Christoph Ruegg
8 years ago
13 changed files with 98 additions and 668 deletions
@ -1,299 +0,0 @@ |
|||
// <copyright file="Fourier.Bluestein.cs" company="Math.NET">
|
|||
// Math.NET Numerics, part of the Math.NET Project
|
|||
// http://numerics.mathdotnet.com
|
|||
// http://github.com/mathnet/mathnet-numerics
|
|||
//
|
|||
// Copyright (c) 2009-2015 Math.NET
|
|||
//
|
|||
// 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
|
|||
// OTHER DEALINGS IN THE SOFTWARE.
|
|||
// </copyright>
|
|||
|
|||
using System; |
|||
using System.Numerics; |
|||
using MathNet.Numerics.Threading; |
|||
|
|||
namespace MathNet.Numerics.IntegralTransforms |
|||
{ |
|||
/// <summary>
|
|||
/// Complex Fast (FFT) Implementation of the Discrete Fourier Transform (DFT).
|
|||
/// </summary>
|
|||
public static partial class Fourier |
|||
{ |
|||
/// <summary>
|
|||
/// Sequences with length greater than Math.Sqrt(Int32.MaxValue) + 1
|
|||
/// will cause k*k in the Bluestein sequence to overflow (GH-286).
|
|||
/// </summary>
|
|||
const int BluesteinSequenceLengthThreshold = 46341; |
|||
|
|||
/// <summary>
|
|||
/// Generate the bluestein sequence for the provided problem size.
|
|||
/// </summary>
|
|||
/// <param name="n">Number of samples.</param>
|
|||
/// <returns>Bluestein sequence exp(I*Pi*k^2/N)</returns>
|
|||
static Complex32[] BluesteinSequence32(int n) |
|||
{ |
|||
double s = Constants.Pi / n; |
|||
var sequence = new Complex32[n]; |
|||
|
|||
// TODO: benchmark whether the second variation is significantly
|
|||
// faster than the former one. If not just use the former one always.
|
|||
if (n > BluesteinSequenceLengthThreshold) |
|||
{ |
|||
for (int k = 0; k < sequence.Length; k++) |
|||
{ |
|||
double t = (s * k) * k; |
|||
sequence[k] = new Complex32((float)Math.Cos(t), (float)Math.Sin(t)); |
|||
} |
|||
} |
|||
else |
|||
{ |
|||
for (int k = 0; k < sequence.Length; k++) |
|||
{ |
|||
double t = s * (k * k); |
|||
sequence[k] = new Complex32((float)Math.Cos(t), (float)Math.Sin(t)); |
|||
} |
|||
} |
|||
|
|||
return sequence; |
|||
} |
|||
|
|||
/// <summary>
|
|||
/// Generate the bluestein sequence for the provided problem size.
|
|||
/// </summary>
|
|||
/// <param name="n">Number of samples.</param>
|
|||
/// <returns>Bluestein sequence exp(I*Pi*k^2/N)</returns>
|
|||
static Complex[] BluesteinSequence(int n) |
|||
{ |
|||
double s = Constants.Pi/n; |
|||
var sequence = new Complex[n]; |
|||
|
|||
// TODO: benchmark whether the second variation is significantly
|
|||
// faster than the former one. If not just use the former one always.
|
|||
if (n > BluesteinSequenceLengthThreshold) |
|||
{ |
|||
for (int k = 0; k < sequence.Length; k++) |
|||
{ |
|||
double t = (s*k)*k; |
|||
sequence[k] = new Complex(Math.Cos(t), Math.Sin(t)); |
|||
} |
|||
} |
|||
else |
|||
{ |
|||
for (int k = 0; k < sequence.Length; k++) |
|||
{ |
|||
double t = s*(k*k); |
|||
sequence[k] = new Complex(Math.Cos(t), Math.Sin(t)); |
|||
} |
|||
} |
|||
|
|||
return sequence; |
|||
} |
|||
|
|||
/// <summary>
|
|||
/// Convolution with the bluestein sequence (Parallel Version).
|
|||
/// </summary>
|
|||
/// <param name="samples">Sample Vector.</param>
|
|||
static void BluesteinConvolutionParallel(Complex32[] samples) |
|||
{ |
|||
int n = samples.Length; |
|||
Complex32[] sequence = BluesteinSequence32(n); |
|||
|
|||
// Padding to power of two >= 2N–1 so we can apply Radix-2 FFT.
