FFTW 3.3.8: Guru Complex DFTs

Chris@82:

fftw_plan fftw_plan_guru_dft(
Chris@82:      int rank, const fftw_iodim *dims,
Chris@82:      int howmany_rank, const fftw_iodim *howmany_dims,
Chris@82:      fftw_complex *in, fftw_complex *out,
Chris@82:      int sign, unsigned flags);
Chris@82: 
Chris@82: fftw_plan fftw_plan_guru_split_dft(
Chris@82:      int rank, const fftw_iodim *dims,
Chris@82:      int howmany_rank, const fftw_iodim *howmany_dims,
Chris@82:      double *ri, double *ii, double *ro, double *io,
Chris@82:      unsigned flags);
Chris@82:

These two functions plan a complex-data, multi-dimensional DFT Chris@82: for the interleaved and split format, respectively. Chris@82: Transform dimensions are given by (rank, dims) over a Chris@82: multi-dimensional vector (loop) of dimensions (howmany_rank, Chris@82: howmany_dims). dims and howmany_dims should point Chris@82: to fftw_iodim arrays of length rank and Chris@82: howmany_rank, respectively. Chris@82:

flags is a bitwise OR (‘|’) of zero or more planner flags, Chris@82: as defined in Planner Flags. Chris@82:

In the fftw_plan_guru_dft function, the pointers in and Chris@82: out point to the interleaved input and output arrays, Chris@82: respectively. The sign can be either -1 (= Chris@82: FFTW_FORWARD) or +1 (= FFTW_BACKWARD). If the Chris@82: pointers are equal, the transform is in-place. Chris@82:

In the fftw_plan_guru_split_dft function, Chris@82: ri and ii point to the real and imaginary input arrays, Chris@82: and ro and io point to the real and imaginary output Chris@82: arrays. The input and output pointers may be the same, indicating an Chris@82: in-place transform. For example, for fftw_complex pointers Chris@82: in and out, the corresponding parameters are: Chris@82:

Chris@82:

ri = (double *) in;
Chris@82: ii = (double *) in + 1;
Chris@82: ro = (double *) out;
Chris@82: io = (double *) out + 1;
Chris@82:

Because fftw_plan_guru_split_dft accepts split arrays, strides Chris@82: are expressed in units of double. For a contiguous Chris@82: fftw_complex array, the overall stride of the transform should Chris@82: be 2, the distance between consecutive real parts or between Chris@82: consecutive imaginary parts; see Guru vector and transform sizes. Note that the dimension strides are applied equally to the Chris@82: real and imaginary parts; real and imaginary arrays with different Chris@82: strides are not supported. Chris@82:

There is no sign parameter in fftw_plan_guru_split_dft. Chris@82: This function always plans for an FFTW_FORWARD transform. To Chris@82: plan for an FFTW_BACKWARD transform, you can exploit the Chris@82: identity that the backwards DFT is equal to the forwards DFT with the Chris@82: real and imaginary parts swapped. For example, in the case of the Chris@82: fftw_complex arrays above, the FFTW_BACKWARD transform Chris@82: is computed by the parameters: Chris@82:

Chris@82:

ri = (double *) in + 1;
Chris@82: ii = (double *) in;
Chris@82: ro = (double *) out + 1;
Chris@82: io = (double *) out;
Chris@82:

4.5.3 Guru Complex DFTs