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// Math.NET Numerics, part of the Math.NET Project
// http://numerics.mathdotnet.com
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using System.Linq;
using Complex = System.Numerics.Complex;
using MathNet.Numerics.Distributions;
using MathNet.Numerics.IntegralTransforms;
using MathNet.Numerics.Statistics;
using NUnit.Framework;

namespace MathNet.Numerics.UnitTests.IntegralTransformsTests
{
    /// <summary>
    /// Parseval's theorem verification tests.
    /// </summary>
    [TestFixture, Category("FFT")]
    public class ParsevalTheoremTest
    {
        /// <summary>
        /// Continuous uniform distribution.
        /// </summary>
        IContinuousDistribution GetUniform(int seed)
        {
            return new ContinuousUniform(-1, 1, new System.Random(seed));
        }

        /// <summary>
        /// Fourier default transform satisfies Parseval's theorem.
        /// </summary>
        /// <param name="count">Samples count.</param>
        [TestCase(0x1000)]
        [TestCase(0x7FF)]
        public void ReferenceDftSatisfiesParsevalsTheorem32(int count)
        {
            var samples = Generate.RandomComplex32(count, GetUniform(1));
            var timeSpaceEnergy = (from s in samples select s.MagnitudeSquared()).Mean();

            var spectrum = new Complex32[samples.Length];
            samples.CopyTo(spectrum, 0);
            ReferenceDiscreteFourierTransform.Forward(spectrum);
            var frequencySpaceEnergy = (from s in spectrum select s.MagnitudeSquared()).Mean();

            Assert.AreEqual(timeSpaceEnergy, frequencySpaceEnergy, 1e-7);
        }

        /// <summary>
        /// Fourier default transform satisfies Parseval's theorem.
        /// </summary>
        /// <param name="count">Samples count.</param>
        [TestCase(0x1000)]
        [TestCase(0x7FF)]
        public void ReferenceDftSatisfiesParsevalsTheorem64(int count)
        {
            var samples = Generate.RandomComplex(count, GetUniform(1));
            var timeSpaceEnergy = (from s in samples select s.MagnitudeSquared()).Mean();

            var spectrum = new Complex[samples.Length];
            samples.CopyTo(spectrum, 0);
            ReferenceDiscreteFourierTransform.Forward(spectrum);
            var frequencySpaceEnergy = (from s in spectrum select s.MagnitudeSquared()).Mean();

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

        /// <summary>
        /// Fourier default transform satisfies Parseval's theorem.
        /// </summary>
        /// <param name="count">Samples count.</param>
        [TestCase(0x1000)]
        [TestCase(0x7FF)]
        public void FourierDefaultTransformSatisfiesParsevalsTheorem32(int count)
        {
            var samples = Generate.RandomComplex32(count, GetUniform(1));
            var timeSpaceEnergy = (from s in samples select s.MagnitudeSquared()).Mean();

            var spectrum = new Complex32[samples.Length];
            samples.CopyTo(spectrum, 0);
            Fourier.Forward(spectrum);
            var frequencySpaceEnergy = (from s in spectrum select s.MagnitudeSquared()).Mean();

            Assert.AreEqual(timeSpaceEnergy, frequencySpaceEnergy, 1e-7);
        }

        /// <summary>
        /// Fourier default transform satisfies Parseval's theorem.
        /// </summary>
        /// <param name="count">Samples count.</param>
        [TestCase(0x1000)]
        [TestCase(0x7FF)]
        public void FourierDefaultTransformSatisfiesParsevalsTheorem64(int count)
        {
            var samples = Generate.RandomComplex(count, GetUniform(1));
            var timeSpaceEnergy = (from s in samples select s.MagnitudeSquared()).Mean();

            var spectrum = new Complex[samples.Length];
            samples.CopyTo(spectrum, 0);
            Fourier.Forward(spectrum);
            var frequencySpaceEnergy = (from s in spectrum select s.MagnitudeSquared()).Mean();

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

        /// <summary>
        /// Hartley default naive satisfies Parseval's theorem.
        /// </summary>
        /// <param name="count">Samples count.</param>
        [TestCase(0x40)]
        [TestCase(0x1F)]
        public void HartleyDefaultNaiveSatisfiesParsevalsTheorem64(int count)
        {
            var samples = Generate.Random(count, GetUniform(1));
            var timeSpaceEnergy = (from s in samples select s*s).Mean();

            var spectrum = new double[samples.Length];
            samples.CopyTo(spectrum, 0);
            spectrum = Hartley.NaiveForward(spectrum, HartleyOptions.Default);

            var frequencySpaceEnergy = (from s in spectrum select s*s).Mean();
            Assert.AreEqual(timeSpaceEnergy, frequencySpaceEnergy, 1e-12);
        }
    }
}
