mathnet-numerics/src/UnitTests/DistributionTests/Continuous/RayleighTests.cs

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

namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
{
    /// <summary>
    /// Rayleigh distribution tests.
    /// </summary>
    [TestFixture]
    public class RayleighTests
    {
        /// <summary>
        /// Set-up parameters.
        /// </summary>
        [SetUp]
        public void SetUp()
        {
            Control.CheckDistributionParameters = true;
        }

        /// <summary>
        /// Can create Rayleigh
        /// </summary>
        /// <param name="scale">Scale value.</param>
        [TestCase(0.1)]
        [TestCase(1.0)]
        [TestCase(10.0)]
        [TestCase(Double.PositiveInfinity)]
        public void CanCreateRayleigh(double scale)
        {
            var n = new Rayleigh(scale);
            Assert.AreEqual(scale, n.Scale);
        }

        /// <summary>
        /// Rayleigh create fails with bad parameters.
        /// </summary>
        /// <param name="scale">Scale value.</param>
        [TestCase(Double.NaN)]
        [TestCase(Double.NegativeInfinity)]
        [TestCase(-1.0)]
        [TestCase(0.0)]
        public void RayleighCreateFailsWithBadParameters(double scale)
        {
            Assert.Throws<ArgumentOutOfRangeException>(() => new Rayleigh(scale));
        }

        /// <summary>
        /// Validate ToString.
        /// </summary>
        [Test]
        public void ValidateToString()
        {
            var n = new Rayleigh(2d);
            Assert.AreEqual("Rayleigh(σ = 2)", n.ToString());
        }

        /// <summary>
        /// Can set scale.
        /// </summary>
        /// <param name="scale">Scale value.</param>
        [TestCase(0.1)]
        [TestCase(1.0)]
        [TestCase(10.0)]
        [TestCase(Double.PositiveInfinity)]
        public void CanSetScale(double scale)
        {
            new Rayleigh(1.0)
            {
                Scale = scale
            };
        }

        /// <summary>
        /// Set scale fails with negative scale.
        /// </summary>
        /// <param name="scale">Scale value.</param>
        [TestCase(-0.0)]
        [TestCase(0.0)]
        [TestCase(-1.0)]
        [TestCase(Double.NegativeInfinity)]
        [TestCase(Double.NaN)]
        public void SetScaleFailsWithNegativeScale(double scale)
        {
            var n = new Rayleigh(1.0);
            Assert.Throws<ArgumentOutOfRangeException>(() => n.Scale = scale);
        }

        /// <summary>
        /// Validate mean.
        /// </summary>
        /// <param name="scale">Scale value.</param>
        [TestCase(0.1)]
        [TestCase(1.0)]
        [TestCase(10.0)]
        [TestCase(Double.PositiveInfinity)]
        public void ValidateMean(double scale)
        {
            var n = new Rayleigh(scale);
            Assert.AreEqual(scale * Math.Sqrt(Constants.PiOver2), n.Mean);
        }

        /// <summary>
        /// Validate variance.
        /// </summary>
        /// <param name="scale">Scale value.</param>
        [TestCase(0.1)]
        [TestCase(1.0)]
        [TestCase(10.0)]
        [TestCase(Double.PositiveInfinity)]
        public void ValidateVariance(double scale)
        {
            var n = new Rayleigh(scale);
            Assert.AreEqual((2.0 - Constants.PiOver2) * scale * scale, n.Variance);
        }

        /// <summary>
        /// Validate standard deviation.
        /// </summary>
        /// <param name="scale">Scale value.</param>
        [TestCase(0.1)]
        [TestCase(1.0)]
        [TestCase(10.0)]
        [TestCase(Double.PositiveInfinity)]
        public void ValidateStdDev(double scale)
        {
            var n = new Rayleigh(scale);
            Assert.AreEqual(Math.Sqrt(2.0 - Constants.PiOver2) * scale, n.StdDev);
        }

        /// <summary>
        /// Validate entropy.
        /// </summary>
        /// <param name="scale">Scale value.</param>
        [TestCase(0.1)]
        [TestCase(1.0)]
        [TestCase(10.0)]
        [TestCase(Double.PositiveInfinity)]
        public void ValidateEntropy(double scale)
        {
            var n = new Rayleigh(scale);
            Assert.AreEqual(1.0 + Math.Log(scale / Constants.Sqrt2) + (Constants.EulerMascheroni / 2.0), n.Entropy);
        }

