performing N independent 1D FFT on a 2D matrix with FFTW - fftw

Question

I have a 2 dimensional matrix with each column corresponding to one independent signal. I am going to perform N 1D fft on each column. In matlab, apply a fft to a 2D matrix will do the trick. But I am porting my code to c++ with fftw. I wonder if there is a way to do so. I try the following code by setting the column size to 1 and row size to 4 (total row number), but it does not help.
#include <iostream>
#include <complex>
#include "fftw3.h"
using namespace std;
int main(int argc, char** argv)
{
complex<double> data[4][2];
data[0][0] = complex<double>(1,1);
data[1][0] = complex<double>(2,1);
data[2][0] = complex<double>(3,1);
data[3][0] = complex<double>(4,1);
data[0][1] = complex<double>(1,1);
data[1][1] = complex<double>(1,2);
data[2][1] = complex<double>(1,3);
data[3][1] = complex<double>(1,4);
cout << "original data ..." << endl;
cout << data[0][0] << '\t' << data[0][1] << endl;
cout << data[1][0] << '\t' << data[1][1] << endl;
cout << data[2][0] << '\t' << data[2][1] << endl;
cout << data[3][0] << '\t' << data[3][1] << endl;
cout << endl << endl;
fftw_plan plan=fftw_plan_dft_2d(4, 1,(fftw_complex*)&data[0][0], (fftw_complex*)&data[0][0], FFTW_FORWARD, FFTW_ESTIMATE);
fftw_execute(plan);
cout << "after fftw ..." << endl;
cout << data[0][0] << '\t' << data[0][1] << endl;
cout << data[1][0] << '\t' << data[1][1] << endl;
cout << data[2][0] << '\t' << data[2][1] << endl;
cout << data[3][0] << '\t' << data[3][1] << endl;
return 0;
}
Above code takes the first and second row and reshape them to 2x2 matrix then perform a 2D fft.
Up to now, the only way that comes to my mind is as follow. Let's say I have NxM (N rows, M columns), I create M fftw plans for M 1D fftw. I execute M fftw in serial to get the result. But in practical application, the matrix is very big, M is so large. It is very inefficient to do this way. Any better idea? Thanks.

Answer 1

For those stumbling across this nowadays, the FFTW devs have implemented routines for this operation, which is faster than looping through each column and taking a separate transform. You certainly don't want to take a 2D transform (as is shown in the question), which is mathematically different than row-wise 1D transforms.
The key to you question is in fftw_plan_many_dft. Here is a link to the full documentation.
Here is an example (modifed from the above link) that illustrates what you're looking for.
#include "fftw3.h"
int main() {
fftw_complex *A; // array of data
A = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*10*3);
// ...
/* Transform each column of a 2d array with 10 rows and 3 columns */
int rank = 1; /* not 2: we are computing 1d transforms */
int n[] = {10}; /* 1d transforms of length 10 */
int howmany = 3;
int idist = 1;
int odist = 1;
/* distance between two elements in the same column */
int istride = 3;
int ostride = 3;
int *inembed = n, *onembed = n;
/* forward, in-place, 1D transform of each column */
fftw_plan p;
p = fftw_plan_many_dft(rank, n, howmany, A, inembed, istride, idist, A, onembed, ostride, odist, FFTW_FORWARD, FFTW_ESTIMATE);
// ...
/* run transform */
fftw_execute_dft(p, A, A);
// ...
/* we don't want memory leaks */
fftw_destroy_plan(p);
fftw_free(A);
}