forked from tsai/mathnet-numerics
Christoph Ruegg
9 years ago
13 changed files with 98 additions and 668 deletions
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// <copyright file="Fourier.Bluestein.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2015 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
|
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System; |
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using System.Numerics; |
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using MathNet.Numerics.Threading; |
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namespace MathNet.Numerics.IntegralTransforms |
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{ |
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/// <summary>
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/// Complex Fast (FFT) Implementation of the Discrete Fourier Transform (DFT).
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/// </summary>
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public static partial class Fourier |
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{ |
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/// <summary>
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/// Sequences with length greater than Math.Sqrt(Int32.MaxValue) + 1
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/// will cause k*k in the Bluestein sequence to overflow (GH-286).
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/// </summary>
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const int BluesteinSequenceLengthThreshold = 46341; |
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/// <summary>
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/// Generate the bluestein sequence for the provided problem size.
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/// </summary>
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/// <param name="n">Number of samples.</param>
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/// <returns>Bluestein sequence exp(I*Pi*k^2/N)</returns>
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static Complex32[] BluesteinSequence32(int n) |
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{ |
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double s = Constants.Pi / n; |
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var sequence = new Complex32[n]; |
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// TODO: benchmark whether the second variation is significantly
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// faster than the former one. If not just use the former one always.
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if (n > BluesteinSequenceLengthThreshold) |
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{ |
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for (int k = 0; k < sequence.Length; k++) |
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{ |
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double t = (s * k) * k; |
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sequence[k] = new Complex32((float)Math.Cos(t), (float)Math.Sin(t)); |
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} |
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} |
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else |
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{ |
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for (int k = 0; k < sequence.Length; k++) |
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{ |
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double t = s * (k * k); |
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sequence[k] = new Complex32((float)Math.Cos(t), (float)Math.Sin(t)); |
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} |
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} |
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return sequence; |
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} |
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/// <summary>
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/// Generate the bluestein sequence for the provided problem size.
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/// </summary>
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/// <param name="n">Number of samples.</param>
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/// <returns>Bluestein sequence exp(I*Pi*k^2/N)</returns>
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static Complex[] BluesteinSequence(int n) |
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{ |
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double s = Constants.Pi/n; |
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var sequence = new Complex[n]; |
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// TODO: benchmark whether the second variation is significantly
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// faster than the former one. If not just use the former one always.
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if (n > BluesteinSequenceLengthThreshold) |
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{ |
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for (int k = 0; k < sequence.Length; k++) |
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{ |
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double t = (s*k)*k; |
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sequence[k] = new Complex(Math.Cos(t), Math.Sin(t)); |
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} |
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} |
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else |
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{ |
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for (int k = 0; k < sequence.Length; k++) |
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{ |
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double t = s*(k*k); |
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sequence[k] = new Complex(Math.Cos(t), Math.Sin(t)); |
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} |
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} |
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return sequence; |
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} |
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/// <summary>
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/// Convolution with the bluestein sequence (Parallel Version).
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/// </summary>
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/// <param name="samples">Sample Vector.</param>
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static void BluesteinConvolutionParallel(Complex32[] samples) |
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{ |
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int n = samples.Length; |
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Complex32[] sequence = BluesteinSequence32(n); |
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// Padding to power of two >= 2N–1 so we can apply Radix-2 FFT.
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int m = ((n << 1) - 1).CeilingToPowerOfTwo(); |
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var b = new Complex32[m]; |
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var a = new Complex32[m]; |
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CommonParallel.Invoke( |
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() => |
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{ |
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// Build and transform padded sequence b_k = exp(I*Pi*k^2/N)
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for (int i = 0; i < n; i++) |
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{ |
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b[i] = sequence[i]; |
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} |
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for (int i = m - n + 1; i < b.Length; i++) |
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{ |
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b[i] = sequence[m - i]; |
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} |
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Radix2(b, -1); |
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}, |
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() => |
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{ |
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// Build and transform padded sequence a_k = x_k * exp(-I*Pi*k^2/N)
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for (int i = 0; i < samples.Length; i++) |
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{ |
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a[i] = sequence[i].Conjugate() * samples[i]; |
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} |
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Radix2(a, -1); |
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}); |
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for (int i = 0; i < a.Length; i++) |
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{ |
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a[i] *= b[i]; |
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} |
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Radix2Parallel(a, 1); |
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var nbinv = 1.0f / m; |
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for (int i = 0; i < samples.Length; i++) |
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{ |
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samples[i] = nbinv * sequence[i].Conjugate() * a[i]; |
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} |
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} |
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/// <summary>
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/// Convolution with the bluestein sequence (Parallel Version).
