diff --git a/src/Numerics/Statistics/KernelDensityEstimator.cs b/src/Numerics/Statistics/KernelDensityEstimator.cs
index 1947b985..fd38641d 100644
--- a/src/Numerics/Statistics/KernelDensityEstimator.cs
+++ b/src/Numerics/Statistics/KernelDensityEstimator.cs
@@ -3,7 +3,7 @@
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
//
-// Copyright (c) 2009-2013 Math.NET
+// Copyright (c) 2009-2018 Math.NET
//
// Permission is hereby granted, free of charge, to any person
// obtaining a copy of this software and associated documentation
@@ -29,172 +29,176 @@
using System;
using System.Collections.Generic;
-using System.Linq;
-using System.Text;
using MathNet.Numerics.Distributions;
using MathNet.Numerics.Threading;
namespace MathNet.Numerics.Statistics
{
- ///
- /// An enum of the methods the supports
- /// for automatic bandwidth selection.
- ///
- public enum KDEBandwidthSelectionMethod
- {
///
- /// TBD
+ /// An enum of the methods the supports
+ /// for automatic bandwidth selection.
///
- SilvermansRuleOfThumb,
- ///
- /// TBD
- ///
- SolveTheEquation
- }
-
- ///
- /// The supports several predefined Kernels.
- /// Note that you can set your own custom kernel by setting
- ///
- public enum KDEKernelType
- {
- ///
- /// A Gaussian kernel (PDF of Normal distribution with mean 0 and variance 1).
- /// This kernel is the default.
- ///
- Gaussian,
+ public enum KDEBandwidthSelectionMethod
+ {
+ ///
+ /// TBD
+ ///
+ SilvermansRuleOfThumb,
- ///
- /// Epanechnikov Kernel
- /// x => Math.Abs(x) <= 1.0 ? 3.0/4.0(1.0-x^2) : 0.0
- ///
- Epanechnikov,
+ ///
+ /// TBD
+ ///
+ SolveTheEquation
+ }
///
- /// Uniform Kernel
- /// x => Math.Abs(x) <= 1.0 ? 1.0/2.0 : 0.0
+ /// The supports several predefined Kernels.
+ /// Note that you can set your own custom kernel by setting
///
- Uniform,
+ public enum KDEKernelType
+ {
+ ///
+ /// A Gaussian kernel (PDF of Normal distribution with mean 0 and variance 1).
+ /// This kernel is the default.
+ ///
+ Gaussian,
- ///
- /// Triangular Kernel
- /// x => Math.Abs(x) <= 1.0 ? (1.0-Math.Abs(x)) : 0.0
- ///
- Triangular,
+ ///
+ /// Epanechnikov Kernel
+ /// x => Math.Abs(x) <= 1.0 ? 3.0/4.0(1.0-x^2) : 0.0
+ ///
+ Epanechnikov,
+
+ ///
+ /// Uniform Kernel
+ /// x => Math.Abs(x) <= 1.0 ? 1.0/2.0 : 0.0
+ ///
+ Uniform,
+
+ ///
+ /// Triangular Kernel
+ /// x => Math.Abs(x) <= 1.0 ? (1.0-Math.Abs(x)) : 0.0
+ ///
+ Triangular,
+
+ ///
+ /// A custom kernel can be set by property
+ ///
+ Custom
+ }
///
- /// A custom kernel can be set by property
+ /// Kernel density estimation
///
- Custom
- }
-
- ///
- ///
- ///
- public class KernelDensityEstimator
- {
- public KernelDensityEstimator(IList samples)
+ public class KernelDensityEstimator
{
- _samples = samples;
- KernelType = KDEKernelType.Gaussian;
- }
+ public KernelDensityEstimator(IList samples)
+ {
+ _samples = samples;
+ KernelType = KDEKernelType.Gaussian;
+ }
- public double EstimateDensity(double x)
- {
- var n = Samples.Count;
- var estimate = CommonParallel.Aggregate(0, n,
- i =>
+
+
+
+ public double EstimateDensity(double x)
{
- var s = Samples[i];
- return Kernel((x - s) / Bandwidth);
- },
- (a, b) => a + b,
- 0d) / (n * Bandwidth);
+ var n = Samples.Count;
