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

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namespace MathNet.Numerics.UnitTests.IntegralTransformsTests
{
    using System;
    using IntegralTransforms;
    using IntegralTransforms.Algorithms;
    using MbUnit.Framework;

    [TestFixture]
    public class InverseTransformTest
    {
        private static void VerifyIsReversibleComplex(
            int count,
            double maximumError,
            Func<Complex[], Complex[]> forward,
            Func<Complex[], Complex[]> inverse)
        {
            var samples = SampleProvider.ProvideComplexSamples(count);
            var work = new Complex[samples.Length];
            samples.CopyTo(work, 0);

            work = forward(work);

            Assert.IsFalse(work.AlmostEqualListWithError(samples, maximumError));

            work = inverse(work);

            AssertHelpers.AlmostEqualList(samples, work, maximumError);
        }

        private static void VerifyIsReversibleReal(
            int count,
            double maximumError,
            Func<double[], double[]> forward,
            Func<double[], double[]> inverse)
        {
            var samples = SampleProvider.ProvideRealSamples(count);
            var work = new double[samples.Length];
            samples.CopyTo(work, 0);

            work = forward(work);

            Assert.IsFalse(work.AlmostEqualListWithError(samples, maximumError));

            work = inverse(work);

            AssertHelpers.AlmostEqualList(samples, work, maximumError);
        }

        [Test]
        [Row(FourierOptions.Default)]
        [Row(FourierOptions.Matlab)]
        public void FourierNaiveIsReversible(FourierOptions options)
        {
            var dft = new DiscreteFourierTransform();

            VerifyIsReversibleComplex(
                0x80,
                1e-12,
                s => dft.NaiveForward(s, options),
                s => dft.NaiveInverse(s, options));
        }

        [Test]
        [Row(FourierOptions.Default)]
        [Row(FourierOptions.Matlab)]
        public void FourierRadix2IsReversible(FourierOptions options)
        {
            var dft = new DiscreteFourierTransform();

            VerifyIsReversibleComplex(
                0x8000,
                1e-12,
                s =>
                {
                    dft.Radix2Forward(s, options);
                    return s;
                },
                s =>
                {
                    dft.Radix2Inverse(s, options);
                    return s;
                });
        }

        [Test]
        [Row(FourierOptions.Default)]
        [Row(FourierOptions.Matlab)]
        public void FourierBluesteinIsReversible(FourierOptions options)
        {
            var dft = new DiscreteFourierTransform();

            VerifyIsReversibleComplex(
                0x7FFF,
                1e-12,
                s =>
                {
                    dft.BluesteinForward(s, options);
                    return s;
                },
                s =>
                {
                    dft.BluesteinInverse(s, options);
                    return s;
                });
        }

        [Test]
        [Row(HartleyOptions.Default)]
        [Row(HartleyOptions.AsymmetricScaling)]
        public void HartleyNaiveIsReversible(HartleyOptions options)
        {
            var dht = new DiscreteHartleyTransform();

            VerifyIsReversibleReal(
                0x80,
                1e-9,
                s => dht.NaiveForward(s, options),
                s => dht.NaiveInverse(s, options));
        }

        [Test]
        public void FourierDefaultTransformIsReversible()
        {
            var samples = SampleProvider.ProvideComplexSamples(0x7FFF);
            var work = new Complex[samples.Length];
            samples.CopyTo(work, 0);

            Transform.FourierForward(work);

            Assert.IsFalse(work.AlmostEqualListWithError(samples, 1e-12));

            Transform.FourierInverse(work);

            AssertHelpers.AlmostEqualList(samples, work, 1e-12);

            Transform.FourierInverse(work, FourierOptions.Default);

            Assert.IsFalse(work.AlmostEqualListWithError(samples, 1e-12));

            Transform.FourierForward(work, FourierOptions.Default);

            AssertHelpers.AlmostEqualList(samples, work, 1e-12);
        }
    }
}