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

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namespace MathNet.Numerics.UnitTests.IntegralTransformsTests
{
    using System;
    using System.Numerics;
    using Distributions;
    using IntegralTransforms;
    using IntegralTransforms.Algorithms;
    using NUnit.Framework;
    using Signals;

    /// <summary>
    /// Matching Naive transform tests.
    /// </summary>
    [TestFixture]
    public class MatchingNaiveTransformTest
    {
        /// <summary>
        /// Continuous uniform distribution.
        /// </summary>
        private readonly IContinuousDistribution _uniform = new ContinuousUniform(-1, 1);

        /// <summary>
        /// Verify matches naive complex.
        /// </summary>
        /// <param name="samples">Samples count.</param>
        /// <param name="maximumError">Maximum error.</param>
        /// <param name="naive">Naive transform.</param>
        /// <param name="fast">Fast delegate.</param>
        private static void VerifyMatchesNaiveComplex(
            Complex[] samples,
            double maximumError,
            Func<Complex[], Complex[]> naive,
            Action<Complex[]> fast)
        {
            var spectrumNaive = naive(samples);

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

            AssertHelpers.AlmostEqualList(spectrumNaive, spectrumFast, maximumError);
        }

        /// <summary>
        /// Fourier Radix2XX matches naive on real sine.
        /// </summary>
        /// <param name="options">Fourier options.</param>
        [TestCase(FourierOptions.Default)]
        [TestCase(FourierOptions.Matlab)]
        [TestCase(FourierOptions.NumericalRecipes)]
        public void FourierRadix2MatchesNaiveOnRealSine(FourierOptions options)
        {
            var dft = new DiscreteFourierTransform();
            var samples = SignalGenerator.EquidistantPeriodic(w => new Complex(Math.Sin(w), 0), Constants.Pi2, 0, 16);

            VerifyMatchesNaiveComplex(
                samples,
                1e-12,
                s => dft.NaiveForward(s, options),
                s => dft.Radix2Forward(s, options));

            VerifyMatchesNaiveComplex(
                samples,
                1e-12,
                s => dft.NaiveInverse(s, options),
                s => dft.Radix2Inverse(s, options));
        }

        /// <summary>
        /// Fourier Radix2XX matches naive on random.
        /// </summary>
        /// <param name="options">Fourier options.</param>
        [TestCase(FourierOptions.Default)]
        [TestCase(FourierOptions.Matlab)]
        [TestCase(FourierOptions.NumericalRecipes)]
        public void FourierRadix2MatchesNaiveOnRandom(FourierOptions options)
        {
            var dft = new DiscreteFourierTransform();
            var samples = SignalGenerator.Random((u, v) => new Complex(u, v), _uniform, 0x80);

            VerifyMatchesNaiveComplex(
                samples,
                1e-12,
                s => dft.NaiveForward(s, options),
                s => dft.Radix2Forward(s, options));

            VerifyMatchesNaiveComplex(
                samples,
                1e-12,
                s => dft.NaiveInverse(s, options),
                s => dft.Radix2Inverse(s, options));
        }

        /// <summary>
        /// Fourier bluestein matches naive on real sine non-power of two.
        /// </summary>
        /// <param name="options">Fourier options.</param>
        [TestCase(FourierOptions.Default)]
        [TestCase(FourierOptions.Matlab)]
        [TestCase(FourierOptions.NumericalRecipes)]
        public void FourierBluesteinMatchesNaiveOnRealSineNonPowerOfTwo(FourierOptions options)
        {
            var dft = new DiscreteFourierTransform();
            var samples = SignalGenerator.EquidistantPeriodic(w => new Complex(Math.Sin(w), 0), Constants.Pi2, 0, 14);

            VerifyMatchesNaiveComplex(
                samples,
                1e-12,
                s => dft.NaiveForward(s, options),
                s => dft.BluesteinForward(s, options));

            VerifyMatchesNaiveComplex(
                samples,
                1e-12,
                s => dft.NaiveInverse(s, options),
                s => dft.BluesteinInverse(s, options));
        }

        /// <summary>
        /// Fourier bluestein matches naive on random power of two.
        /// </summary>
        /// <param name="options">Fourier options.</param>
        [TestCase(FourierOptions.Default)]
        [TestCase(FourierOptions.Matlab)]
        [TestCase(FourierOptions.NumericalRecipes)]
        public void FourierBluesteinMatchesNaiveOnRandomPowerOfTwo(FourierOptions options)
        {
            var dft = new DiscreteFourierTransform();
            var samples = SignalGenerator.Random((u, v) => new Complex(u, v), _uniform, 0x80);

            VerifyMatchesNaiveComplex(
                samples,
                1e-12,
                s => dft.NaiveForward(s, options),
                s => dft.BluesteinForward(s, options));

            VerifyMatchesNaiveComplex(
                samples,
                1e-12,
                s => dft.NaiveInverse(s, options),
                s => dft.BluesteinInverse(s, options));
        }

        /// <summary>
        /// Fourier bluestein matches naive on random non-power of two.
        /// </summary>
        /// <param name="options">Fourier options.</param>
        [TestCase(FourierOptions.Default)]
        [TestCase(FourierOptions.Matlab)]
        [TestCase(FourierOptions.NumericalRecipes)]
        public void FourierBluesteinMatchesNaiveOnRandomNonPowerOfTwo(FourierOptions options)
        {
            var dft = new DiscreteFourierTransform();
            var samples = SignalGenerator.Random((u, v) => new Complex(u, v), _uniform, 0x7F);

            VerifyMatchesNaiveComplex(
                samples,
                1e-12,
                s => dft.NaiveForward(s, options),
                s => dft.BluesteinForward(s, options));
            VerifyMatchesNaiveComplex(
                samples,
                1e-12,
                s => dft.NaiveInverse(s, options),
                s => dft.BluesteinInverse(s, options));
        }
    }
}