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

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

namespace MathNet.Numerics.UnitTests.IntegralTransformsTests
{

#if !NOSYSNUMERICS
    using System.Numerics;
#endif

    /// <summary>
    /// Matching Naive transform tests.
    /// </summary>
    [TestFixture, Category("FFT")]
    public class MatchingNaiveTransformTest
    {
        /// <summary>
        /// Continuous uniform distribution.
        /// </summary>
        IContinuousDistribution GetUniform(int seed)
        {
            return new ContinuousUniform(-1, 1, new System.Random(seed));
        }

        static void Verify(
            Complex[] samples,
            int maximumErrorDecimalPlaces,
            FourierOptions options,
            Func<Complex[], FourierOptions, Complex[]> naive,
            Action<Complex[], FourierOptions> fast)
        {
            var spectrumNaive = naive(samples, options);

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

            AssertHelpers.AlmostEqual(spectrumNaive, spectrumFast, maximumErrorDecimalPlaces);
        }

        /// <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 FourierRadix2MatchesNaive_RealSine(FourierOptions options)
        {
            var samples = Generate.PeriodicMap(16, w => new Complex(Math.Sin(w), 0), 16, 1.0, Constants.Pi2);

            Verify(samples, 12, options, Fourier.NaiveForward, Fourier.Radix2Forward);
            Verify(samples, 12, options, Fourier.NaiveInverse, Fourier.Radix2Inverse);
        }

        /// <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 FourierRadix2MatchesNaive_Random(FourierOptions options)
        {
            var samples = Generate.RandomComplex(0x80, GetUniform(1));

            Verify(samples, 10, options, Fourier.NaiveForward, Fourier.Radix2Forward);
            Verify(samples, 10, options, Fourier.NaiveInverse, Fourier.Radix2Inverse);
        }

        /// <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 FourierBluesteinMatchesNaive_RealSine_Arbitrary(FourierOptions options)
        {
            var samples = Generate.PeriodicMap(14, w => new Complex(Math.Sin(w), 0), 14, 1.0, Constants.Pi2);

            Verify(samples, 12, options, Fourier.NaiveForward, Fourier.BluesteinForward);
            Verify(samples, 12, options, Fourier.NaiveInverse, Fourier.BluesteinInverse);
        }

        /// <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 FourierBluesteinMatchesNaive_Random_PowerOfTwo(FourierOptions options)
        {
            var samples = Generate.RandomComplex(0x80, GetUniform(1));

            Verify(samples, 10, options, Fourier.NaiveForward, Fourier.BluesteinForward);
            Verify(samples, 10, options, Fourier.NaiveInverse, Fourier.BluesteinInverse);
        }

        /// <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 FourierBluesteinMatchesNaive_Random_Arbitrary(FourierOptions options)
        {
            var samples = Generate.RandomComplex(0x7F, GetUniform(1));

            Verify(samples, 10, options, Fourier.NaiveForward, Fourier.BluesteinForward);
            Verify(samples, 10, options, Fourier.NaiveInverse, Fourier.BluesteinInverse);
        }

        [Test, Explicit("Long-Running")]
        public void AlgorithmsMatchNaive_PowerOfTwo_Large()
        {
            // 65536 = 2^16
            const FourierOptions options = FourierOptions.NoScaling;
            var samples = Generate.RandomComplex(65536, GetUniform(1));
            var naive = Fourier.NaiveForward(samples, options);

            Verify(samples, 10, options, (a, b) => naive, Fourier.Radix2Forward);
            Verify(samples, 10, options, (a, b) => naive, Fourier.BluesteinForward);
        }

        [Test, Explicit("Long-Running")]
        public void AlgorithmsMatchNaive_Arbitrary_Large()
        {
            // 30870 = 2*3*3*5*7*7*7
            const FourierOptions options = FourierOptions.NoScaling;
            var samples = Generate.RandomComplex(30870, GetUniform(1));
            var naive = Fourier.NaiveForward(samples, options);

            Verify(samples, 10, options, (a, b) => naive, Fourier.BluesteinForward);
        }

        [Test, Explicit("Long-Running")]
        public void AlgorithmsMatchNaive_Arbitrary_Large_GH286()
        {
            const FourierOptions options = FourierOptions.NoScaling;
            var samples = Generate.RandomComplex(46500, GetUniform(1));
            var naive = Fourier.NaiveForward(samples, options);

            Verify(samples, 10, options, (a, b) => naive, Fourier.BluesteinForward);
        }
    }
}