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/// </summary>
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/// <param name="samples">Sample Vector.</param>
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static void BluesteinConvolutionParallel(Complex[] samples) |
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{ |
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int n = samples.Length; |
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Complex[] sequence = BluesteinSequence(n); |
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// Padding to power of two >= 2N–1 so we can apply Radix-2 FFT.
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int m = ((n << 1) - 1).CeilingToPowerOfTwo(); |
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var b = new Complex[m]; |
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var a = new Complex[m]; |
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CommonParallel.Invoke( |
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() => |
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{ |
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// Build and transform padded sequence b_k = exp(I*Pi*k^2/N)
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for (int i = 0; i < n; i++) |
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{ |
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b[i] = sequence[i]; |
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} |
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for (int i = m - n + 1; i < b.Length; i++) |
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{ |
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b[i] = sequence[m - i]; |
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} |
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Radix2(b, -1); |
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}, |
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() => |
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{ |
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// Build and transform padded sequence a_k = x_k * exp(-I*Pi*k^2/N)
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for (int i = 0; i < samples.Length; i++) |
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{ |
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a[i] = sequence[i].Conjugate()*samples[i]; |
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} |
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Radix2(a, -1); |
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}); |
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for (int i = 0; i < a.Length; i++) |
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{ |
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a[i] *= b[i]; |
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} |
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Radix2Parallel(a, 1); |
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var nbinv = 1.0/m; |
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for (int i = 0; i < samples.Length; i++) |
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{ |
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samples[i] = nbinv*sequence[i].Conjugate()*a[i]; |
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} |
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} |
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/// <summary>
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/// Swap the real and imaginary parts of each sample.
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/// </summary>
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/// <param name="samples">Sample Vector.</param>
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static void SwapRealImaginary(Complex32[] samples) |
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{ |
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for (int i = 0; i < samples.Length; i++) |
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{ |
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samples[i] = new Complex32(samples[i].Imaginary, samples[i].Real); |
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} |
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} |
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/// <summary>
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/// Swap the real and imaginary parts of each sample.
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/// </summary>
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/// <param name="samples">Sample Vector.</param>
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static void SwapRealImaginary(Complex[] samples) |
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{ |
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for (int i = 0; i < samples.Length; i++) |
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{ |
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samples[i] = new Complex(samples[i].Imaginary, samples[i].Real); |
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} |
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} |
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/// <summary>
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/// Bluestein generic FFT for arbitrary sized sample vectors.
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/// </summary>
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/// <param name="samples">Time-space sample vector.</param>
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/// <param name="exponentSign">Fourier series exponent sign.</param>
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internal static void Bluestein(Complex32[] samples, int exponentSign) |
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{ |
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int n = samples.Length; |
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if (n.IsPowerOfTwo()) |
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{ |
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Radix2Parallel(samples, exponentSign); |
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return; |
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} |
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if (exponentSign == 1) |
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{ |
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SwapRealImaginary(samples); |
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} |
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BluesteinConvolutionParallel(samples); |
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if (exponentSign == 1) |
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{ |
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SwapRealImaginary(samples); |
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} |
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} |
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/// <summary>
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/// Bluestein generic FFT for arbitrary sized sample vectors.
