Initial version of VectorNormal distribution.

src/Numerics/Distributions/Multivariate/VectorNormal.cs

@@ -0,0 +1,283 @@
+// <copyright file="VectorNormal.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://mathnet.opensourcedotnet.info
+//
+// Copyright (c) 2009 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.Distributions
+{
+    using System;
+    using Properties;
+    using MathNet.Numerics.LinearAlgebra.Double;
+
+    /// <summary>
+    /// This class implements functionality for the multivariate normal distribution. This distribution
+    /// is parameterized by a mean vector and a covariance matrix.
+    /// </summary>
+    /// <remarks><para>The distribution will use the <see cref="System.Random"/> by default. 
+    /// Users can get/set the random number generator by using the <see cref="RandomSource"/> property.</para>
+    /// <para>The statistics classes will check all the incoming parameters whether they are in the allowed
+    /// range. This might involve heavy computation. Optionally, by setting Control.CheckDistributionParameters
+    /// to false, all parameter checks can be turned off.</para></remarks>
+    public class VectorNormal
+    {
+
+
+
+
+
+
+        // The Dirichlet distribution parameters.
+        private double[] _alpha;
+
+        /// <summary>
+        /// The distribution's random number generator.
+        /// </summary>
+        private Random _random;
+
+        /// <summary>
+        /// Initializes a new instance of the Dirichlet class. The distribution will
+        /// be initialized with the default <seealso cref="System.Random"/> random number generator.
+        /// </summary>
+        /// <param name="alpha">An array with the Dirichlet parameters.</param>
+        public Dirichlet(double[] alpha)
+        {
+            SetParameters(alpha);
+            RandomSource = new Random();
+        }
+
+        /// <summary>
+        /// Constructs a new symmetric Dirichlet distribution. The distribution will
+        /// be initialized with the default <seealso cref="System.Random"/> random number generator.
+        /// </summary>
+        /// <param name="alpha">The value of each parameter of the Dirichlet distribution.</param>
+        /// <param name="k">The dimension of the Dirichlet distribution.</param>
+        public Dirichlet(double alpha, int k)
+        {
+            // Create a parameter structure.
+            double[] parm = new double[k];
+            for (int i = 0; i < k; i++)
+            {
+                parm[i] = alpha;
+            }
+
+            SetParameters(parm);
+            RandomSource = new Random();
+        }
+
+        /// <summary>
+        /// Checks whether the parameters of the distribution are valid: no parameter can be less than zero and
+        /// at least one parameter should be larger than zero.
+        /// </summary>
+        /// <param name="alpha">The parameters of the Dirichlet distribution.</param>
+        /// <returns>True when the parameters are valid, false otherwise.</returns>
+        public static bool IsValidParameterSet(double[] alpha)
+        {
+            bool allzero = true;
+
+            for (int i = 0; i < alpha.Length; i++)
+            {
+                if (alpha[i] < 0.0)
+                {
+                    return false;
+                }
+                else if (alpha[i] > 0.0)
+                {
+                    allzero = false;
+                }
+            }
+
+            if (allzero)
+            {
+                return false;
+            }
+
+            return true;
+        }
+
+        /// <summary>
+        /// Sets the parameters of the distribution after checking their validity.
+        /// </summary>
+        /// <param name="alpha">The parameters of the Dirichlet distribution.</param>
+        /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
+        private void SetParameters(double[] alpha)
+        {
+            if (Control.CheckDistributionParameters && !IsValidParameterSet(alpha))
+            {
+                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
+            }
+
+            _alpha = (double[]) alpha.Clone();
+        }
+
+        /// <summary>
+        /// A string representation of the distribution.
+        /// </summary>
+        public override string ToString()
+        {
+            return "Dirichlet(Dimension = " + this.Dimension + ")";
+        }
+
+        /// <summary>
+        /// Gets the dimension of the Dirichlet distribution.
+        /// </summary>
+        public int Dimension
+        {
+            get { return _alpha.Length; }
+        }
+
+        /// <summary>
+        /// Gets or sets the parameters of the Dirichlet distribution.
+        /// </summary>
+        public double[] Alpha
+        {
+            get
+            {
+                return _alpha;
+            }
+            set
+            {
+                SetParameters(value);
+            }
+        }
+
+        /// <summary>
+        /// The sum of the Dirichlet parameters.
+        /// </summary>
+        private double AlphaSum
+        {
+            get
+            {
+                double s = 0.0;
+                for (int i = 0; i < _alpha.Length; i++)
+                {
+                    s += _alpha[i];
+                }
+                return s;
+            }
+        }
+
+        /// <summary>
+        /// Gets the mean of the Dirichlet distribution.
+        /// </summary>
+        public double[] Mean
+        {
+            get
+            {
+                double sum = AlphaSum;
+                double[] parm = new double[Dimension];
+                for (int i = 0; i < Dimension; i++)
+                {
+                    parm[i] = _alpha[i] / sum;
+                }
+
+                return parm;
+            }
+        }
+
+        /// <summary>
+        /// Gets the variance of the Dirichlet distribution.
+        /// </summary>
+        public double[] Variance
+        {
+            get
+            {
+                double s = this.AlphaSum;
+                double[] v = new double[_alpha.Length];
+                for (int i = 0; i < _alpha.Length; i++)
+                {
+                    v[i] = _alpha[i]*(s - _alpha[i])/(s*s*(s + 1.0));
+                }
+                return v;
+            }
+        }
+
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public Random RandomSource
+        {
+            get
+            {
+                return _random;
+            }
+
+            set
+            {
+                if (value == null)
+                {
+                    throw new ArgumentNullException();
+                }
+
+                _random = value;
+            }
+        }
+
+        /// <summary>
+        /// Samples a Dirichlet distributed random vector.
+        /// </summary>
+        public double[] Sample()
+        {
+            return Sample(RandomSource, _alpha);
+        }
+
+        /// <summary>
+        /// Samples a Dirichlet distributed random vector.
+        /// </summary>
+        /// <param name="rnd">The random number generator to use.</param>
+        /// <param name="alpha">The Dirichlet distribution parameter.</param>
+        public static double[] Sample(System.Random rnd, double[] alpha)
+        {
+            if (Control.CheckDistributionParameters && ! IsValidParameterSet(alpha))
+            {
+                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
+            }
+
+            int n = alpha.Length;
+            double[] gv = new double[n];
+            double sum = 0.0;
+            for (int i = 0; i < n; i++)
+            {
+                if (alpha[i] == 0.0)
+                {
+                    gv[i] = 0.0;
+                }
+                else
+                {
+                    gv[i] = Gamma.Sample(rnd, alpha[i], 1.0);
+                }
+
+                sum += gv[i];
+            }
+
+            for (int i = 0; i < n; i++)
+            {
+                gv[i] /= sum;
+            }
+
+            return gv;
+        }
+    }
+}

