mathnet-numerics/src/Numerics.Tests/DistributionTests/Multivariate/MultinomialTests.cs

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using System;
using System.Linq;
using MathNet.Numerics.Distributions;
using MathNet.Numerics.Statistics;
using NUnit.Framework;

namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
{
    /// <summary>
    /// Multinomial distribution tests.
    /// </summary>
    [TestFixture, Category("Distributions")]
    public class MultinomialTests
    {
        /// <summary>
        /// Bad proportion of ratios.
        /// </summary>
        private double[] _badP;

        /// <summary>
        /// Another bad proportion of ratios.
        /// </summary>
        private double[] _badP2;

        /// <summary>
        /// Small array with proportion of ratios
        /// </summary>
        private double[] _smallP;

        /// <summary>
        /// Large array with proportion of ratios
        /// </summary>
        private double[] _largeP;

        /// <summary>
        /// Set-up tests parameters.
        /// </summary>
        [SetUp]
        public void SetUp()
        {
            Control.CheckDistributionParameters = true;
            _badP = new[] { -1.0, 1.0 };
            _badP2 = new[] { 0.0, 0.0 };
            _smallP = new[] { 1.0, 1.0, 1.0 };
            _largeP = new[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 };
        }

        /// <summary>
        /// Can create Multinomial
        /// </summary>
        [Test]
        public void CanCreateMultinomial()
        {
            var m = new Multinomial(_largeP, 4);
            CollectionAssert.AreEqual(_largeP, m.P);
        }

        /// <summary>
        /// Can create Multinomial from a histogram.
        /// </summary>
        [Test]
        public void CanCreateMultinomialFromHistogram()
        {
            double[] smallDataset = { 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5 };
            var hist = new Histogram(smallDataset, 10, 0.0, 10.0);
            var m = new Multinomial(hist, 7);

            foreach (var t in m.P)
            {
                Assert.AreEqual(1.0, t);
            }
        }

        /// <summary>
        /// Multinomial create fails with <c>null</c> histogram.
        /// </summary>
        [Test]
        public void MultinomialCreateFailsWithNullHistogram()
        {
            Histogram h = null;
// ReSharper disable once ExpressionIsAlwaysNull
            Assert.That(() => new Categorical(h), Throws.TypeOf<ArgumentNullException>());
        }

        /// <summary>
        /// Multinomial create fails with negative ratios.
        /// </summary>
        [Test]
        public void MultinomialCreateFailsWithNegativeRatios()
        {
            Assert.That(() => new Multinomial(_badP, 4), Throws.ArgumentException);
        }

        /// <summary>
        /// Multinomial create fails with all zero ratios.
        /// </summary>
        [Test]
        public void MultinomialCreateFailsWithAllZeroRatios()
        {
            Assert.That(() => new Multinomial(_badP2, 4), Throws.ArgumentException);
        }

        /// <summary>
        /// Validate ToString.
        /// </summary>
        [Test]
        public void ValidateToString()
        {
            System.Threading.Thread.CurrentThread.CurrentCulture = System.Globalization.CultureInfo.InvariantCulture;
            var b = new Multinomial(_smallP, 4);
            Assert.AreEqual("Multinomial(Dimension = 3, Number of Trails = 4)", b.ToString());
        }

        /// <summary>
        /// Validate skewness.
        /// </summary>
        /// <param name="p">Proportion of ratios.</param>
        /// <param name="n">Number of trials.</param>
        /// <param name="res">Expected value.</param>
        [TestCase(new[] { 0.3, 0.7 }, 5, new[] { 0.390360029179413, -0.390360029179413 })]
        [TestCase(new[] { 0.1, 0.3, 0.6 }, 10, new[] { 0.843274042711568, 0.276026223736942, -0.129099444873581 })]
        [TestCase(new[] { 0.15, 0.35, 0.3, 0.2 }, 20, new[] { 0.438357003759605, 0.140642169281549, 0.195180014589707, 0.335410196624968 })]
        public void ValidateSkewness(double[] p, int n, double[] res)
        {
            var b = new Multinomial(p, n);
            for (var i = 0; i < b.P.Length; i++)
            {
                AssertHelpers.AlmostEqualRelative(res[i], b.Skewness[i], 12);
            }
        }

