mathnet-numerics/src/Numerics/IntegralTransforms/Algorithms/DiscreteFourierTransform.Naive.cs

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namespace MathNet.Numerics.IntegralTransforms.Algorithms
{
    using System;
    using System.Numerics;
    using Threading;

    /// <summary>
    /// Complex Fast (FFT) Implementation of the Discrete Fourier Transform (DFT).
    /// </summary>
    public partial class DiscreteFourierTransform
    {
        /// <summary>
        /// Naive generic DFT, useful e.g. to verify faster algorithms.
        /// </summary>
        /// <param name="samples">Time-space sample vector.</param>
        /// <param name="exponentSign">Fourier series exponent sign.</param>
        /// <returns>Corresponding frequency-space vector.</returns>
        internal static Complex[] Naive(Complex[] samples, int exponentSign)
        {
            var w0 = exponentSign * Constants.Pi2 / samples.Length;
            var spectrum = new Complex[samples.Length];

            CommonParallel.For(
               0,
               samples.Length,
               index =>
               {
                   var wk = w0 * index;
                   var sum = Complex.Zero;
                   for (var n = 0; n < samples.Length; n++)
                   {
                       var w = n * wk;
                       sum += samples[n] * new Complex(Math.Cos(w), Math.Sin(w));
                   }

                   spectrum[index] = sum;
               });

            return spectrum;
        }

        /// <summary>
        /// Naive forward DFT, useful e.g. to verify faster algorithms.
        /// </summary>
        /// <param name="timeSpace">Time-space sample vector.</param>
        /// <param name="options">Fourier Transform Convention Options.</param>
        /// <returns>Corresponding frequency-space vector.</returns>
        public Complex[] NaiveForward(Complex[] timeSpace, FourierOptions options)
        {
            var frequencySpace = Naive(timeSpace, SignByOptions(options));
            ForwardScaleByOptions(options, frequencySpace);
            return frequencySpace;
        }

        /// <summary>
        /// Naive inverse DFT, useful e.g. to verify faster algorithms.
        /// </summary>
        /// <param name="frequencySpace">Frequency-space sample vector.</param>
        /// <param name="options">Fourier Transform Convention Options.</param>
        /// <returns>Corresponding time-space vector.</returns>
        public Complex[] NaiveInverse(Complex[] frequencySpace, FourierOptions options)
        {
            var timeSpace = Naive(frequencySpace, -SignByOptions(options));
            InverseScaleByOptions(options, timeSpace);
            return timeSpace;
        }
    }
}