|
|||
int m = ((n << 1) - 1).CeilingToPowerOfTwo(); |
|||
var b = new Complex32[m]; |
|||
var a = new Complex32[m]; |
|||
|
|||
CommonParallel.Invoke( |
|||
() => |
|||
{ |
|||
// Build and transform padded sequence b_k = exp(I*Pi*k^2/N)
|
|||
for (int i = 0; i < n; i++) |
|||
{ |
|||
b[i] = sequence[i]; |
|||
} |
|||
|
|||
for (int i = m - n + 1; i < b.Length; i++) |
|||
{ |
|||
b[i] = sequence[m - i]; |
|||
} |
|||
|
|||
Radix2(b, -1); |
|||
}, |
|||
() => |
|||
{ |
|||
// Build and transform padded sequence a_k = x_k * exp(-I*Pi*k^2/N)
|
|||
for (int i = 0; i < samples.Length; i++) |
|||
{ |
|||
a[i] = sequence[i].Conjugate() * samples[i]; |
|||
} |
|||
|
|||
Radix2(a, -1); |
|||
}); |
|||
|
|||
for (int i = 0; i < a.Length; i++) |
|||
{ |
|||
a[i] *= b[i]; |
|||
} |
|||
|
|||
Radix2Parallel(a, 1); |
|||
|
|||
var nbinv = 1.0f / m; |
|||
for (int i = 0; i < samples.Length; i++) |
|||
{ |
|||
samples[i] = nbinv * sequence[i].Conjugate() * a[i]; |
|||
} |
|||
} |
|||
|
|||
/// <summary>
|
|||
/// Convolution with the bluestein sequence (Parallel Version).
|
|||
/// </summary>
|
|||
/// <param name="samples">Sample Vector.</param>
|
|||
static void BluesteinConvolutionParallel(Complex[] samples) |
|||
{ |
|||
int n = samples.Length; |
|||
Complex[] sequence = BluesteinSequence(n); |
|||
|
|||
// Padding to power of two >= 2N–1 so we can apply Radix-2 FFT.
|
|||
int m = ((n << 1) - 1).CeilingToPowerOfTwo(); |
|||
var b = new Complex[m]; |
|||
var a = new Complex[m]; |
|||
|
|||
CommonParallel.Invoke( |
|||
() => |
|||
{ |
|||
// Build and transform padded sequence b_k = exp(I*Pi*k^2/N)
|
|||
for (int i = 0; i < n; i++) |
|||
{ |
|||
b[i] = sequence[i]; |
|||
} |
|||
|
|||
for (int i = m - n + 1; i < b.Length; i++) |
|||
{ |
|||
b[i] = sequence[m - i]; |
|||
} |
|||
|
|||
Radix2(b, -1); |
|||
}, |
|||
() => |
|||
{ |
|||
// Build and transform padded sequence a_k = x_k * exp(-I*Pi*k^2/N)
|
|||
for (int i = 0; i < samples.Length; i++) |
|||
{ |
|||
a[i] = sequence[i].Conjugate()*samples[i]; |
|||
} |
|||
|
|||
Radix2(a, -1); |
|||
}); |
|||
|
|||
for (int i = 0; i < a.Length; i++) |
|||
{ |
|||
a[i] *= b[i]; |
|||
} |
|||
|
|||
Radix2Parallel(a, 1); |
|||
|
|||
var nbinv = 1.0/m; |
|||
for (int i = 0; i < samples.Length; i++) |
|||
{ |
|||
samples[i] = nbinv*sequence[i].Conjugate()*a[i]; |
|||
} |
|||
} |
|||
|
|||
/// <summary>
|
|||
/// Swap the real and imaginary parts of each sample.
|
|||
/// </summary>
|
|||
/// <param name="samples">Sample Vector.</param>
|
|||
static void SwapRealImaginary(Complex32[] samples) |
|||
{ |
|||
for (int i = 0; i < samples.Length; i++) |
|||
{ |
|||
samples[i] = new Complex32(samples[i].Imaginary, samples[i].Real); |
|||
} |
|||
} |
|||
|
|||
/// <summary>
|
|||
/// Swap the real and imaginary parts of each sample.
|
|||
/// </summary>
|
|||
/// <param name="samples">Sample Vector.</param>
|
|||
static void SwapRealImaginary(Complex[] samples) |
|||
{ |
|||
for (int i = 0; i < samples.Length; i++) |
|||
{ |
|||
samples[i] = new Complex(samples[i].Imaginary, samples[i].Real); |
|||
} |
|||
} |
|||
|
|||
/// <summary>
|
|||
/// Bluestein generic FFT for arbitrary sized sample vectors.
|
|||
/// </summary>
|
|||
/// <param name="samples">Time-space sample vector.</param>
|
|||
/// <param name="exponentSign">Fourier series exponent sign.</param>
|
|||
internal static void Bluestein(Complex32[] samples, int exponentSign) |
|||
{ |
|||
int n = samples.Length; |
|||
if (n.IsPowerOfTwo()) |
|||
{ |
|||
Radix2Parallel(samples, exponentSign); |
|||
return; |
|||
} |
|||
|
|||
if (exponentSign == 1) |
|||
{ |
|||
SwapRealImaginary(samples); |
|||
} |
|||
|
|||
BluesteinConvolutionParallel(samples); |
|||
|
|||
if (exponentSign == 1) |
|||
{ |
|||
SwapRealImaginary(samples); |
|||
} |
|||
} |
|||
|
|||
/// <summary>
|
|||
/// Bluestein generic FFT for arbitrary sized sample vectors.
