FFTW 3.3.8: Guru Complex DFTs

cannam@167:

fftw_plan fftw_plan_guru_dft(
cannam@167:      int rank, const fftw_iodim *dims,
cannam@167:      int howmany_rank, const fftw_iodim *howmany_dims,
cannam@167:      fftw_complex *in, fftw_complex *out,
cannam@167:      int sign, unsigned flags);
cannam@167: 
cannam@167: fftw_plan fftw_plan_guru_split_dft(
cannam@167:      int rank, const fftw_iodim *dims,
cannam@167:      int howmany_rank, const fftw_iodim *howmany_dims,
cannam@167:      double *ri, double *ii, double *ro, double *io,
cannam@167:      unsigned flags);
cannam@167:

These two functions plan a complex-data, multi-dimensional DFT cannam@167: for the interleaved and split format, respectively. cannam@167: Transform dimensions are given by (rank, dims) over a cannam@167: multi-dimensional vector (loop) of dimensions (howmany_rank, cannam@167: howmany_dims). dims and howmany_dims should point cannam@167: to fftw_iodim arrays of length rank and cannam@167: howmany_rank, respectively. cannam@167:

flags is a bitwise OR (‘|’) of zero or more planner flags, cannam@167: as defined in Planner Flags. cannam@167:

In the fftw_plan_guru_dft function, the pointers in and cannam@167: out point to the interleaved input and output arrays, cannam@167: respectively. The sign can be either -1 (= cannam@167: FFTW_FORWARD) or +1 (= FFTW_BACKWARD). If the cannam@167: pointers are equal, the transform is in-place. cannam@167:

In the fftw_plan_guru_split_dft function, cannam@167: ri and ii point to the real and imaginary input arrays, cannam@167: and ro and io point to the real and imaginary output cannam@167: arrays. The input and output pointers may be the same, indicating an cannam@167: in-place transform. For example, for fftw_complex pointers cannam@167: in and out, the corresponding parameters are: cannam@167:

cannam@167:

ri = (double *) in;
cannam@167: ii = (double *) in + 1;
cannam@167: ro = (double *) out;
cannam@167: io = (double *) out + 1;
cannam@167:

Because fftw_plan_guru_split_dft accepts split arrays, strides cannam@167: are expressed in units of double. For a contiguous cannam@167: fftw_complex array, the overall stride of the transform should cannam@167: be 2, the distance between consecutive real parts or between cannam@167: consecutive imaginary parts; see Guru vector and transform sizes. Note that the dimension strides are applied equally to the cannam@167: real and imaginary parts; real and imaginary arrays with different cannam@167: strides are not supported. cannam@167:

There is no sign parameter in fftw_plan_guru_split_dft. cannam@167: This function always plans for an FFTW_FORWARD transform. To cannam@167: plan for an FFTW_BACKWARD transform, you can exploit the cannam@167: identity that the backwards DFT is equal to the forwards DFT with the cannam@167: real and imaginary parts swapped. For example, in the case of the cannam@167: fftw_complex arrays above, the FFTW_BACKWARD transform cannam@167: is computed by the parameters: cannam@167:

cannam@167:

ri = (double *) in + 1;
cannam@167: ii = (double *) in;
cannam@167: ro = (double *) out + 1;
cannam@167: io = (double *) out;
cannam@167:

4.5.3 Guru Complex DFTs