Guru Real-data DFTs - FFTW 3.3.4
Description: FFTW 3.3.4

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#### 4.5.4 Guru Real-data DFTs

         fftw_plan fftw_plan_guru_dft_r2c(
              int rank, const fftw_iodim *dims,
              int howmany_rank, const fftw_iodim *howmany_dims,
              double *in, fftw_complex *out,
              unsigned flags);

         fftw_plan fftw_plan_guru_split_dft_r2c(
              int rank, const fftw_iodim *dims,
              int howmany_rank, const fftw_iodim *howmany_dims,
              double *in, double *ro, double *io,
              unsigned flags);

         fftw_plan fftw_plan_guru_dft_c2r(
              int rank, const fftw_iodim *dims,
              int howmany_rank, const fftw_iodim *howmany_dims,
              fftw_complex *in, double *out,
              unsigned flags);

         fftw_plan fftw_plan_guru_split_dft_c2r(
              int rank, const fftw_iodim *dims,
              int howmany_rank, const fftw_iodim *howmany_dims,
              double *ri, double *ii, double *out,
              unsigned flags);

Plan a real-input (r2c) or real-output (c2r), multi-dimensional DFT with transform dimensions 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. As for the basic and advanced interfaces, an r2c transform is `FFTW_FORWARD` and a c2r transform is `FFTW_BACKWARD`.

The last dimension of `dims` is interpreted specially: that dimension of the real array has size `dims[rank-1].n`, but that dimension of the complex array has size `dims[rank-1].n/2+1` (division rounded down). The strides, on the other hand, are taken to be exactly as specified. It is up to the user to specify the strides appropriately for the peculiar dimensions of the data, and we do not guarantee that the planner will succeed (return non-`NULL`) for any dimensions other than those described in Real-data DFT Array Format and generalized in Advanced Real-data DFTs. (That is, for an in-place transform, each individual dimension should be able to operate in place.)

`in` and `out` point to the input and output arrays for r2c and c2r transforms, respectively. For split arrays, `ri` and `ii` point to the real and imaginary input arrays for a c2r transform, and `ro` and `io` point to the real and imaginary output arrays for an r2c transform. `in` and `ro` or `ri` and `out` may be the same, indicating an in-place transform. (In-place transforms where `in` and `io` or `ii` and `out` are the same are not currently supported.)

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

In-place transforms of rank greater than 1 are currently only supported for interleaved arrays. For split arrays, the planner will return `NULL`.