+ var estimate = CommonParallel.Aggregate(0, n,
+ i =>
+ {
+ var s = Samples[i];
+ return Kernel((x - s) / Bandwidth);
+ },
+ (a, b) => a + b,
+ 0d) / (n * Bandwidth);
- return estimate;
- }
+ return estimate;
+ }
- private readonly IList _samples;
- public IList Samples
- {
- get { return _samples; }
- }
+ private readonly IList _samples;
- private double _bandwidth = 1;
- public double Bandwidth
- {
- get
- {
- return _bandwidth;
- }
- set
- {
- if (value <= 0)
+ public IList Samples
{
- throw new ArgumentException("The bandwidth must be a positive number!");
+ get { return _samples; }
}
- _bandwidth = value;
- }
- }
- private KDEKernelType _kernelType;
- public KDEKernelType KernelType
- {
- get { return _kernelType; }
- set
- {
- switch (value)
+ private double _bandwidth = 1;
+
+ public double Bandwidth
{
- case KDEKernelType.Gaussian:
- {
- Kernel = x => Normal.PDF(0.0, 1.0, x);
- _kernelType = KDEKernelType.Gaussian;
- }
- break;
- case KDEKernelType.Epanechnikov:
+ get { return _bandwidth; }
+ set
{
- Kernel = x => Math.Abs(x) <= 1.0 ? 0.75 * (1 - x * x) : 0.0;
- _kernelType = KDEKernelType.Epanechnikov;
+ if (value <= 0)
+ {
+ throw new ArgumentException("The bandwidth must be a positive number!");
+ }
+
+ _bandwidth = value;
}
- break;
- case KDEKernelType.Uniform:
+ }
+
+ private KDEKernelType _kernelType;
+
+ public KDEKernelType KernelType
+ {
+ get { return _kernelType; }
+ set
{
- Kernel = x => ContinuousUniform.PDF(-1.0, 1.0, x);
- _kernelType = KDEKernelType.Uniform;
+ switch (value)
+ {
+ case KDEKernelType.Gaussian:
+ {
+ Kernel = x => Normal.PDF(0.0, 1.0, x);
+ _kernelType = KDEKernelType.Gaussian;
+ }
+ break;
+ case KDEKernelType.Epanechnikov:
+ {
+ Kernel = x => Math.Abs(x) <= 1.0 ? 0.75 * (1 - x * x) : 0.0;
+ _kernelType = KDEKernelType.Epanechnikov;
+ }
+ break;
+ case KDEKernelType.Uniform:
+ {
+ Kernel = x => ContinuousUniform.PDF(-1.0, 1.0, x);
+ _kernelType = KDEKernelType.Uniform;
+ }
+ break;
+ case KDEKernelType.Triangular:
+ {
+ Kernel = x => Triangular.PDF(-1.0, 1.0, 0.0, x);
+ _kernelType = KDEKernelType.Triangular;
+ }
+ break;
+ case KDEKernelType.Custom:
+ throw new ArgumentException("In order to set a custom Kernel, property Kernel must be set directly.");
+ }
}
- break;
- case KDEKernelType.Triangular:
+ }
+
+ private Func _kernel;
+
+ ///
+ /// Sets or Gets the Kernel used for the density estimate.
+ /// Setting the Kernel changes the to
+ /// A Kernel is a real function with Integral 1. Typically, it is also positive and symmetric about 0.
+ /// Note that none of these properties are checked.
+ ///
+ public Func Kernel
+ {
+ get { return _kernel; }
+ set
{
- Kernel = x => Triangular.PDF(-1.0, 1.0, 0.0, x);
- _kernelType = KDEKernelType.Triangular;
+ _kernel = value;
+ _kernelType = KDEKernelType.Custom;
}
- break;
- case KDEKernelType.Custom:
- throw new ArgumentException("In order to set a custom Kernel, property Kernel must be set directly.");
}
- }
- }
-
- private Func _kernel;
- ///
- /// Sets or Gets the Kernel used for the density estimate.
- /// Setting the Kernel changes the to
- /// A Kernel is a real function with Integral 1. Typically, it is also positive and symmetric about 0.
- /// Note that none of these properties are checked.