|
|||
/// </summary>
|
|||
/// <param name="samples">Time-space sample vector.</param>
|
|||
/// <param name="exponentSign">Fourier series exponent sign.</param>
|
|||
internal static void Bluestein(Complex[] samples, int exponentSign) |
|||
{ |
|||
int n = samples.Length; |
|||
if (n.IsPowerOfTwo()) |
|||
{ |
|||
Radix2Parallel(samples, exponentSign); |
|||
return; |
|||
} |
|||
|
|||
if (exponentSign == 1) |
|||
{ |
|||
SwapRealImaginary(samples); |
|||
} |
|||
|
|||
BluesteinConvolutionParallel(samples); |
|||
|
|||
if (exponentSign == 1) |
|||
{ |
|||
SwapRealImaginary(samples); |
|||
} |
|||
} |
|||
} |
|||
} |
|||
@ -1,225 +0,0 @@ |
|||
// <copyright file="Fourier.RadixN.cs" company="Math.NET">
|
|||
// Math.NET Numerics, part of the Math.NET Project
|
|||
// http://numerics.mathdotnet.com
|
|||
// http://github.com/mathnet/mathnet-numerics
|
|||
//
|
|||
// Copyright (c) 2009-2014 Math.NET
|
|||
//
|
|||
// 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
|
|||
// OTHER DEALINGS IN THE SOFTWARE.
|
|||
// </copyright>
|
|||
|
|||
using System; |
|||
using System.Numerics; |
|||
using System.Runtime.CompilerServices; |
|||
using MathNet.Numerics.Properties; |
|||
using MathNet.Numerics.Threading; |
|||
|
|||
namespace MathNet.Numerics.IntegralTransforms |
|||
{ |
|||
/// <summary>
|
|||
/// Complex Fast (FFT) Implementation of the Discrete Fourier Transform (DFT).
|
|||
/// </summary>
|
|||
public static partial class Fourier |
|||
{ |
|||
/// <summary>
|
|||
/// Radix-2 Reorder Helper Method
|
|||
/// </summary>
|
|||
/// <typeparam name="T">Sample type</typeparam>
|
|||
/// <param name="samples">Sample vector</param>
|
|||
static void Radix2Reorder<T>(T[] samples) |
|||
{ |
|||
var j = 0; |
|||
for (var i = 0; i < samples.Length - 1; i++) |
|||
{ |
|||
if (i < j) |
|||
{ |
|||
var temp = samples[i]; |
|||
samples[i] = samples[j]; |
|||
samples[j] = temp; |
|||
} |
|||
|
|||
var m = samples.Length; |
|||
|
|||
do |
|||
{ |
|||
m >>= 1; |
|||
j ^= m; |
|||
} |
|||
while ((j & m) == 0); |
|||
} |
|||
} |
|||
|
|||
/// <summary>
|
|||
/// Radix-2 Step Helper Method
|
|||
/// </summary>
|
|||
/// <param name="samples">Sample vector.</param>
|
|||
/// <param name="exponentSign">Fourier series exponent sign.</param>
|
|||
/// <param name="levelSize">Level Group Size.</param>
|
|||
/// <param name="k">Index inside of the level.</param>
|
|||
#if !NET40
|
|||
[MethodImpl(MethodImplOptions.AggressiveInlining)] |
|||
#endif
|
|||
static void Radix2Step(Complex32[] samples, int exponentSign, int levelSize, int k) |
|||
{ |
|||
// Twiddle Factor
|
|||
var exponent = (exponentSign * k) * Constants.Pi / levelSize; |
|||
var w = new Complex32((float)Math.Cos(exponent), (float)Math.Sin(exponent)); |
|||
|
|||
var step = levelSize << 1; |
|||
for (var i = k; i < samples.Length; i += step) |
|||
{ |
|||
var ai = samples[i]; |
|||
var t = w * samples[i + levelSize]; |
|||
samples[i] = ai + t; |
|||
samples[i + levelSize] = ai - t; |
|||
} |
|||
} |
|||
|
|||
/// <summary>
|
|||
/// Radix-2 Step Helper Method
|
|||
/// </summary>
|
|||
/// <param name="samples">Sample vector.</param>
|
|||
/// <param name="exponentSign">Fourier series exponent sign.</param>
|
|||
/// <param name="levelSize">Level Group Size.</param>
|
|||
/// <param name="k">Index inside of the level.</param>
|
|||
#if !NET40
|
|||
[MethodImpl(MethodImplOptions.AggressiveInlining)] |
|||
#endif
|
|||
static void Radix2Step(Complex[] samples, int exponentSign, int levelSize, int k) |
|||
{ |
|||
// Twiddle Factor
|
|||
var exponent = (exponentSign*k)*Constants.Pi/levelSize; |
|||
var w = new Complex(Math.Cos(exponent), Math.Sin(exponent)); |
|||
|
|||
var step = levelSize << 1; |
|||
for (var i = k; i < samples.Length; i += step) |
|||
{ |
|||
var ai = samples[i]; |
|||
var t = w*samples[i + levelSize]; |
|||
samples[i] = ai + t; |
|||
samples[i + levelSize] = ai - t; |
|||
} |
|||
} |
|||
|
|||
/// <summary>
|
|||
/// Radix-2 generic FFT for power-of-two sized sample vectors.
|
|||
/// </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 Radix2(Complex32[] 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 sized sample vectors.
|
|||
/// </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 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