Changeset 13033 for trunk/sources/HeuristicLab.Tests/HeuristicLab.Common-3.3/EnumerableStatisticExtensions.cs

Timestamp:

10/19/15 16:13:14 (9 years ago)

Author:

gkronber

Message:

#2418: implemented O(n) algorithm for median (and general quantiles) determination.

File:

• trunk/sources/HeuristicLab.Tests/HeuristicLab.Common-3.3/EnumerableStatisticExtensions.cs (modified) (2 diffs)

trunk/sources/HeuristicLab.Tests/HeuristicLab.Common-3.3/EnumerableStatisticExtensions.cs

@@ -20 +20 @@
 #endregion
 
+using System;
+using System.Collections.Generic;
+using System.Diagnostics;
+using System.Diagnostics.Contracts;
 using System.Linq;
 using HeuristicLab.Common;
+using HeuristicLab.Random;
 using Microsoft.VisualStudio.TestTools.UnitTesting;
 
@@ -31 +36 @@
     [TestProperty("Time", "short")]
     public void QuantileTest() {
+      {
+        Assert.AreEqual(2.0, new double[] { 2.0 }.Quantile(0.5));
+        Assert.AreEqual(2.0, new double[] { 2.0 }.Quantile(0.01));
+        Assert.AreEqual(2.0, new double[] { 2.0 }.Quantile(0.99));
+      }
+
+      {
+        Assert.AreEqual(1.5, new double[] { 1.0, 2.0 }.Median());
+        Assert.AreEqual(2.0, new double[] { 1.0, 2.0 }.Quantile(0.99));
+        Assert.AreEqual(1.0, new double[] { 1.0, 2.0 }.Quantile(0.01));
+      }
+      {
+        Assert.AreEqual(2.0, new double[] { 3.0, 1.0, 2.0 }.Median());
+        Assert.AreEqual(3.0, new double[] { 3.0, 1.0, 2.0 }.Quantile(0.99));
+        Assert.AreEqual(1.0, new double[] { 3.0, 1.0, 2.0 }.Quantile(0.01));
+      }
+
+
       var xs = new double[] { 1, 1, 1, 3, 4, 7, 9, 11, 13, 13 };
       {
-        var q = xs.Quantile(0.3);
-        Assert.AreEqual(q, 2.0, 1E-6);
+        var q0 = Quantile(xs, 0.3); // naive implementation using sorting
+        Assert.AreEqual(q0, 2.0, 1E-6);
+
+        var q1 = xs.Quantile(0.3); // using select
+        Assert.AreEqual(q1, 2.0, 1E-6);
       }
       {
-        var q = xs.Quantile(0.75);
-        Assert.AreEqual(q, 11.0, 1E-6);
+        var q0 = Quantile(xs, 0.75); // naive implementation using sorting
+        Assert.AreEqual(q0, 11.0, 1E-6);
+
+        var q1 = xs.Quantile(0.75); // using select
+        Assert.AreEqual(q1, 11.0, 1E-6);
       }
       // quantile = 0.5 is equivalent to median
       {
         // even number of elements
-        Assert.AreEqual(xs.Quantile(0.5), xs.Median(), 1E-6);
+        var expected = Median(xs);
+        Assert.AreEqual(expected, Quantile(xs, 0.5), 1E-6); // using sorting
+        Assert.AreEqual(expected, xs.Quantile(0.5), 1E-6); // using select
       }
       {
         // odd number of elements
-        Assert.AreEqual(xs.Take(9).Quantile(0.5), xs.Take(9).Median(), 1E-6);
+        var expected = Median(xs.Take(9));
+        Assert.AreEqual(expected, Quantile(xs.Take(9), 0.5), 1E-6); // using sorting
+        Assert.AreEqual(expected, xs.Take(9).Quantile(0.5), 1E-6); // using select
+      }
+
+      // edge cases
+      {
+        try {
+          new double[] { }.Quantile(0.5); // empty
+          Assert.Fail("expected exception");
+        }
+        catch (Exception) {
+        }
+      }
+      {
+        try {
+          Enumerable.Repeat(0.0, 10).Quantile(1.0); // alpha < 1 
+          Assert.Fail("expected exception");
+        }
+        catch (Exception) {
+        }
+      }
+    }
+
+    [TestMethod]
+    [TestCategory("General")]
+    [TestProperty("Time", "medium")]
+    public void QuantilePerformanceTest() {
+      int n = 10;
+      var sw0 = new Stopwatch();
+      var sw1 = new Stopwatch();
+      const int reps = 1000;
+      while (n <= 1000000) {
+        for (int i = 0; i < reps; i++) {
+          var xs = RandomEnumerable.SampleRandomNumbers(0, 10000, n + 1).Select(x => (double)x).ToArray();
+          sw0.Start();
+          var q0 = Median(xs); // sorting
+          sw0.Stop();
+
+
+          sw1.Start();
+          var q1 = xs.Median(); // selection
+          sw1.Stop();
+          Assert.AreEqual(q0, q1, 1E-9);
+        }
+        Console.WriteLine("{0,-10} {1,-10} {2,-10}", n, sw0.ElapsedMilliseconds, sw1.ElapsedMilliseconds);
+
+        n = n * 10;
+      }
+    }
+
+
+    // straight forward implementation of median function (using sorting)
+    private static double Median(IEnumerable<double> values) {
+      // iterate only once 
+      double[] valuesArr = values.ToArray();
+      int n = valuesArr.Length;
+      if (n == 0) throw new InvalidOperationException("Enumeration contains no elements.");
+
+      Array.Sort(valuesArr);
+
+      // return the middle element (if n is uneven) or the average of the two middle elements if n is even.
+      if (n % 2 == 1) {
+        return valuesArr[n / 2];
+      } else {
+        return (valuesArr[(n / 2) - 1] + valuesArr[n / 2]) / 2.0;
+      }
+    }
+
+    // straight forward implementation of quantile function (using sorting)
+    private static double Quantile(IEnumerable<double> values, double alpha) {
+      Contract.Assert(alpha > 0 && alpha < 1);
+      // iterate only once 
+      double[] valuesArr = values.ToArray();
+      int n = valuesArr.Length;
+      if (n == 0) throw new InvalidOperationException("Enumeration contains no elements.");
+
+      Array.Sort(valuesArr);
+      //  starts at 0
+
+      // return the element at Math.Ceiling (if n*alpha is fractional) or the average of two elements if n*alpha is integer.
+      var pos = n * alpha;
+      Contract.Assert(pos >= 0);
+      Contract.Assert(pos < n);
+      bool isInteger = Math.Round(pos).IsAlmost(pos);
+      if (isInteger) {
+        return 0.5 * (valuesArr[(int)pos - 1] + valuesArr[(int)pos]);
+      } else {
+        return valuesArr[(int)Math.Ceiling(pos) - 1];
       }
     }