mathnet-numerics/src/UnitTests/IntegralTransformsTests/ParsevalTheoremTest.cs

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namespace MathNet.Numerics.UnitTests.IntegralTransformsTests
{
    using System.Linq;
    using Distributions;
    using IntegralTransforms;
    using IntegralTransforms.Algorithms;
    using MbUnit.Framework;
    using Sampling;
    using Statistics;
    using System.Numerics;

    [TestFixture]
    public class ParsevalTheoremTest
    {
        private IContinuousDistribution _uniform = new ContinuousUniform(-1, 1);

        [Test]
        [Row(0x1000)]
        [Row(0x7FF)]
        public void FourierDefaultTransformSatisfiesParsevalsTheorem(int count)
        {
            var samples = Sample.Random((u, v) => new Complex(u, v), _uniform, count);

            var timeSpaceEnergy = (from s in samples select s.MagnitudeSquared()).Mean();

            var work = new Complex[samples.Length];
            samples.CopyTo(work, 0);

            // Default -> Symmetric Scaling
            Transform.FourierForward(work);

            var frequencySpaceEnergy = (from s in work select s.MagnitudeSquared()).Mean();

            Assert.AreApproximatelyEqual(timeSpaceEnergy, frequencySpaceEnergy, 1e-12);
        }

        [Test]
        [Row(0x40)]
        [Row(0x1F)]
        public void HartleyDefaultNaiveSatisfiesParsevalsTheorem(int count)
        {
            var samples = Sample.Random(x => x, _uniform, count);

            var timeSpaceEnergy = (from s in samples select s * s).Mean();

            var work = new double[samples.Length];
            samples.CopyTo(work, 0);

            // Default -> Symmetric Scaling
            var dht = new DiscreteHartleyTransform();
            work = dht.NaiveForward(work, HartleyOptions.Default);

            var frequencySpaceEnergy = (from s in work select s * s).Mean();

            Assert.AreApproximatelyEqual(timeSpaceEnergy, frequencySpaceEnergy, 1e-12);
        }
    }
}