        /// <summary>
        /// Validate skewness.
        /// </summary>
        /// <param name="scale">Scale value.</param>
        /// <param name="skn">Expected value.</param>
        [TestCase(0.1, 0.63111065781893638)]
        [TestCase(1.0, 0.63111065781893638)]
        [TestCase(10.0, 0.63111065781893638)]
        [TestCase(Double.PositiveInfinity, 0.63111065781893638)]
        public void ValidateSkewness(double scale, double skn)
        {
            var n = new Rayleigh(scale);
            AssertHelpers.AlmostEqual(skn, n.Skewness, 17);
        }

        /// <summary>
        /// Validate mode.
        /// </summary>
        /// <param name="scale">Scale value.</param>
        [TestCase(0.1)]
        [TestCase(1.0)]
        [TestCase(10.0)]
        [TestCase(Double.PositiveInfinity)]
        public void ValidateMode(double scale)
        {
            var n = new Rayleigh(scale);
            Assert.AreEqual(scale, n.Mode);
        }

        /// <summary>
        /// Validate median.
        /// </summary>
        /// <param name="scale">Scale value.</param>
        [TestCase(0.1)]
        [TestCase(1.0)]
        [TestCase(10.0)]
        [TestCase(Double.PositiveInfinity)]
        public void ValidateMedian(double scale)
        {
            var n = new Rayleigh(scale);
            Assert.AreEqual(scale * Math.Sqrt(Math.Log(4.0)), n.Median);
        }

        /// <summary>
        /// Validate minimum.
        /// </summary>
        /// <param name="scale">Scale value.</param>
        [TestCase(0.1)]
        [TestCase(1.0)]
        [TestCase(10.0)]
        [TestCase(Double.PositiveInfinity)]
        public void ValidateMinimum(double scale)
        {
            var n = new Rayleigh(scale);
            Assert.AreEqual(0.0, n.Minimum);
        }

        /// <summary>
        /// Validate maximum.
        /// </summary>
        /// <param name="scale">Scale value.</param>
        [TestCase(0.1)]
        [TestCase(1.0)]
        [TestCase(10.0)]
        [TestCase(Double.PositiveInfinity)]
        public void ValidateMaximum(double scale)
        {
            var n = new Rayleigh(1.0);
            Assert.AreEqual(Double.PositiveInfinity, n.Maximum);
        }

        [TestCase(0.1, 0.1)]
        [TestCase(1.0, 1.0)]
        [TestCase(10.0, 10.0)]
        [TestCase(Double.PositiveInfinity, Double.PositiveInfinity)]
        public void ValidateDensity(double scale, double x)
        {
            var n = new Rayleigh(scale);
            double expected = (x/(scale*scale))*Math.Exp(-x*x/(2.0*scale*scale));
            Assert.AreEqual(expected, n.Density(x));
            Assert.AreEqual(expected, Rayleigh.PDF(scale, x));
        }

        [TestCase(0.1, 0.1)]
        [TestCase(1.0, 1.0)]
        [TestCase(10.0, 10.0)]
        [TestCase(Double.PositiveInfinity, Double.PositiveInfinity)]
        public void ValidateDensityLn(double scale, double x)
        {
            var n = new Rayleigh(scale);
            double expected = Math.Log(x/(scale*scale)) - (x*(x/(2.0*(scale*scale))));
            Assert.AreEqual(expected, n.DensityLn(x));
            Assert.AreEqual(expected, Rayleigh.PDFLn(scale, x));
        }

        [TestCase(0.1, 0.1)]
        [TestCase(1.0, 1.0)]
        [TestCase(10.0, 10.0)]
        public void ValidateInverseCumulativeDistribution(double scale, double x)
        {
            var n = new Rayleigh(scale);
            double cdf = 1.0 - Math.Exp(-x*x/(2.0*scale*scale));
            Assert.AreEqual(x, n.InverseCumulativeDistribution(cdf));
            Assert.AreEqual(x, Rayleigh.InvCDF(scale, cdf));
        }

        /// <summary>
        /// Can sample.
        /// </summary>
        [Test]
        public void CanSample()
        {
            var n = new Rayleigh(1.0);
            n.Sample();
        }

        /// <summary>
        /// Can sample sequence.
        /// </summary>
        [Test]
        public void CanSampleSequence()
        {
            var n = new Rayleigh(1.0);
            var ied = n.Samples();
            ied.Take(5).ToArray();
        }
    }
}