- ///
- public Func Kernel
- {
- get { return _kernel; }
- set
- {
- _kernel = value;
- _kernelType = KDEKernelType.Custom;
- }
- }
- public double SelectBandwidth(KDEBandwidthSelectionMethod bandwidthSelectionMethod)
- {
- throw new NotImplementedException();
+ public double SelectBandwidth(KDEBandwidthSelectionMethod bandwidthSelectionMethod)
+ {
+ throw new NotImplementedException();
+ }
}
- }
}
diff --git a/src/UnitTests/StatisticsTests/KernelDensityEstimatorTests.cs b/src/UnitTests/StatisticsTests/KernelDensityEstimatorTests.cs
index 3ed56a21..eee46c35 100644
--- a/src/UnitTests/StatisticsTests/KernelDensityEstimatorTests.cs
+++ b/src/UnitTests/StatisticsTests/KernelDensityEstimatorTests.cs
@@ -3,7 +3,7 @@
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
//
-// Copyright (c) 2009-2016 Math.NET
+// Copyright (c) 2009-2018 Math.NET
//
// Permission is hereby granted, free of charge, to any person
// obtaining a copy of this software and associated documentation
@@ -28,165 +28,161 @@
//
using System;
-using System.Collections.Generic;
-using System.Linq;
-using System.Text;
-using System.Threading.Tasks;
using NUnit.Framework;
using MathNet.Numerics.Statistics;
namespace MathNet.Numerics.UnitTests.StatisticsTests
{
- ///
- /// Kernel Density Estimator tests.
- ///
- [TestFixture, Category("Statistics")]
- public class KernelDensityEstimatorTests
- {
- private readonly double[] _testData =
+ ///
+ /// Kernel Density Estimator tests.
+ ///
+ [TestFixture, Category("Statistics")]
+ public class KernelDensityEstimatorTests
{
- 0.899822328897223,
- -0.300111005615676,
- 1.029365712103099,
- -0.345065971567321,
- 1.012801864262980,
- 0.629334584931419,
- -0.213015082641055,
- -0.865697308360524,
- -1.043108301337627,
- -0.270068812648099
- };
-
- [Test]
- public void KDETestGaussianKernelBandwidth1()
- {
- var kde = new KernelDensityEstimator(_testData);
-
- Assert.AreEqual(KDEKernelType.Gaussian, kde.KernelType);
- Assert.AreEqual(1.0d, kde.Bandwidth);
- AssertHelpers.AlmostEqualRelative(0.398942280401433, kde.Kernel(0), 10); //Density of standard normal distribution at 0
-
- var estimate = kde.EstimateDensity(-3.5);
- AssertHelpers.AlmostEqualRelative(0.004115405028907, estimate, 10);
-
- estimate = kde.EstimateDensity(0);
- AssertHelpers.AlmostEqualRelative(0.310485907659139, estimate, 10);
-
- estimate = kde.EstimateDensity(2);
- AssertHelpers.AlmostEqualRelative(0.099698581377801, estimate, 10);
- }
-
- [Test]
- public void KDETestTriangularKernelBandwidth1()
- {
- var kde = new KernelDensityEstimator(_testData);
- kde.KernelType = KDEKernelType.Triangular;
+ private readonly double[] _testData =
+ {
+ 0.899822328897223,
+ -0.300111005615676,
+ 1.029365712103099,
+ -0.345065971567321,
+ 1.012801864262980,
+ 0.629334584931419,
+ -0.213015082641055,
+ -0.865697308360524,
+ -1.043108301337627,
+ -0.270068812648099
+ };
+
+ [Test]
+ public void KDETestGaussianKernelBandwidth1()
+ {
+ var kde = new KernelDensityEstimator(_testData);
+
+ Assert.AreEqual(KDEKernelType.Gaussian, kde.KernelType);
+ Assert.AreEqual(1.0d, kde.Bandwidth);
+ AssertHelpers.AlmostEqualRelative(0.398942280401433, kde.Kernel(0), 10); //Density of standard normal distribution at 0
+
+ var estimate = kde.EstimateDensity(-3.5);
+ AssertHelpers.AlmostEqualRelative(0.004115405028907, estimate, 10);
+
+ estimate = kde.EstimateDensity(0);
+ AssertHelpers.AlmostEqualRelative(0.310485907659139, estimate, 10);
+
+ estimate = kde.EstimateDensity(2);