        /// <summary>
        /// Validate variance.
        /// </summary>
        /// <param name="p">Proportion of ratios.</param>
        /// <param name="n">Number of trials.</param>
        /// <param name="res">Expected value.</param>
        [TestCase(new[] { 0.3, 0.7 }, 5, new[] { 1.05, 1.05 })]
        [TestCase(new[] { 0.1, 0.3, 0.6 }, 10, new[] { 0.9, 2.1, 2.4 })]
        [TestCase(new[] { 0.15, 0.35, 0.3, 0.2 }, 20, new[] { 2.55, 4.55, 4.2, 3.2 })]
        public void ValidateVariance(double[] p, int n, double[] res)
        {
            var b = new Multinomial(p, n);
            for (var i = 0; i < b.P.Length; i++)
            {
                AssertHelpers.AlmostEqualRelative(res[i], b.Variance[i], 12);
            }
        }

        /// <summary>
        /// Validate mean.
        /// </summary>
        /// <param name="p">Proportion of ratios.</param>
        /// <param name="n">Number of trials.</param>
        /// <param name="res">Expected value.</param>
        [TestCase(new[] { 0.3, 0.7 }, 5, new[] { 1.5, 3.5 })]
        [TestCase(new[] { 0.1, 0.3, 0.6 }, 10, new[] { 1.0, 3.0, 6.0 })]
        [TestCase(new[] { 0.15, 0.35, 0.3, 0.2 }, 20, new[] { 3.0, 7.0, 6.0, 4.0 })]
        public void ValidateMean(double[] p, int n, double[] res)
        {
            var b = new Multinomial(p, n);
            for (var i = 0; i < b.P.Length; i++)
            {
                AssertHelpers.AlmostEqualRelative(res[i], b.Mean[i], 12);
            }
        }

        /// <summary>
        /// Validate probability.
        /// </summary>
        /// <param name="p">Proportion of ratios.</param>
        /// <param name="x">Input X value.</param>
        /// <param name="res">Expected value.</param>
        [TestCase(new[] { 0.3, 0.7 }, new[] { 1, 9 }, 0.121060821)]
        [TestCase(new[] { 0.1, 0.3, 0.6 }, new[] { 1, 3, 6 }, 0.105815808)]
        [TestCase(new[] { 0.15, 0.35, 0.3, 0.2 }, new[] { 1, 1, 1, 7 }, 0.000145152)]
        public void ValidateProbability(double[] p, int[] x, double res)
        {
            var b = new Multinomial(p, x.Sum());
            AssertHelpers.AlmostEqualRelative(b.Probability(x), res, 12);
        }

        /// <summary>
        /// Validate probability log.
        /// </summary>
        /// <param name="x">Input X value.</param>
        [TestCase(new[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 })]
        [TestCase(new[] { 1, 1, 1, 2, 2, 2, 3, 3, 3 })]
        [TestCase(new[] { 5, 6, 7, 8, 7, 6, 5, 4, 3 })]
        public void ValidateProbabilityLn(int[] x)
        {
            var b = new Multinomial(_largeP, x.Sum());
            AssertHelpers.AlmostEqualRelative(b.ProbabilityLn(x), Math.Log(b.Probability(x)), 12);
        }

        /// <summary>
        /// Can sample static.
        /// </summary>
        [Test]
        public void CanSampleStatic()
        {
            Multinomial.Sample(new System.Random(0), _largeP, 4);
        }

        /// <summary>
        /// Sample static fails with bad parameters.
        /// </summary>
        [Test]
        public void FailSampleStatic()
        {
            Assert.That(() => Multinomial.Sample(new System.Random(0), _badP, 4), Throws.ArgumentException);
        }

        /// <summary>
        /// Can sample.
        /// </summary>
        [Test]
        public void CanSample()
        {
            var n = new Multinomial(_largeP, 4);
            n.Sample();
        }
    }
}