本征FFT库 [英] Eigen FFT library

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问题描述

我正在尝试通过FFTW后端使用Eigen不支持的FFT库.具体来说,我想进行2D FFT.这是我的代码:

I am trying to use Eigen unsupported FFT library using FFTW backend. Specifically I am want to do a 2D FFT. Here's my code :

void fft2(Eigen::MatrixXf * matIn,Eigen::MatrixXcf * matOut)
{
    const int nRows = matIn->rows();
    const int nCols = matIn->cols();

    Eigen::FFT< float > fft;

    for (int k = 0; k < nRows; ++k) {
        Eigen::VectorXcf tmpOut(nRows);
        fft.fwd(tmpOut, matIn->row(k));
        matOut->row(k) = tmpOut;
    }

    for (int k = 0; k < nCols; ++k) {
        Eigen::VectorXcf tmpOut(nCols);
        fft.fwd(tmpOut, matOut->col(k));
        matOut->col(k) = tmpOut;
    }

}

我有2个问题:

  • 首先,在某些矩阵上使用此代码时遇到分段错误.并非所有矩阵都将发生此错误.我想这与对齐错误有关.我通过以下方式使用这些功能:

  • First, I get a segmentation fault when using this code on some matrix. This error doesn't happen for all matrixes. I guess it's related to an alignment error. I use the functions in the following way :

Eigen :: MatrixXcf matFFT(mat.rows(),mat.cols());fft2(& matFloat,& matFFT);

Eigen::MatrixXcf matFFT(mat.rows(),mat.cols()); fft2(&matFloat,&matFFT);

其中mat可以是任何矩阵.有趣的是,仅当我在第二维上计算FFT时才植入代码,而在第一维上却没有.KissFFT后端不会发生这种情况.

where mat can be any matrix. Funnily, the code plants only when I compute the FFT over the 2nd dimension, never on the first one. This doesn't happen with kissFFT backend.

  • 第二,当函数正常工作时,我得到的结果与Matlab(使用FFTW)不同.例如:

输入矩阵:

[2, 1, 2]
[3, 2, 1]
[1, 2, 3]

本征给出:

[           (0,5),    (0.5,0.86603),          (0,0.5)]
[  (-4.3301,-2.5),     (-1,-1.7321), (0.31699,-1.549)]
[ (-1.5,-0.86603),       (2,3.4641),       (2,3.4641)]

Matlab给出了:

Matlab gives :

   17 +          0i          0.5 +    0.86603i          0.5 -    0.86603i
   -1 +          0i           -1 -     1.7321i            2 -     3.4641i
   -1 +          0i            2 +     3.4641i           -1 +     1.7321i 

只有中央部分是相同的.

Only the central part is the same.

任何帮助都将受到欢迎.

Any help would be welcome.

推荐答案

在我的第一个解决方案中,我未能激活EIGEN_FFTW_DEFAULT,激活它揭示了在fftw支持的Eigen实现中出现错误.以下作品:

I failed to activate EIGEN_FFTW_DEFAULT in my first solution, activating it reveals an error in the fftw-support implementation of Eigen. The following works:

#define EIGEN_FFTW_DEFAULT
#include <iostream>
#include <unsupported/Eigen/FFT>

int main(int argc, char *argv[])
{
    Eigen::MatrixXf A(3,3);
    A << 2,1,2,  3,2,1,  1,2,3;
    const int nRows = A.rows();
    const int nCols = A.cols();

    std::cout << A << "\n\n";

    Eigen::MatrixXcf B(3,3);

    Eigen::FFT< float > fft;

    for (int k = 0; k < nRows; ++k) {
        Eigen::VectorXcf tmpOut(nRows);
        fft.fwd(tmpOut, A.row(k));
        B.row(k) = tmpOut;
    }
    std::cout << B << "\n\n";
    Eigen::FFT< float > fft2;  // Workaround: Using the same FFT object for a real and a complex FFT seems not to work with FFTW
    for (int k = 0; k < nCols; ++k) {
        Eigen::VectorXcf tmpOut(nCols);
        fft2.fwd(tmpOut, B.col(k));
        B.col(k) = tmpOut;
    }
    std::cout << B << '\n';
}

我得到以下输出:

2 1 2
3 2 1
1 2 3

     (17,0)  (0.5,0.866025) (0.5,-0.866025)
     (-1,0)   (-1,-1.73205)     (2,-3.4641)
     (-1,0)      (2,3.4641)    (-1,1.73205)

与您的Matlab结果相同.

Which is the same as your Matlab result.

N.B.:FFTW似乎本机支持2D实数->复杂FFT(无需使用单独的FFT).这可能会更有效.

N.B.: FFTW seems to support 2D real->complex FFT natively (without using individual FFTs). This is likely more efficient.

fftwf_plan fftwf_plan_dft_r2c_2d(int n0, int n1,               
                                 float *in, fftwf_complex *out, unsigned flags);

这篇关于本征FFT库的文章就介绍到这了,希望我们推荐的答案对大家有所帮助,也希望大家多多支持IT屋!

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