src/Numerics/Numerics.csproj

@@ -61,6 +61,7 @@
     <Compile Include="Distributions\IContinuousDistribution.cs" />
     <Compile Include="Distributions\IDiscreteDistribution.cs" />
     <Compile Include="Distributions\IDistribution.cs" />
+    <Compile Include="Distributions\Multivariate\VectorNormal.cs" />
     <Compile Include="Distributions\Multivariate\Dirichlet.cs" />
     <Compile Include="Distributions\Multivariate\Multinomial.cs" />
     <Compile Include="IntegralTransforms\Algorithms\DiscreteHartleyTransform.Naive.cs" />

src/UnitTests/DistributionTests/CommonDistributionTests.cs

@@ -41,13 +41,15 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
         [SetUp]
         public void SetupDistributions()
         {
-            dists = new IDistribution[5];
+            dists = new IDistribution[7];
 
             dists[0] = new Beta(1.0, 1.0);
             dists[1] = new ContinuousUniform(0.0, 1.0);
             dists[2] = new Gamma(1.0, 1.0);
             dists[3] = new Normal(0.0, 1.0);
             dists[4] = new Bernoulli(0.6);
+            dists[5] = new Weibull(1.0, 1.0);
+            dists[6] = new DiscreteUniform(1, 10);
         }
 
         [Test]

