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fftw3: Guru Complex DFTs

 
 4.5.3 Guru Complex DFTs
 -----------------------
 
      fftw_plan fftw_plan_guru_dft(
           int rank, const fftw_iodim *dims,
           int howmany_rank, const fftw_iodim *howmany_dims,
           fftw_complex *in, fftw_complex *out,
           int sign, unsigned flags);
 
      fftw_plan fftw_plan_guru_split_dft(
           int rank, const fftw_iodim *dims,
           int howmany_rank, const fftw_iodim *howmany_dims,
           double *ri, double *ii, double *ro, double *io,
           unsigned flags);
 
    These two functions plan a complex-data, multi-dimensional DFT for
 the interleaved and split format, respectively.  Transform dimensions
 are given by ('rank', 'dims') over a multi-dimensional vector (loop) of
 dimensions ('howmany_rank', 'howmany_dims').  'dims' and 'howmany_dims'
 should point to 'fftw_iodim' arrays of length 'rank' and 'howmany_rank',
 respectively.
 
    'flags' is a bitwise OR ('|') of zero or more planner flags, as
 defined in Planner Flags.
 
    In the 'fftw_plan_guru_dft' function, the pointers 'in' and 'out'
 point to the interleaved input and output arrays, respectively.  The
 sign can be either -1 (= 'FFTW_FORWARD') or +1 (= 'FFTW_BACKWARD').  If
 the pointers are equal, the transform is in-place.
 
    In the 'fftw_plan_guru_split_dft' function, 'ri' and 'ii' point to
 the real and imaginary input arrays, and 'ro' and 'io' point to the real
 and imaginary output arrays.  The input and output pointers may be the
 same, indicating an in-place transform.  For example, for 'fftw_complex'
 pointers 'in' and 'out', the corresponding parameters are:
 
      ri = (double *) in;
      ii = (double *) in + 1;
      ro = (double *) out;
      io = (double *) out + 1;
 
    Because 'fftw_plan_guru_split_dft' accepts split arrays, strides are
 expressed in units of 'double'.  For a contiguous 'fftw_complex' array,
 the overall stride of the transform should be 2, the distance between
 consecutive real parts or between consecutive imaginary parts; see 
 Guru vector and transform sizes.  Note that the dimension strides are
 applied equally to the real and imaginary parts; real and imaginary
 arrays with different strides are not supported.
 
    There is no 'sign' parameter in 'fftw_plan_guru_split_dft'.  This
 function always plans for an 'FFTW_FORWARD' transform.  To plan for an
 'FFTW_BACKWARD' transform, you can exploit the identity that the
 backwards DFT is equal to the forwards DFT with the real and imaginary
 parts swapped.  For example, in the case of the 'fftw_complex' arrays
 above, the 'FFTW_BACKWARD' transform is computed by the parameters:
 
      ri = (double *) in + 1;
      ii = (double *) in;
      ro = (double *) out + 1;
      io = (double *) out;
 

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