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/// </summary>
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/// <param name="samples">Time-space sample vector.</param>
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/// <param name="exponentSign">Fourier series exponent sign.</param>
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internal static void Bluestein(Complex[] samples, int exponentSign) |
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{ |
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int n = samples.Length; |
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if (n.IsPowerOfTwo()) |
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{ |
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Radix2Parallel(samples, exponentSign); |
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return; |
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} |
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if (exponentSign == 1) |
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{ |
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SwapRealImaginary(samples); |
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} |
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BluesteinConvolutionParallel(samples); |
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if (exponentSign == 1) |
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{ |
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SwapRealImaginary(samples); |
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} |
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} |
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} |
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} |
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@ -1,225 +0,0 @@ |
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// <copyright file="Fourier.RadixN.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2014 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
|
|
||||
// obtaining a copy of this software and associated documentation
|
|
||||
// files (the "Software"), to deal in the Software without
|
|
||||
// restriction, including without limitation the rights to use,
|
|
||||
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
|
||||
// copies of the Software, and to permit persons to whom the
|
|
||||
// Software is furnished to do so, subject to the following
|
|
||||
// conditions:
|
|
||||
//
|
|
||||
// The above copyright notice and this permission notice shall be
|
|
||||
// included in all copies or substantial portions of the Software.
|
|
||||
//
|
|
||||
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
|
||||
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
|
||||
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
|
||||
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
|
||||
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
|
||||
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
|
||||
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
|
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// OTHER DEALINGS IN THE SOFTWARE.
|
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// </copyright>
|
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using System; |
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using System.Numerics; |
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using System.Runtime.CompilerServices; |
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using MathNet.Numerics.Properties; |
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using MathNet.Numerics.Threading; |
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namespace MathNet.Numerics.IntegralTransforms |
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{ |
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/// <summary>
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/// Complex Fast (FFT) Implementation of the Discrete Fourier Transform (DFT).
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/// </summary>
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public static partial class Fourier |
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{ |
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/// <summary>
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/// Radix-2 Reorder Helper Method
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/// </summary>
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/// <typeparam name="T">Sample type</typeparam>
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/// <param name="samples">Sample vector</param>
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static void Radix2Reorder<T>(T[] samples) |
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{ |
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var j = 0; |
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for (var i = 0; i < samples.Length - 1; i++) |
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{ |
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if (i < j) |
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{ |
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var temp = samples[i]; |
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samples[i] = samples[j]; |
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samples[j] = temp; |
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} |
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var m = samples.Length; |
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do |
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{ |
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m >>= 1; |
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j ^= m; |
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} |
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while ((j & m) == 0); |
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} |
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} |
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/// <summary>
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/// Radix-2 Step Helper Method
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/// </summary>
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/// <param name="samples">Sample vector.</param>
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/// <param name="exponentSign">Fourier series exponent sign.</param>
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/// <param name="levelSize">Level Group Size.</param>
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/// <param name="k">Index inside of the level.</param>
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#if !NET40
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[MethodImpl(MethodImplOptions.AggressiveInlining)] |
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#endif
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static void Radix2Step(Complex32[] samples, int exponentSign, int levelSize, int k) |
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{ |
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// Twiddle Factor
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var exponent = (exponentSign * k) * Constants.Pi / levelSize; |
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var w = new Complex32((float)Math.Cos(exponent), (float)Math.Sin(exponent)); |
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var step = levelSize << 1; |
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for (var i = k; i < samples.Length; i += step) |
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{ |
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var ai = samples[i]; |
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var t = w * samples[i + levelSize]; |
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samples[i] = ai + t; |
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samples[i + levelSize] = ai - t; |
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} |
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} |
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/// <summary>
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/// Radix-2 Step Helper Method
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/// </summary>
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/// <param name="samples">Sample vector.</param>
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/// <param name="exponentSign">Fourier series exponent sign.</param>
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/// <param name="levelSize">Level Group Size.</param>
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/// <param name="k">Index inside of the level.</param>
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#if !NET40
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[MethodImpl(MethodImplOptions.AggressiveInlining)] |
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#endif
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static void Radix2Step(Complex[] samples, int exponentSign, int levelSize, int k) |
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{ |
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// Twiddle Factor
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var exponent = (exponentSign*k)*Constants.Pi/levelSize; |
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var w = new Complex(Math.Cos(exponent), Math.Sin(exponent)); |
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var step = levelSize << 1; |
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for (var i = k; i < samples.Length; i += step) |
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{ |
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var ai = samples[i]; |
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var t = w*samples[i + levelSize]; |
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samples[i] = ai + t; |
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samples[i + levelSize] = ai - t; |
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} |
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} |
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/// <summary>
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/// Radix-2 generic FFT for power-of-two sized sample vectors.