src/UnitTests/DistributionTests/Multivariate/VectorNormalTests.cs

@@ -0,0 +1,213 @@
+// <copyright file="VectorNormalTests.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://mathnet.opensourcedotnet.info
+//
+// Copyright (c) 2009 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.UnitTests.DistributionTests
+{
+    using System;
+    using System.Linq;
+    using MbUnit.Framework;
+    using MathNet.Numerics.Distributions;
+
+    [TestFixture]
+    public class VectorNormalTests
+    {
+        [SetUp]
+        public void SetUp()
+        {
+            Control.CheckDistributionParameters = true;
+        }
+
+        //[Test]
+        //[ExpectedException(typeof(ArgumentOutOfRangeException))]
+        //public void NormalConstructorFail()
+        //{
+        //    Matrix cov = new DenseMatrix(new double[,] { { 1.0, 1.0 }, { -1.0, 2.0 } });
+        //    Vector mean = new DenseVector(new double[] { 5.0, 5.0 });
+
+        //    // Build a new vector normal distribution.
+        //    VectorNormal normal = new VectorNormal(mean, cov);
+        //}
+
+        [Test]
+        public void StandardNormal()
+        {
+            VectorNormal normal = new VectorNormal(5);
+
+            // Test the mean.
+            for (int i = 0; i < 5; i++)
+            {
+                Assert.AreEqual(0.0, normal.Mean[i]);
+            }
+
+            // Test the covariance.
+            for (int i = 0; i < 5; i++)
+            {
+                for (int j = 0; j < 5; j++)
+                {
+                    if (i == j)
+                    {
+                        Assert.AreEqual(1.0, normal.Covariance[i, j]);
+                    }
+                    else
+                    {
+                        Assert.AreEqual(0.0, normal.Covariance[i, j]);
+                    }
+                }
+            }
+
+            // Test the pdf.
+            Assert.AreEqual(0.010105326013812, normal.Density(new DenseVector(5, 0.0)), mAcceptableError);
+            Assert.AreEqual(8.294956719377678e-004, normal.Density(new DenseVector(5, 1.0)), mAcceptableError);
+
+            // Test the mode.
+            for (int i = 0; i < 5; i++)
+            {
+                Assert.AreEqual(0.0, normal.Mode[i]);
+            }
+
+            // Test the median.
+            for (int i = 0; i < 5; i++)
+            {
+                Assert.AreEqual(0.0, normal.Median[i]);
+            }
+
+            // Test the entropy.
+            Assert.AreEqual(7.094692666023364, normal.Entropy, mAcceptableError);
+        }
+
+        [Test]
+        public void NormalFromCovariance()
+        {
+            Matrix cov = new DenseMatrix(new double[,] { { 1.0, 0.9 }, { 0.9, 1.0 } });
+            Vector mean = new DenseVector(new double[] { 5.0, 5.0 });
+
+            // Check that these are valid mean and covariances.
+            Assert.DoesNotThrow(() => VectorNormal.CheckParameters(mean, cov));
+
+            // Build a new vector normal distribution.
+            VectorNormal normal = new VectorNormal(mean, cov);
+
+            // Test the mean.
+            Assert.AreEqual(5.0, normal.Mean[0]);
+            Assert.AreEqual(5.0, normal.Mean[1]);
+
+            // Test the covariance.
+            Assert.AreEqual(1.0, normal.Covariance[0, 0]);
+            Assert.AreEqual(0.9, normal.Covariance[0, 1]);
+            Assert.AreEqual(0.9, normal.Covariance[1, 0]);
+            Assert.AreEqual(1.0, normal.Covariance[1, 1]);
+
+            // Test the mode.
+            Assert.AreEqual(5.0, normal.Mode[0]);
+            Assert.AreEqual(5.0, normal.Mode[1]);
+
+            // Test the median.
+            Assert.AreEqual(5.0, normal.Median[0]);
+            Assert.AreEqual(5.0, normal.Median[1]);
+
+            // Test the entropy.
+            Assert.AreEqual(2.007511462998520, normal.Entropy, mAcceptableError);
+
+            // Get the RNG.
+            System.Random rnd = normal.RandomNumberGenerator;
+        }
+
+
+
+
+
+
+
+
+        [Test]
+        public void HasRandomSource(int i)
+        {
+            VectorNormal d = new VectorNormal(0.3, 5);
+            Assert.IsNotNull(d.RandomSource);
+        }
+
+        [Test]
+        public void CanSetRandomSource(int i)
+        {
+            VectorNormal d = new VectorNormal(0.3, 5);
+            d.RandomSource = new Random();
+        }
+
+        [Test]
+        [ExpectedException(typeof(ArgumentNullException))]
+        public void FailSetRandomSourceWithNullReference(int i)
+        {
+            VectorNormal d = new VectorNormal(0.3, 5);
+            d.RandomSource = null;
+        }
+
+        [Test]
+        public void CanGetDimension()
+        {
+            VectorNormal d = new VectorNormal(0.3, 10);
+            Assert.AreEqual(10, d.Dimension);
+        }
+
+        [Test]
+        public void ValidateMean()
+        {
+            VectorNormal d = new VectorNormal(0.3, 5);
+
+            for (int i = 0; i < 5; i++)
+            {
+                AssertHelpers.AlmostEqual(0.3/1.5, d.Mean[i], 15);
+            }
+        }
+
+        [Test]
+        public void ValidateVariance()
+        {
+            double[] alpha = new double[10];
+            double sum = 0.0;
+            for (int i = 0; i < 10; i++)
+            {
+                alpha[i] = i;
+                sum += i;
+            }
+
+            VectorNormal d = new VectorNormal(alpha);
+
+            for (int i = 0; i < 10; i++)
+            {
+                AssertHelpers.AlmostEqual(i * (sum - i) / (sum * sum * (sum + 1.0)), d.Variance[i], 15);
+            }
+        }
+
+        [Test]
+        public void CanSampleVectorNormal()
+        {
+            VectorNormal d = new VectorNormal(1.0, 5);
+            double[] s = d.Sample();
+        }
+    }
+}

src/UnitTests/UnitTests.csproj

@@ -72,6 +72,7 @@
     <Compile Include="DistributionTests\Continuous\NormalTests.cs" />
     <Compile Include="DistributionTests\Discrete\BernoulliTests.cs" />
     <Compile Include="DistributionTests\Discrete\DiscreteUniformTests.cs" />
+    <Compile Include="DistributionTests\Multivariate\VectorNormalTests.cs" />
     <Compile Include="DistributionTests\Multivariate\DirichletTests.cs" />
     <Compile Include="DistributionTests\Multivariate\MultinomialTests.cs" />
     <Compile Include="IntegralTransformsTests\HartleyTest.cs" />