             double[] data = null;
-            Assert.Throws<ArgumentNullException>(() => data.Mean());
+            Assert.Throws<ArgumentNullException>(() => Statistics.Mean(data));
         }
 
         /// <summary>
@@ -136,7 +137,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
         public void StandardDeviation(string dataSet, int digits)
         {
             var data = _data[dataSet];
-            AssertHelpers.AlmostEqual(data.StandardDeviation, data.Data.StandardDeviation(), digits);
+            AssertHelpers.AlmostEqual(data.StandardDeviation, Statistics.StandardDeviation(data.Data), digits);
         }
 
         /// <summary>
@@ -155,7 +156,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
         public void NullableStandardDeviation(string dataSet, int digits)
         {
             var data = _data[dataSet];
-            AssertHelpers.AlmostEqual(data.StandardDeviation, data.DataWithNulls.StandardDeviation(), digits);
+            AssertHelpers.AlmostEqual(data.StandardDeviation, Statistics.StandardDeviation(data.DataWithNulls), digits);
         }
 
         /// <summary>
@@ -165,7 +166,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
         public void StandardDeviationThrowsArgumentNullException()
         {
             double[] data = null;
-            Assert.Throws<ArgumentNullException>(() => data.StandardDeviation());
+            Assert.Throws<ArgumentNullException>(() => Statistics.StandardDeviation(data));
         }
 
         /// <summary>
@@ -175,8 +176,16 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
         public void ShortMinMax()
         {
             var samples = new[] {-1.0, 5, 0, -3, 10, -0.5, 4};
-            Assert.That(samples.Minimum(), Is.EqualTo(-3), "Min");
+            Assert.That(Statistics.Minimum(samples), Is.EqualTo(-3), "Min");
-            Assert.That(samples.Maximum(), Is.EqualTo(10), "Max");
+            Assert.That(Statistics.Maximum(samples), Is.EqualTo(10), "Max");
+            Assert.That(ArrayStatistics.Minimum(samples), Is.EqualTo(-3), "Min");
+            Assert.That(ArrayStatistics.Maximum(samples), Is.EqualTo(10), "Max");
+
+            var sorted = new double[samples.Length];
+            Array.Copy(samples, sorted, samples.Length);
+            Array.Sort(sorted);
+            Assert.That(SortedArrayStatistics.Minimum(sorted), Is.EqualTo(-3), "Min");
+            Assert.That(SortedArrayStatistics.Maximum(sorted), Is.EqualTo(10), "Max");
         }
 
         /// <summary>
@@ -187,11 +196,16 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
         {
             // -3 -1 -0.5 0  1  4 5 6 10
             var samples = new[] {-1, 5, 0, -3, 10, -0.5, 4, 1, 6};
-            Assert.That(samples.Median(), Is.EqualTo(1), "Median");
+            Assert.That(Statistics.Median(samples), Is.EqualTo(1), "Median");
             Assert.That(Statistics.OrderStatistic(samples, 1), Is.EqualTo(-3), "Order-1");
             Assert.That(Statistics.OrderStatistic(samples, 3), Is.EqualTo(-0.5), "Order-3");
             Assert.That(Statistics.OrderStatistic(samples, 7), Is.EqualTo(5), "Order-7");
             Assert.That(Statistics.OrderStatistic(samples, 9), Is.EqualTo(10), "Order-9");
+
+            var sorted = new double[samples.Length];
+            Array.Copy(samples, sorted, samples.Length);
+            Array.Sort(sorted);
+            Assert.That(SortedArrayStatistics.Median(sorted), Is.EqualTo(1), "Median");
         }
 
         /// <summary>
@@ -208,9 +222,9 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
                     RandomSource = new Numerics.Random.MersenneTwister(100)
                 };
 
-            AssertHelpers.AlmostEqual(1e+9, gaussian.Samples().Take(10000).Mean(), 11);
+            AssertHelpers.AlmostEqual(1e+9, Statistics.Mean(gaussian.Samples().Take(10000)), 11);
-            AssertHelpers.AlmostEqual(4d, gaussian.Samples().Take(10000).Variance(), 1);
+            AssertHelpers.AlmostEqual(4d, Statistics.Variance(gaussian.Samples().Take(10000)), 1);
-            AssertHelpers.AlmostEqual(2d, gaussian.Samples().Take(10000).StandardDeviation(), 2);
+            AssertHelpers.AlmostEqual(2d, Statistics.StandardDeviation(gaussian.Samples().Take(10000)), 2);
         }
 
         /// <summary>
@@ -219,8 +233,12 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
         [Test]
         public void Median_CodeplexIssue5667()
         {
-            var seq = File.ReadLines("./data/Codeplex-5667.csv").Select(s => double.Parse(s));
+            var seq = File.ReadLines("./data/Codeplex-5667.csv").Select(double.Parse);
-            Assert.AreEqual(1.0, seq.Median());
+            Assert.AreEqual(1.0, Statistics.Median(seq));
+
+            var sorted = seq.ToArray();
+            Array.Sort(sorted);
+            Assert.AreEqual(1.0, SortedArrayStatistics.Median(sorted));
         }
     }
 #endif