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POFFTW: size of output array for 2D Fourier Transform of 3D data
 

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  1. POFFTW: size of output array for 2D Fourier Transform of 3D data
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    <p>I have a real 3D array of dimensions Nx*Ny*Nz and want to take a 2D Fourier transform for each z value <a href="http://www.fftw.org/doc/Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs" rel="nofollow">using FFTW</a>. Here the z index is the fastest varying in memory. Currently the following code works as expected:</p> <pre><code>int Nx = 16; int Ny = 8; int Nz = 3; // allocate memory const int dims = Nx * Ny * Nz; // input data (pre Fourier transform) double *input = fftw_alloc_real(dims); // why is this the required output size? const int outdims = Nx * (Ny/2 + 1) * Nz; // we want to perform the transform out of place // (so seperate array for output) fftw_complex *output = fftw_alloc_complex(outdims); // setup "plans" for forward and backward transforms const int rank = 2; const int howmany = Nz; const int istride = Nz; const int ostride = Nz; const int idist = 1; const int odist = 1; int n[] = {Nx, Ny}; int *inembed = NULL, *onembed = NULL; fftw_plan fp = fftw_plan_many_dft_r2c(rank, n, howmany, input, inembed, istride, idist, output, onembed, ostride, odist, FFTW_PATIENT); fftw_plan bp = fftw_plan_many_dft_c2r(rank, n, howmany, output, onembed, ostride, odist, input, inembed, istride, idist, FFTW_PATIENT); </code></pre> <p>As I understand it, transforming a 1D sequence of length N requires (N/2 + 1) complex values so why does the above code crash if instead I set <code>outdims = (Nx/2 + 1)*(Ny/2 + 1)*Nz</code> as one might expect for a 2D transform?</p> <p>Secondly am I right in thinking that I can access the real and imaginary parts of modes from <code>qx = 0 to Nx/2</code> (inclusive) using the following:</p> <pre><code>#define outputRe(qx,qy,d) ( output[(d) + Nz * ((qy) + (Ny/2 + 1) * (qx))][0] ) #define outputIm(qx,qy,d) ( output[(d) + Nz * ((qy) + (Ny/2 + 1) * (qx))][1] ) </code></pre> <p><strong>EDIT</strong>: <a href="http://pastebin.com/N9Qww2cz" rel="nofollow">Full code</a> and <a href="http://pastebin.com/Rnsdabzb" rel="nofollow">Makefile</a> for those who want to play around. Assumes fftw and gsl installed.</p> <p><strong>EDIT2:</strong> If I understand correctly, the indexing (allowing positive and negative frequencies) should be (probably getting too messy for a macro!):</p> <pre><code>#define outputRe(qx,qy,d) ( output[(d) + Nz * ((qy) + (Ny/2 + 1) * ( ((qx) &gt;= 0) ? (qx) : (Nx + (qx)) ) ) ][0] ) #define outputIm(qx,qy,d) ( output[(d) + Nz * ((qy) + (Ny/2 + 1) * ( ((qx) &gt;= 0) ? (qx) : (Nx + (qx)) ) ) ][1] ) for (int qx = -Nx/2; qx &lt; Nx/2; ++qx) for (int qy = 0; qy &lt;= Ny/2; ++qy) outputRe(qx, qy, d) = ... </code></pre> <p>where <code>outputRe(-Nx/2, qy, d)</code> points to the same data as <code>outputRe(Nx/2, qy, d)</code>. In practice I would probably just to loop over the first index and convert to a frequency, rather than the other way round!</p>
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