+ AssertHelpers.AlmostEqualRelative(0.099698581377801, estimate, 10);
+ }
+
+ [Test]
+ public void KDETestTriangularKernelBandwidth1()
+ {
+ var kde = new KernelDensityEstimator(_testData);
+ kde.KernelType = KDEKernelType.Triangular;
+
+ Assert.AreEqual(KDEKernelType.Triangular, kde.KernelType);
+ Assert.AreEqual(1.0d, kde.Bandwidth);
+ Assert.AreEqual(1.0d, kde.Kernel(0)); //Density of standard normal distribution at 0
+
+ var estimate = kde.EstimateDensity(-3.5);
+ AssertHelpers.AlmostEqualRelative(0, estimate, 10);
+
+ estimate = kde.EstimateDensity(0);
+ AssertHelpers.AlmostEqualRelative(0.347688490533868, estimate, 10);
+
+ estimate = kde.EstimateDensity(2);
+ AssertHelpers.AlmostEqualRelative(0.004216757636608, estimate, 10);
+ }
+
+ [Test]
+ public void KDETestUniformKernelBandwidth1()
+ {
+ var kde = new KernelDensityEstimator(_testData);
+ kde.KernelType = KDEKernelType.Uniform;
+
+ Assert.AreEqual(KDEKernelType.Uniform, kde.KernelType);
+ Assert.AreEqual(1.0d, kde.Bandwidth);
+ Assert.AreEqual(0.5d, kde.Kernel(0));
+
+ var estimate = kde.EstimateDensity(-3.5);
+ AssertHelpers.AlmostEqualRelative(0, estimate, 10);
+
+ estimate = kde.EstimateDensity(0);
+ AssertHelpers.AlmostEqualRelative(0.35, estimate, 10);
+
+ estimate = kde.EstimateDensity(2);
+ AssertHelpers.AlmostEqualRelative(0.1, estimate, 10);
+ }
+
+ [Test]
+ public void KDETestEpanechnikovKernelBandwidth1()
+ {
+ var kde = new KernelDensityEstimator(_testData);
+ kde.KernelType = KDEKernelType.Epanechnikov;
+
+ Assert.AreEqual(KDEKernelType.Epanechnikov, kde.KernelType);
+ Assert.AreEqual(1.0d, kde.Bandwidth);
+ Assert.AreEqual(0.75d, kde.Kernel(0));
+
+ var estimate = kde.EstimateDensity(-3.5);
+ AssertHelpers.AlmostEqualRelative(0, estimate, 10);
+
+ estimate = kde.EstimateDensity(0);
+ AssertHelpers.AlmostEqualRelative(0.353803214812608, estimate, 10);
+
+ estimate = kde.EstimateDensity(2);
+ AssertHelpers.AlmostEqualRelative(0.006248168996717, estimate, 10);
+ }
+
+ [Test]
+ public void KDETestGaussianKernelBandwidth0p5()
+ {
+ var kde = new KernelDensityEstimator(_testData);
+ kde.Bandwidth = 0.5d;
+
+ var estimate = kde.EstimateDensity(-3.5);
+ AssertHelpers.AlmostEqualRelative(5.311490430807364e-007, estimate, 10);
+
+ estimate = kde.EstimateDensity(0);
+ AssertHelpers.AlmostEqualRelative(0.369994803886827, estimate, 10);
+
+ estimate = kde.EstimateDensity(2);
+ AssertHelpers.AlmostEqualRelative(0.032447347007482, estimate, 10);
+ }
+
+ [Test]
+ public void KDETestGaussianKernelBandwidth2()
+ {
+ var kde = new KernelDensityEstimator(_testData);
+ kde.Bandwidth = 2.0d;
- Assert.AreEqual(KDEKernelType.Triangular, kde.KernelType);
- Assert.AreEqual(1.0d, kde.Bandwidth);
- Assert.AreEqual(1.0d, kde.Kernel(0)); //Density of standard normal distribution at 0
+ var estimate = kde.EstimateDensity(-3.5);
+ AssertHelpers.AlmostEqualRelative(0.046875864115900, estimate, 10);
- var estimate = kde.EstimateDensity(-3.5);
- AssertHelpers.AlmostEqualRelative(0, estimate, 10);
+ estimate = kde.EstimateDensity(0);
+ AssertHelpers.AlmostEqualRelative(0.186580447512078, estimate, 10);
- estimate = kde.EstimateDensity(0);
- AssertHelpers.AlmostEqualRelative(0.347688490533868, estimate, 10);
-
- estimate = kde.EstimateDensity(2);
- AssertHelpers.AlmostEqualRelative(0.004216757636608, estimate, 10);
- }
-
- [Test]
- public void KDETestUniformKernelBandwidth1()
- {
- var kde = new KernelDensityEstimator(_testData);
- kde.KernelType = KDEKernelType.Uniform;
-