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/// </summary>
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/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
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/// <param name="exponentSign">Fourier series exponent sign.</param>
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/// <exception cref="ArgumentException"/>
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internal static void Radix2(Complex32[] samples, int exponentSign) |
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{ |
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if (!samples.Length.IsPowerOfTwo()) |
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{ |
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throw new ArgumentException(Resources.ArgumentPowerOfTwo); |
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} |
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Radix2Reorder(samples); |
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for (var levelSize = 1; levelSize < samples.Length; levelSize *= 2) |
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{ |
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for (var k = 0; k < levelSize; k++) |
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{ |
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Radix2Step(samples, exponentSign, levelSize, k); |
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} |
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||||
} |
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||||
} |
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/// <summary>
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||||
/// Radix-2 generic FFT for power-of-two sized sample vectors.
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||||
/// </summary>
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||||
/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
|
|
||||
/// <param name="exponentSign">Fourier series exponent sign.</param>
|
|
||||
/// <exception cref="ArgumentException"/>
|
|
||||
internal static void Radix2(Complex[] samples, int exponentSign) |
|
||||
{ |
|
||||
if (!samples.Length.IsPowerOfTwo()) |
|
||||
{ |
|
||||
throw new ArgumentException(Resources.ArgumentPowerOfTwo); |
|
||||
} |
|
||||
|
|
||||
Radix2Reorder(samples); |
|
||||
for (var levelSize = 1; levelSize < samples.Length; levelSize *= 2) |
|
||||
{ |
|
||||
for (var k = 0; k < levelSize; k++) |
|
||||
{ |
|
||||
Radix2Step(samples, exponentSign, levelSize, k); |
|
||||
} |
|
||||
} |
|
||||
} |
|
||||
|
|
||||
/// <summary>
|
|
||||
/// Radix-2 generic FFT for power-of-two sample vectors (Parallel Version).
|
|
||||
/// </summary>
|
|
||||
/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
|
|
||||
/// <param name="exponentSign">Fourier series exponent sign.</param>
|
|
||||
/// <exception cref="ArgumentException"/>
|
|
||||
internal static void Radix2Parallel(Complex32[] samples, int exponentSign) |
|
||||
{ |
|
||||
if (!samples.Length.IsPowerOfTwo()) |
|
||||
{ |
|
||||
throw new ArgumentException(Resources.ArgumentPowerOfTwo); |
|
||||
} |
|
||||
|
|
||||
Radix2Reorder(samples); |
|
||||
for (var levelSize = 1; levelSize < samples.Length; levelSize *= 2) |
|
||||
{ |
|
||||
var size = levelSize; |
|
||||
|
|
||||
CommonParallel.For(0, size, 64, (u, v) => |
|
||||
{ |
|
||||
for (int i = u; i < v; i++) |
|
||||
{ |
|
||||
Radix2Step(samples, exponentSign, size, i); |
|
||||
} |
|
||||
}); |
|
||||
} |
|
||||
} |
|
||||
|
|
||||
/// <summary>
|
|
||||
/// Radix-2 generic FFT for power-of-two sample vectors (Parallel Version).
|
|
||||
/// </summary>
|
|
||||
/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
|
|
||||
/// <param name="exponentSign">Fourier series exponent sign.</param>
|
|
||||
/// <exception cref="ArgumentException"/>
|
|
||||
internal static void Radix2Parallel(Complex[] samples, int exponentSign) |
|
||||
{ |
|
||||
if (!samples.Length.IsPowerOfTwo()) |
|
||||
{ |
|
||||
throw new ArgumentException(Resources.ArgumentPowerOfTwo); |
|
||||
} |
|
||||
|
|
||||
Radix2Reorder(samples); |
|
||||
for (var levelSize = 1; levelSize < samples.Length; levelSize *= 2) |
|
||||
{ |
|
||||
var size = levelSize; |
|
||||
|
|
||||
CommonParallel.For(0, size, 64, (u, v) => |
|
||||
{ |
|
||||
for (int i = u; i < v; i++) |
|
||||
{ |
|
||||
Radix2Step(samples, exponentSign, size, i); |
|
||||
} |
|
||||
}); |
|
||||
} |
|
||||
} |
|
||||
} |
|
||||
} |
|
||||
Loading…
Reference in new issue