FFTW 3.3.5: Guru Complex DFTs

cannam@127:

fftw_plan fftw_plan_guru_dft(
cannam@127:      int rank, const fftw_iodim *dims,
cannam@127:      int howmany_rank, const fftw_iodim *howmany_dims,
cannam@127:      fftw_complex *in, fftw_complex *out,
cannam@127:      int sign, unsigned flags);
cannam@127: 
cannam@127: fftw_plan fftw_plan_guru_split_dft(
cannam@127:      int rank, const fftw_iodim *dims,
cannam@127:      int howmany_rank, const fftw_iodim *howmany_dims,
cannam@127:      double *ri, double *ii, double *ro, double *io,
cannam@127:      unsigned flags);
cannam@127:

These two functions plan a complex-data, multi-dimensional DFT cannam@127: for the interleaved and split format, respectively. cannam@127: Transform dimensions are given by (rank, dims) over a cannam@127: multi-dimensional vector (loop) of dimensions (howmany_rank, cannam@127: howmany_dims). dims and howmany_dims should point cannam@127: to fftw_iodim arrays of length rank and cannam@127: howmany_rank, respectively. cannam@127:

flags is a bitwise OR (‘|’) of zero or more planner flags, cannam@127: as defined in Planner Flags. cannam@127:

In the fftw_plan_guru_dft function, the pointers in and cannam@127: out point to the interleaved input and output arrays, cannam@127: respectively. The sign can be either -1 (= cannam@127: FFTW_FORWARD) or +1 (= FFTW_BACKWARD). If the cannam@127: pointers are equal, the transform is in-place. cannam@127:

In the fftw_plan_guru_split_dft function, cannam@127: ri and ii point to the real and imaginary input arrays, cannam@127: and ro and io point to the real and imaginary output cannam@127: arrays. The input and output pointers may be the same, indicating an cannam@127: in-place transform. For example, for fftw_complex pointers cannam@127: in and out, the corresponding parameters are: cannam@127:

cannam@127:

ri = (double *) in;
cannam@127: ii = (double *) in + 1;
cannam@127: ro = (double *) out;
cannam@127: io = (double *) out + 1;
cannam@127:

Because fftw_plan_guru_split_dft accepts split arrays, strides cannam@127: are expressed in units of double. For a contiguous cannam@127: fftw_complex array, the overall stride of the transform should cannam@127: be 2, the distance between consecutive real parts or between cannam@127: consecutive imaginary parts; see Guru vector and transform sizes. Note that the dimension strides are applied equally to the cannam@127: real and imaginary parts; real and imaginary arrays with different cannam@127: strides are not supported. cannam@127:

There is no sign parameter in fftw_plan_guru_split_dft. cannam@127: This function always plans for an FFTW_FORWARD transform. To cannam@127: plan for an FFTW_BACKWARD transform, you can exploit the cannam@127: identity that the backwards DFT is equal to the forwards DFT with the cannam@127: real and imaginary parts swapped. For example, in the case of the cannam@127: fftw_complex arrays above, the FFTW_BACKWARD transform cannam@127: is computed by the parameters: cannam@127:

cannam@127:

ri = (double *) in + 1;
cannam@127: ii = (double *) in;
cannam@127: ro = (double *) out + 1;
cannam@127: io = (double *) out;
cannam@127:

4.5.3 Guru Complex DFTs