- Assert.AreEqual(KDEKernelType.Uniform, kde.KernelType);
- Assert.AreEqual(1.0d, kde.Bandwidth);
- Assert.AreEqual(0.5d, kde.Kernel(0));
-
- var estimate = kde.EstimateDensity(-3.5);
- AssertHelpers.AlmostEqualRelative(0, estimate, 10);
-
- estimate = kde.EstimateDensity(0);
- AssertHelpers.AlmostEqualRelative(0.35, estimate, 10);
-
- estimate = kde.EstimateDensity(2);
- AssertHelpers.AlmostEqualRelative(0.1, estimate, 10);
- }
-
- [Test]
- public void KDETestEpanechnikovKernelBandwidth1()
- {
- var kde = new KernelDensityEstimator(_testData);
- kde.KernelType = KDEKernelType.Epanechnikov;
+ estimate = kde.EstimateDensity(2);
+ AssertHelpers.AlmostEqualRelative(0.123339405007761, estimate, 10);
+ }
- Assert.AreEqual(KDEKernelType.Epanechnikov, kde.KernelType);
- Assert.AreEqual(1.0d, kde.Bandwidth);
- Assert.AreEqual(0.75d, kde.Kernel(0));
-
- var estimate = kde.EstimateDensity(-3.5);
- AssertHelpers.AlmostEqualRelative(0, estimate, 10);
-
- estimate = kde.EstimateDensity(0);
- AssertHelpers.AlmostEqualRelative(0.353803214812608, estimate, 10);
-
- estimate = kde.EstimateDensity(2);
- AssertHelpers.AlmostEqualRelative(0.006248168996717, estimate, 10);
- }
-
- [Test]
- public void KDETestGaussianKernelBandwidth0p5()
- {
- var kde = new KernelDensityEstimator(_testData);
- kde.Bandwidth = 0.5d;
-
- var estimate = kde.EstimateDensity(-3.5);
- AssertHelpers.AlmostEqualRelative(5.311490430807364e-007, estimate, 10);
-
- estimate = kde.EstimateDensity(0);
- AssertHelpers.AlmostEqualRelative(0.369994803886827, estimate, 10);
-
- estimate = kde.EstimateDensity(2);
- AssertHelpers.AlmostEqualRelative(0.032447347007482, estimate, 10);
- }
-
- [Test]
- public void KDETestGaussianKernelBandwidth2()
- {
- var kde = new KernelDensityEstimator(_testData);
- kde.Bandwidth = 2.0d;
-
- var estimate = kde.EstimateDensity(-3.5);
- AssertHelpers.AlmostEqualRelative(0.046875864115900, estimate, 10);
-
- estimate = kde.EstimateDensity(0);
- AssertHelpers.AlmostEqualRelative(0.186580447512078, estimate, 10);
-
- estimate = kde.EstimateDensity(2);
- AssertHelpers.AlmostEqualRelative(0.123339405007761, estimate, 10);
- }
-
- [Test]
- public void KDETestCustomKernelBandwidth1()
- {
- var kde = new KernelDensityEstimator(_testData);
- kde.Bandwidth = 1.0d;
- kde.Kernel = x => 0.5d * Math.Exp(-Math.Abs(x)); //Picard-Kernel
+ [Test]
+ public void KDETestCustomKernelBandwidth1()
+ {
+ var kde = new KernelDensityEstimator(_testData);
+ kde.Bandwidth = 1.0d;
+ kde.Kernel = x => 0.5d * Math.Exp(-Math.Abs(x)); //Picard-Kernel
- Assert.AreEqual(KDEKernelType.Custom, kde.KernelType);
- Assert.AreEqual(1.0d, kde.Bandwidth);
- Assert.AreEqual(0.5d, kde.Kernel(0));
+ Assert.AreEqual(KDEKernelType.Custom, kde.KernelType);
+ Assert.AreEqual(1.0d, kde.Bandwidth);
+ Assert.AreEqual(0.5d, kde.Kernel(0));
- var estimate = kde.EstimateDensity(-3.5);
- AssertHelpers.AlmostEqualRelative(0.018396636706009, estimate, 10);
+ var estimate = kde.EstimateDensity(-3.5);
+ AssertHelpers.AlmostEqualRelative(0.018396636706009, estimate, 10);
- estimate = kde.EstimateDensity(0);
- AssertHelpers.AlmostEqualRelative(0.272675897096678, estimate, 10);
+ estimate = kde.EstimateDensity(0);
+ AssertHelpers.AlmostEqualRelative(0.272675897096678, estimate, 10);
- estimate = kde.EstimateDensity(2);
- AssertHelpers.AlmostEqualRelative(0.092580285110347, estimate, 10);
+ estimate = kde.EstimateDensity(2);
+ AssertHelpers.AlmostEqualRelative(0.092580285110347, estimate, 10);
+ }
}
- }
}